Primary 4

Class 4 / D Date : / / 2021

Unit one: Place Value concept 1 : Reinforcing Place Value

Lesson : Review digit , Numeral , Number
-------------------------------------------------------------------------------------------------------------------
Learning outcomes
At the end of the lesson students will be able to
• Explain the difference between a digit, numeral, and number.
• Discuss how the value of a digit can change
Resources
Student book
Digital source
Video – using QR code

Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page 54

The tools : white papers , Cards
Vocabulary Building: digit, numeral, and number.
ACCESS
Large Numbers with Small Animals
Ask students: Read Ant Facts for Kids to learn about amazing ants.
Then, highlight or circle all the numbers you see
BUILD (40 minutes)
Ask students to Write any large number on a piece of paper
And try to get the differences between digit, numeral, and number.
Vocabulary Building: (20 minutes)
Ask students
In your own words, write a brief definition of the terms digit, number, and numeral.
Record the definitions that were written by the class
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CONNECT
Writing About Math Consider the numbers 26, 260, and 62
. Explain what strategies you would use to determine the greatest number.
Try to use the words digit, numeral, and number to explain your thinking.
Be prepared to share your thinking with the class

Practice:
Write each number in the appropriate column

Check Understanding:
Reinforcing the place value
Correct the new Vocabulary Building: digit, numeral, and number.
Students should be remembering the place value when comparing between numbers, then
asking students to move to the practice part

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Unit one: Place Value concept 1 : Reinforcing Place Value
Lesson : Big Numbers
-------------------------------------------------------------------------------------------------------------------
Learning outcomes
In this lesson
• Students will identify all whole number place values through the One Milliard place.
• Students will explain how the value of a digit changes based on its place in a number

Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page 60

Resources
Place value chart – cards
Digital source
Video – using QR code
Vocabulary Building: digit, milliard, period, place value.
ACCESS
COMMON MISCONCEPTIONS AND ERRORS
• Students may not understand that the position of a digit in a numeral determines its value.
• Students may not recognize that there are relationships between place values. For example, in
the number 333, the value of the 3 in the Tens place is 10 times greater than the value of the 3
in the Ones place. The value of the 3 in the Hundreds place is 10 times greater than the value of
the 3 in the Tens place.
• Students may struggle to read large numbers correctly utilizing Ones, Thousands, Millions,
and Milliards
Ask students:
Exploring Place Value

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BUILD (40 minutes)
Reading the Place Value Chart
Creating Really Big Numbers
Give students 10–15 minutes to play.
Then, stop and ask one student to write their greatest numeral on the board.
Ask students to walk through each digit.
ASK • What is this digit?
• What is this digit’s value?
• What would happen to the value of this
digit if it were here (point to another place in the numeral)?
• Why did the value of the digit change when its location changed
Vocabulary Building: (20 minutes)
Ask students
In your own words, write a brief definition of the terms digit, number, and numeral.
Record the definitions that were written by the class

CONNECT
Writing About Math
1. Direct students to Lesson 2 CONNECT Writing About
Math and respond to the prompt.
WRAP-UP (3 min)
One Million Ants!
1. Ask students to reflect on the statement shared during ACCESS and then consider
the question: If there are 1,000,000 ants for every 1 person, how many people do you
think it would take to have one milliard ants?
Practice:
Direct students to Lesson 2 PRACTICE and have them complete the problems.
Address student errors and misconceptions around very large numbers.
Check Your Understanding
1. Use the digits 3, 5, 7, 8, 8, 1, 6, 2 to make the greatest number you can. Then use the
same digits to make the smallest number you can.
Greatest: 88,765,321
Smallest: 12,356,788

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Big numbers

Thousands
H T O H T O

Standard form : ---------------------------------------------------------------------------------------------

Word form :----------------------------------------------------------------------------------------------------
-------------------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------------
Expand form :------------------------------------------------------------------- ----------------------

H T O H T O H T O
5 8 3 4 6 0 9 0 5

Standard form : ---------------------------------------------------------------------------------------

Check
The Value of the digit 5 in the number 1 ,578 ,416 is -------------
The value of the digit 3 in the number 356 , 546 is ----------------
Complete
5 tens = ……………..
3 hundred thousand =………………
400 tens = ………………..thousands

Write the greatest and the smallest number formed from 3 , 5 , 7 ,8 ,1 ,6 ,2

The greatest number is -------------------------------

The smallest number is -------------------------------

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Unit one: Place Value concept 1 : Reinforcing Place Value

Lesson : Changing Values
-------------------------------------------------------------------------------------------------------------------
Learning outcomes
In this lesson
• Students will explain how the value of a digit changes as it moves to the left in a whole
number.
• Students will describe patterns they observe in
changing place values.
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page 65

