Unit 7 Grade 7

Fractions and Decimals

Lesson Outline

Big Picture

Students will:
• explore fraction relationships;
• develop an understanding of strategies related to addition and subtraction of fractions (proper, improper, and mixed);
• explore multiplication of fractions through repeated addition;
• explore division of whole numbers by simple fractions;
• understand the percent/decimal/fraction relationship;
• solve problems involving whole number percents, fractions, and decimals;
• add, subtract, multiply, and divide decimals;
• investigate experimental probabilities and compare to theoretical probabilities and independent events.
Day Lesson Title Math Learning Goals Expectations
1 Fraction Puzzles • Explore/review fractional parts of geometric shapes. 7m11, 7m15
• Order fractions.
CGE 3c, 5a, 5e
2 Adding Fractions • Investigate adding fractions using manipulatives. 7m11

CGE 3b, 3c, 5a

3 Adding Fractions with • Add fractions by connecting concrete to symbolic. 7m11, 7m12
Different • Recognize the need for and find equivalent fractions with
Denominators common denominators. CGE 4b, 5e
4 Exploring Fractions • Explore fractions using relational rods. 7m24
Using Relational Rods
CGE 3c, 4a
5 Adding and • Add and subtract fractions using relational rods. 7m24
Subtracting Fractions
Using Relational Rods CGE 2c, 3b, 3c, 5e
6 Subtracting Fractions • Develop strategies for subtracting fractions using equivalent 7m24
Using Equivalent fractions with common denominators.
Fractions • Add and subtract fractions. CGE 4e, 5g
7 Adding and • Demonstrate understanding and skills while performing 7m24
Subtracting Fractions operations with fractions.
CGE 2b, 3c
8 Exploring Fractions • Explore repeated addition of fractions and addition and 7m24, 7m25
Further subtraction of mixed numbers.
CGE 3b, 4f, 5a
9 Dividing Whole • Divide whole numbers by simple fractions using concrete 7m18
Numbers by Fractions materials, e.g., divide 3 by , using fraction strips.
Using Concrete
Materials

10 Summative • Demonstrate understanding of fractions and operations with 7m11, 7m19,

Assessment fractions on an open-ended, problem-solving task. 7m24, 7m25

CGE 2b, 3c, 4f

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 1

Day Lesson Title Math Learning Goals Expectations
11 Fractions and • Explore the relationships between fractions and decimals. 7m15, 7m27
Decimals
CGE 2c, 3c
12 Decimals • Compare and order decimals to hundredths, using a variety of 7m11, 7m15, 7m23
tools, e.g., number lines, relational rods, base-ten materials,
calculators. CGE 2c, 3e
• Determine whether a fraction or a decimal is the most appropriate
way to represent a given quantity, e.g., I would use a fraction to
express part of an hour, saying “quarter hour” instead of “.25 of
an hour.”
• Add and subtract decimals.
13 Mental Math and • Use a variety of mental strategies to add and subtract decimals, 7m19, 7m23
Decimals e.g., use the distributive property.
• Divide whole numbers by decimal numbers to hundredths using CGE 3c, 4b
concrete materials.
14 Multiplying Decimals • Multiply decimal numbers to thousandths by one-digit whole 7m18, 7m20
numbers, using concrete materials, calculators, estimation, and
algorithms. CGE 3e, 4b
• Solve problems involving the multiplication of decimal numbers.
15 Dividing Decimals • Divide whole numbers by decimal numbers to hundredths, using 7m18, 7m20
concrete materials, e.g., base-ten materials to divide 4 by 0.8.
• Divide decimal numbers to thousandths by one-digit whole CGE 3a, 3c
numbers, using concrete materials, estimation, and algorithms,
e.g., estimate 16.75 ÷ 3 as 18 ÷ 3 ! 6, then calculate, predicting an
answer slightly less than 6.
• Solve everyday problems involving division with decimals.
16 Solving Multi-Step • Solve multi-step problems involving whole numbers and 7m21, 7m22
Problems Involving decimals.
Decimals • Justify solutions using concrete materials, calculators, estimation, CGE 2b, 3c
and algorithms.
• Use estimation when solving problems involving decimals to
judge the reasonableness of a solution, e.g., A book costs $18.49.
The salesperson tells you that the total price, including taxes, is
$22.37. How can you tell if the total price is reasonable without
using a calculator?
17 Summative • Demonstrate an understanding of decimals and operations with
Assessment of decimals.
Decimals

18 Percent • Investigate and represent the relationships among fractions, 7m15, 7m22, 7m27
decimals, and percents.
• Identify common uses of percents, fractions, and decimals. CGE 2b, 2c, 3e
• Estimate percents visually, e.g., shade 60% of a rectangle, and
mentally, e.g., 3 out of 11 hockey players missed practice means
approximately 25% were absent.
19 Solving Percent • Solve problems that involve determining whole-number percents, 7m28
Problems with using concrete materials, e.g., base-ten materials, 10 " 10 square.
Concrete Materials CGE 2b, 2c, 3e

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 2

Day Lesson Title Math Learning Goals Expectations
20 Finding the Percent of • Solve problems that involve determining the percent of a number, 7m22, 7m28
a Number e.g., CDs are on sale for 50% of the regular price. What is the sale
price of a $14.98 CD? Relate the percent to fraction and decimal CGE 3c, 3e
versions, e.g., The CD is half price.
• Estimate to judge the reasonableness of the answer.
• Solve problems that involve determining whole-number percents
with and without calculators.
21 Connecting Fractions • Determine what percent one number is of another, e.g., 4 out of 7m15, 7m28
to Percent 16 shapes are hearts. What percent are hearts?
• Connect this type of problem to converting a fraction to a percent, CGE 3c, 3e
e.g., 4 out of 16 = = 25%.
22 Using Percent to Make • Use percent to make comparisons, e.g., students won ribbons 7m28
Comparisons
in one class and won in the other class. Which had the better CGE 3e
performance?
• Pose and solve comparison problems using a calculator.
23 Using Percent to Find • Calculate the size of the whole when a percentage of the whole is 7m27, 7m28, 7m84
the Whole known, e.g., 6 students in a class have juice for snack. If that is
20% of the class, how large is the class? CGE 2b, 2c
• Relate to probability e.g., if 20% of the students have juice, what
is the probability that a student chosen at random will have juice?
Term 3
24 Using Tables and Lists • Determine all possible outcomes of an event using a chart, table, 7m85
to Determine or systematic list, e.g., If you threw three coins simultaneously,
Outcomes what are all the possible combinations of heads and tails? CGE 2c, 3e
• Determine all possible sums when rolling two number cubes.

25 Probability • Distinguish between theoretical probability and experimental 7m27, 7m85, 7m86
probability.
• Express probability as a fraction, decimal, and percent. CGE 3c, 3e
• Calculate probability of specific outcomes using Day 24 charts
and tables, e.g., what is the probability of three coin flips being
HHH?
26 Designing Games and • Understand the connections between percent and probability by: 7m84
Experiments # designing a fair game (each player has a 50% chance of
winning), e.g., Two players take turns rolling one numbered CGE 2c, 3c, 4b, 4c
cube. If the number is odd, player A scores a point. If the
number is even, player B scores a point.
# designing an experiment where the chance of a particular
outcome is 1 in 3, e.g., use a bag of 2 red and 4 green balls.
27 Making Predictions • Make predictions about a population given a probability, e.g., if 7m84
Based on Probability the probability of catching a fish at the conservation is 30%, how
many students in our class of 28 will catch a fish, if we all go to CGE 3c, 3e
the conservation to fish?
28 Tree Diagrams • Understand that two events are independent when one does not 7m85
affect the probability of the other, e.g., rolling a number cube,
then flipping a coin.
• Determine all possible outcomes for two independent events by
completing tree diagrams, e.g., spinning a three-section spinner
two consecutive times; rolling a number cube, then spinning a
four-section spinner. CGE 3c

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 3

Day Lesson Title Math Learning Goals Expectations
29 Probability of a • Determine the probability of a specific outcome from two 7m85
Specific Event independent events using tree diagrams, e.g., when flipping a coin
and then rolling a number cube, what is the probability of getting CGE 3a
a head and an even number?
30 Comparing Theoretical • Perform a simple probability experiment. 7m86
and Experimental • Compare theoretical probability with the results of the experiment
Probability using both a small sample (individual student results) and a large
sample (the combined results from all students in the class). CGE 2e, 3c
• Understand that probability results can be misleading if an
experiment has too few trials.
31 Applications of • Examine everyday applications of probability, e.g., batting 7m27, 7m83
Probability in the averages, goalie statistics, weather forecasts, opinion polls.
World • Research and report on probabilities expressed in fraction, CGE 3c, 4c, 4e, 4f
decimal, and percent form.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 4

Unit 7: Day 1: Fraction Puzzles Grade 7
Math Learning Goals Materials
• Explore/review fractional parts of geometric shapes. • pattern blocks

• Order fractions. • overhead pattern

blocks
• BLM 7.1.1, 7.1.2,
7.1.3, 7.1.4
• 2 or 3 large
imperial socket
wrench sets in
cases
Assessment
Opportunities
Minds On… Whole Class ! Solving a Problem
Students solve an area fraction puzzle: See Continuum and
Connections
• With your pattern blocks build two different triangles each with an area that Fractions in LMS
is one-half green and one-half blue. library.

Students share their solutions, using the overhead pattern blocks. Virtual pattern
Discuss whether rearranging the blocks makes the solution “different.” blocks are available
at:
http://arcytech.org/ja
va/patterns/patterns
_j.shtml

Action! Pairs ! Problem Solving

Students complete questions 1 to 5 on BLM 7.1.1, using pattern blocks. They Briefly review the
show the graphic solution, labelling each colour with the appropriate fraction meaning of
parallelogram (blue
of the whole triangle (BLM 7.1.2). or beige block) and
Students complete questions 1 to 5 (BLM 7.1.3) individually. Pairs of trapezoid (red
block).
students take turns, completing question 6, using an imperial set of socket
Some methods
wrenches. students may use
include physical size
Curriculum Expectations/Demonstration/Marking Scheme: Assess of each socket,
students’ understanding of equivalent fractions and ordering fractions. ordering of the
sockets could also
be accomplished
using equivalent
fractions, converting
to decimals, or
measuring in
millimetres.
Consolidate Whole Class ! Sharing/Discussion
Debrief Pairs of students share their solutions to an area puzzle using the overhead
pattern blocks and explain how they know their solution is correct.
Discuss possible answers to question 5 on the student worksheet (BLM
7.1.1).
Several different pairs of students share their solutions, even if the solution is
merely another arrangement of the same pattern blocks. This allows more
students to be recognized and reinforces multiple solutions and explanations.
Discuss the various methods students used to solve the socket set problem.
Students explain why they placed a certain socket between two others.

Home Activity or Further Classroom Consolidation Provide a tangram

Concept Practice Complete worksheet 7.1.4. pattern.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 5

7.1.1: Pattern Block Area Fraction Puzzles
Name:
Date:

Use pattern blocks to solve each of the area fraction puzzles below. Draw each solution on
pattern block paper. Label each colour with its fraction of the whole shape.

1. Build a parallelogram with an area that is green, blue, and red.

2. Build a parallelogram with an area that is green, yellow, red, and blue.

3. Build a trapezoid with an area that is green and red.

4. Rebuild each of the puzzles above in a different way.

5. Explain why it is not possible to build a parallelogram with an area that is one-half yellow,
one-third green, and one-quarter blue.

Pattern Block Area Fraction Puzzles

Name:
Date:

Use pattern blocks to solve each of the area fraction puzzles below. Draw each solution on
pattern block paper. Label each colour with its fraction of the whole shape.

1. Build a parallelogram with an area that is green, blue, and red

2. Build a parallelogram with an area that is green, yellow, red, and blue.

3. Build a trapezoid with an area that is green and red.

4. Rebuild each of the puzzles above in a different way.

5. Explain why it is not possible to build a parallelogram with an area that is one-half yellow,
one-third green, and one-quarter blue.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 6

7.1.2: Pattern Block Paper

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 7

7.1.3: Socket to You!
Name:
Date:

1. is an equivalent fraction for . Write two more equivalent fractions for .

2. Write two equivalent fractions for .

3. Circle which is larger: or .! ! Explain how you know.

4. Circle which is smaller: or . ! ! Explain how you know.

5. Circle the fraction that fits between and . Verify your answer using a method of your

choice.

6. Often mechanics use socket wrench sets with openings measured in fractions of an inch.
These fractions are stamped on the fronts of the sockets.
Arrange the sockets from smallest to largest.
Explain how you decided on the order you chose.
Check by placing the sockets in the case.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 8

7.1.4: Area with Tangrams

Name:
Date:

1. Use your tangram pieces to complete the table. Consider the area
of D to be one square unit.

Tangram Calculated Area of Fraction of the Entire Set

Piece Tangram Piece (by Area)
A
B
C
D 1 unit 2
E
F
G

2. What fraction of part D is E?

3. What fraction of part A is C?

4. What fraction of part B is C?

5. If the area of C is 4 cm2, find the area of each of the other parts.

6. If the area of F is 3 cm2, find the area of each of the other parts.

Calculated Area Calculated Area

A
B
C 4 cm 2
D
E
F 3 cm 2
G

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 9

Unit 7: Day 2: Adding Fractions Grade 7
Math Learning Goals Materials
• Investigate combinations of fractions using manipulatives. • pattern blocks
• overhead pattern
blocks
• BLM 7.2.1

Assessment
Opportunities
Minds On… Whole Class ! Introducing Problems
One way: Using the
Using pattern blocks, students show that . Several students share hexagon as one
their methods. whole, the triangle
can be one-sixth,
Students show that and share which pattern block they chose to three triangles (or
the trapezoid) can
represent one whole. be one-half, and
together they form
Demonstrate the use of different pattern blocks to represent one whole. four-sixths (two-
thirds).

Action! Pairs ! Exploration Fractions, both

Students answer several questions involving combining fractions that can be proper and
improper, that have
modelled with pattern blocks. For example, . denominators of 2,
3, or 6 work well
Students explain each solution, and identify which pattern block they used to with pattern blocks.
represent the whole.

Consolidate Whole Class ! Sharing/Discussion

Debrief Students demonstrate their strategies to add fractions using overhead pattern As students explore
blocks. and discuss they
gain a deeper
Discuss the idea of equivalent fractions with common denominators as it understanding of
relates to the pattern blocks, e.g., using smaller blocks helps to combine equivalent fractions
fractions with different denominators. and of the algorithm
for determining a
For example, to add , students may choose to use the hexagon as the common
denominator.
one whole. They would use the trapezoid to represent and five triangles to
represent . To combine the fractions, students need to express the answer in
triangles (one whole and two triangles, or one- and two-sixths, which can be
simplified to one and one-third using the blue rhombi).
Students should use a variety of methods to determine the common
denominator.

Curriculum Expectations/Demonstration/Checklist: Assess students’

ability to add fractions using manipulatives.

Home Activity or Further Classroom Consolidation For virtual pattern

Complete the worksheet, Combining Fractions (7.2.1). blocks and related
Concept Practice
activities see:
http://math.rice.edu/
~lanius/Patterns/

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 10

7.2.1: Combining Fractions
Name:
Date:

Use pattern blocks to solve each problem. Record your solutions on the pattern block paper.
Include the symbolic fractions as well as the drawings.
1. Show that:

a) b) c)

2. Add and .

3. Add .

4. Show three different ways of adding three fractions to get two wholes.

5. Show that is less than 1. How much less than 1 is this sum?

Combining Fractions
Name:
Date:

Use pattern blocks to solve each problem. Record your solutions on the pattern block paper.
Include the symbolic fractions as well as the drawings.
1. Show that:
a) b) c)

2. Add and .

3. Add .

4. Show three different ways of adding three fractions to get two wholes.

5. Show that is less than 1. How much less than 1 is this sum?

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 11

Unit 7: Day 3: Adding Fractions with Different Denominators Grade 7
Math Learning Goals Materials
• Add fractions by connecting concrete to symbolic. • BLM 7.3.1, 7.3.2

• Recognize the need for and find equivalent fractions with common • pattern blocks

denominators.

Assessment
Opportunities
Minds On… Whole Class ! Teacher Directed Instruction
Some students share their solutions to question 3 from the previous day’s
Home Activity ( ) using overhead pattern blocks.
1 whole
Record the symbolic form of each solution, i.e., the fractions. Discuss how to
get the solution without using pattern blocks.
Through questioning, students consider the use of equivalent fractions with a
common denominator, in this case, 6. They may determine the common
denominator in different ways.

Action! Pairs ! Think/Pair/Share

Students think individually about solving each of the questions from the
Home Activity, Day 2, using equivalent fractions with a common
denominator. Then with a partner, they discuss their strategies for finding
equivalent fractions with a common denominator. Pairs share their strategies
with a small group and/or the whole class.

Curriculum Expectations/Observation/Checklist: Assess students’

understanding of addition of fractions with common denominators.

Consolidate Whole Class ! Note Making

Debrief Create a note together that outlines the process for adding fractions using
equivalent fractions with a common denominator. Include the multiples
method of finding common denominators.
Students determine the steps to follow in the process.
Students work independently on differentiated practice, based on the
teacher’s observations in Action (see BLM 7.3.1, 7.3.2). BLM 7.3.2 shows
scaffolding.

Home Activity or Further Classroom Consolidation Provide student with

Differentiated
Complete the worksheet, Adding Fractions with Different Denominators, and appropriate practice
Concept Practice
the practice questions. questions.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 12

7.3.1: Adding Fractions with Different Denominators
Name:
Date:

1. Use multiples to find three common denominators for the following pair of fractions:

Multiples of 2:

Multiples of 8:

My three common denominators are _______, _______, and ______.

2. Find a common denominator for the following fraction pairs:

a) b)

Common denominator: ___________ Common denominator: ___________

Rewrite each pair with a common denominator using equivalent fractions.

3. Rewrite each of the following expressions using equivalent fractions with a common
denominator. Add the fractions.

a)

b)

c)

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 13

7.3.2: Adding Fractions with Different Denominators
Name:
Date:

1. Use multiples to find two common denominators for the following pair of fractions.
Multiples of 2: 2, 4, ___, ___, ___, ___, ___, ___, ___, ___, ___

Multiples of 8: 8, 16, ___, ___, ___, ___, ___, ___, ___, ___

My two common denominators are _______ and _______.

2. Find a common denominator for the following fraction pairs.

a) b)

4: 4, ___, ___, ___, ___, ___, ___, ___ 5: ___, ___, ___, ___, ___, ___, ___

3: 3, ___, ___, ___, ___, ___, ___, ___ 8: ___, ___, ___, ___, ___, ___, ___

Common denominator: ________ Common denominator: ________

—=— =—

—= =—

3. Rewrite the following expression using equivalent fractions with a common denominator.
Add the fractions.

3: ___, ___, ___, ___, ___, ___, ___

a)
5: ___, ___, ___, ___, ___, ___, ___

— — ! —+— = —

b)

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 14

Unit 7: Day 4: Exploring Fractions Using Relational Rods Grade 7
Math Learning Goals Materials
• Explore fractions using relational rods. • overhead
relational rods
• sets of relational
rods
• BLM 7.4.1, 7.4.2,
7.4.3

Assessment
Opportunities
Minds On… Whole Class ! Introducing the Problem
As pairs of students follow along with their own sets of relational rods, place
If students have not
the blue and black overhead relational rods together to form one whole worked with
(BLM 7.4.2). Students decide how they would determine the value of a relational rods
particular coloured rod in relation to this blue-black whole. before, some time
should be allocated
Invite a student to demonstrate that the brown rod (8 units) is one-half of the to exploration. They
blue-black whole (16 units). may benefit from
some discussion of
Repeat with the dark green rod. Students determine the fractional value of the “unit” in the rods.
dark green rod in relation to the blue-black whole. Write this relation as a
fraction ( ). If sets of relational
rods are not readily
Guide their thinking with questions: available, use
BLM 7.4.1.
• What rod(s) may represent one unit for this whole?
• How many units is the dark green rod? Students use other rods to determine
equivalent fractions in lowest terms.