Resources
Place value chart – cards
Digital source
Video – using QR code
Vocabulary Building: amateur, milliard, myrmecologist, period, place valu e
ACCESS
COMMON MISCONCEPTIONS AND ERRORS
Students may be able to identify the place values and periods but may not recognize the pattern
or relationship between each place
Multiplying by Ten
1. Distribute 2 Tens rods to each student.
2. Direct students to Lesson 3 ACCESS Multiplying by Ten. Ask students to read the directions
and answer the first question.
Solve several problems together using multiplication by 10. Record on the board.
For example:
• If 5 people were in the small group, how many
would there be? How do you know?
(5 × 10 = 50)
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• If 11 people were in the small group, how many would there be? How do you know?
(11 × 10 = 110)
BUILD (40 minutes)
What value does this digit have when I put it in the Ones place?
• What value does this digit have when I put it in the Tens place?
Exploring Place Value Relationships
1 Ten is 10 times as much as 1 One. 10 × 1 = 10
• 1 Hundred is 10 times as much as 1 Ten. 10 × 10 = 100
• 1 Thousand is 10 times as much as 1 Hundred. 10 × 100 = 1,000
• 1 Ten Thousand is 10 times as much as 1 Thousand. 10 × 1,000 = 10,000
• 1 Hundred Thousand is 10 times as much as 1 Ten Thousand. 10 × 10,000 = 100,000
• 1 Million is 10 times as much as 1 Hundred Thousand. 10 × 100,000 = 1,000,000

CONNECT
Direct students to Lesson 3 CONNECT Multiplying Ants and ask them to complete the
learning activity.
Practice:
Direct students to Lesson 3 PRACTICE and have them complete the problems. Address
student errors and misconceptions around changing values.
Check Your Understanding
1. Fill in the blanks below.
One million/1,000,000 is 10 times greater than one hundred thousand.
Two thousand/2,000 is 10 times greater than two hundred.
Seventy thousand/70,000 is 10 times greater than seven thousand
2. What is the value of the following:
a. 9 in the Tens place? 90
b. 3 in the Hundreds place? 300
c. 60 Tens? 600
d. 80 Thousands? 80,000

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Unit one: Place Value concept 1 : Reinforcing Place Value

Lesson : Review Comparing Values

Learning outcomes
In this lesson
• Students will explain the relationship between a given place value and the place value
to its left.
• Students will use multiplication to compare place values.
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page 63

Resources
Place value chart – cards
Digital source
Video – using QR code
Vocabulary Building: Review vocabulary as needed
ACCESS
COMMON MISCONCEPTIONS AND ERRORS
• Students may be able to identify the place values and periods, but may not recognize the
pattern or relationship between each place.

BUILD (40 minutes)

Exploring Place Value
1. Remind students that they have already learned that the value of a digit depends on its
location within a number. Explain that they should also know that it can be helpful to understand
the relationship between a given place value and the place value to its left.
2. Ask students to describe the patterns they saw in the ACCESS problems. Students should
describe a pattern of multiplying by 10 each time they move one place to the left.

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place Value and the Pharaoh Ant (25 min)

1. Direct students to Lesson 4 BUILD Place Value and the Pharaoh Ant and ask them to
work in pairs to solve Problems 1–3.
2. Ask volunteers to share their thinking and ask them how these problems relate to what
we know about relationships between place values.
3. Have students work in pairs or small groups to complete Problems 4–7 in BUILD.
CONNECT
Step to the Left
Have students turn to Lesson 4 CONNECT Step to the Left. Go over the directions with
students and have them work independently to complete the activity, which relates to the
Essential Question for this lesson
Practice:
Direct students to Lesson 4 PRACTICE and have them complete the problems. Address
student errors and misconceptions.
Check Your Understanding
1. (3 Tens and 9 Ones) × 10 = 390
2. (5 Thousands and 2 Hundreds) × 100 = 520,000
3. (9 Hundred and 9 Tens) × 1,000 = 990,000
4. 56 Thousands × 100 = 5,600,000
5. Highlight or circle the number that is 100 times larger than 42.
420 or 4,200
6. Highlight or circle the number that is 1,000 times larger than 12 3.
123,000 or 12,300

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Unit one: Place Value concept 1 : Reinforcing Place Value

Lesson : Many Ways to Write
-------------------------------------------------------------------------------------------------------------------
Learning outcomes
In this lesson
• Students will write numerals in standard, word, and expanded forms.
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page 79

Resources
Digital cards
Digital source
Video – using QR code
Vocabulary Building: expanded form, standard form, word form
ACCESS
COMMON MISCONCEPTIONS AND ERRORS
• Students may be confused about how to represent a place value with a 0 digit in expanded
form. For example: 30,456 = 30,000 + 400 + 50 + 6. The 0 is not represented in expanded form
because in standard form the 0 represents that there is nothing in tha t place value.
• Students may struggle to say large numbers and need to be reminded to group the numbers
into periods as they read them aloud.
• Students may forget to use commas when writing
numbers in word form.

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BUILD (40 minutes)
Numeral Form Exploration (10 min)
1. Direct students to Lesson 5 BUILD Numeral Form Exploration section of their Student
Materials.Show students the number 9,231,043,204 written in standard form, expanded form,
and word form.
Read the numbers aloud with students.
2. Ask students to share their thinking about the following questions:
ASK •
What do you remember about these forms
of writing numerals?
• What was easy?
• What was challenging?
CONNECT
Writing About Math
Direct students to Lesson 5 CONNECT Writing About Math and ask them to respond to
the prompt. Students should have used place value and an
understanding of the value of each digit to create the greatest numbers possible. For
example, it would not make sense to write the smallest digit in the highes t place, since
that would not allow you to create the greatest numeral possible. Students should
recognize that they should write the greatest digit in the greatest place and list them in
decreasing value in the numeral they create.
Practice:
Direct students to Lesson 5 PRACTICE and have them complete the problems. Address
student errors and misconceptions around the many ways to write numbers.
Check Your Understanding
Complete the table below:

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Unit one: Place Value concept 1 : Reinforcing Place Value
Lesson : Composing and Decomposing
-------------------------------------------------------------- -----------------------------------------------------
Learning outcomes
In this lesson
• Students will compose and decompose numerals in multiple forms.
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page 85

Resources
Place value chart – cards
Digital source
Video – using QR code
Vocabulary Building: compose, decompose, decomposed form, expanded form,
standard form, word form
ACCESS
COMMON MISCONCEPTIONS AND ERRORS
Students may not be sure how to represent a zero in a place when the number is decomposed.
• Students may incorrectly use parentheses to group place values .
• Students may not connect digits in their place values, expanded notation, and decomposing
numbers.
• Students may confuse the terms compose and decompose
Build:
Composing and Decomposing (2 min)
1. Ask students to talk to their Shoulder Partner and predict what might happen to an anthill after
a strong wind or rainstorm.
2. Direct students to Lesson 6 BUILD Composing and Decomposing.
Ask students to look at the images of the anthills and briefly describe their observations.
Composing 145
3. Explain that numbers, like an anthill, can be composed (put together) and decomposed
(broken apart). Ask students to work independently to complete the activity Composing
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145 in their Student Materials. Encourage students to use a variety of operations as they
compose 145.
4. After a few minutes, tell students to share with a Shoulder Partner some of the ways
they composed 145.
5. Show students the place value chart on the board. Ask students to share ways that the
chart might help them decompose numbers. (Students may say that a place value chart
helps them more easily see how to write numbers in expanded notation.)
6. Write or display the following numbers on the board:
60,000 + 7,000 + 800 + 90 + 1(6 × 10,000) + (7 × 1,000) + (8 × 100) + (9 × 10) + (1 × 1)
PRACTICE
Direct students to Lesson 6 PRACTICE and have them complete the problems. Address
student errors and misconceptions around composing and decomposing
numbers.
Check Your Understanding
Decompose the numeral below using expanded form.
1. 67 million, 38 thousand, 1260,000,000 + 7,000,000 + 30,000 + 8,000 + 10 + 2
Decompose the numerals below as you did in BUILD:
2. nine million, four hundred forty thousand, two hundred twenty
(9 × 1,000,000) + (4 × 100,000) + (4 × 10,000) + (2 × 100) + (2 × 10)
3. six milliard, nine hundred million, ten thousand four
(6 × 1,000,000,000) + (9 × 100,000,000) + (1 × 10,000) + (4 × 1)
4. eight million, seventy thousand, two hundred
(8 × 1,000,000) + (7 × 10,000) + (2 × 100)

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Unit one: Place Value concept 2 : Using Place Value

Lesson : Review Comparing Really Big Numbers
------------------------------------------------------------- ------------------------------------------------------
Learning outcomes
In this lesson
• Students will use place value to compare large numerals.
• Students will use symbols to express numerical comparisons.

Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page 105

Resources
Digital Cards – Comparison symbols
Digital source
Video – using QR code
Vocabulary Building: digit, milliard, period, place value.
ACCESS
COMMON MISCONCEPTIONS AND ERRORS
Students sometimes compare the number of digits in a numeral rather than the value of the
largest digit.
• Students sometimes forget to consider how many digits are in a numeral when they compare

BUILD (40 minutes)

. Ask students to discuss how they can use place value helps to compare really big numbers.
NOTE: Help students connect this activity to their learning in Lesson 6, reinforcing this with
writing and modeling on the blackboard as needed.
For example, with Ant Hills 3 and 4, students should note that each numeral has the same digit
in the Ten
Thousands place, but Ant Hill 3 has 4 × 1,000 in the
Thousands place and Ant Hill 4 has 5 × 1,000 in the
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Thousands place. • What is this digit’s value?
• What would happen to the value of this digit if it were here (point to another place in the
numeral)?
• Why did the value of the digit change when its location changed
Practice:
PRACTICE
Direct students to Lesson 7 PRACTICE and have them
complete the problems. Address student errors and
misconceptions.
Check Your Understanding
1. Circle the symbol to compare the numbers.
1,231,425,234 < 1,321,454,435
67,353,622 < 67,353,630
40,243,021 > 40,209,314
999,999,999 < 1,000,000,000
Create a number in the Hundred Thousands that is less than (<) 893,824.Students must
create a number less than 893,824.
3. Create a number in the Ten Millions that is greater than (>) 34,450,600,125.Students
must create a number greater than 34,450,600,125.
4. Create a number in the Milliards that is greater than (>) 3,456,789,000.Students must
create a number greater than 3,456,789,000

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Unit one: Place Value concept 2 : Using Place Value
Lesson : Comparing Numbers in Multiple Forms
-------------------------------------------------------------------------------------------------------------------
Learning outcomes
In this lesson
• Students will compare numbers in multiple forms.
• Students will describe strategies for comparing numbers in multiple forms
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page 105

Resources
Digital Cards – chart paper
Digital source
Video – using QR code
Vocabulary Building: n
decomposed form, efficient, expanded form, standard form, word form
ACCESS
COMMON MISCONCEPTIONS AND ERRORS
• Students may struggle with comparing numbers in word form or expanded notation.
• Students may struggle with finding a system that helps them compare numbers in different
forms
BUILD (40 minutes)
. Strategies for Comparison
Number Battle Directions
• The game requires 3 players. 2 players are “builders” and 1 player is the “reader.”
• Each player needs a set of digit cards 0–9.
1. Players will combine the 3 decks (30 cards), shuffle the cards, and p lace them
face down in the middle.
2. Each builder draws 11 cards.
3. Each builder uses 10 of their cards to create the greatest number possible and
discards the 11th card.
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4. The reader will read each builder’s number aloud.
5. The builders write their number and their partner’s number in the table in their
Student Materials. Be sure to pay attention to how the numbers should be
recorded for each round.
6. The builders compare their numbers and record the appropriate sign (< or >).
7. The builders discuss: Which place value did you use to determine which
number was greater?
8. Rotate roles and play again.

Practice:
PRACTICE
Direct students to Lesson 8 PRACTICE and have them
complete the problems. Address student errors and
misconceptions.
Check Your Understanding
1. Compare these anthills. Circle the one with the greatest number of ants.
Put a box around the one with the least number of ants and draw stars on the
two with an equal number of ants.
(1 × 1,000,000,000) + (3 × 100,000) + 10

456,320,126

400,000,000 + 50,000,000 +6,000,000 + 300,000 + 20,000 + 100

four hundred fifty-six million, three hundred twenty thousand, one hundred twenty -six

(4 × 100,000,000) + (8 × 10,000,000) + (6 × 1,000,000) + (9 × 10,000) + (9 × 1,000) + (4

× 100) + (3 × 10) +1

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Unit one: Place Value concept 2 : Using Place Value
Lesson : Descending and Ascending Numbers
-------------------------------------------------------------------------------------------------------------------
Learning outcomes
In this lesson
• Students will order numbers in multiple forms.
• Students will describe strategies for ordering numbers in multiple forms.

Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page 115

Resources
Digital Cards
Digital source
Video – using QR code
Vocabulary Building:
ascending, compare, decomposed form, descending, expanded form, order, standard
form, word form
ACCESS
COMMON MISCONCEPTIONS AND ERRORS
• Students may not understand the place value relationships between the standard, word, and
expanded forms of a number.
• Students may not understand that numbers can be ordered in multiple forms (standard, word,
or expanded form).
• Students may struggle to compare and order numbers with similar digits and need to be
reminded to start on the left and compare each digit while moving to the right of a number

. BUILD (40 minutes)

Ascending and Descending Numbers

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Practice:
Direct students to Lesson 9 PRACTICE and have them
complete the problems. Address student errors and
misconceptions.
Check Your Understanding
1. Rewrite the numerals below in standard form. Then, list the numerals in
descending order (greatest to least).
six hundred forty-three thousand, nine hundred
nineteen; 634,920; (6 × 100,000) + (4 × 10,000) + (3 × 1,000) + (9 × 100) + (2 × 10);
600,000 + 40,000 + 4,000 + 10; six hundred forty-four thousand, two hundred ninety-nine

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Unit one: Place Value concept 2 : Using Place Value
Lesson : Predicting the Unpredictable
-------------------------------------------------------------------- -----------------------------------------------
Learning outcomes
In this lesson
• Students will explain front-end estimation.
• Students will use front-end estimation to approximate large numbers.
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page 120

Resources
Digital Cards
Digital source
Video – using QR code
Vocabulary Building:
estimation, front-end estimation, reasonable
ACCESS
COMMON MISCONCEPTIONS AND ERRORS
Students may struggle with knowing when to estimate and when an exact number is needed to
solve a problem.
• Students may confuse front-end estimation with other rounding strategies.
• Students may not understand the value of determining the reasonablene ss of answers.
. BUILD (40 minutes)
Exact or Not?
1. Tell students that there are times when they need an exact answer and times when an
estimate is good enough.
2. Play Pop-Up to help students consider when it is okay to estimate and when they should find
exact numbers

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Practice:

Direct students to Lesson 10 PRACTICE and have them complete the problems. Address
student errors and misconceptions.
Check Your Understanding
1. Define front-end estimation in your own words.
Students should mention using the digit in the largest place in the numeral or the digit
with the highest place value.
Use front-end estimation for the following numbers.
2. 86,433,920
80,000,000
3. 6,627,513,202
6,000,000,000
4. One hundred sixty-three million, four hundred thirty thousand, eight hundred two
100,000,000
5. (9 × 1,000,000) + (2 × 100,000) + (7 × 10,000) + (3 × 100) + (6 × 1)9,000,000
6. 700,000 + 7,000 + 70

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Unit one: Place Value concept 2 : Using Place Value
Lesson : Rounding Rules
---------------------------------------------------------------------------------- ---------------------------------
Learning outcomes
In this lesson
• Students will apply multiple strategies to round numbers.
Students will discuss whether rounding or front-end estimation provide a more accurate
estimate
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page 125

Resources
Digital Cards
Digital source
Video – using QR code
Vocabulary Building:
accurate, estimation, nearest, reasonable, rounding
ACCESS
COMMON MISCONCEPTIONS AND ERRORS
• Students may misapply the rule for rounding down and actually lower the value of the digit in
the designated place instead of keeping it the same or increasing it by one.
• Students may misapply the rule for rounding up and change the digit in the designated place,
while not changing digits in smaller places to zeroes.
• Students often only use front-end estimation for determining the reasonableness of answers.
Rounding provides more accurate estimates.
BUILD (40 minutes)
Rounding Using the Midpoint Strategy