Action! Pairs ! Exploration

Students explore the fractional value of each of the relational rods relative to
the blue-black whole.
Students organize their work in a table to clearly show how they have
determined the fractional value of all of the coloured rods in relation to the
blue-black whole and their relationships to each other (fractions less than one
only). See BLM 7.4.3.

Curriculum Expectations/Observation/Mental Note: Assess students’

understanding of equivalent fractions.

Consolidate Whole Class ! Sharing/Discussion

Debrief Students share the reasoning they used to determine the fractional value for
each coloured rod in relation to the blue-black whole and to each other.
Several different pairs share their strategies.
Pairs share their methods for organizing the information to show the
relationships among the rods.

Home Activity or Further Classroom Consolidation Provide students

Complete practice questions. with appropriate
Concept Practice
practice questions.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 15

7.4.1: Template for Relational Rods
Teachers may want to print
the coloured rods on acetate
and cut them apart to use on
the overhead transparency.

Students can colour the

rods as indicated and cut
them apart to make their
own set of relational rods.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 16

7.4.2: Relational Rods as a Fraction of One Blue-Black Whole
Name:
Date:

Write the value of each coloured rod as a fraction of the blue-black rod. Simplify any fraction
that is not in lowest terms.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 17

7.4.3: Fractions Using Relational Rods

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 18

Unit 7: Day 5: Adding and Subtracting Fractions Using Relational Rods Grade 7
Math Learning Goals Materials
• Add and subtract fractions using relational rods. • sets of relational
rods
• BLM 7.5.1

Assessment
Opportunities
Minds On… Whole Class ! Review
Discuss strategies that different students used for expressing one rod as a
fraction of another.

Action! Pairs ! Game

Play one game as a whole class. This would allow for
some reinforcement
Students work with the relational rods to create and complete addition and of appropriate
subtraction problems (BLM 7.5.1). language and
problem-solving
They use various strategies to prove that their statement is correct –
skills.
modelling with the rods, using symbolic manipulation and equivalent
fractions, using a calculator.

Curriculum Expectations/Demonstration/Anecdotal Note: Assess

students’ ability to add and subtract fractions, using relational rods and
equivalent fractions.

Consolidate Whole Class ! Discussion

Debrief Each pair of students shares one addition or subtraction expression they
created for the class to solve.
Discuss students’ strategies for solving, e.g., using rods, mentally, finding
equivalent fractions with a common denominator.

Home Activity or Further Classroom Consolidation Assign these tasks

• Create a new game that would require the use of relational rods to add or to specific groups of
Application
Reflection subtract fractions, e.g., purple-brown whole. students based on
their skill levels.
Exploration OR
• Create a new whole based on two or more rods combined (not blue-black). Provide students
Find the fractional value that each rod is of the whole. with appropriate
practice questions
OR involving equivalent
fractions.
• Complete the practice questions about determining equivalent fractions.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 19

7.5.1: Fraction Game with Relational Rods
Name:
Date:

Work with a partner.

Use the worksheet 7.4.2: Relational Rods as a Fraction of One Blue-Black Whole to help you
with the fractional value of each rod.

1. One partner randomly selects 5 rods from the set and lays them out on the table. The other
partner chooses from these, 2 rods to add and subtract.

2. Individually, create two addition-of-fractions equations and two subtraction-of-fractions

equations using the rods. Record your equations using the colours as well as the fractional
values in terms of the blue-black rod.
For example,
Addition
dark green + purple = orange

blue-black + blue-black = blue-black

Use equivalent fractions to reduce to:

blue-black + blue-black = blue-black

Subtraction
orange # purple = dark green

blue-black # blue-black = blue-black,

Use equivalent fractions to reduce to:

blue-black # blue-black = blue-black

3. Compare your two sets of equations.

• For each equation hat is common, check the answer using another method. If it is
correct award your team 2 points.
• For each equation that is different, explain your solution to your partner. When you agree
on the correct equation, check the answer. If it is correct, award you team 1 point.
• No points are awarded for incorrect equations.

4. Record each person’s score for that round.

5. For each round, take turns, randomly selecting 5 rods from the set.

6. Play continues until one person reaches 20 points.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 20

Unit 7: Day 6: Subtracting Fractions Using Equivalent Fractions Grade 7
Math Learning Goals Materials
• Develop rules for subtracting fractions using equivalent fractions with • BLM 7.6.1, 7.6.2

common denominators. • relational rods

• pattern blocks
• Add and subtract fractions.

Assessment
Opportunities
Minds On… Whole Class ! Game
Consider including
Play the concentration game with the class (BLM 7.6.1, 7.6.2).
visual
representations of
the fractions on the
game board, e.g.,
coloured rods,
pattern blocks.

Action! Whole Class ! Note making

Alternatives to this
Students summarize their understanding of subtracting fractions using whole-class activity
equivalent fractions with a common denominator. include working in
Work together to pose questions, create examples related to the questions, and pairs or small
groups or creating
work the examples. Students add to their notes. Highlight different methods poster notes. Make
that students have developed for determining equivalent fractions and for manipulatives
subtracting fractions. available.
Students develop the steps in the process, including as much detail as they
require.

Consolidate Individual ! Practice

Debrief Students work independently to add and subtract fractions by completing
assigned questions. Make manipulatives available.

Curriculum Expectations/Quiz/Marking Scheme: Assess students’ ability

to add and subtract fractions, using a variety of tools.

Home Activity or Further Classroom Consolidation

Application • Complete the practice questions. Provide students
Concept Practice OR with appropriate
Reflection practice questions.
• Create a card game based on fractions.
Skill Drill

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 21

7.6.1: A Concentration Game (Teacher)

A B C D

E F G H

I J K L

M N O P

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 22

7.6.2: Instructions for the Concentration Game (Teacher)

This game can be used to introduce a topic or to help students consolidate a concept.
Choose only one concept for each game.

For example:
• equivalent fractions
• fractions in simplest form
• converting between fractions and decimals, decimals and percent, or fractions and percent
• converting between mixed numbers and improper fractions

To prepare the game:

Randomly write eight fractions in different boxes on an acetate copy of the game board. In the
remaining eight boxes, write the match to the original eight. Cut out and number 16 paper
squares to hide the contents of each box as the game is projected on the overhead screen.
Label the blank squares that you use to cover the boxes.

To play the game:

The class forms two teams. A student from the starting team requests that two boxes be
uncovered. The student tells if there is a match. If the two items revealed match, the team gets
a point. If not, the boxes are covered again and a student from the next team gets a turn. Play
continues until all matches have been found.

Note: Students can work in pairs to quietly discuss the correctness of the match. This may also
reduce self-consciousness for some students.

Alternate playing suggestions:

• If a team makes a match, they get another turn.

• All students must have at least one turn before anyone can take a second turn.

• To prevent students from automatically saying that everything revealed is matching, the
team loses a point if a student declares an incorrect match.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 23

Unit 7: Day 7: Adding and Subtracting Fractions Grade 7
Math Learning Skills Materials
• Demonstrate understanding and skills while performing operations with • BLM 7.7.1, 7.7.2

fractions.

Assessment
Opportunities
Minds On… Whole Class ! Review/Four Corners
Refer to Think
Students go to the corner where the question they are most interested in
Literacy:
discussing is posted, e.g., adding fractions, subtracting fractions, equivalent Mathematics,
fractions, using manipulatives to understand fractions. In this corner students Grades 7–9,
discuss their understanding. Visit each corner and ask relevant questions and pp. 106–109.
redirect the discussion, as needed.

Action! Individual ! Applying Understanding

Students work independently to complete the Fraction Flag task (BLM 7.7.1).
Students may measure using a ruler or use manipulatives to cover the area.
They may use any of the manipulative materials they have been using to add
and subtract fractions, if they choose.
For some students, the flag could be superimposed on grid paper (or grid
paper on acetate could be used) to provide an additional option for counting
squares to determine area.

Curriculum Expectations/Application/Checkbric: Assess students’ ability

to apply their understanding of fractions.

Consolidate Whole Class ! Sharing

Debrief Students share their strategies for completing the task.

Home Activity or Further Classroom Consolidation

Exploration Create your own flag using fractional sections. Include solutions. See BLM 7.7.2.
Reflection Post flags in the
classroom.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 24

7.7.1: Fraction Flag
Name:
Date:

The flag to the right was designed with four colours.

1. Determine the fraction of the flag that is:
a. Orange

b. Blue

c. Yellow

d. Green

2. What fraction of the flag is not green?

Explain your reasoning.

3. How much more of the flag is orange than blue? Show all of your work.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 25

7.7.2: Create Your Own Fraction Flag
_____________’s Fraction Flag Date: __________________

Note: Your flag must have at least 8 sections and use only straight lines.
You must include orange, blue, yellow, and green.
Identify what fraction of the whole flag is represented by each colour?

orange = ________ blue = ________ yellow = ________ green = ________

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 26

Unit 7: Day 8: Exploring Fractions Further Grade 7
Math Learning Goals Materials
• Explore repeated addition of fractions and addition and subtraction of mixed • BLM 7.8.1, 7.8.2
• overhead
numbers.
manipulatives

Assessment
Opportunities
Minds On… Whole Class ! Introducing the Problems
Identify and describe types of fractions and operations with fractions that Have manipulatives
available for
have not been addressed (mixed numbers, multiplication and division of students to use to
fractions, etc.). Focus on mixed fractions. Students can build the fractions add and subtract
with manipulatives, as well as represent them symbolically. mixed fractions.

Action! Pairs ! Exploration

Students develop solutions for the various fraction problems (BLM 7.8.1). Students should
consult with their
Students can use manipulatives of their choice. partner before they
ask for assistance.
Problem Solving/Application/Checklist: Assess students’ ability to solve
problems involving the addition and subtraction of fractions.

Consolidate Whole Class ! Sharing

Debrief Students share the strategies they used to solve the problems, providing a Have overhead
complete explanation of how they attempted the solution and how they can manipulatives
available.
prove their solution is correct.
Record the different methods students used and lead them to see that there is
more than one valid strategy, e.g., is the same as
.

Home Activity or Further Classroom Consolidation

Application
Complete worksheet 7.8.2, Food Fractions.
Concept Practice

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 27

7.8.1: Fraction Party Problems
Solve the following problems involving fractions. Show or explain your strategies.

1. A recipe for Pink Party Punch calls for cups of raspberry juice, cups of ginger ale,

and cups of raspberry sherbet. How many cups of punch will the recipe make?

2. Sam filled 6 glasses with L of juice in each glass. How many litres of juice did he use?

3. Xia has 16 metres of rope. She cuts off of the rope to use as a skipping rope for a party

activity. How long is Xia’s skipping rope?

4. Tyson cut some bagels in half and some apples into eighths. At the end of the party, there
were 5 pieces of bagel and 11 slices of apple left. How many bagels and how many apples
were not eaten?

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 28

7.8.2: Food Fractions

Solve the following problems involving food and fractions. Show and/or explain the strategies
you used.

1. Three people shared a mega nutrition bar.

Which of the following statements are possible? Explain your reasoning.

a. Greg ate of the bar, Gursharan ate, and Mo ate .

b. Greg ate of the bar, Gursharan ate , and Mo ate .

c. Greg ate of the bar, Gursharan ate , and Mo ate .

d. Greg ate of the bar, Gursharan ate , and Mo ate .

2. Ms. Legume wants to use of her garden for lettuce and for beans.

What fraction of the garden does she have left for each of her carrots and her peas if they
both are to get the same amount of space?

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 29

Unit 7: Day 9: Dividing Whole Numbers by Fractions Using Concrete
Materials Grade 7
Math Learning Goals Materials
• Divide whole numbers by simple fractions using concrete materials, e.g., divide 3 • Fraction strips
• Linking cubes
by , using fraction strips. • Relational Rods
• Ruler
• Graph paper
• BLM 7.9.1
• BLM 7.9.2
Assessment (A) and DI (D)
Opportunities
Minds On… Whole Class & Pairs ! Solving a Problem
Pose the following questions related to division and have students solve Typical student
misconception:
questions in pairs using manipulatives.
4 =2
4 2= 4 = 6 3= 6 = 6 =
Suggest translating this
Encourage students to solve questions in a variety of ways and be prepared to into words: How many
explain their thinking / reasoning. halves are there in four
OR
Students share their solutions, using the blackboard or overhead.
show 4 circles each cut
Discuss the different representations (numerical, graphical, concrete in half. Count the
materials) of student solutions. halves to show the
answer of 8.
Action! Whole Class & Pairs ! Create a Problem & Gallery Walk
As a class – discuss and list the various real-life examples and applications of
dividing whole numbers by fractions. When dividing whole
numbers by whole
numbers the answer
In pairs, students will use BLM 7.9.1 to create and solve a realistic problem gets smaller
(division of whole numbers by fractions) and represent their solution in 2 BUT when dividing
ways (manipulatives, pictures, numbers, etc.) whole numbers by
fractions (smaller than
1) the answer gets
Students do a gallery walk (walk around and observe various questions and larger.
solutions).

Students complete the reflection part of BLM 7.9.1.

Curriculum Expectations/Demonstration/Marking Scheme: Assess

students’ understanding of dividing whole numbers by simple fractions.
Consolidate Whole Class ! Sharing/Discussion All activities are
assessment for learning
Debrief Briefly discuss the observations of the students during the gallery walk through discussion and
(context of questions, representations used, any number solutions, etc.). student work.

Have several different students share their problems and solutions.

Discuss and list the various representations students used to solve their Use various
representations
problems.
Home Activity or Further Classroom Consolidation Watch a 4 minute
Complete worksheet 7.9.2. video on dividing
fractions for a step-by-
Application
step how-to using
Concept Practice
algorithms:
http://www.mathplaygr
ound.com/howto_divid
e_fractions.html

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 30

7.9.1: Dividing Whole Numbers by Fractions Grade 7

Problem:

Representation 1: Representation 2:

What did you learn or notice during your gallery walk?

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 31

7.9.2: Dividing Whole Numbers by Fractions Grade 7
Name: _________________________ Date:_____________

Solve the following problems involving fractions. Show or explain your strategies.

1. How many quarters are in a roll of quarters ($10.00)? Explain.

2. For a class party, the teacher buys 3 bottles of 2 L pop. Each cup holds L. Will the
teacher have enough pop to fill 33 cups full?

3. It takes Mason of an hour to walk 4.6 km. How far can he walk in 1 hour?

4. Complete the chart below showing division of whole numbers by fractions.

Whole Fraction Quotient Diagram

10

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 32

7.9.2: Dividing Whole Numbers by Fractions Grade 7
Solutions
Solve the following problems involving fractions. Show or explain your strategies.

1. How many quarters are in a roll of quarters ($10.00)?

$10 = 40 OR $1 = 4 and 4 x 10 = 40 OR Draw 40 quarters OR

2. For a class party, the teacher buys 3 bottles of 2 L pop. Each cup holds L. Will the teacher
have enough pop to fill 33 cups full?

With 3 bottles, there are 6 L total. 6 ÷ = 30. Each 1 ÷ = 5. (Each whole can be
partitioned into 5 fifths.) Therefore 6 wholes can be partitioned into 30 fifths.
Therefore, the teacher will not have enough pop to fill 33 cups full.

3. It takes Mason of an hour to walk 4.6 km. How far can he walk in 1 hour?

In hour, Mason walks 2.3 km ( ÷2= and 4.6 km ÷ 2 = 2.3 km.) Therefore in
of an hour (or 1 whole hour), Mason can walk 6.9 km ( X 3 = and 2.3 km X 3 = 6.9 km).
*Note* This calculation is really “inverting and multiplying” but by first finding the unit
part ( ) and then the whole, the student is able to see why this works.
h h h h

0 km 2.3 km 4.6 km 6.9 km

4. Complete the chart below showing division of whole numbers by fractions.

Whole Fraction Answer Diagram

3 6

4 16

4 10

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 33

Unit 7: Day 10: Summative Assessment Grade 7
Math Learning Goals Materials
• Demonstrate an understanding of fractions and operations with fractions on • BLM 7.10.1
an open-ended, problem-solving task

Assessment (A) and DI (D)

Opportunities
Minds On… Small Group ! Placemat Activity Refer to Think
Literacy:
Have small groups of students use a Placemat organizer to solve one of the
Mathematics,
sample problems below. Gr. 7-9, pp. 102-104
Prompt students to write their full solution to the problem, including an
explanation of their thinking and strategy used
Consider making
In the centre of the placemat, each group writes a “model” solution to their homogeneous
problem student groupings
for the Placemat
Sample Problems activity
• divide 10 chocolate bars into quarters
• add 1 cup + cup Consider having
different groups
• pour out of a pail of water that is only full solve different
problems
• a student has already run of a lap in a 3 lap race – how many laps
remain?
• hour on computer, hour watching TV, hour playing video
games – what is total screen time?

As a whole class, discuss similarities, common misconceptions and possible

strategies to solve problems with fractions.
Action! Individual ! Assessment Task
Students work independently to complete BLM 7.10.1

Consolidate Whole Class ! Discussion

Debrief Discuss any questions that arise during the independent work period.

Curriculum Expectations/Quiz/Marking Scheme: Assess students’ ability to

solve problems involving operations with fractions, using a variety of tools.

Home Activity or Further Classroom Consolidation

After individual work has been assessed, teacher should select a variety of
solutions to highlight a range of solutions to share through congress or
Differentiated Bansho. Students look for similarities in solutions, reflect on their solution
Exploration and identify strategies to improve/clarify.
Reflection

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 34

7.10.1: Operations with Fractions Grade 7
Summative Assessment
You have been asked by your principal to help re-design a new eco yard at your school. The yard will
have to include the following sections:

of the yard will be a flower and vegetable garden

of the yard will be used for a creative play space with trees and shrubbery

of the yard will be used for open field space for soccer, football, etc.

The remainder of the yard will be used for basketball nets and 4-square.

1. Determine the total fraction of the yard used for garden, creative play and open field.
Explain your thinking.

Show your work and explain your thinking.

Final Answer:

2. The principal wants to know if there will be of the yard left over for basketball and

4-square. Show your calculations and draw a diagram that explains your answer to
the principal.

SCHOOL YARD

Explanation

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 35

7.10.1: Operations with Fractions Grade 7
Summative Assessment (Continued)
3. In the part of the yard used for basketball and 4-square, the area of each basketball
court is twice as big as each 4-square court.

a) The principal wants two basketball courts and four 4-square courts in this part of the yard. What
fraction of this part of the yard would be taken up by one 4-square court?

Show your work and explain your thinking.

Final Answer:

b) What fraction of the entire yard would each 4-square court be? Explain the strategy you used to
calculate the answer.

Explain your thinking.

Final Answer:

4. The area of the creative play space will only be used by the primary students. The
2
total area of the yard is 800 m . Calculate the area of the yard that will be used by
junior and intermediate students.

Show your work and explain your thinking.

Final Answer:

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 36

7.10.1: Operations with Fractions Grade 7
Summative Assessment Solutions
You have been asked by your principal to help re-design a new eco yard at your school. The yard will
have to include the following sections:

of the yard will be a flower and vegetable garden

of the yard will be used for a creative play space with trees and shrubbery

of the yard will be used for open field space for soccer, football, etc.