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Practice:
Direct students to Lesson 11 PRACTICE and have them complete the problems. Address
student errors and misconceptions.
Check Your Understanding
Use the Rounding Rule strategy to solve the problems below. Remember to circle the
digit you are rounding to.
Round the numbers below to the Thousands place.
1. 9,621 ≈ 10,000
2. 42,502 ≈ 43,000
3. 824,157 ≈ 824,000
Round the numbers below to the Hundreds place.
4. 10,671 ≈ 10,700
5. 423,502 ≈ 423,500
6. 1,632,542 ≈ 1,632,500

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Unit two: Addition and subtraction strategies
Theme 1 | Number Sense and Operations
Concept 1 : Using addition and subtraction strategies
LESSON 1 Properties of Addition
-------------------------------------------------------------------------------------------------------------------
Learning outcomes
In this lesson
• Students will identify the properties of addition and subtraction.
• Students will explain the properties of addition and subtraction.

• Students will investigate to determine whether the properties of addition apply to

subtraction

Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page 151

Resources
• Properties of Addition anchor chart on chart paper (see the example at the end of this
volume)
• Mathematics Tool Kit anchor chart on chart paper (see the example at the end of this
volume)
Digital source
Video – using QR code
Vocabulary Building: addend, Additive Identity Property, Associative Property,
Commutative Property, minuend, property, subtrahend.
ACCESS
COMMON MISCONCEPTIONS AND ERRORS

• Students may not understand that, although the order of numbers does not matter in an
addition problem, it matters greatly and changes the answer in a subtraction problem.

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• Students may struggle to remember the difference between the Associative and Commutative
Properties.
• Students may struggle to read large numbers correctly utilizing Ones, Thousands, Millions,
and Milliards
Ask students:
Read the following numbers aloud and ask students to write them in standard form:
1. 3,000 + 400 + 20 + 7
2. 9,000 + 800 + 10
3. 600,000 + 30,000 + 9,000 + 800
4. 1,000,000,000 + 5,000,000 + 8,000
BUILD (40 minutes)
Additive Identity Property
properties are characteristics that belong to a set of numbers. Properties are always true, so a property
of addition will always be true.
Commutative Property and Associative Property
The Commutative Property of Addition states that addends can be combined in any order
and the answer will remain the same.
• The Associative Property of Addition states that addends can be grouped in any way and the
sum will remain the same
Do you think these properties apply to subtraction problems? • How can we figure out whether or not they
do?
• Examples o Additive Identity: 6 – 0 = 6, but 0 – 6 = –6 (a number less than 0)
o Commutative: 2 + 3 + 5 = 10 and 3 + 2 + 5 = 10 but 5 – 2 – 3 = 0 and 2 – 3 – 5 = –6 (or a number less
than 0)
o Associative: (2 + 3) + 5 = 10 and 2 + (3 + 5) = 10 but (5 – 2) – 3 = 0 and 5 – (2 – 3) = 6
Vocabulary Building: (20 minutes)
Ask students
In your own words, write a brief definition of the terms digit, number, and numeral.
Record the definitions that were written by the class

Check Your Understanding

Solve the problems. Then list the property illustrated
by each problem (Additive Identity, Commutative, or Associative).
1. 18 + 34 + 20 = 72 Property: Commutative
2. (20 + 37) + 40 = 97 Property: Associative
3. 56,248 + 0 = 56,248 Property: Additive Identity
4. 50 + 12 + 8 = 70 Property: Commutative

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Class 4 / D Date : / / 2021

Unit two: Addition and subtraction strategies

Concept 1 : Using addition and subtraction strategies
LESSON 2: Review Mental Math Strategies
-------------------------------------------------------------------------------------------------------------------
Learning outcomes
In this lesson
Students will apply a variety of strategies to add and subtract mentally.
• Students will explain the importance of mental math skills
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page 151

Resources
• Properties of Addition anchor chart on chart paper (see the example at the end of this
volume)
• Mathematics Tool Kit anchor chart on chart paper (see the example at the end of this
volume)
Digital source
Video – using QR code
Vocabulary Building:
benchmark numbers, estimate, mental math, round
ACCESS
COMMON MISCONCEPTIONS AND ERRORS
When using compensation to mentally add and subtract, students are often unclear how to
balance the amount compensated.

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BUILD (40 minutes)

: Mental math refers to fact learning, mental computation, and computational estimation. This
lesson introduces some common strategies along with estimation and rounding which have
already been discussed. These mental math strategies help students think flexibly and are best
applied in brief practice sessions over a period of time and introduced with small numbers before
applying to larger ones. These strategies will be included periodically in Number Talk
experiences throughout Primary4
ASK
• Which benchmark number should we make for 37? In other words, what number
is 37 close to that is easier to add in our heads? (Most likely students will answer
40. If students have other ideas, let them explain their thinking, but use rounding as
a strategy to guide students to choose 40

ASK • How many Ones do we need to add to 37 to get to this benchmark?