The remainder of the yard will be used for basketball nets and 4-square.

1. Calculate the total fraction of the yard used for garden, creative play and open field.
Explain your thinking.

Show your work and explain your thinking.

+ + = + + = =

Students could also draw a diagram.

Final Answer:

The total fraction of the yard used for garden, creative play & open field is .

2. The principal wants to know if there will be of the yard left over for basketball and

4-square. Show your calculations and draw a diagram that explains your answer to
the principal.

This diagram represents the schoolyard divided

into 12ths:

+ +

Because 1/3 of the yard would be 4/12, and only

3/12 is left over, there is only of the yard left

for basketball and 4-square.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 37

7.10.1: Operations with Fractions Grade 7
Summative Assessment Solutions
3. In the part of the yard used for basketball and 4-square, the area of each basketball
court is twice as big as each 4-square court.

c) The principal wants two basketball courts and four 4-square courts in this part of the yard. What
fraction of this part of the yard would be taken up by one 4-square court?

Each basketball court takes up of the

space. Because the basketball courts

are twice as big as the 4-square court,
each 4-square court would represent 1/8
of this part of the yard.

d) What fraction of the entire yard would each 4-square court be? Explain the strategy you used to
calculate the answer.

Explain your thinking

Each 4-square court is of of the entire yard. This means that there are

8 x 4 = 32 areas the same size as one 4-square court. Therefore each 4-square court
represents 1/32 of the entire yard.
Final Answer: 1/32 of the entire yard

4. The area of the creative play space will only be used by the primary students. The
2
total area of the yard is 800 m . Calculate the area of the yard that will be used by
junior and intermediate students.

The primary students will use ! of the

yard. This leaves " for the junior and
intermediate students.
2
Each quarter represents 200 m of the
yard. Three of these sections would be
2
600 m .

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 38

Unit 7: Day 11: Fractions and Decimals Grade 7
Math Learning Goals Materials
• Explore the relationship between fractions and decimals. • BLM 7.11.1,
7.11.2

Assessment
Opportunities
Minds On… Whole Class ! Review and Introduce New Problem
Ask students to think of any two fractions that are “really close.” Record a
few of their suggestions on the board.
Challenge them to choose one pair of fractions from the board and to find two
numbers that are between the two listed. Ask what types of numbers they
might use to solve this problem. Identify that they could use fractions or
decimals.

Action! Pairs ! Problem Solving

Two methods to
Students find two numbers between one pair of fractions listed on the board. change a fraction to
Pairs develop their own strategies and methods independently, share their a decimal on a
solutions to the problem, and their reasoning in finding the two numbers. If calculator are:
• divide the
they use decimals, they should make the connection to fractions.
numerator by the
denominator
Communicating/Observation/Anecdotal Note: Assess students’ ability to • enter the fraction
communicate their thinking using correct mathematical language. using the fraction
key ( ), press
ENTER, then
press the fraction
key again

Consolidate Whole Class ! Sharing The definition of

Debrief multiple may need to
Some discussion around the connection between fractions and decimals and be reviewed with
how to use a calculator to convert fractions to decimals would be useful. students.
Include number systems, common relationships that students are familiar
with, and applications/appropriateness of each in daily contexts.

Pairs ! Practice
Reinforce understanding of the fraction-decimal relationship (BLM 7.11.1).

Home Activity or Further Classroom Consolidation

Create three determine-the-decimal questions. Each one should have either Provide students
Concept Practice
Exploration two or three clues and all the clues should be needed to determine the with appropriate
decimal. practice questions
Reflection for exploring the
Complete the practice questions. relationship of
fractions to
decimals.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 39

7.11.1: Determine the Decimal
Determine the mystery decimal number from the clues listed.

1. The decimal is… Clue #1: greater than

Clue #2: less than

Clue #3: a multiple of

2. The decimal is… Clue #1: between and

Clue #2: greater than

Clue #3: a multiple of 0.11

3. The decimal is… Clue #1: a multiple of

Clue #2: between 2 and 3

4. The decimal is… Clue #1: less than

Clue #2: greater than

Clue #3: a multiple of 0.17

5. The decimal is… Clue #1: greater than

Clue #2: a multiple of 0.22

Clue #3: less than 1

6. The decimal is… Clue #1: between and

Clue #2: closer to than to one-half

Clue #3: a multiple of

7. The decimal is… Clue #1: multiple of

Clue #2: closer to 6 than to 3.5

Clue #3: not a whole number

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 40

7.11.2: Determine the Decimal Answers (Teacher)
Determine the mystery decimal number from the clues listed.

1. The decimal is… Clue #1: greater than

(0.15) Clue #2: less than

Clue #3: a multiple of

2. The decimal is… Clue #1: between and

(0.55) Clue #2: greater than

Clue #3: a multiple of 0.11

3. The decimal is… Clue #1: a multiple of

(2.25) Clue #2: between 2 and 3

4. The decimal is… Clue #1: less than

(0.85) Clue #2: greater than

Clue #3: a multiple of 0.17

5. The decimal is… Clue #1: greater than

(0.88) Clue #2: a multiple of 0.22

Clue #3: less than 1

6. The decimal is… Clue #1: between and

(0.3) Clue #2: closer to than to one-half

Clue #3: a multiple of

7. The decimal is… Clue #1: multiple of

(5.5) Clue #2: closer to 6 than to 3.5

Clue #3: not a whole number

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 41

Unit 7: Day 12: Decimals Grade 7
Math Learning Goals Materials
• Compare and order decimals to hundredths, using a variety of tools, e.g., • BLM 7.12.1
number lines, base-ten materials, calculators. • BLM 7.12.2
• Determine whether a fraction or a decimal is the most appropriate way to • Number lines
represent a given quantity, e.g., I would use a fraction to express part of an • Base-ten blocks
• Calculators
hour, saying “quarter hour” instead of “.25 of an hour.” • 10 x 10 grid
• Add and subtract decimals.

Assessment (A) and DI (D)

Opportunities
Minds On… Whole Class ! Discussion This lesson
Discuss and identify the connection between fractions and decimals from Lesson 11 reinforces students’
experience from the
and have students individually list real-life examples that use fractions and decimals.
junior grades with
Discuss whether the fraction or decimal notation is the most appropriate way to decimals.
represent a given quantity depending on the situation.
i.e., a measuring cup is in fractions but monetary value is usually in decimals
Have students label their list (F for fraction or D for decimal). Encourage use of
As a class, quickly discuss any problems that students faced (i.e., a quarter is the same manipulatives (base-
as $.25 and both are used in different scenarios). ten blocks and 10 x
10 grids) or use
Write 3 decimals on the board between 0 and 2 – using tenths and hundredths Gizmos: Ordering
(e.g., 0.4, 0.35 and 1.25). Fractions and
Have pairs of students represent one of these numbers using various manipulatives Decimals
(number line, base-ten blocks, 10x10 grid).
Choice of decimal in
Order these decimals on the board (possibly reviewing place value up to hundredths if activity allows for
needed). students to choose
decimals that are
Action! Whole Class ! Activity appropriate for them
Have students make up a decimal between 0 and 2 and write it on a small piece of (e.g., 0.5 or 1.31).
scrap paper. Students will stand up and place themselves in order around the outside Teacher Note:
of the room. You may choose to
Once they are in order, have students call out their numbers. do the same
Decide as a class whether everybody is in the correct order. Discuss a few examples ordering activity
on the board and/or using manipulatives to clarify any difficulties or misconceptions. including a choice of
fractions or decimals
Complete BLM 7.12.1 in pairs to consolidate these concepts. To clarify “hard” and to extend and
“easy”, the teacher could provide some criteria. E.g., “easy” means comparing up to 3 connect these
concepts further.
decimals, or the decimals are all written with the same place value i.e. hundredths.
“Hard” could mean that at least 4 decimals are compared and/or decimals are written
using different place values.

Curriculum Expectations/Demonstration/Marking scheme: Assess students’

understanding of comparing and ordering decimals as well as adding and subtracting
decimals.
Consolidate Whole Class ! Sharing/Discussion
Debrief Have students share strategies to represent, compare and order decimals as well as add
and subtract decimals.

Take up activity BLM 7.12.1 as a class and discuss any difficulties with the activity –
have pairs of students explain their reasoning. Share part E from handout where
students created their own problems.

Home Activity or Further Classroom Consolidation

Concept Practice Complete BLM 7.12.2

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 42

7.12.1: Decimals Grade 7
Name: Date:

1. Four students ran a 200m race. They each ran in a heat and in the finals. The times for the
two races were as follows:

Student Heat Time Final Time

A 25.34 s 25.29 s
B 26.12 s 25.13 s
C 25.89 s 25.45 s
D 25.45 s 25.01 s

A. In the Final race what place did each runner finish in?

B. Place the final running times for each runner on the number line below.

25 26

C. If the winner was decided by adding the heat time to the final time, which student would win
the race? Did they finish in the same order compared to the final? Show your work.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 43

7.12.1: Decimals (Continued) Grade 7
D. Which student showed the most improvement in their times from the heat to the final race?
Show your work.

E. Make up two problems using decimals. One problem has to be easy and the other problem
must be difficult. Solve each of your problems.

Problem One Problem Two

Solution One Solution Two

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 44

7.12.1: Decimals Solutions Grade 7
Name: Date:

1. Four students ran a 200m race. They each ran in a heat and in the finals. The times for the
two races were as follows:

Student Heat Time Final Time

A 25.34 s 25.29 s
B 26.12 s 25.13 s
C 25.83 s 25.45 s
D 25.45 s 25.01 s

A. What place did each runner finish in the final race?

Student A - first
Student B - fourth
Student C - third
Student D - second

B. Order the final running times from least to greatest on a number line.

25.01 s 25.13 s 25.29 s 25.45 s

25 25.50 26

C. If the winner was decided by adding the heat time to the final time which student would win
the race? Did they finish in the same order compared to the final? Show your work.

Student A Student B Student C Student D

25.34 s 26.12 s 25.83 s 25.45 s

+ 25.29 s + 25.13 s + 25.45 s + 25.01 s
50.63 s 51.25 s 51.28 s 51.46 s

Student A still came first, but Student B came second instead of fourth.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 45

7.12.1: Decimals Solutions (Continued) Grade 7
D. Which student showed the most improvement in their times from the heat to the final race?
Show your work.

Student A Student B Student C Student D

25.34 s 26.12 s 25.83 s 25.45 s

-25.29 s - 25.13 - 25.45 s - 25.01 s
0.05 s 0.99 s 0.38 s 0.44 s

Student B showed the greatest improvement from the heat to the final race.

E. Make up two problems using decimals. One problem has to be easy and the other problem
must be difficult. Solve each of your problems.

Problem One Problem Two

Solution One Solution Two

Answers will vary. Answers will vary.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 46

7.12.2: Decimals Grade 7
Name: Date:

1. Represent the following decimals using these 10x10 grids provided.

a. 0.4 b. 0.17

2. Compare the following decimals (<, > or =)

a. 0.8 __ 0.65
b. 14.5 __ 14.50
c. 1.68 __ 1.61

3. Place the following decimals in order on the number line below.

0.5, 1.37, 0.73, 0.7, 1.32

0 1 2

4. Add and subtract the following decimals.

34.51 17.82 524.79

+5.39 +18.27 - 32.85

9 – 3.25 = 780.05 + 17.9 =

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 47

7.12.2: Decimals Solutions Grade 7
Name: Date:

1. Represent the following numbers using these 10x10 grids.

a. 0.4 b. 0.17

2. Compare the following decimals (<, > or =)

a. 0.8 _>_ 0.65
b. 14.5 _=_ 14.50
c. 1.68 _>_ 1.61

3. Place the following decimals in order on the number line below.

0.5, 1.37, 0.73, 0.7, 1.32

0.5 0.7 0.73 1.32 1.37

0 1
2

4. Add and subtract the following decimals.

34.51 17.82 524.79

+5.39 +18.27 - 32.85
39.90 36.09 491.94

9 – 3.25 = 5.75 780.05 + 17.9 = 797.95

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 48

Unit 7: Day 13: Mental Math and Decimals Grade 7
Math Learning Goals Materials
• Use a variety of mental strategies to add and subtract decimals, e.g., use • 10x10 grid
the distributive property. • Money
• Divide whole numbers by decimal numbers to hundredths using concrete • Number line
materials. • BLM 7.13.1

Assessment (A) and DI (D)

Opportunities
Minds On… Whole Class! Solving a Problem When dividing whole
Present the problems below to the class in order to explore mental math strategies with numbers by whole
numbers the answer
decimals.
gets smaller
BUT when dividing
John went to the corner store to buy a big bag of chips that costs $2.89 and a bottle of whole numbers by
pop for $1.49. How much did he spend? If he brought $5, how much change did he decimals (smaller
get? Note: You may not use a pencil or calculator. than 1) the answer
(Note: Ignore taxes for the purpose of today’s activities – focus on mental math aspect gets larger.
of the lesson.)
Distributive property
– allows numbers to
Students share and discuss strategies they used to solve the problem.
be decomposed
using place value.
Jenny had a $5 bill and wanted to get quarters to play the video game at the store. E.g. 3.92 is 3 + 0.9 +
How many quarters did the store owner give Jenny? Show this as a division question. 0.02
(Answer: 5 0.25 = 20).
Instructions
Be sure to discuss mental math strategies including: rounding, distributive property explicitly state not to
(e.g. 2.89 + 1.49 = 2 + 1 + 0.90 + 0.50), number lines, adding whole numbers then use a calculator –
decimals, etc. some students may
Action! Groups ! Solving a Problem require a calculator
or paper/pencil to
Distribute chart paper and BLM 7.13.1 to students in same-ability groupings (2-4
complete these
students per group). Have students explain their solution to question #4 in detail on a tasks.
piece of chart paper.
Access Gizmo:
Curriculum Expectations/Demonstration/Marking scheme: Assess students’
Sums and
understanding of mental math strategies involved in addition and subtraction of differences with
decimals decimals

Consolidate Whole Class ! Presentation/Discussion/Sharing Strategies

Debrief Teacher leads a discussion about the solutions to questions 1-3. Even though students
may have the same final answers, their strategies may be quite different and these
variations can be highlighted.

Post chart papers showing solutions to question #4 on the blackboard. Have groups
present their answers and have students share their mental math strategies. Encourage
the class to question their peers to help them deepen their understanding of each
other’s strategies.

Practise some of the key mental math strategies that were used through a few new
questions such as: How much would it cost for a package of bubble gum and a
container of white milk? (Solve this using the idea of distributive property).
Home Activity or Further Classroom Consolidation
Have students take an advertisement from a local grocery store flyer and buy 3
Application
different items for as close to $10 as possible. Explain the mental math strategy that
Concept Practice
they used.
Differentiated

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 49

7.13.1: Mental Math and Decimals Grade 7
Names: Date:

You are going to the corner store. The following items can be purchased:
(Remember you are not allowed to use a calculator and the strategies you use must be doable
without a pencil)

Small bag of chips .............................................. $1.29

Chocolate Bar ...................................................... $0.89
Package of Liquorice ........................................... $3.43
Package of Bubble Gum ..................................... $1.48

Chocolate Milk (500 mL) ..................................... $1.15

White Milk (500 mL) ............................................ $1.15
Bottle of Pop ......................................................... $1.49
Bottle of Water...................................................... $2.41

Giant Freezie ....................................................... $0.87

Popsicle ................................................................ $0.50
Slushie ................................................................. $3.27

1. a) How much would it cost to buy a chocolate bar and a bottle of water? Show the mental
math strategy you used.

b) How much change would you receive from a $5.00 bill?

2. If you and your friends wanted to buy 3 chocolate milks, 3 bags of chips and a package of
liquorice. If you had a $10.00 bill, would you have enough money?

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 50

7.13.1: Mental Math and Decimals (Continued) Grade 7
3. a) How much would it cost to buy a Slushie, a freezie and a package of gum? Show the
mental math strategy that you used.

b) You had a toonie, three loonies, 5 quarters, 8 dimes and 10 nickels. How much change
would you receive from your purchase?

4. You have $8.00 to spend. What would you buy? What is the total cost? How much change
did you receive? (Whatever money you don’t spend goes back to your parents so be sure to
spend as close to $8 as you can)

5. You have $4.00, how many freezies can you buy? (Show a division equation in your
answer).

6. You have $10.00. Jasdeep thinks you can buy 7 bottles of pop. Is she right? Explain your
thinking.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 51

7.13.1: Mental Math and Decimals Solutions Grade 7
Name: Date:

You are going to the corner store. The following items can be purchased:
(Remember you are not allowed to use a calculator and the strategies you use must be able to
have been done without a pencil)

Small bag of chips .............................................. $1.29

Chocolate Bar ...................................................... $0.89
Package of Liquorice ........................................... $3.43
Package of Bubble Gum ..................................... $1.48

Chocolate Milk (500 mL) ..................................... $1.15

White Milk (500 mL) ............................................ $1.15
Bottle of Pop ......................................................... $1.49
Bottle of Water...................................................... $2.41

Giant Freezie ....................................................... $0.87

Popsicle ................................................................ $0.50
Slushie ................................................................. $3.27

1. a) How much would it cost to buy a chocolate bar and a bottle of water? Show the mental
math strategy you used.

$0.89 + $2.41 = $3.30

(Students will use various strategies – we will provide a few examples but many
others will arise)
$1 - .11 +2.41 = 3.41 - .11 = 3.30
$.90 - .01 +2.41 = 3.31 - .01 = 3.30
$.90 + $2.40 = $3.30

Strategies: Number line

Money - change

b) How much change would you receive from a $5.00 bill?

$5 - $3.30 = $1.70
Many strategies should be explored

2. If you and your friends wanted to buy 3 chocolate milks, 3 bags of chips and a package of
liquorice. If you had a $10.00 bill, would you have enough money?

3 Chocolate Milks: $1.15 + $1.15 + $1.15 = $3 + .45 = $3.45

3 Chips: $1.29 + $1.29 +$1.29 = $1.30 x 3 - .01 x 3 = $3.90 - .03
= $3.87
Liquorice: $3.43 = $3.43
$10.75
By inspection – you can see that with $.87 and $9, as well as $.45 and $.43 it is easily
more than $10.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 52

7.13.1: Mental Math and Decimals Solutions Grade 7
Continued
3. a) How much would it cost to buy a Slushie, a freezie and a package of gum? Show the
mental math strategy that you used.

Slushie $3.27 $3 and $1 = $4 .48 and .27 = .75 and .87

Freezie $0.87 Many strategies should be explored
Gum $1.48
$5.62

b) You had a toonie, three loonies, 5 quarters, 8 dimes and 10 nickels. How much change
would you receive from your purchase?

$2 + $3 + $1.25 + $.80 + $.50 = $6 + $.25 + $1.30 = $7.55

$7.55 - $5.62 = almost $2 = $2 - .07 = $1.93

4. You have $8.00 to spend. What would you buy? What is the total cost? How much change
did you receive? (Whatever money you don’t spend goes back to your parents so be sure to
spend as close to $8 as you can)

Answers will vary and mental math strategies should be explored in discussion!

5. You have $4.00, how many freezies can you buy? (Show a division equation in your
answer).

$4 .50 = 8

6. You have $10.00. Jasdeep thinks you can buy 7 bottles of pop. Is she right? Explain your
thinking.

$10 $1.49 = ? $1.50 + 1.50 + 1.50 + 1.50 + 1.50 + 1.50 + 1.50 = $10.50 - .07 = $10.43

OR $10 $1.50 = 7 would be $10.50 so not enough

$10 $1.50 = 6 would get you $1 left over
Jasdeep was wrong – she doesn’t quite have enough!