• Where could I get those 3 Ones?
Do a Think Aloud as you write the following on the board, explaining each step aloud. Be
sure to remind students that this strategy makes mental computation much easier.
37 + 8 = _______
–3
37 + 5 = _______
40 + 5 = 45

Check Your Understanding

Decide which mental math strategy would work best for each problem. There may be
more than one best answer.
Compensate to Make a Benchmark-Break Up and Bridge Add to Subtract
1. 169 + 32 Compensate to Make a Benchmark
2. 802 – 789 Add to Subtract
3. 64 + 89 Compensate to Make a Benchmark
4. 44 – 23 Break Up and Bridge
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Unit two: Addition and subtraction strategies

Concept 1 : Using addition and subtraction strategies
LESSON 3: Addition with Regrouping
-------------------------------------------------------------------------------------------------------------------
Learning outcomes
In this lesson
• Students will add multidigit whole numbers.
• Students will estimate to determine if their answer is re asonable.
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page 160

Resources
• No additional materials needed
Digital source
Video – using QR code
Vocabulary Building: Algorithm

ACCESS
COMMON MISCONCEPTIONS AND ERRORS
• Students may struggle with regrouping whether using the standard algorithm or decomposing
by place value.
• Students may always start a number line at 0. In problems that use large numbers, it is
important to start a number line with numbers other than 0.

BUILD (40 minutes)

Using the Standard Addition
1. Explain to students that mental math strategies are helpful, but they also need to know the
standard algorithms for solving problems. An algorithm is a procedure or set of steps.

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2. Write 466 + 221 vertically on the board. Ask students to help you solve the problem. If
students do not remember the steps, remind them they have to start at the Ones place, and ask
them to solve 6 plus 1. Record 7. Repeat with the Tens place and theHundreds place. 687

Connect
Answer Key for Bridging Ants and Addition:
1. 142 + 165 = 307. Possible estimates:
100 + 200 = 300; 140 + 170 = 310.

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Class 4 / D Date : / / 2021

Unit two: Addition and subtraction strategies

Concept 1 : Using addition and subtraction strategies
LESSON 4: Subtraction Strategies
-------------------------------------------------------------------------------------------------------------------
Learning outcomes
In this lesson
• Students will use decomposition of numbers to subtract multidigit whole numbers.
• Students will explain the importance of finding patterns and relationships in
mathematics
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page 160

Resources
• Mental Math Strategies anchor chart
• Thinking Like a Mathematician anchor chart
Digital source
Video – using QR code
Vocabulary Building: difference, minuend, subtrahend
ACCESS
COMMON MISCONCEPTIONS AND ERRORS
• Students may struggle with decomposing numbers in meaningful ways (ways that make
sense to them).
• Students may struggle with where to place numbers on an open number line.
Answer Key for Using 10s:
1. 10
2. 15 (7 + 3 = 10, 10 + 5 = 15)
3. 16 (7 + 3 = 10, 10 + 6 = 16 or +1 from the previous problem)
4. 10
5. 17 (9 + 1 = 10, 10 + 7 = 17)
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6. 16 (9 + 1 = 10, 10 + 6 = 16 or -1 from the previous problem)
7. 20 (7 + 3 = 10, 10 + 10 = 20 or 10 × 2 = 20)
8. 20 (9 + 1 = 10, 10 + 10 = 20 or 10 × 2 = 20)
BUILD (40 minutes)
Counting Back with Decomposition
• Write 263 – 135 = _______ on the board

Check Your Understanding

Solve the problems using a strategy of your choice.
1. 8,497 – 1,246 = 7,251
2. 1,325 – 920 = 405
3. 310 – 106 = 204
4. 10,000 – 350 = 9,650
5. 766 – 564 = 202

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Unit two: Addition and subtraction strategies
Concept 1 : Using addition and subtraction strategies
LESSON 5: Subtraction with Regrouping
-------------------------------------------------------------------------------------------------------------------
Learning outcomes
In this lesson
• Students will use place value to subtract using the standard algorithm.
• Students will subtract with regrouping.
• Students will estimate to check the reasonableness of their answers.
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page 178

Resources
• Subtraction strategy signs
Digital source
Video – using QR code
Vocabulary Building: algorithm, regroup
ACCESS
COMMON MISCONCEPTIONS AND ERRORS
• Students struggle to understand the standard algorithm for subtraction when regrouping is
required. They do not decompose into smaller units to solve.
• Students tend to model both the subtrahend and minuend instead of recognizing that the
minuend is the only number to model since the subtrahend will be taken away from that larger
number.

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BUILD (40 minutes)

Subtraction with Regrouping

Answer Key for Ant Facts and Algorithms:

1. 4,000 – 2,000 = 2,000; 3.548 – 1,672 = 1,876
2. 3,000 – 1,000 = 2,000; 3,452 – 1,267 = 2,185
3. 255,000 – 6,000 = 249,000; 255,000 – 6,200 = 248,800
Check Your Understanding
. Use the standard subtraction algorithm to solve the problem. Then, round each number to the nearest
Thousand to check the reasonableness of your answers..
13,526 – 2,834 = 10,692; 14,000 – 3,000 = 11,000
2. Use the standard subtraction algorithm to sol ve the story problem. Record your equation and show
your thinking. Then, round each number to the nearest Hundred to check the reasonableness of your
answer. A local bakery sold 1,232 zalabya in one day. If they sold 876 zalabya in the morning, how many
were sold during the rest of the day?
1,232 – 876 = 356 zalabya; 1,200 – 900 = 300 zalabya
Solve the following problems using the standard subtraction algorithm. Then, round each number to the
nearest Thousand to check the reasonableness of your answers. Y ou may draw a place value chart to
organize the problems, if needed.
3. 17,525 – 13,708 = 3817; 18,000 – 14,000 = 4,000
4. 431,925 – 204,835 = 227,090; 432,000 – 205,000 = 227,000
5. 61,851 – 52,670 = 9,181; 62,000 – 53,000 = 9,000

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Unit two: Addition and subtraction strategies

Concept 2 : Solving Multistep Problems
LESSON 6: Bar Models, Variables, and Story Problems
-------------------------------------------------------------------------------------------------------------------
Learning outcomes
In this lesson
• Students will use letters to represent unknown quantities in equations.
• Students will use bar models to represent and solve story problems.
• Students will solve for the variable in an equation.
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page 193

Resources
No addition resources needed
Digital source
Video – using QR code
Vocabulary Building: bar model, variable

ACCESS
COMMON MISCONCEPTIONS AND ERRORS
• Students may struggle to determine what a variable represents and how to find the value.
• Students may not demonstrate flexibility in how they find a variable in a fact family. They may
not be able to see that there are several relationships between the other numbers.

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BUILD (40 minutes)

Check Your Understanding

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Class 4 / D Date : / / 2021

Unit two: Addition and subtraction strategies

Concept 2 : Solving Multistep Problems
LESSON 7: Solving Multistep Story Problems with Addition and Subtraction
-------------------------------------------------------------------------------------------------------------------
Learning outcomes
In this lesson
• Students will solve multistep story problems.
• Students will explain how they solved multistep story problems.
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page 202

Resources
No addition resources are needed
Digital source
Video – using QR code
Vocabulary Building: Review vocabulary as needed

ACCESS
COMMON MISCONCEPTIONS AND ERRORS
• Students often look for keywords to indicate which operations are needed to solve story
problems. However, keywords do not always work.
• Students may not be able to formulate or implement a plan for solving multistep problems.
• Students may not realize there is often a “hidden” question they must answer before they can
solve multistep problems.
Answer Key for Hidden Question:
1. 1,025 – 101 = 924 ants
2. 1,555 – 924 = 631 ants

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BUILD (40 minutes)

Answer Key for Putting It Together:
1. 1,725 + 22,750 + 6,075 = 30,550 ants (counted by Mariam)
50,750 – 30,550 = 20,200 ants (left to be counted by Mariam)

Answer Key for Solving Multistep Story Problems:

1. 6 I subtracted 870 from 2,000.
2. The answer is 1,130, so Ahmed can eat 1,130 more calories today.
3 I drew a box around “how many more.”
5 I added the calories of the foods Ahmed has eaten to answer the hidden question (how many
calories Ahmed has already eaten). The answer is 870 calories.
1 I circled 340 calories, 190 calories, 85 calories, 255 calories, and 2,000 calories

Check Your Understanding

Use the problem-solving steps to solve the multi-step story problems. Show your work.
1. The Suez Canal extends from Port Said to the city of Suez and is 193,120 meters long. If a
boat travels 38,620 meters each day for 5 days, how many more
meters will it need to travel to reach the end of the canal?
38,620 + 38,620 + 38,620 + 38,620 + 38,620 = 193,100 or 38,620 × 5 = 193,100
193,120 – 193,100 = 20 meters

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Unit two: Addition and subtraction strategies

Concept 2 : Solving Multistep Problems
LESSON 8 : Solving Multistep Story Problems with Addition and Subtraction
-------------------------------------------------------------------------------------------------------------------
Learning outcomes
In this lesson
• Students will solve multistep story problems.
• Students will explain how they solved multistep story problems.
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page 202

Resources
No addition resources are needed
Digital source
Video – using QR code
Vocabulary Building: Review vocabulary as needed

ACCESS
COMMON MISCONCEPTIONS AND ERRORS
• Students often look for keywords to indicate which operations are needed to solve story
problems. However, keywords do not always work.
• Students may not be able to formulate or implement a plan for solving multistep problems.
• Students may not realize there is often a “hidden” question they must answer before they can
solve multistep problems.
Answer Key for Hidden Question:
1. 1,025 – 101 = 924 ants
2. 1,555 – 924 = 631 ants

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Class 4 / D Date : / / 2021

BUILD (40 minutes)

Answer Key for Putting It Together:
1. 1,725 + 22,750 + 6,075 = 30,550 ants (counted by Mariam)
50,750 – 30,550 = 20,200 ants (left to be counted by Mariam)

Answer Key for Solving Multistep Story Problems:

1. 6 I subtracted 870 from 2,000.
2. The answer is 1,130, so Ahmed can eat 1,130 more calories today.
3 I drew a box around “how many more.”
5 I added the calories of the foods Ahmed has eaten to answer the hidden question (how many
calories Ahmed has already eaten). The answer is 870 calories.
1 I circled 340 calories, 190 calories, 85 calories, 255 calories, and 2,000 calories

Check Your Understanding

Use the problem-solving steps to solve the multi-step story problems. Show your work.
1. The Suez Canal extends from Port Said to the city of Suez and is 193,120 meters long. If a
boat travels 38,620 meters each day for 5 days, how many more
meters will it need to travel to reach the end of the canal?
38,620 + 38,620 + 38,620 + 38,620 + 38,620 = 193,100 or 38,620 × 5 = 193,100
193,120 – 193,100 = 20 meters

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Class 4 / D Date : / / 2021

Unit three: Concepts of measurement

Theme one : Number senses and operations
Concept 1: metric measurement
LESSON 1: Ant Travel
-------------------------------------------------------------------------------------------------------------------
Learning outcomes
In this lesson
• Students will explain the relationship between metric units of length.
• Students will convert between metric units of length.
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page 193