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 53

Unit 7: Day 14: Multiplying Decimals Grade 7
Math Learning Goals Materials
•Multiply decimal numbers to thousandths by one-digit whole numbers, using • BLM 7.14.1
concrete materials, calculators, estimation, and algorithms • BLM 7.14.2
•Solve problems involving the multiplication of decimal numbers • BLM 7.14.3
• Bingo chips

Assessment (A) and DI (D)

Opportunities
Minds On… Whole Class! Discussion Encourage students to
Pose this problem: reason out the answer
There were 3 mini-watermelons that weighed 2.132 kilograms each. How much was and placement of the
decimal, rather than
the total weight?
the need to count the
decimal places when
As a class discuss an estimation for the following question: multiplying decimals.
2.132 x 3 =
(The answer will be more than 6 because 2 X 3 = 6)
Using base-ten
blocks and grids helps
Students complete the following questions: visual and tactile
21 x 3 = (63) learners. Blackline
2.1 x 3 = (6.3) masters for base-ten
grids can found on
213 x 3 = (639) eworkshop under
2.13 x 3 = (6.39) printable documents.

2 132 x 3 = (6 396) Use Gizmo:

2.132 x 3 = (6.396) Multiplying with
Decimals
Students will check their answers with a calculator. Ask the following questions:
• What patterns do you notice? Students need to
The answers are the same without the decimal but the placement of the decimal is make sure that they
determined by looking at the question and figuring out where the decimal goes in have four answers for
the answer. each column in the
Math Bingo Game,
• What happens when you add 2.132 + 2.132 + 2.132 = ?
therefore they only
• Can you represent 2.132 x 3 in a different way? (Distributive Property) need to complete four
(2 x3) + (0.1 x 3) + (0.03 x 3) + (0.002 x 3) = questions. (Calculators
may be used by
Do another question with the class: students if needed.)
3175 x 4 = (12 700 or Can you have an answer of 127?)
3.175 x 4 = 12.700 or 12.7 For an expansion of
Discuss the placement of the zeroes in the question without a decimal and with a the Distributive Model
using area, see these
decimal.
two Gizmos from
Action! Individual and Whole Class ! Math Bingo Game www.explorelearning.
com: Multiplying with
Students complete the questions on BLM 7.14.2 prior to playing the Math Bingo
Decimals and
Game. They must also fill out their chart. Multiplying Decimals
(Area Model). Watch
Teacher plays Math Bingo Game with students. the Demo movie for
the latter Gizmo to see
Curriculum Expectations/Observations/Anecdotal Notes: Assess students’ ability an excellent
to multiply decimals by whole numbers. explanation of the
model in action.
Consolidate Whole Class!Sharing
Debrief Have students come up with real-life examples of multiplication of decimals by whole Identify ahead of time
numbers (money, gas, weight, distance, time, etc.). students who have
Identify any misconceptions (the placement of the decimal in the answer and the interesting strategies
relationship to the question) that were observed when multiplying decimals by whole to share with the class.
numbers and effective strategies that were used by students to find solutions.

Application
Home Activity or Further Classroom Consolidation If used for classroom
Complete problems on BLM 7.14.3 that reinforce the multiplication of decimals. consolidation, BLM
Concept Practice 7.14.4 could be
completed in pairs.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 54

7.14.1 Multiplying Decimals Overhead Transparency Grade 7

21 X 3 = ___________

2.1 X 3 = ___________

213 X 3 = ___________

2.13 X 3 = ___________

2132 X 3 = ___________

2.132 X 3 = ___________

Represent 2.132 X 3 as a sum:

Use the Distributive Property to represent

this sum another way:

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 55

7.14.2: Multiplying Decimals Grade 7

Name: ____________________ Date:___________

Complete the questions below. Place any 16 of the answers in the MATH Chart at the
bottom for a quick game your teacher will lead when you are done. Your answers
should be placed in the appropriate columns M (0-1), A (1-10), T (11-20), H (20+)

3.42 x 2 = 72 55
34.2 x 2 = x 0.25 x 0.25
0.342 x 2 =

1.75 x 5 =
.175 x 5 =
0. 125 0. 125
8 x 1.23 = x 99 x 88
8 x .123 =

1 x .333 =
3 x .333 =
4 x .333 = 8. 58 8. 58
x 42 x 37
7 x 2.25 =

2. 651 2. 651 2. 651

x 3 x 23 x 78

M (0-1) A (1-10) T (11-20) H (20+)

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 56

7.14.2: Multiplying Decimals (Teacher Copy) Grade 7
Name: ____________________ Date:___________

When students have completed their work, read out questions from the worksheet
below randomly (ensuring to choose questions with answers in each category).
Students will circle their answers in their MATH Chart (if they got the right answer and
placed it in their chart). The first student to get MATH in a row wins! Continue to
correct the rest of the worksheet when finished the game.

3.42 x 2 = 6.84 A 72 55
34.2 x 2 = 68.4 H x.25 x.25
.342 x 2 = .684 M 18.00 T 13.75 T

1.75 x 5 = 8.75 A
.175 x 5 = .875 M
.125 .125
8 x 1.23 = .984 M x 99 x 88
8 x .123 = 9.84 A 12.375 T 11.000 T

1 x .333 = .333 M
3 x .333 = .999 M
4 x .333 = 1.332 A 8.58 8.58
x 42 x 37
7 x 2.25 = 15.75 T 360.36 H 317.46 H

2.651 2.651 2.651

x 3 x 23 x 78
7.953 A 60.973 H 206.778 H

M (0-1) A (1-10) T (11-20) H (20+)

Any of:
.684 6.84 15.75 68.4
.875 8.75 18.00 360.36
.984 9.84 13.75 317.46
.333 1.332 12.375 60.973
.999 7.953 11.000 206.778

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 57

7.14.3 Multiplying Decimals Grade 7
Name: ____________________ Date:___________

1. Manuel went to the store to buy three pairs of jeans that cost $ 29.89 per pair. What is the
total cost of the purchase?

2. Ishmael’s dad had to purchase gas for his car 5 times in one month. Gas costs 97.7 cents
per litre and he purchased 65 L each time. How much would gas cost him for the one month?

3. Lisa lives 1.357 km from school and walks everyday.

How many kilometres does she walk in a week? (HINT: She also has to walk home.)

4. Chicken costs $8.80 a kilogram. The recipe you are making for a party requires you to buy 6
kilograms of chicken. How much will the chicken cost you?

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 58

7.14.3 Multiplying Decimals Solutions Grade 7
Name: ____________________ Date:___________

1. Manuel went to the store to buy three pairs of jeans. The jeans cost $29.89, how much was
the cost of the jeans?

$29.89 x 3 = $89.67

2. Ishmael’s dad had to fill up his car 5 times in one month. Gas costs 97.7 cents per litre. If
his car requires 65 L, how much would gas cost him for the one month?

97.7 x 65 = 6350.5 cents

6350.5 x 5 = 31752.5 cents

How many dollars is this? $317.525 rounded to $317.53

OR $0.977 x 65 = $63.505
$63.505 x 5 = $317.525 rounded to $317.53

3. Lisa walks 1.357 km to school everyday. How many kilometres does she walk in a week?
(HINT: She also has to walk home.)

1.357 km x 2 = 2.714 km
2.714 km x 5 (number of days in a normal school week) = 13.57 km

OR 1.357 km x 10 = 13.57 km

4. Chicken costs $8.80 a kilogram. The recipe you are making for a party requires you to buy 6
kilograms of chicken. How much will the chicken cost you?

$8.80 x 6 = $52.80

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 59

Unit 7: Day 15: Dividing Decimals Grade 7
Math Learning Goals Materials
• Divide whole numbers by decimals to hundredths, using concrete materials, • Hundredths Grids
e.g. base-ten materials to divide 4 by 0.8 • Play money
• Divide decimal numbers to thousandths by one-digit whole numbers, using • Fraction strips
concrete materials, estimation, and algorithms, e.g., estimate 16.75 3 as • BLM 7.15.1
• BLM 7.15.2
18 3 6, then calculate, predicting an answer slightly less than 6
• Solve everyday problems involving division with decimals.

Assessment (A) and DI (D)

Opportunities
Minds On… Whole Class! Discussion Identify with the
students that the
Using hundredths grids or fraction strips have students complete the
whole is the one
following: 4 2 = (Answer: 2); 4 0.2 = ( Answer: 20); hundredths grid, or
4 0.25 = ( Answer: 16) show them what the
• What did you notice about your solution when you divided a whole whole is with fraction
strips.
number by a whole number and a whole number by a decimal? (The
answer gets larger when dividing by decimals rather than a whole.)
• Why did the answer get smaller when dividing by 0.25 compared to 0.2?

Use the fraction strips or hundreds chart to create two questions that show a
whole number being divided by a decimal number and explain your thinking.
(e.g. 3 0.5 or 4 0.8)
Instead of dividing a whole by a decimal number, students will now solve a
problem that involves dividing a decimal number by a whole number.
15 3 = 5
1.5 3 = 0.5
0.15 3 = 0.05
0.015 3 = 0.005
Use a drawing or number line to represent the solutions. Discuss with Students may
students the placement of the decimal in the answer and the size of the need to use play
money.
answer. Ask students if their answer seems reasonable.
Action! Pairs! Problem Solving
Pose the following question to students:
Math
You and your two friends did some work around the house for your family. Congress is a format
They emptied their penny jar and gave you and your friends $22.86 to share that allows for the
evenly. How much did each of you make? sharing and
Students are not allowed to use a calculator. Students in pairs solve the discussing of
various student
question on chart paper or on BLM 7.15.1. Encourage students to use solutions. During
manipulatives and different strategies to solve the problem. the congress various
Scaffolding: Why can’t the answer be $8 or more? strategies and big
What if it was only you and ONE friend? ideas are
highlighted.
Communicating/Observation/Anecdotal Note: Assess students’ ability to
communicate their thinking using correct mathematical language.
Consolidate Choose different students to share their answer (math congress), making sure
Debrief that the answers displayed show different strategies.
Identify the key ideas and different strategies that were used.
Home Activity or Further Classroom Consolidation The concept of
Application Students will complete BLM 7.15.2. rounding repeating
Concept Practice decimals needs to
Discuss with students the answer to question 5 because the concepts of be discussed.
Skill Drill estimation and repeating decimals are encountered with these questions.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 60

7.15.1: Dividing Decimals Grade 7
Name: Date:

You and your two friends did some work around the house for your family. They
emptied their penny jar and gave you and your friends $22.86 to share evenly. How
much did each of you make?

A. Estimate your answer and explain your reasoning.

B. Solve and show your thinking.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 61

7.15.1: Dividing Decimals: Grade 7
Answers and Discussion Sheet
Name: Date:

You and your two friends did some work around the house for your family. They emptied their penny jar
and gave you and your friends $21.86 to share evenly. How much did each of you make?

A. Estimate your answer and explain your reasoning.

As a class discuss an estimation for the following question:

21 3 = 7
Talk about using “friendly numbers” - the closest number that can be divisible by
3 that is closest to $22.86 is $21.00 without going over the original amount. Each
person will receive more than $7. (Each person would not receive $8.00 because
$8 x 3 = $24.00)

B. Solve and show your thinking.

Possible student solutions:

A. $22.86 3=

22 3 = 7 remainder 1 ! 1.86 3 = 0.62

$7.62

B. Some students will have use the standard algorithm.

C. Some students might use a number line.

D. Some students are going to draw money or use play money if available. (DI)

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 62

7.15.2: Division with Decimals Grade 7

Name:______________________________ Date:___________________

Represent the following questions using diagrams.

1) 2 0.5 = 2) 5 0.25 = 3) 0.75 3=

Solve the following problems.

4) You made $90 at work in a week. Your hourly wage is $7.50. How many hours did you
work that week?

5) a) You bought $8 worth of gas for your lawnmower. The cost of the gas was
$0.925 per litre. Estimate how many litres of gas you bought. Explain your
thinking. Is your estimate higher or lower than you believe the final answer
should be?

b) Exactly how much did you buy (correct to thousandth decimal place)?

6) You and 3 friends bought 2.36 kg of candy. You need to share the candy equally. How
much candy does each person get?

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 63

7.15.2: Division with Decimals Solutions Grade 7

Name: Date:

Represent the following questions using diagrams.

1) 2 0.5 = 4 2) 5 0.25 = 20 3) 0.75 3 = 0.25

0 0.25 0.5 0.75

Solve the following problems.

4) You made $90 at work in a week. Your hourly wage is $7.50. How many hours did you
work that week?

$90 per hour $7.50 = 12 hours

5) a) You bought $8 worth of gas for your lawnmower. The cost of the gas was $0.925 per
litre. Estimate how many litres of gas you bought. Explain your thinking. Is your
estimate higher or lower than you believe the final answer to be?

$8 $1 per litre = 8 litres

Our estimate will be slightly too low because we divided by a whole dollar but the
cost was less than a dollar.

OR $8 $0.90 per litre = almost 9 litres

Our estimate will be slightly too high because we divided by less than the cost of
the gas.

b) Exactly how much did you buy (correct to thousandth decimal place)?

$8 $0.925 per litre = 8.648648648 litres

rounded to 8.649 litres

6) You and 3 friends bought 2.36 kg of candy. You need to share the candy equally. How
much candy does each person get?

2.36 kg 4 = 0.59

OR 2 4 = 0.5 and .36 4 = 0.09 so 2.36 4 = 0.50 + 0.09 = 0.59

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 64

Day 16: Solving Multi-Step Problems Involving Decimals Grade 7
Math Learning Goals Materials
• Solve multi-step problems involving whole numbers and decimals. • Calculators
• Justify solutions using concrete materials, calculators, estimation, and • Various concrete
algorithms. materials to
• Use estimation when solving problems involving decimals to judge the represent
fractions and
reasonableness of a solution, e.g. A book costs $18.49. The salesperson
decimals
tells you that the total price, including taxes, is $22.37. How can you tell if • BLM 7.16.1
the total price is reasonable without using a calculator? BLM 7.16.2
Assessment (A) and DI (D)
Opportunities
Minds On… Whole Class! Small Group! Review Operations with Decimals
Give each small group the following organizer:
Addition with Decimals Subtraction with Decimals Students may
need to use a
calculator.
Multiplication with Decimals Division with Decimals

Groups then work together to fill in each section with important ideas,
reminders and strategies when solving problems involving the particular
operations and decimals. Each section must have at least one sample problem
and solution.

Time permitting – have groups conduct a gallery walk to see what other
groups have written and then return to their original placemat and
record/discuss their observations from other group’s organizer. Discuss as a
class any “aha” moments.
Math
Action! Small Group! Whole Group! Problem Solving
Congress is a format
In small homogeneous groups, students complete BLM 7.16.1. Encourage that allows for the
students to use manipulatives and different strategies to solve the problems. sharing and
Students are to put their solutions for question number 4 on a piece of chart discussing of
various student
paper. solutions. During
the congress various
Choose different students to share their answer (math congress), making sure strategies and big
that the answers displayed show different strategies. ideas are
highlighted.
Curriculum Expectations/Observations/Checklist: Assess students’ ability to
solve multi-step problems involving whole numbers and decimals.
Consolidate Whole Group! Group Discussion
Debrief Discuss the student solutions, identifying big ideas involving the operations
of decimals (estimation, arithmetic properties, thinking of decimals as parts).
Home Activity or Further Classroom Consolidation An online game that
Students can fill out an exit card that identifies questions they still have about requires students to
multiply and divide
the operation of decimals and anything they found interesting or an “aha” decimals is
Differentiated moment that they encountered when adding, subtracting, multiplying and “Midnight at the
Reflection dividing decimals. See sample on BLM 7.16.2. Super Big”.
http://www.learningw
ave.com/lwonline/deci
mal13/midnight_worki
ng/midnight.html

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 65

7.16.1: Solving Multi-Step Problems Involving Decimals Grade 7

Name: ___________________________ Date:___________________

Solve the following problems. Show your work.

Riley and Caileigh go shopping at a mall. They are each planning on buying 1 pair of jeans and
2 shirts. They each brought $100. (No taxes on their purchases.)

Store A Store B Store C

Jeans A $39.97 Jeans B $44.99 Jeans C $49.95
2 Shirts A for $44.48 Shirt B $22.49 Shirt C $19.45

1. At what store should Riley and Caileigh shop to spend the least amount of money?

2. Riley really likes the jeans from Store B, a shirt from Store A and another shirt from
Store C. Does she have enough money to buy these clothes? If so, how much money
would she get back?

3. Caileigh decides that she really wants to get 2 pairs of jeans and 1 shirt. Is it possible
for her to do this if she shops at different stores? Explain.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 66

7.16.1: Solving Multi-Step Problems Involving Decimals Grade 7
Continued

4. The stores are offering different discounts. Please figure out the best deal to buy one
pair of jeans and 2 shirts from the same store.

Store A (10% off)

Store B (Buy one jeans, get one shirt at 50% off)
Store C (25% off jeans)

a) Spend a few minutes discussing which you think will be the best deal.

b) Determine the exact answer.

Store A Store B Store C

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 67

7.16.1: Solving Multi-Step Problems Grade 7
Involving Decimals (Teacher Answers)
Name: ___________________________ Date:___________________

Riley and Caileigh go shopping at a mall. They are each planning on buying 1 pair of jeans and 2 shirts.
They each brought $100. (No taxes on their purchases.)

Store A Store B Store C

Jeans A $39.97 Jeans B $44.99 Jeans C $49.96
2 Shirts A for $44.48 Shirt B $22.48 Shirt C $20.46

1. At what store should Riley and Caileigh shop to spend the least amount of money?

Store A Store B Store C

$39.97 + 44.48 = $84.45 $44.99 + 22.48 + 22.48 = $89.95 $49.96 + 20.46 + 20.46 = $90.88

2. Riley really likes the Jeans from Store C, a shirt from Store A and another shirt from Store B.
Does she have enough money to buy these clothes? If so, how much money would she get
back?

Jeans C $49.96 Cost: 49.95 + 22.24 + 22.48 = $94.68

Shirt A $44.48 2 = $22.24 Yes, she has enough money to buy them.
Shirt B $22.48 Change: 100 – 94.68 = $5.32

3. Caileigh really wants to get 2 pairs of jeans and 1 shirt. Is it possible for her to do this if she
shops at different stores? Explain.

Cheapest jeans are from Store A: $39.97 x 2 = $79.94

Cheapest shirt is from Store C: $20.46

79.94 + 20.46 = $100.40

Caileigh does not have enough money to do this – she is short $0.40.

4. The stores are offering different discounts. Please figure out the best deal to buy one pair of
jeans and 2 shirts from the same store.
Store A (10% off)
Store B (Buy one jeans, get one shirt at 50% off)
Store C (25% off jeans)

a) Estimate: Answers will vary – discussion/reasoning in groups is important

Many students will presume that Store B will have the best deal because it has 50%
off.
Other students will estimate that Store A will have the best deal because Store A
was the cheapest from question 1.
Other students will estimate that Store C will have the best deal because jeans are
the most expensive.
b) Actual:
Store A Store B Store C
Cost at store A (from 1) One shirt is 50% off Jeans 25% off
$84.46 $22.48 2 = $11.24 $49.96 4 = $12.49
10% off is $8.45 Jeans cost:
(84.46 x .10) $49.96 – 12.49
= $37.47
Cost: Cost:
84.46 – 8.45 44.99 + 11.24 + 22.48 Cost:
= $76.01 = $78.71 37.47 + 20.46 + 20.46
= $78.39
TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 68
7.16.2: Solving Multi-Step Problems Grade 7
Involving Decimals

EXIT CARD

NAME: DATE:__________________

1. Rate your confidence (1-5) when doing the following operations with decimals.
(1 is not confident and 5 is very confident)

Adding Subtracting Multiplying Dividing

2. What questions do you still have about operations with decimals?

3. What did you learn about doing operations with decimals or what was an “aha” moment
for you?

EXIT CARD
NAME: DATE:__________________

1. Rate your confidence (1-5) when doing the following operations with decimals.
(1 is not confident and 5 is very confident)

Adding Subtracting Multiplying Dividing

2. What questions do you still have about operations with decimals?

3. What did you learn about doing operations with decimals or what was an “aha” moment
for you?

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 69

Unit 7: Day 17: Summative Assessment of Decimals Grade 7
Math Learning Goals Materials
• Demonstrate an understanding of decimals and operations with decimals • BLM 7.17.1
• Calculators

Assessment (A) and DI (D)

Opportunities
Minds On… Whole Class ! Review and Discussion Students may
Ask the class to bring out their exit cards from the previous day and discuss use calculators or
answers. work in pairs

See online
Or, if the students did not complete exit cards, ask and discuss the following resource list for
questions: suggested online
• Are there any questions about the operation of decimals? games and tools to
• Are there any ideas they found interesting or an “aha” moment that they support previous
concepts.
encountered when adding, subtracting, multiplying and dividing
decimals?
• Are there any big ideas or strategies to remember when working with
decimals?
Have students
work in groups for
Action! Individual ! Summative Assessment Piece a few minutes to
Students independently will complete BLM 7.17.1. discuss their initial
thoughts /
strategies about
Curriculum Expectations/Quiz/Marking Scheme: Assess students’ ability to solve the problems (but
problems involving operations with decimals, using a variety of tools. they are not
allowed to write
anything on their
paper).
Consolidate Whole Class ! Discussion
Debrief Collect papers and identify solutions that show different strategies.
Ask students if there were any questions that they had difficulty with. Ask
students to discuss and display the different ways that they solved the
identified problem(s).

Follow up activity
Identify a variety of solutions that effectively displayed the ability to clearly Assessment as
Learning
communicate a solution. Discuss the attributes that made the solution a clear opportunity as
Reflection example of effective communication. students reflect on
their learning.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 70

7.17.1: Summative Assessment Grade 7
Name: Date:

Below is a diagram of your new bedroom. (Note: The diagram is not exactly to scale.)

1.0 m

3.00 m
1.85 m
Bed 1.0 m

0.6 m
Dresser

3.24 m
1. a) You are going to get flooring for your new room. You need to know the area of the
floor in order to determine how much it will cost to buy hardwood floors. What is the
area of the room?

b)The total cost for the hardwood floor was $425.00. How much did it cost per square
metre?

2. a) You are also putting baseboards around the room. Baseboards come in pieces that
are 1.5 m long. How many pieces will you need?

b) The cost of baseboards is $8.97 per piece from part a. Estimate, using whole
numbers, how much it will cost you to put baseboards in your room. Make a second
more accurate estimation that includes a decimal. Explain your thinking.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 71

7.17.1: Summative Assessment Continued Grade 7

3. a) A cousin is coming to live with you and you need to share your room with him/her.
You have been told that you have to give your cousin half of the room. How much floor
space will your cousin get?

b) Your cousin is bringing a bed and a desk that are the same size as yours. How much
floor space will be left in the room after your cousin moves in?

c) Your parents are bugging you to practice your math. They ask you if you can figure
out about what fraction of the room is covered? Explain your thinking to them.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 72

7.17.1 Summative Assessment Solutions Grade 7
Name: Date:

Below is a diagram of your new bedroom. (Note: The diagram is not exactly to scale)

1.0 m

3.00 m
1.85 m
Bed
1.0 m

0.6 m
Dresser

3.24 m
1. a) You are going to get flooring for your new room. You need to know the area of the
floor in order to determine how much it will cost to buy hardwood floors. What is the
area of the room?

Area =lxw
= 3.24 m x 3 m
= 9.72 m2

b) The total cost for the hardwood floor was $425.00. How much did it cost per square
metre?

Solution: $425 9.72 m2

= $ 43.7242798
Rounded to 43.72
Final Answer: $43.72 per m2

2. a) You are also putting baseboards around the room. Baseboards come in pieces that
are 1.5 m long. How many pieces will you need?

Perimeter of the room = 3 + 3 + 3.24 + 3.24

= 12.48 m
One solution: Another solution:
1.5 x 8 pieces = 12m 3.0 m side ! 2 pieces (3 1.5 = 2)
1.5 x 9 pieces = 13.5m 3.24 m side ! 2 and a bit pieces Total of 8+ pieces
(9)

OR 12.48 1.5 = 8.32 (not an expected solution for grades 7)

So, you need 9 pieces.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 73

7.17.1 Summative Assessment Solutions Grade 7
b) The cost of baseboards is $8.47 per piece from part a. Estimate how much it will cost
you to put baseboards in your room. Make a second more accurate estimation that
includes a decimal. Explain your thinking.

Possible Answers
Estimate 1: $10 x 9 pieces = $90

OR $9 x 9 pieces = $81

Estimate including a decimal: $8.5 x 9 pieces = $76.50

3. a) A cousin is coming to live with you and you need to share your room with them.
You have been told that you have to give your cousin half of the room. How much floor
space will they get?

Possible Solutions
Solution 1: Area 2 = 9.72 2 = 4.86 m2

Solution 2: length 2 x width = 3.24 2 x 3 = 1.62 x 3 = 4.86 m2

Solution 3: length x width 2 = 3.24 x 3 2 = 3.24 x 1.5 = 4.86 m2

b) Your cousin is bringing a bed and a desk that are the same size as yours. How much
floor space will be left in the room after your cousin moves in?

Solution: Area of desks = 1.85 x 1 x 2 = 3.7 m2

Area of dressers = 0.6 x 1 x 2 = 1.2 m2

Answer: Area of Room – Area of Desks – Area of Dressers

= 9.72 – 3.7 – 1.2
= 4.82 m2

c) Your parents are bugging you to practice your math. They ask you if you can figure
out about what fraction of the room is covered? Explain your thinking to them.

4.82 m2 is covered
9.72 m2 is the total area

4.82 is very close to 5

9.72 is very close to 10

5 is half of 10. Therefore, of the room is covered with furniture.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 74

Unit 7: Day 18: Percent Grade 7
Math Learning Goals Materials
• Investigate and represent the relationships among fractions, decimals, and • BLM 7.18.1
percents • Van de Walle
• Identify common uses of percents, fractions and decimals hundredths disk
• Estimate percents visually, e.g., shade 60% of a rectangle, and mentally,
e.g., 3 out of 11 hockey players missed practice means approximately 25%
were absent

Assessment (A) and DI (D)

Opportunities
Minds On… Small Group ! Think Pair Share
Students activate prior knowledge by discussing familiar uses of percents (e.g.
discounts at stores, basketball statistics, 2% milk, etc.), fractions (e.g. baking) and
decimals (e.g. batting averages, money). Make connection to
French: “per” = of;
Whole Class ! Discussion “cent” = 100.
Teacher constructs a familiar shape (see samples below) and asks students what Percent means “out
fraction each section represents. Students may use a variety of strategies but should of 100” or
“hundredth” and
recognize the relative fraction as part of the whole.
percent represents a
fraction out of 100.
Teacher prompts students: “If this shape was divided into 100 equal pieces, how (E.g. 40/100 = 40%)
many pieces would be shaded? (e.g. 2/5 would be 40/100; ! would be 50/100) How
would this be expressed as a fraction?” See Teaching
Student Centred
Teacher models relationship with Van de Walle hundredths disks. Make these disks Mathematics, Van
available for student use as needed. de Walle page 108
or www.
ablongman.com/van
Teacher discusses the meaning of “percent.” Teacher makes a connection between a dewalleseries
fraction out of 100 and the equivalent decimal (e.g. 40% = 40/100 = 0.4).
Students should make connection between place value of decimals and percent (e.g.
0.58 = 58 hundredths ! 58%).
Teacher can access
Gizmos “Percents
Fractions &
Decimals” at
www.
explorelearning.com

There is an attached
assessment in this
Action! Individual or Pairs Gizmo that students
Complete BLM 7.18.1 or Gizmo “Percent, Fractions & Decimals”. can use to confirm
their understanding
Curriculum Expectations/Demonstration/Marking Scheme: assess students’
understanding of relationship between fractions, decimals and percent
Consider
Consolidate Whole Class ! Discussion photocopying BLM
Debrief Discuss answers to BLM 7.18.1, reinforcing the connection between fractions out of 7.18.2 (Teacher’s
100, decimals and percent. Answers) and
having students cut
and paste
Students describe in their math journals the relationship between fractions, decimals
appropriate answers
and percent. into template

Home Activity or Further Classroom Consolidation

Teacher gives the student a number and students judge which format (fraction,
Application decimal or percent) is “best” to represent this statistic.
Judging what representation is the best should involve students determining suitable
criteria (i.e. 1/10 on a test….the best representation would probably be 10%).

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 75

7.18.1: Fractions, Decimals & Percent Grade 7
1. Use the shaded areas to complete the chart.

Fraction out of 100 Decimal Percent

2. Complete the following chart.

Fraction out of 100 Decimal Percent

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 76

7.18.1: Fractions, Decimals & Percent Solutions Grade 7

1. Use the shaded areas to complete the chart.

Fraction out of 100 Decimal Percent

0.2 20%

0.25 25%

0.64 64%

2. Complete the following chart

Fraction out of 100 Decimal Percent

0.25 25%

0.8 80%

0.24 24%

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 77

Unit 7: Day 19: Solving Percent Problems with Concrete Materials Grade 7

Math Learning Goals Materials

• Solve problems that involve determining whole-number percents, using • BLM 7.19.1
concrete materials, e.g., base-ten materials, 10 x 10 square. • BLM 7.19.2
• BLM 7.19.3
• Relational Rods
• 2 Colour
Counters
• 30 cm Rulers
• Cube-a-links
• Newspapers
Assessment (A) and DI (D)
Opportunities
Minds On… Small Group ! Investigation
In small groups, students skim through newspapers for a few minutes and
locate examples of each of the following: percents, fractions and decimals.
Students record their examples on chart paper under the appropriate heading.
Students then post and share their group’s media examples with the class.
(Some examples may include: 30% chance of rain, 40% of the popular vote
for an election, tax, sporting averages, product studies/improvements).

After student groups have shared their examples with the class, the teacher
asks:
• Which representation is used most frequently?
• Which representation is the easiest to comprehend at a glance? If sets of relational rods
are not readily
available, use BLM
Students suggest possible reasons why a given number or statistic may be
7.4.1. (Template for
represented as a fraction/decimal/percent. (Possible answers: Percents are relational rods)
easiest to read because “out of 100” is a friendly benchmark for comparison;
they also may be most widely used. Fractions are perceived as difficult to
understand so may not be as frequently used.)
Action! Small Groups ! Carousel Investigations
In groups, students rotate through the stations described by BLM 7.19.1. They
record their work on BLM 7.19.2.

For Station 1, part c) provides an extension for students needing a further

challenge.
By completing the problems at each of the four stations, students will work
with percentages using an area, linear and set model.

Curriculum Expectations/Observation/Mental Note:

Assess students’ understanding of representing percentages, with particular
attention to effective use of each model.
Consolidate Whole Class ! Sharing/Discussion
Debrief Students share their findings and record any corrections on their worksheet.
For Station 4, encourage students to take notice of the relationship between
part b) and part c).
Home Activity or Further Classroom Consolidation Provide students with
Application appropriate practice
Further practice can be given with each manipulative as needed.
Concept Practice questions.
Skill Drill

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 78

7.19.1: Stations for Small Group Investigations Grade 7
– Percent with Concrete Materials

Station 1: Relational Rods

If the yellow rod represents 100%:

a) Which rod represents 20%?

b) Which rod represents 60%?

c) Which rod represents 200%?

_________________________________________

Station 2: 2 Colour Counters

Using 2 colour counters:

Count out 8 red counters and 2 yellow counters:

a) What percent are yellow?

b) What percent are not yellow?

c) If you take away 50% of the red counters, what

percent of the counters are now yellow?

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 79

7.19.1: Stations for Small Group Investigations Grade 7
– Percent with Concrete Materials

Station 3: 10 x 10 Grid

Shade in 50 squares on a 10 x 10 grid. This represents

100%.

a) What percent is represented by 10 squares?

b) What percent is represented by 45 squares?

c) How many squares would represent 11%?

Station 4: Ruler or Cube-a-Links

Draw a 12 cm line segment labelled AB.

AB represents 75% of a longer line segment called AC:

a) What is the length of AC? Draw AC.

b) What is the length of 25% of AC?

c) What is the length of 50% of 50% of AC?

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 80

7.19.2: Stations for Small Group Investigations Grade 7
– Percent with Concrete Materials Student Record Sheet
Station 1: Relational Rods Station 2: 2 Colour Counters

a) a)

b) b)

c) c)

Station 3: 10 x 10 Grid Station 4: Ruler or Cube-a-Links

a) a)

b) b)

c) c)

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 81

7.19.2: Stations for Small Group Investigations Grade 7
– Percent with Concrete Materials Solutions

Station 1: Relational Rods Station 2: 2 Colour Counters

If the yellow rod represents 100%: Using 2 colour counters:

a) What rod represents 20%? (white) If you have 8 red counters and 2 yellow
b) What rod represents 60%? (green) counters:
c) What rod represents 200%?
(orange) a) What percent are yellow? (20%)
b) What percent are not yellow?
(80%)
c) If you take away 50% of the red
counters, now what percent of the
counters are yellow? (33%)

Station 3: 10 x 10 Grid Station 4: Ruler or Cube-a-Links

Shade in 50 squares on a 10 x 10 grid. If a 12 cm line segment AB represents

This represents 100%. 75% of a longer line segment AC:

a) What percent is represented by 10 a) What is the length of AC? Draw

squares? (20%) AC. (16 cm)
b) What percent is represented by 45 b) What is the length of 25% of AC?
squares? (90%) (4 cm)
c) How many squares would c) What is the length of 50% of 50%
represent 11%? (5.5 squares) of AC? (4 cm)

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 82

7.19.3: 10 x 10 Grid Grade 7

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 83

Unit 7: Day 20: Finding the Percent of a Number Grade 7
Math Learning Goals Materials
• Solve problems that involve determining the percent of a number, e.g. CDs are on sale for • BLM 7.20.1
50% off the regular price. What is the sale price of a $14.98 CD? Relate the percent to • BLM 7.20.2
fraction and decimal versions, e.g., the CD is half price. • Fraction circles
• Estimate to judge the reasonableness of the answer & rings
• Solve problems that involve determining whole-number percents with and without
calculators

Assessment (A) and DI (D)

Opportunities
Minds On… Pairs ! Think Pair Share
Students share examples of real life situations in which they would need to calculate the
percent of a number (e.g., finding the percent of a test score).

Whole Class ! Pair Problem Solving

Teacher presents a sample problem involving finding percent of a number and students work
in pairs to solve the problem and explain their solution.
Sample Problem 1: Students may use
In a class of 28 students, 50% are wearing jeans. How many students are wearing jeans? calculators if
necessary; encourage
• Students should be able to represent 50% as !, and that ! of 28 is 14. students to round
using mental math,
• Ask students to represent this problem using a number line.
but they may use the
• Discuss solution strategies as a class, reinforcing options to solve the problem (e.g. calculator for
convert percent to a decimal and multiply by number). calculations

1/3 and 2/3 are

common benchmark
Sample Problem 2: fractions/percents;
On your vacation, you travel 600 km north and 300 km west. What percent of your trip did students should think
you travel north? about 1/3 = 33.3%
and 2/3 = 66.6%
• Students should calculate the total distance travelled as 600 + 300 = 900; is the
Teacher can access
Gizmos “Percent of
same as = = 66.6% Change” at www.
explorelearning.com.
This is a manipulative
“percent ruler” tool.

Gizmo – Percent
of Change gives a
good visual
representation for the
Action! and/or
Consolidate sections

Action! Small Group ! Problem Solving Select

Students work in groups to solve problems on BLM 7.20.1 homogeneous or
heterogeneous
Curriculum Expectations/Demonstration/Marking Scheme: Assess students’ understanding groupings
of calculating percent of a number
Be aware of
Consolidate Whole Class ! Discussion misconceptions in
Debrief Teacher prompts students to identify similarities and differences in solutions & addresses students’ work and
common misconceptions (e.g. identifying the “whole”). Students do a Gallery Walk in order address as a class
to identify various methods of solving problems and graphic representations.

Application
Home Activity or Further Classroom Consolidation This provides an
Students work independently to complete the problem on BLM 7.20.2 opportunity for
Concept Practice individual assessment

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 84

7.20.1: Finding Percent of a Number Grade 7
Practice Problems

For each problem, first estimate your answer. Then use pictures, numbers and words to
explain your answer.

1. Two different video game systems are on sale. The regular price of game
system A is $280 and it is on sale for 15% off. The regular price of game
system B is $360 and it is on sale for 25% off. Which game system costs
less after the discount?

2. In a new marketing campaign to sell a new bag of chips, the manufacturer

advertises “20% more for free!” If a standard bag of chips is 50g, what size is
the new chip bag?

3. The average height of a grade 7 student in September is 120cm. In June, the average
height is 150 cm. What is the percent growth in height over the year?

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 85

 7.20.1: Finding Percent of a Number Grade 7
Practice Problems Solutions

For each problem, first estimate your answer. Then use pictures, numbers and words to
explain your answer.

1. Two different video games are on sale. The regular price of game system
A is $280 and it is on sale for 15% off. The regular price of game system B is
$360 is 25% off. Which game system costs less after the discount?

Answer: System A costs 85% of the original price. 0.85 X $280 = $238.
System B is 75% of the original price. 0.75 X $360 = $270. Therefore game
system A costs less after the discount.

2. In a new marketing campaign to sell a new bag of chips, the manufacturer

advertises “20% more for free!” If a standard bag of chips is 50 g, what size is
the new chip bag?

Answer: 20% of 50 g is 10 g. (Mental math: 10% is 5 g.) So the new chip bag
is 20% more, or 10 g more. Its new size is 60 g.

3. 3. The average height of a grade 7 student in September is 120 cm. In June,

the average height is 150 cm. What is the percent growth in height over the
year?

Answer: Growth is 150 cm – 120 cm = 30 cm. 30 cm compared to 120 cm (the

original height) is ! or 25%. [Note: an incorrect answer may be obtained as
follows. If you compare 120 cm to 150 cm, there is a 20% difference. This
“difference” is not the same as “percent growth”. To look at growth, the “whole”
is the original height.]

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 86

7.20.2: Finding Percent of a Number Grade 7
Independent Practice

For this problem, first estimate your answer. Then use pictures, numbers
and words to explain your answer.

A pair of jeans costs $50. They are on sale for 20% off. You have to
add PST and GST to the final cost of the jeans.

PST in Ontario = ____________ %

GST = _____________ %

Which method of calculating the final price results in a lower price?

a) calculating the sales tax on the jeans BEFORE taking the 20%
discount
OR
b) calculating the sales tax on the jeans AFTER taking the 20%
discount

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 87

7.20.2: Finding Percent of a Number Grade 7
Independent Practice Solutions

For this problem, first estimate your answer. Then use pictures, numbers and words to
explain your answer.

A pair of jeans costs $50. They are on sale for 20% off. You have to add PST
and GST to the final cost of the jeans.

PST in Ontario = ________________%

GST = _______________ %

Which method of calculating the final price results in a lower price:

a) calculating the sales tax on the jeans BEFORE taking the 20% discount,
or
b) calculating the sales tax on the jeans AFTER taking the 20% discount

ANSWER:

Option a) If PST & GST is 13%, the sales tax on the jeans is 0.13 X 50 =
$6.50, so the total price is $56.50. 20% of $56.50 is $11.30, for a final price of
$56.50 - $11.30 = $45.20.

Option b) Take the 20% discount first off $50.00. 20% of $50.00 is $10.00 so
the before-tax price is $40.00. The sales tax on the jeans is 0.13 X $40 = $5.20
for a total price of $45.20.

Therefore, both methods will give the same final price.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 88

Unit 7: Day 21: Connecting Fractions to Percents Grade 7
Math Learning Goals Materials
• Determine what percent one number is of another, e.g., 4 out of 16 • String
shapes are hearts. What percent are hearts? • Rulers
• Connect this type of problem to converting a fraction to a percent, e.g., 4 • Chart Paper
out of 16 = 4/16 = 25%. • Calculators
• Cube-a-links
• BLM 7.21.1
• BLM 7.21.2
• BLM 7.21.3
Assessment (A) and DI (D)
Opportunities
Minds On… Whole Class ! Sharing Activity Students having difficulty
may choose to use
In order to calculate percents, students need to clearly understand that a
calculators or other
fraction is really a division expression. 18/5 is “18 fifths” or “18 ÷5”. manipulatives such as
So the following activity reinforces this concept. cube-a-links.

Discuss the question on BLM 7.21.1 with the class. Teaching Note:
A “quadrat” is a square or
Make an overhead of BLM 7.21.1. Provide students with 3m of string rectangular area of land
per group. marked off for the study of
Action! Pairs ! Problem Solving plants & animals
Students complete BLM 7.21.2 (may be used as an overhead) and Do not suggest
solution is discussed. procedures.
Students then complete BLM 7.21.3. Introduce the problems and have Interchange the words
students individually complete the first two steps: “fraction” and
“percent/hundredth” while
1. Individual - estimate each answer and justify thinking. speaking with students.
(e.g. relate to benchmarks) Refer to the concepts of
2. Individual – identify each number as a part, a whole or a fraction. “whole”, “part” and
3. Then in pairs, solve the problems using chart paper to display “fraction/percent”
Use both set and area
solutions. models because it seems
that most percent
Curriculum Expectations/Demonstration/Marking Scheme: Assess problems are sets but
students are more familiar
student’s understanding of connecting fractions and percents using the with areas. Students
consolidation activity below. should use models or
Consolidate Whole Class ! Debrief and Consolidate pictures to explain their
Debrief answers; this will more
Students participate in sharing of solutions (Math Congress). They fully develop the
explain their solutions and explain how they know their solution is relationships.
correct. Several different pairs of students share their solutions. This Encourage mental
allows more students to be recognized and reinforces multiple solutions computation.
and explanations. Math Congress is the
sharing of student
answers. Teacher
chooses a variety of
problem solving
approaches to highlight
and validate various
strategies.
Home Activity or Further Classroom Consolidation
Application Students complete the same problems but substitute fractions for the
Concept Practice percentages.
Exploration
Teacher Prompt: How would the solutions be different?
-It would also be appropriate to use a Gizmo: Percents and Proportions

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 89

7.21.1:Connecting Fractions to Percents (Overhead) Grade 7

A student is making a quadrat for a field study in her Ecosystems

unit. She has 3 m of string and uses ! of this to create the
square quadrat. How much string did she use for this task?

Which of the following answers are correct? Which answer is

“best”?

(A) Draw a sketch of a 3 m string split into fourths to show that

3m ÷ 4 = 0.75 m

(B) This means ! of 3 m or 3 groups of ! or 3 x !

(C) This means " m because you’re sharing the string into 4ths
and taking 3 of them.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 90

7.21.2: Connecting Fractions to Percents Grade 7

Four out of 16 shapes are hearts. What percent are hearts?

1. Estimate the answer.

2. Identify each number as the part, the whole or the
fraction/percent.
3. Solve the problem.

-----------------------------------------------------------------------------------
Teacher Answers
1. Estimate:
4 out of 16 is the same as ! or 25% (a very easy estimation here!).

2. Identify each number as a part, a whole or a fraction / percent.

Part: 4 , Whole: 16, Fraction / percent: 4/16 or 25%
i.e., the numerator counts and the denominator tells you what you’re
counting.

3. Solve the problem.

- 4/16 is equivalent to !, which is equivalent to 25/100 or 25%
- 4/16 means 4 ÷16 or 0.25. This is “twenty five hundredths” or “twenty
five percent”.

DI: An area model (simpler version) of this question is provided below:

A chocolate bar is split into 16 squares and you eat 4 of them. What percent of the
chocolate bar did you eat? You have 4 parts (here a part is a “1/16”), so again the
numerator counts and the denominator tells you what you’re counting.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 91

7.21.3: Connecting Fractions to Percents Grade 7
Student Practice

For each problem:

1. Estimate.
Hint: identify each number as a part, a whole or a fraction.
2. Solve the problem.
1. a) In a Grade 7 class, 18 out of 30 students play on extra-curricular sports teams.
What percent of students play on a team?

b) In the same class, 20% of students are on the Honour Roll. How many students
are on the Honour Roll?

2. Bill buys a skateboard. The price tag shows an original price of $120, but it has
been marked down to $90. What percentage did he save by buying this
skateboard on sale?

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 92

7.21.3: Connecting Fractions to Percents Solutions Grade 7
Solutions
1. a) In a Grade 7 class, 18 out of 30 students play on extra-curricular sports teams.
What percent of students play on a team?

Answer:

- 18 ÷ 30 = 0.6 or “six tenths” or “sixty hundredths” or “sixty percent”

- 18 / 30 = 6 / 10 = 60 / 100 = 60%

b) In the same class, 20% of students are on the Honour Roll. How many
students is that?

Answer:

- 20% is 20/100 or 2/10 or 6/30

- If 60% was 18 students, then 30% is 9 students and 10% is 3 students, so 20%
is 6 students
- 20% is 0.20 and 0.20 X 30 = 6

2. Bill buys a skateboard. The price tag shows an original price of $120, but it has
been marked down to $90.

What percentage did he save by buying this skateboard on sale?

Answer:
- Saved $30
- 30/120 = ! = 0.25 = 25%
- Therefore Bill saved 25% on his purchase

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 93

Unit 7: Day 22: Using Percent to Make Comparisons Grade 7
Math Learning Goals Materials
• BLM 7.22.1
• Use percent to make comparisons, e.g., students won ribbons in one • BLM 7.22.2

class and won in the other class. Which had the better performance?

• Pose and solve comparison problems using a calculator.

Assessment (A) and DI (D)
Opportunities
Minds On… Pairs ! Activity Smartboard Activity:
Use BLM 7.22.1 – photocopy one copy for each pair of students. Comparing Percents
available:
Students cut out all questions and match equivalent fractions, decimals and U7L22_notebook1
percents. Once they have matched equivalent fraction/decimal/percent,
students need to arrange the items from smallest to largest on a number line;
students decide what is the “best” label for the number line (e.g. 0% - 100%,
A variety of fractions
decimal or fraction). have been included
to give students the
Whole Class! Discussion opportunity to see
“friendly” numbers
as well as less
Teacher asks students how they compared the fractions and familiar fractions.

BLM 7.22.1: The

E.g. 1: Both fractions are 1 piece less than a whole; is a larger fraction decimals have been
rounded to the
th
nearest 100 , and
than so therefore taking away a larger fraction would give a smaller “left the percents have
been rounded to the
nearest whole
number.
over” which means that would be the larger fraction
Gizmo: Ordering
Percents, Fractions,
E.g. 2: Calculate / compare percent for each fraction: = 88% and = and Decimals gives
a visual
90% representation for
the ‘Minds On...’
Action! Whole Class ! Discussion section.
Students should discuss which form is “easiest” to compare – fraction vs.
fraction, or percent vs. percent.
Teacher reviews idea from Lesson 21 – a fraction is a division expression. In
order to calculate the equivalent percent of a given fraction, divide the
numerator by the denominator to get a decimal with 2 decimal places and
convert to percent.

e.g. ! 5 ÷ 7 = 0.71 ! 71% (numerator ÷ denominator x 100 = % )

Pair Activity ! Practice Solving Percent Comparison Problems

Students work in pairs to complete BLM 7.22.2
Curriculum Expectations/Demonstration/Marking Scheme: Assess students’
understanding of comparing percents/fractions/decimals
Consolidate Whole Class! Discussion
Debrief Discuss answers to problems on BLM 7.22.2
Home Activity or Further Classroom Consolidation
Application Students complete the “Independent Practice” activity from BLM 7.22.2.
Concept Practice Students can share their problems with other students in a follow-up class
Exploration (see Unit 7 Lesson 23).

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 94

7.22.1: Matching Fractions, Decimals and Percents Grade 7

1. Cut out the cards.

2. Match cards (fraction, decimal and percent) that represent the same quantity
3. Order the fractions/decimals/percents from smallest to largest.

0.20

0.67 0.15 90%

74% 0.47 67%
20% 0.33 15%
0.89 33% 0.90
0.74 89% 47%

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 95

7.22.1: Matching Fractions, Decimals and Percents Grade 7
Solutions

2/13 0.15 15%

10/50 0.20 20%

9/27 0.33 33%

14/30 0.47 47%

2/3 0.67 67%

23/31 0.74 74%

8/9 0.89 89%

9/10 0.90 90%

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 96

7.22.2: Problem Solving – Comparing Percents Grade 7

1. During a hockey season, Terry scored 9 goals in 14 games. Cory scored 10

goals in 17 games. Casey scored 8 goals in 13 games. Represent each
player’s statistics as a fraction, decimal and percent. (Round each decimal to
the nearest 100th)

2. If the coach wants to pick the player who is best at scoring for the All-Star
team, what player should she pick?

3. The coach is able to pick 2 players for the All-Star team and selects Casey
and Terry. In the All-Star game, Terry scores 1 goal and Casey scores 2
goals. Which player is now the best / highest scoring player?

Independent Practice
You are the coach of this hockey team. Create a problem that compares
percents using statistics that YOU invent about the team (E.g. penalties, assists,
wins/losses, ice time, etc.). Write the problem on one side of a page and solve
the problem on the reverse of the same page.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 97

7.22.2: Problem Solving – Comparing Percents Grade 7
Solutions

1. During a hockey season, Terry scored 9 goals in 14 games. Cory scored 10

goals in 17 games. Casey scored 8 goals in 13 games. Represent each
player’s statistic as a fraction, decimal and percent.

Answer:
Fraction Decimal Percent
Terry 0.64 64%

Cory 0.59 59%

Casey 0.62 62%

2. If the coach wants to pick the highest scoring player for the All-Star team, what
player should she pick?

Answer: The coach should pick Terry (64%).

3. The coach is able to pick 2 players for the All-Star team and selects Casey and
Terry. In the All-Star game, Terry scores 1 goal and Casey scores 2 goals.
Which player is now the best / highest scoring player?

Answer: Now, Casey has now scored a total of 10/14 games or 71%. Terry has
now scored in 10/15 games or 67%.
Casey is now the highest scoring player.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 98

Unit 7: Day 23: Using Percent to Find the Whole Grade 7
Math Learning Goals Materials
• Calculate the size of the whole when a percentage of the whole is known, • BLM 7.23.1
e.g. 6 students in a class have juice for snack. If that is 20% of the class, • BLM 7.23.2
how large is the class? • BLM 7.23.3
• Relate to probability; e.g. if 20% of the students have juice, what is the • BLM 7.23.4
• Manipulatives
probability that a student chosen at random will have juice?
(relational rods)
• Post-it notes
Assessment (A) and DI (D)
Opportunities
Minds On… Whole Class ! Modified Four Corners
Pose questions to the class from BLM 7.23.1. For each question, ask students If relational rods are
not available, use
to write their answer on a page and get up and go make a group with students BLM 7.4.1 –
around the room with whom they can share their answers. After all students Relational Rods
have grouped, discuss each answer as a class to determine correct answers. If Template
all students correctly identify the questions but without enough information,
then give them a second prompt: What information is missing?
Answers:
1. Not enough information; we don’t know the area of the walls.
2. 25% of a 1 m rope is 0.25 m and 50% of a 2 m rope is 1 m.
3. Not enough information; we don’t know the heights of either grade
ten student.
4. Not enough information; we don’t know.

Action! Whole Class ! Exploration (Representing) Make manipulatives

from previous
Give students the problem from BLM 7.23.2. The teacher should focus on lessons available,
the representation of the answer and encourage students to connect to especially relational
previous understanding. rods.

After students have produced solutions, have them do a gallery walk and jot
down on a post-it note one more representation of a solution that they find Use Gizmo: Percents
and Proportions for a
effective. visual representation
Possible student answers are on BLM 7.23.3.

Whole Class ! Sharing

Consolidate ideas through discussion. Pointing out working through decimals
and fractions is effective. Ask the class, “What is the probability that a
student selected at random will have a litterless lunch?” Answer: 1/5
Consolidate Individual ! Practice
Debrief Students work on BLM 7.23.4 individually.

Curriculum Expectations/Recorded Solutions/Rubric:

Assess students’ solutions using a rubric based on the mathematical process
of representing.
Home Activity or Further Classroom Consolidation
When taking up students’ independent practice, students record the
probability of each event for each question.
Answers:
Application
1. What is probability that a team won the next game played?
Reflection
Answer: 40/100 or 2/5
2. What is the probability that a randomly selected student has already
paid? Answer: 2/3
3. What is the probability that a randomly selected seat is taken?
Answer: 95/100 or 19/20

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 99

7.23.1: Using Percent to Find the Whole Grade 7
(Overhead)

1. If I paint 25% of one wall in my house green and

1/3 of another wall white, which wall used more
paint?

2. Which is longer: 25% of a 1 m rope or 50% of a

2 m rope?

3. A grade ten male is 15% taller than a grade eight

male. A grade ten female is 10% taller than a
grade eight female. Which of these students is
the tallest?

4. In 2007, 17% of Canada’s population was under

the age of 15. In 1971, 29% of Canada’s
population was the same age. In which year were
there more children in Canada?

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 100

7.23.2: Using Percent to Find the Whole Grade 7
(Gallery Walk Problem)

Six (6) students in a class have litterless lunches. If

that is 20% of the class, how large is the class?
Clearly explain your thinking.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 101

7.23.3: Using Percent to Find the Whole Grade 7
(Teacher Answers)

Six (6) students in a class have litterless lunches. If that is 20% of the class, how large
is the class?

Sample Answers:

1. 20% = = Using equivalent fractions, = ! 30 students in class

2. 20% + 20% + 20% + 20% + 20% = 100% Therefore,

6 + 6 + 6 + 6 + 6 = 30 ! 30 students in the class

3. 20% = 0.2 ! Let y represent the number of students in the class

0.2 x y = 6
y = 30

4. + + + + = 30

+ + + + =

20% + 20% + 20% + 20% + 20% = 100%

5. Using relational rods as a model: The red rod is 1/5 or 20 % of the orange rod

6 + 6 + 6 + 6 + 6 + 6

Red Red Red Red Red Red

Orange Rod

Total Class = 30

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 102

7.23.4: Using Percent to Find the Whole Grade 7
Student Practice

1. If a baseball team won 8 games and this represented a 0.4

winning percentage, how many games did they play?

2. The Grade 7 class had collected 67% (2/3) of their class trip
money. The amount collected was $210. How much money
will be collected in total?

3. The movie theatre was 95% full for the opening show. If there
are 250 people seated, how many more can fit?

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 103

7.23.4: Using Percent to Find the Whole Grade 7
Student Practice Solutions

1. If a baseball team won 8 games and this represented a 0.4

winning percentage, how many games did they play?
8 games represents winning 40% of their games

If 8 games is 40%, 4 games is 20% and 2 games represents 10%,

Then 2 games multiplied by 10 equals 20 games.
Answer : 20 games

2. The Grade 7 class had collected 67% (2/3) of their class trip
money. The amount collected was $210. How much money
will be collected in total?
67% or 2/3 divided by 2 is equal to 1/3.

If 1/3 is $105 ($210/2) then 3/3 is $105 x 3 = $315

1/3 = $105 1/3 = $105 1/3= $105

OR
1/3 is 105/? (Solve for the equivalent fraction)
Answer: $315 will be collected in total

Answer $315 games

3. The movie theatre was 95% full for the opening show. If there
are 250 people seated, how many more can fit?

.95x = 250
.95/.95x = 250/.95
x = 263 (rounded to the nearest whole number)

To find how many more people can fit:

263- 250 = 13
Answer: 13 more people can fit in the theatre

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 104

Unit 7: Day 24: Using Tables and Lists to Determine Outcomes Grade 7
Math Learning Goals Materials
• Determine all possible outcomes of an event using a chart, table, or • BLM 7.24.1
systematic list, e.g., if you threw 3 coins simultaneously, what are all the • Coins
possible combinations of heads and tails? • Number cubes
• Determine all possible sums when rolling 2 number cubes • Counters

Assessment (A) and DI (D)

Opportunities
Minds On… Whole Class Activity ! Introduce Vocabulary
Write vocabulary words on board (see below) so that students can begin to
This activity
use the terms during the demonstration. addresses a
Teacher demonstrates flipping a coin at least 8 times and recording outcomes. possible
Either use coins, or National Library of Virtual Manipulatives ! grade 6-8 ! misconception that
successive events
data analysis & probability ! coin toss. depend on the
http://nlvm.usu.edu/en/nav/frames_asid_305_g_3_t_5.html?from=category_g previous event
_3_t_5.html or the Probability Simulations gizmo from
www. explorelearning.com.
Ask students what they think the next outcome will be. Reinforce with
students that both H or T are equally likely because these are independent
events.
Discuss and define “outcome”, “likely”, “impossible”, “most likely”,
“certain”.
Action! Small Group Activity ! Number Cube Race Game
Each group of students plays the game on BLM 7.24.1.

Instructions for Game:

In each small group, students pick numbers (like a draft) until all numbers
between 1 and 12 are taken. Roll 2 number cubes and calculate the sum.
Each time a sum is rolled, students move a marker up the game board for that
sum. The first sum to reach the top of the game board “wins”.
At the end of the game, students record all possible outcomes of calculating
the sum of 2 number cubes.

Curriculum Expectations/Demonstration/Marking Scheme: Assess

students’ understanding of determining outcomes and possible outcomes.
Consolidate Whole Class Activity
Debrief Teacher explains that an outcome is a possible event of a probability
experiment. Teacher prompts:
“What were possible/impossible/likely/unlikely/most likely outcomes of the
number cube game?”
After discussing the game, students should identify that the sum of 7 is the
most likely outcome.
Teacher asks students to reflect on other methods of recording the results of
this game (e.g. tally chart, table).
Home Activity or Further Classroom Consolidation
Students write a reflection (e.g. rap) using probability vocabulary (likely,
Reflection
most likely, impossible, certain, etc.) to reflect the number cube race game
outcomes.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 105

7.24.1: Number Cube Race Grade 7
Groups: 2, 3, 4 or 6.
Materials: 2 number cubes and game markers (e.g., counters)

Instructions:
1. Students take turns choosing numbers between 1-12 (until all the numbers have been chosen) that
they will “race”.
2. Taking turns, students roll the number cubes and calculate the sum. For each roll, they move the
marker for that sum up one space on the game board towards the Finish Line.
3. The first counter to reach the finish line is the winner.
4. Upon completion of the game, make a bar graph to represent the frequency (final positions of the
counters) from rolling and recording the sum of the two number cubes.

Frequency
FINISH LINE

1 2 3 4 5 6 7 8 9 10 11 12

List all the possible sums (outcomes) of rolling 2, 6-sided number cubes.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 106

Unit 7: Lesson 25: Probability Grade 7
Math Learning Goals Materials
• Distinguish between theoretical probability and experimental probability • BLM 7.25.1
• Express probability as a fraction, decimal and percent • BLM 7.25.2
• Calculate probability of specific outcomes using Lesson 24 charts and • BLM 7.25.3
tables, e.g., what is the probability of 3 coin flips being HHH? • Number cubes,
coins

Assessment (A) and DI (D)

Opportunities
Minds On… Pair Activity ! Exploring
Give pairs of students a coin; one student will pick heads (H) and the other
student will pick tails (T). Students predict the number of heads/tails for a
total of 50 flips.
Students perform 50 coin flips and record their results in a tally chart.
Students also write the actual number of heads/tails as a fraction out of 50.
Action! Whole Class ! Discussion Theoretical
Teacher prompts: probability: the
• “What are the possible outcomes of flipping a coin?” chance that
something should
An outcome that you “want” to happen is called a “favourable outcome” happen based on
• “What is the total number of outcomes when flipping a coin?” calculating:
# favourable
Show how to calculate theoretical probability = # favourable outcomes
outcomes/ total #
total # outcomes outcomes
Teacher prompt:
Experimental
“What is the theoretical probability of flipping a head?” probability: the
Students compare theoretical probability to the results of their experiments chance that
(record results from various pairs’ experiments on board). something will
Students should recognize that experimental probability and theoretical happen based on
results from an
probability are often not the same. experiment

Pair Activity Teacher can access

Students complete BLM 7.25.1 using previous day’s results from Number Gizmos “Theoretical
and Experimental
Cube Race on their charts. Probability” at
www.
Curriculum Expectations/Demonstration/Marking Scheme: Assess explorelearning.com
students’ understanding of the difference between theoretical and
Here the teacher
experimental probability. can design a spinner
Consolidate Whole Class ! Discussion (and use multiple
Debrief Compare pairs’ results as a class; what different experimental probabilities spinners) and select
were observed? the favourable
outcome and tally
the results.
Whole Class ! Probability Game “SKUNK”
Students use BLM 7.25.2 to play SKUNK (instructions for playing the game
are included on BLM).
Teacher prompts: “How did you know when to sit down?”
Students use BLM 7.25.3 to record all possible outcomes for sums of number
cubes.
Home Activity or Further Classroom Consolidation
Application Take the SKUNK game home to teach someone else the game and play it,
Concept Practice
discussing their strategies for winning. Teachers may copy the game board
Exploration
Reflection to send home.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 107

7.25.1: Probability – Number Cube Game Grade 7
Probabilities
1. Using the data from the Number Cube Game, complete the chart.

Probability of the actual event (P) = frequency of the outcome

Total # of trials

Frequency of Total # of Probability as Probability as a Probability as a

Outcome Trials a Fraction Decimal Percent (%)
(From Number (round to nearest
Cube Race) hundredth)
2

10

11

12

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 108

7.25.2: “SKUNK” Probability Game Board Grade 7

Game Instructions:
• Teacher rolls 2 number cubes
• Players record the sum of the numbers in the appropriate column (i.e. sums for round 1
are recorded under "S", sums for round 2 are recorded under the first “K”, etc.)
• Players must now individually choose to either remain standing or to sit down (if a
student sits down, this ends the round for them)
• Players still standing continue to record the sums of future rolls (and must decide to
remain standing or sit down after each roll)
• The round ends when a double is rolled.
• Players who are standing when a double is rolled get 0 points for that round.
• For players who are sitting when a double is rolled, their score for that round is the sum
of all the numbers they recorded while standing.
• There are 5 rounds: "S", "K", "U", "N", "K" and the final score is sum of all 5 rounds

Roll S K U N K
1

10

11

12

Score for
Round

Total Final Score: .

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 109

7.25.3: Probability of a Double Roll Grade 7
with 2 Number Cubes

1 2 3 4 5 6

Total number of outcomes: _________

Circle all the outcomes that result in a double roll (“favourable” outcomes)

Theoretical Probability = # favourable outcomes = __________

total # of outcomes

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 110

Unit 7: Lesson 26: Designing Games and Experiments Grade 7
Math Learning Goals Materials
• Understand the connections between percent and probability by: • Number cubes
o Designing a fair game (each player has a 50% chance of winning) e.g., • Spinners
two players take turns rolling one numbered cube. If the number is odd, • Playing cards
player A scores a point. If the number is even, player B scores a point. • Coins,
• Marbles,
o Designing an experiment where the chance of a particular outcome is 1
• Modifiable
in 3, e.g., use a bag of red and green balls spinner
• BLM 7.26.1
Assessment (A) and DI (D)
Opportunities
Minds On… Whole Class ! Spinner Game
Demonstrate a fair game using a regular spinner or the default fair spinner
(with equivalent sections) from the National Library of Virtual Manipulatives
! data analysis & probability ! spinners. Students get a point for each time
the arrow lands on the colour they selected.
http://nlvm.usu.edu/en/nav/frames_asid_186_g_3_t_5.html?open=activities&
from=topic_t_5.html
Discuss and record the theoretical probability of getting each of the colours to
prove that this is a fair game (e.g., equal chance of each outcome).
Modify the spinner to increase the size of one section to make one outcome
more likely than others (e.g., increase 1 region’s value from 1 ! 2).
Discuss and record the theoretical probability of getting each of the colours to
prove that this is an unfair game (unequal chance of each outcome).
Discuss ways to make the modified spinner a fair game (see below).
To make this “unfair” spinner a
fair game, award ! a point for
landing on yellow and 1 point
for landing on all others.
Or, players could select yellow
as their option, or 2 other
colours. Fair Game Design
incorporates
procedural writing
(instructions for
Action! Pair Activity ! Design a Fair Game
playing the game)
Students use BLM 7.26.1 and play their own game that can be
Curriculum Expectations/Demonstration/Marking Scheme: Assess assessed separately
students’ understanding of fair games using a rubric for problem solving. for a writing mark

Consolidate Whole Class

Debrief Students play each other’s games, identifying whether particular games are Students may
fair or not. modify existing
games

Individual Practice
Students complete a journal entry proving mathematically that their game is
fair.
Exploration Home Activity or Further Classroom Consolidation
Discuss / explore the fairness of other games at home (board games, card
games, etc.).

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 111

7.26.1 BLM Designing Games and Experiments Grade 7
Task: Working with a partner, you must design a fair game that
uses any of number cubes, coins, playing cards, marbles or spinners.
(If you have another creative idea, consult with your teacher for
approval.)

Game Criteria:
• Your game must result in a winner (should take 5-10 minutes to play).
• You must state the object of the game.
• Your game must include clearly written rules that are easy to follow
• Your game must be fair.
• Your game must be fun for other Grade 7 students.
• Your game may be a modification of an existing game.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 112

Unit 7: Lesson 27: Making Predictions Based on Probability Grade 7
Math Learning Goals Materials
• Make predictions about a population given a probability, e.g., if the • BLM 7.27.1
probability of catching a fish is 30%, how many students in a class of 28
will catch a fish if they all go fishing together?

Assessment (A) and DI (D)

Opportunities
Minds On… Whole Class ! Discussion
Discuss real life applications of probability in which you use “chance” to
determine your willingness to participate (e.g., weather ! 30% chance of
rain; getting picked to be on a sports team; investment risk; lottery ticket,
etc.).
Discuss with students the lowest probability needed to motivate them to
participate (personal risk factor) e.g., the chance of winning a national lottery
prize might be very low vs. the chance of winning a prize in a school draw.

Action! Individual Practice

Teacher reviews how to convert fractions to percent and how to calculate
percent of a number.
Students complete BLM 7.27.1.

Curriculum Expectations/Demonstrations/Marking Scheme: Assess students’

understanding of making predictions based on probability.

Consolidate Small Group Sharing

Debrief Students form small groups and share their solutions for BLM 7.27.1 #2
within their group. The teacher can group similar solutions together on the
board to highlight particular strategies in a Bansho or Congress and discuss
how fractions, decimals, and percents relate to probability.

Application Home Activity or Further Classroom Consolidation

Concept Practice Select a variety of appropriate textbook problems.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 113

7.27.1: Making Predictions Based on Probability Grade 7

Answer these questions individually and show your work clearly.

1. a) If the chance of winning a prize on a coffee cup rim is 10%, and a class of 30
Grade 7 students each bought one cup, how many winners would you expect?

b) If the students who did not win a prize on their first cup each bought a second
cup, how many winners would you expect on the second cups, if the probability of winning
is still 10%?

2. The school baseball team played 24 games. Sean scored 6 home runs, Carole hit home
runs in 5% of her games and Mitch hit home runs 1/8 of the time.

a) Based on these probabilities, who has best chance of hitting a home run in the next
game?

b) If the probabilities stayed the same for the next season where 30 games are played,
how many homeruns would you expect each player to hit?

3. A multiple-choice test has four options for each question. If you randomly answered
a test with 60 questions, how many questions would you expect to get correct?

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 114

7.27.1: Making Predictions Based on Probability Grade 7
Solutions
1. a) If the chance of winning a prize on a coffee cup rim is 10%, and a class of 30
Grade 7 students each bought one cup, how many winners would you
expect?

Answer: 0.10 X 30 = 3, ! 3 winners would be expected

b) If the students who did not win a prize on their first cups each bought a second
cup, how many winners would you expect on the second cups, if the probability of
winning is still 10%?

Answer: 0.10 X 27 = 2.7, ! 2 or 3 winners would be expected

2. The school baseball team played 24 games. Sean scored 6 homeruns, Carole hit
homeruns in 5% of her games and Mitch hit homeruns 1/8 of the time.

a. Based on these probabilities, who has best chance of hitting a home run in the next
game?

Answer: Sean ! 6/24 = 0.25 = 25%

Carole ! 5%
Mitch ! 1/8 = 0.125 = 12.5%

Sean has the best chance.

b. If the probabilities stayed the same for the next season where 30 games are played, how
many homeruns would you expect each player to hit?

Answer: Sean ! 0.25 X 30 = 12.5 or 13

Carole ! 0.05 X 30 = 1.5 or 2
Mitch ! 0.125 X 30 = 3.75 or 4

3. A multiple-choice test has four options for each question. If you randomly answered
a test of 60 questions, how many questions would you expect to get correct?

Answer: You have a ! chance of getting the question correct. So on a test with 60
questions, you would get 0.25 X 60 = 15 questions correct.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 115

Unit 7: Day 28: Tree Diagrams Grade 7
Math Learning Goals Materials
• Understand that two events are independent when one does not affect the • BLM 7.28.1
probability of the other, e.g., rolling a number cube, then flipping a coin.
• Determine all possible outcomes for two independent events by completing
tree diagrams, e.g., spinning a three-section spinner two consecutive times;
rolling a number cube, then spinning a four-section spinner.
Assessment (A) and DI (D)
Opportunities
Minds On… Pairs (Problem Solving) ! Whole Class (Discussion) This example is to
show how to do a tree
Pose the following problem to the class, and have them solve it in pairs. diagram. The
• You are going to an ice-cream store to make your own sundae. You have to discussion during the
choose one type of ice-cream, one topping and a sauce. consolidation and
The following options are on the menu: debrief section will
Ice -Cream Topping Sauce expose students to
Vanilla (V) Sprinkles (Sp) Fudge (F) understanding that
Chocolate (C) Cherries (Ch) Strawberry (S) when two events are
independent of each
Caramel (Ca)
other, one will not
With your partner, display all of the different combinations of sundaes that could be affect the probability
made. Then discuss the number of the combinations. Have students display different of the other event.
ways they organized their work (e.g., lists, charts, random combinations, etc.). If a
pair of students has done a tree diagram, have that group explain their solution. If no Recall generating lists
and tables from
one used a tree diagram, model how to draw one. Lesson 24 and how
tree diagrams
Fudge VSpF organize outcomes in
Sprinkles Strawberry VSpS a logical sequence.
Tree diagrams are
Caramel VSpCa more suitable when
there are more events
Vanilla Fudge VChF
and combinations
Cherries Strawberry VChS (hard to show 3
events on a table).
Caramel VChCa

Students may
Fudge CSpF need to use a coin or
a spinner to
Sprinkles Strawberry CSpS understand how many
outcomes there are
Caramel CSpCa
for each. See Lesson
Chocolate Fudge CChF 24 for online tools.
Cherries Strawberry CChS Independent Events-
Caramel CChCa Two or more events
where one does not
There are 12 different combinations. affect the probability
(2 types of ice cream x 2 toppings x 3 sauces = 12) of another.
Ask students questions like the sample question below:
The Gizmo
• How many combinations have strawberry sauce?
“Compound
Independent and
Action! Pairs! Exploration Dependent Events”
Students complete questions on BLM 7.28.1 in pairs. could be used to
model an
Consolidate Whole Class! Discussions independent and a
Debrief Pairs of students share their solutions for question 1. dependent event.
Discuss question number 2 with students, identifying when events are dependent and See
www.explorelearning.
independent and how that would affect the possible outcomes. Point out that we will com
always be working with independent events and that using dependent events becomes
much more complex.
Curriculum Expectations/ Observation/Mental Note: Assess students’
understanding of being able to identify possible outcomes for two or more independent
events using tree diagrams.

Application Home Activity Provide scenarios

Reflection Write a reflection about the usefulness of organizing your possible outcomes using a so students can
practice using tree
tree diagram. Think of real-life scenarios where you would need to find all of the
diagrams.
possible outcomes.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 116

7.28.1: Tree Diagrams Grade 7

Name: ______________________________ Date:___________________

1. Create a tree diagram and list all of the outcomes for the following situations.

a) Rolling a 6-sided die and flipping a coin

b) Flipping a coin 3 times

c) Spinning the spinner twice and then flipping a coin Spinner

B
A

2. a) In the situations above, do any of those events depend on the results of another
event? Explain why or why not.

b) Can you think of another situation where the outcome of one event depends on the
outcome from a previous event?

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 117

7.28.1: Tree Diagrams Solutions Grade 7

Name: ______________________________ Date:___________________

1. Complete a tree diagram and list all of the outcomes for the following situations.

a) Rolling a 6-sided die and flipping a coin

Outcomes
(12)
H
1–H
1 T 1–T
H 2–H
2 T 2–T

H 3–H
3 T 3–T

H 4–H
4 T 4–T

H 5–H
5 5–T
T 6–H
H
6 6–T
T

b) Flipping a coin 3 times

Possible Outcomes (8)

H - HHH
- HHT
H T - HTH
H T H - HTT
T - THH

H H - THT
T T - TTH
- TTT
T H
T

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 118

7.28.1: Tree Diagrams Solutions Continued Grade 7

c) Spinning the spinner below twice and flipping a coin

18 Outcomes
- AAH
B
- AAT A
- ABH
- ABT C
- ACH
- ACT
- BAH
- BAT
- BBH
- BBT
- BCH
- BCT
- CAH
- CAT
- CBH
- CBT
- CCH
- CCT

2. a) In the situations above, do any of those events depend on the results of another
event? Explain why or why not.

None of them do. Whether you get a heads on a flip of a coin doesn’t impact what
you’ll get the next time. All of these are “independent” of each other.

b) Can you think of another situation where the outcome of one event depends on the
outcome from a previous event?

If you drew a coloured marble from a bag and did not put the marble back, it
would change the possible outcomes for the colour of the next marble you grab
from the bag (and therefore it “depends” on the colour of the first marble).

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 119

Unit 7: Day 29: Probability of Specific Event Grade 7
Math Learning Goals Materials
• Determine the probability of a specific outcome from two independent • BLM 7.29.1
events using tree diagram, e.g., when flipping a coin and then rolling a • BLM 7.29.2
number cube, what is the probability of getting a head and an even • Spinners
number?

Assessment (A) and DI (D)

Opportunities
Minds On… Whole Class! Discussion
Refer to the tree diagrams on BLM 7.28.1 from Day 28. Have students create Students can
3 probability based questions that identify specific outcomes from the tree use calculators to
diagrams in question 1a), i.e., What is the probability of flipping heads and help them determine
the theoretical
rolling a 3? What is the probability of rolling an even number and flipping probability (in
tails? percent form).

Ask students to solve their questions and then discuss how they represented
their answers (fractions, words, percent, decimals, etc.).
Action! Pairs ! Exploration ! Discussion Virtual Spinners are
In pairs students complete BLM 7.29.1. available at:
http://nlvm.usu.edu/
en/nav/topic_t_5.ht
Discuss question number two from BLM 7.29.1. Ask students to explain ml or the Gizmo
their thinking and display different ways they represented their answer. “Probability
Simulations” from
www.explorelearnin
Individual ! Practice g.com
Individually complete BLM 7.29.2.

Curriculum Expectations/ Observation/Mental Note: Assess students’

understanding of using tree diagrams to determine the probability of a
specific outcome from two independent events.

Consolidate Whole Class! Discussion/Sharing

Debrief Discuss how tree diagrams gives access to all possible outcomes for
probability experiments, and how they are useful for determining / calculating
theoretical probability.

Discuss any difficulties or “aha” moments arising from BLM 7.29.2.

Further Consolidation or Home Activity

Using BLM 7.29.1, have students consider changing the size of the second
Application spinner to have 6 equally sized sections (by removing brown and purple).
Concept Practice How would this change your answers on the BLM? What would the new
Exploration answers be?

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 120

7.29.1: Probability of a Specific Event Grade 7
Name: Date:

At the school fun fair there was a game with two spinners like the ones below. You must spin both
spinners once; if they land on the same colour, you win a prize.

Spinner 1 Spinner 2

brown red

red green
purple yellow

orange
green
blue yellow
blue
black

1. Draw a tree diagram and list all of the possible outcomes.

2. What is the theoretical probability that you will win a prize?

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 121

 7.29.1: Probability of a Specific Event Solutions Grade 7
Name: Date:

At the school fun fair there was a game with two spinners like the ones below. You must spin both
spinners once; if they land on the same colour, you win a prize.

Spinner 1 Spinner 2

brown red

red green
purple yellow

orange
green
blue yellow
blue
black

1. Draw a tree diagram and list all of the possible outcomes. Purple

Red – Purple Green -Purple Blue – Purple Yellow – Purple

Red – Brown Green – Brown Blue – Brown Yellow – Brown
Red – Red Green – Red Blue – Red Yellow – Red
Red – Yellow Green – Yellow Blue – Yellow Yellow – Yellow
Red – Orange Green – Orange Blue – Orange Yellow – Orange
Red – Black Green – Black Blue – Black Yellow – Black
Red – Blue Green – Blue Blue – Blue Yellow – Blue
Red – Green Green – Green Blue – Green Yellow - Green

2. What is the theoretical probability that you will win a prize?

Theoretical Probability = Favourable Outcomes

Total Outcomes

= or

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 122

7.29.2: Probability of a Specific Event Grade 7
Name: Date:

Complete the following questions determining the probability of the given events. You can use
the tree diagrams from Lesson 28.

1. Rolling a 6-sided die and flipping a coin

a) P(3, H) =

b) P(4 or 5, T) =

c) P(<5,T) =

d) P(Even number, T) =

e) P(Prime number, H) =

f) P(Odd number, H or T) =

g) P(Any number, H) =

2. Flipping a coin 3 times

a) P(3 Heads) =

b) P(3 Tails) =

c) P(2 Heads and 1 Tails) =

d) P(1 Heads and 2 Tails) =

e) P(Heads first, then 1 Heads and 1 Tail in any order) =

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 123

7.29.2: Probability of a Specific Event Continued Grade 7
3. Spinning the spinner below twice and flipping a coin

Spinner

B
A

a) P(A and B and Heads) =

b) P(B and C and Tails) =

c) P(2 Cs and Tails) =

d) P(Both the same letter and Tails) =

e) P(Any letters and Heads) =

4. Make up your own situation with 3 events where there are 12 outcomes.

5. Create and answer three probability questions (similar to questions above) dealing with
the situation you created in question 4.

a)

b)

c)

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 124

7.29.2: Probability of a Specific Event (Teacher Answers) Grade 7

Name: Date:

Complete the following questions determining the probability of the given events. You can use
the tree diagrams from Lesson 28.

1. Rolling a 6-sided die and flipping a coin

a) P(3, H) =

b) P(4 or 5, T) = or

c) P(<5,T) = or

d) P(Even number, T) = or

e) P(Prime number, H) = or

f) P(Odd number, H or T) = or

g) P (Any number, H) = or

2. Flipping a coin 3 times

a) P(3 Heads) =

b) P(3 Tails) =

c) P(2 Heads and 1 Tails) =

d) P(1 Heads and 2 Tails) =

e) P(Heads first, then 1 Heads and 1 Tail in any order) = or

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 125

3. Spinning the spinner below twice and flipping a coin
Spinner

B
A

a) P(A and B and Heads) = or

b) P(B and C and Tails) = or

c) P(2 Cs and Tails) =

d) P(Both the same letter and Tails) = or

e) P(Any letters and Heads) = or

4. Make up your own situation with 3 events where there are 12 outcomes.

Many options: Flipping 2 coins and spinning 1 three-section spinner

Rolling 2 dice (even numbers) and spinning 1three-section spinner
Rolling 2 dice (odd numbers) and rolling another die (getting a 5 or 6)

Any situation with 2 outcomes, 2 outcomes, and 3 outcomes

5. Create and answer three probability questions (similar to questions above) dealing with
the situation you created in question 4.

Answers will vary.

Sample from first option above (flipping 2 coins and three-section spinner)

a) P(2 Heads and a B) =

b) P(Heads and Tails and a C) = or

c) P(2 Heads and any letter) = or

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 126

Unit 7: Day 30: Comparing Theoretical to Experimental Probability Grade 7
Math Learning Goals Materials
• Perform simple probability experiments. • BLM 7.29.1
• Compare theoretical probability with the results of the experiment using both a small • BLM 7.30.1
sample (individual student results) and a large sample (the combined results from all • Paper clips
students in the class). • Dice
• Understand that probability results can be misleading if an experiment has too few • Coins
trials.
Assessment (A) and DI (D)
Opportunities
Minds On… Teacher Directed! Whole Class! Discussion
Give students a paper clip to act as the pointer on a spinner. Have students do the Theoretical
probability – A
game 8 times from BLM 7.29.1 from the previous lesson. Have the students keep
mathematical
track of their results. Remind them of the terms “theoretical probability” and calculation of the
“experimental probability”. Looking at the tree diagram from Day 29, compare the chances that an
results of their spin (experimental probability) to the theoretical probability. event will happen in
theory.
On a chart, record the results of 4 students. Compare the results of the 4 students
(experimental probability) to the theoretical probability. Experimental
On a different chart, record the results of the whole class. Compare the results of the Probability – The
likelihood of an
whole class to the theoretical probability.
event occurring,
determined from
Depending on the results, discuss how the results on each chart can be misleading if an experimental results
experiment has too few trials or the sample size is too small. (e.g. if nobody won the rather than from
game based on the first sample size, someone might assume that if you played the theoretical
game you would never win if they saw the first chart) reasoning.

Define the term “sample size” and discuss how the sample size is 32 for the first chart. Sample Size – A
representative group
Ask the question: Do the results from these 32 trials represent what should happen to
chosen from a
other people who will play the game? population and
examined in order to
For the chart showing the results from the whole class, ask the question: Does this make predictions
sample size represent what will happen to people who will play this game? about the
Action! Individual! Exploration! Apply Understanding populations.
Have students conduct a probability experiment, using BLM 7.30.1.
Students are familiar with this question from Day 28 BLM 7.28.1 question 1.
OR Use the second
If you have access to Gizmos (and it has not already used), students can use the Gizmo
following probability experiments online from www.explorelearning.com :
a) Compound Independent Events
http://www.explorelearning.com/index.cfm?method=cResource.dspResourcesForCour
se&CourseID=233
b) Theoretical or Experimental Probability
http://www.explorelearning.com/index.cfm?method=cResource.dspResourcesForCour
se&CourseID=233

Curriculum Expectations/ Application/Checklist: Assess students’ understanding

of being able to conduct a probability experiment and being able to compare
theoretically probability to experimental probability based on sample size.
Consolidate Whole Class! Discussions
Debrief Discuss how the sample size will reflect the accuracy of theoretical probability when
compared to experimental probability. Also, discuss that probability games have an
element of chance (somebody has to win the lottery).
Discuss the importance of an appropriate sample size when comparing theoretical
probability to experimental probability.
Discuss real life examples where probability, percents, fractions and decimals could be
misleading (e.g., advertisements’ claims based on percentages where sample sizes are
not known, or the number of trials of a given event are not shared).
Home Activity
Application
To prepare for Lesson 31, think of everyday applications of probability and bring in
Reflection
samples from: magazines, the internet, books, newspapers etc.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 127

7.30.1: Comparing Theoretical and Grade 7
Experimental Probability
Below is a tally chart for flipping a coin and rolling a 6-sided die. Conduct the
experiment 24 times and complete the chart.
(All of the possible outcomes have been provided for you in the first column)

Experimental Experimental Theoretical Theoretical Experimental

Tally Total Probability Probability Probability Probability =
Outcome (Fraction) (Percent) (Fraction) (Percent) Theoretical?
(yes or no)
Flip Roll
H 1
H 2
H 3
H 4
H 5
H 6
T 1
T 2
T 3
T 4
T 5
T 6

1. For how many of the outcomes were your experimental probabilities equal to the
theoretical probability? How many were close? Which was the furthest away?
Does that make sense?

2. If we gathered the whole class’ data, would you expect similar results to what you
obtained individually?

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 128

Unit 7: Day 31: Application of Probability in the World Grade 7
Math Learning Goals Materials
• Examine everyday applications of probability, e.g. batting averages, goalie • BLM 7.31.1
statistics, weather forecasts, opinion polls, etc. • BLM 7.31.2
• Research and report on probabilities expressed in fraction, decimal, and • BLM 7.31.3
percent form.
Assessment (A) and DI (D)
Opportunities
Minds On… Whole Class! Discussion
Display and discuss real life examples of probability that students brought in from the
Day 30 ‘At Home Activity’. If students didn’t bring any; brainstorm examples and
discuss what each example means in terms of probability. How are these examples
represented? (words, fractions, decimals and percents) Possibilities: weather results,
lotteries or gaming, sports betting, “risks” in the financial world, demographic
predictions based on population statistics, car insurance rates based on probabilities of
certain ages/genders getting in accidents, etc. Statistics on
smoking can be
Discuss a few examples in sports where knowledge of probability can help provide found at:
http://www.familyfirst
information about more favourable outcomes. These outcomes can help predict who
aid.org/teen-
has a better chance of winning and aid in decision-making. smoking.html.

Discuss a few examples where the outcomes are affected by chance even when the
probability of an event has been given (e.g., weather, lotteries, scratch tickets, etc.).
Also talk about statistics that apply to teenagers. What are your chances of becoming
a smoker? What are the chances that someone in this class will smoke?
Action! Pairs or Individual! Research and Application Remind students
Students will complete BLM 7.31.1 using BLM 7.31.2 (which is a collection of about equivalent
sample statistical data) or the Internet. Students could use the following sentence fractions when trying
starter: What are the odds that ... to relate statistics to
Examples: Someone will be struck by lightning once? Twice? Or win the Roll up the a different sample
Rim to Win Contest at Tim Hortons?) size.
Use any website that gives statistics. Students could change the population or sample
size to match their school size, class or town/city. (Comparing statistical data with
different sample sizes)

Possible Ideas/ Websites

Statistics Canada (students can also look at census data for their city or town)
http://www.statcan.gc.ca/
Tim Hortons Roll Up the Rim to Win Contest
http://www.rolluptherimtowin.com/en/rules.php
Sports Statistics www.mlb.com, www.nhl.com, www.nba.com
Weather http://www.theweathernetwork.com/ This would allow
Lottery Statistics http://www.lotto649stats.com/lotto649.html students to make
connections to
http://www.cbc.ca/news/background/gambling/lotteries.html transfer and apply
knowledge.
Curriculum Expectations/ Application/Rubric: Assess students’ ability to research
a real life example of probability and their ability to effectively communicate and
apply their knowledge.

Consolidate Gallery Walk! Whole Group Discussion

Debrief Have students walk around the room and read other students’ work.
After students have completed a gallery walk discuss anything they found interesting
or questions they still might have.
Home Activity or Further Consolidation Highlight the
Application Challenge the students to try to find an interesting or bizarre math fact that is a real life appropriate columns
Exploration example of probability OR complete BLM 7.31.3. in the data table
and/or discuss
headings.

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 129

7.31.1 Applications of Probability in the World Grade 7

Name: ________________________________ Date:__________________

Find out the probability (could be a decimal, percent or fraction) of something happening in the
real world and fill out the following chart. Refer to BLM 7.31.2.

Math Fact(s) that is a Real Life Example of Probability:

Source:

Explain how the math fact you have chosen is a good real life example of probability.

How would people use your fact?

Who would use your math fact and why?

Can you apply your statistic to the population of your class? School? Town or city? Future events?

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 130

7.31.2: Applications of Probability in the World Grade 7
Name: ________________________________ Date:__________________

Use any of the following real-life statistics to complete the worksheet 7.31.1.

Roll Up the Rim to Win!!! Lotto 649 Odds

Total Cups: 281 686 000 Jackpot Winner: 1 in 13 983 816
Cars: 35 5 out of 6 numbers: 1 in 55 491
$100 Gift Card: 25 000 4 out of 6 numbers: 1 in 1032
3 out of 6 numbers: 1 in 57
Statistics from one study by CDC Hockey
(High school students smoking) Goalie Goals Against Average (GAA): 3.15
23% in 2005 Goalie Save Percentage: .913
22% in 2003
36% in 1997

Unemployment Rate Total Sales at a Store

Overall: 8.6% Year: Up 3.5%
Ages 15-24: 15.9% Month: Down 1.1%

Long Term Forecast Updated: Friday, July 10, 2009, 8:00 EDT

(from: theweathernetwork.com)
Saturday Sunday Monday Tuesday Wednesday Thursday
Jul. 11 Jul. 12 Jul. 13 Jul. 14 Jul. 15 Jul. 16

Thunderstorms Cloudy periods Sunny Sunny Isolated showers Variable cloudiness

P.O.P. 90% 0% 0% 0% 40% 20%
High 26°C 22°C 23°C 23°C 24°C 16°C
Feels Like 35 - - - - -
Low 15°C 15°C 15°C 15°C 13°C 13°C
Wind SW 20 km/h W 15 km/h W 15 km/h W 15 km/h SE 10 km/h W 20 km/h
24-Hr Rain 2-4 mm - - - less than 1 mm -
(Note: P.O. P. is probability of precipitation)

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 131

7.31.3: Applications of Probability in the World Grade 7
Name: ________________________________ Date:__________________

2007 Raptors Playoffs Statistics

PLAYER AVERAGES
REBOUNDS
Player G GS MPG FG% 3p% FT% OFF DEF TOT APG SPG BPG TO PF PPG
Chris Bosh 6 6 37.0 .396 .200 .842 1.20 7.80 9.00 2.5 .83 1.83 2.00 3.20 17.5
T.J. Ford 6 5 22.7 .487 .500 .810 .80 .80 1.70 4.0 1.17 .33 2.33 1.20 16.0
Anthony Parker 6 6 40.0 .419 .400 .795 .50 4.80 5.30 1.0 1.50 .33 1.17 3.00 15.2
Jose Calderon 6 1 24.3 .507 .250 .833 .30 1.30 1.70 5.3 .83 .00 2.50 2.00 13.0
Andrea Bargnani 6 3 30.2 .478 .412 .789 .50 3.50 4.00 1.0 .83 .50 1.17 2.70 11.0
Morris Peterson 6 2 30.5 .517 .500 .833 .80 3.70 4.50 .3 .33 .33 1.00 3.30 6.8
Rasho Nesterovic 5 4 14.2 .467 .000 1.000 2.00 2.60 4.60 .6 .00 .40 .80 .80 3.4
Juan Dixon 6 0 10.5 .381 .250 .000 .00 .70 .70 .5 1.17 .00 1.67 1.00 3.0
Joey Graham 6 3 18.2 .286 .000 .800 .20 3.20 3.30 .3 .67 .00 1.00 2.00 2.7
Luke Jackson 3 0 3.7 .000 .000 1.000 .30 1.30 1.70 .3 .33 .00 .33 1.00 2.0
Kris Humphries 6 0 11.5 .333 .000 .375 1.20 1.70 2.80 .2 .17 .33 .50 1.80 1.5
Darrick Martin 2 0 4.0 .000 .000 1.000 .00 .50 .50 1.0 .00 .00 .00 .00 1.0

A. Using the table (Toronto Raptors 2007 Playoffs) complete the following questions.

1. Which players made just less than half of their shots (FG%) during the playoffs?

2. If you were the coach who would you want shooting a foul shot (FT%) at the end of a
game?

3. If Jose Calderon were to shoot 20 3-pointers (3p%), how many do you think he would
make?

4. Would it be better for Morris Peterson to focus on the percentage statistics (FG%, 3p%
and FT%) or the other ones (Rebounds, Assists-APG, Points-PPG, etc.) when
discussing a new contract with the Raptors? Justify your answer.

B. As a team, The Toronto Blue Jays were batting .275 at one point in the season.

1. If they had 40 bats in a game, how many hits would you expect them to get?

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 132

7.31.3: Applications of Probability in the World Grade 7
Solutions
Name: ________________________________ Date:__________________

2007 Raptors Playoffs Statistics

PLAYER AVERAGES
REBOUNDS
Player G GS MPG FG% 3p% FT% OFF DEF TOT APG SPG BPG TO PF PPG
Chris Bosh 6 6 37.0 .396 .200 .842 1.20 7.80 9.00 2.5 .83 1.83 2.00 3.20 17.5
T.J. Ford 6 5 22.7 .487 .500 .810 .80 .80 1.70 4.0 1.17 .33 2.33 1.20 16.0
Anthony Parker 6 6 40.0 .419 .400 .795 .50 4.80 5.30 1.0 1.50 .33 1.17 3.00 15.2
Jose Calderon 6 1 24.3 .507 .250 .833 .30 1.30 1.70 5.3 .83 .00 2.50 2.00 13.0
Andrea Bargnani 6 3 30.2 .478 .412 .789 .50 3.50 4.00 1.0 .83 .50 1.17 2.70 11.0
Morris Peterson 6 2 30.5 .517 .500 .833 .80 3.70 4.50 .3 .33 .33 1.00 3.30 6.8
Rasho Nesterovic 5 4 14.2 .467 .000 1.000 2.00 2.60 4.60 .6 .00 .40 .80 .80 3.4
Juan Dixon 6 0 10.5 .381 .250 .000 .00 .70 .70 .5 1.17 .00 1.67 1.00 3.0
Joey Graham 6 3 18.2 .286 .000 .800 .20 3.20 3.30 .3 .67 .00 1.00 2.00 2.7
Luke Jackson 3 0 3.7 .000 .000 1.000 .30 1.30 1.70 .3 .33 .00 .33 1.00 2.0
Kris Humphries 6 0 11.5 .333 .000 .375 1.20 1.70 2.80 .2 .17 .33 .50 1.80 1.5
Darrick Martin 2 0 4.0 .000 .000 1.000 .00 .50 .50 1.0 .00 .00 .00 .00 1.0

A. Using the table (Toronto Raptors 2007 Playoffs), complete the following questions:

1. Which players made just less than half of their shots (FG%) during the playoffs?
T.J. Ford, Andrea Bargnani and Rasho Nesterovic

2. If you were the coach, who would you want shooting a foul shot (FT%) at the end of a
game?
Rasho Nesterovic, Luke Jackson or Darrick Martin

3. If Jose Calderon were to shoot 20 3-pointers (3p%), how many do you think he would
make?
.250% = .25 = ! He would make a quarter of the 20 shots = 5

4. Would it be better for Morris Peterson to focus on the percentage statistics (FG%, 3p%
and FT%) or the other ones (Rebounds, Assists-APG, Points-PPG, etc.) when
discussing a new contract with the Raptors? Justify your answer.

He would be better to use the percentage statistics because he is the highest on

the team in FG% and 3p% and very good at FT% (.833). However, using the other
statistics he is not the highest (rebounds-4th, points-6th, assists-almost last)

B. As a team, The Toronto Blue Jays were batting .275 at one point in the season.

1. If they had 40 bats in a game, how many hits would you expect them to get?

Many solutions possible:

.275 = = or .275 x 40 = 11

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 133

Online Student-Friendly Resources for Decimals
Using Decimals
! tenths “Railroad Repair” http://pbskids.org/cyberchase/games/decimals/decimals.html

! estimating and reading tenths, hundredths and thousandths “Decimal Darts”

http://www.decimalsquares.com/dsGames/games/darts.html

! tenths, hundredths and thousandths using a grid “Beat the Clock”

http://www.decimalsquares.com/dsGames/games/beatclock.html and “Concentration”
http://www.decimalsquares.com/dsGames/games/concentration.html

! online number line for tenths, hundredths and thousandths

http://www.mathsonline.co.uk/freesite_tour/resource/whiteboard/decimals/dec_notes.html

Ordering Decimals
! online number line for tenths, hundredths and thousandths
http://www.mathsonline.co.uk/freesite_tour/resource/whiteboard/decimals/dec_notes.html

! ordering tenths and hundredths “Switch” http://www.interactivestuff.org/sums4fun/switch.html

! ordering tenths and hundredths “Builder Ted”

http://www.bbc.co.uk/education/mathsfile/shockwave/games/laddergame.html

! ordering tenths, hundredths and thousandths “Place Value”

http://www.decimalsquares.com/dsGames/games/placevalue.html

! ordering hundredths using Olympic scores “The Award Ceremony”

http://www.mathsonline.co.uk/nonmembers/gamesroom/awards/awardc.html

! ordering thousandths and ten thousandths (hard!) “Decimals in Space”

http://themathgames.com/arithmetic-games/place-value/decimal-place-value-math-game.php

Adding Decimals
! adding tenths, hundredths or thousandths “Decimal Squares Blackjack”
http://www.decimalsquares.com/dsGames/games/blackjack.html

Subtracting Decimals
! subtracting tenths, hundredths or thousandths “Rope Tug”
http://www.decimalsquares.com/dsGames/games/tugowar.html

Multiplying Decimals
! estimating, multiplying decimals “Decimal Speedway”
http://www.decimalsquares.com/dsGames/games/speedway.html

Converting Fractions and Decimals

! online converter between fractions and decimals
http://www.shodor.org/interactivate/activities/Converter/

TIPS4RM: Grade 7: Unit 7 – Fractions and Decimals 134