Resources
• Metric Conversion chart
• Meter stick
• Centimeter ruler
Digital source
Video – using QR code (optional )
Vocabulary Building:
centi-, centimeter, convert, decompose, kilo-, kilometer, length, meter, metric system,
milli-,
millimeter

ACCESS
COMMON MISCONCEPTIONS AND ERRORS
Students may struggle to remember conversions for metric units of length.
• Students may confuse the units of measurement with what is being measured (length, mass,
capacity).
• Students may compare or try to convert numbers without considering the units of measurement

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Class 4 / D Date : / / 2021

BUILD (40 minutes)

Metric Units (10 min) For this activity, create a Metric Conversion
chart for display, such as the one shown here:

CONNECT
PRACTICE
Direct students to Lesson 1 PRACTICE and have them complete the problems. Address student
errors and misconceptions.
Check Your Understanding
Convert to centimeters:
1. 6 m = 600 cm
2. 20 m 10 cm = 2,010 cm
Convert to meters:
3. 23 km = 23,000 m
4. 800 km 50 m = 800,050 m
5. 5,950 m = 5 km 950 m

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Class 4 / D Date : / / 2021

Unit three: Concepts of measurement

Theme one : Number senses and operations
Concept 1: metric measurement
LESSON 2: The Weight Can Wait
-------------------------------------------------------------------------------------------------------------------
Learning outcomes
In this lesson
• Students will explain the relationship between metric units of mass.
• Students will convert between metric units of mass
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page 240

Resources
An object that weighs about a gram (paper clip or pen)
• An object that weighs about a kilogram (a liter bottle of water, bag of rice, pineapple

Digital source
Video – using QR code (optional )
Vocabulary Building:
grams, kilograms, mass, weight
ACCESS
COMMON MISCONCEPTIONS AND ERRORS
• Students may struggle to remember conversions for units of mass.
• Students often confuse the units of measurement with what is being measured (length, mass,
volume).
• Students may compare or try to convert numbers wit hout considering the units of
measurement.

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BUILD (40 minutes)

Conversion and Application (30 min)
1. Ask students to turn to Lesson 2 BUILD Conversion and Application and
look at the Conversion
Example.
2 kg 300 g= 2,300 g
Remind students this is a bar model and is a tool to help us as
mathematicians. Discuss how 2,300 grams can be converted to 2 kil ograms
300 grams.
The mass is the same, but the units to express the mass are different.
3. Remind students that the prefix “kilo-” means 1,000 and there are 1,000
grams in 1 kilogram.
4. Ask students to work with a partner to solve Problems 1–10. If students are
struggling, regroup the class and work through the problems together.
5. During the last 5 minutes of BUILD, go over answers with the students.
Ask students to discuss any questions they still have and strategies they
used that helped them solve the problems

Check Your Understanding

Convert.
1. 3,806 g = 3 kg 806 g
2. 8 kg 50 g = 8,050 g
3. 3,425 g = 3 kg 425 g
4. 1 kg 10 g = 1,010 g
5. 10,452 g = 10 kg 452g

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Class 4 / D Date : / / 2021

Unit three: Concepts of measurement

Theme one : Number senses and operations
Concept 1: metric measurement
LESSON 3: Fill It Up
-------------------------------------------------------------------------------------------------------------------
Learning outcomes
In this lesson
• Students will explain the relationship between metric units of capacity.
• Students will convert between metric units of capacity
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page 193

Resources

Digital source
Video – using QR code (optional )
Vocabulary Building:
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capacity, liter, milliliter, volume
ACCESS
COMMON MISCONCEPTIONS AND ERRORS
• Students may struggle to remember conversions for metric units of capacity.
• Students may struggle with story problems that require converting to the same units before
solving.
• Students often confuse the units of measurement with what is being measu red (length, mass,
volume).
• Students may compare or try to convert numbers
without considering the units of measurement
BUILD (40 minutes)

PRACTICE
Direct students to Lesson 3 PRACTICE and have them complete the problems. Address
student errors and misconceptions.
Check Your Understanding
Express the answers in milliliters.
1. 21 L + 2 L 800 mL = 23,800 mL
2. 4 L 485 mL − 323 mL = 4,162 mL
Convert.
3. 11 L 342 mL = 11,342 mL 4. 16,783 mL = 16 L 783 m
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Class 4 / D Date : / / 2021

Unit three: Concepts of measurement

Theme one : Number senses and operations
Concept 1: metric measurement
LESSON 4: Measurement and Unit Conversions
-------------------------------------------------------------------------------------------------------------------
Learning outcomes
In this lesson
Students will compare place value relationships and measurement conversions.
• Students will use multiplication and division to convert units of measurement.
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page 193

Resources

Metric Conversion chart (From Lesson 1

Digital source
Video – using QR code (optional )
Vocabulary Building:
Review vocabulary as needed.
ACCESS
COMMON MISCONCEPTIONS AND ERRORS
When converting units, students often divide instead of multiplying and vice versa.

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BUILD (40 minutes)
More Conversions (25 min)
1. Ask students what operation they used to convert from larger units, like kilograms, to
smaller units, like grams. (Multiplication)
2. Reinforce this by writing the following on the board:
5 kg = ______ g
5 kg × 1,000 g/kg = ________ g
3. Share with the students that we multiply 5 by 1,000 because we know that there are
1,000 grams in 1 kilogram. Notice that it is like the place value chart.
As we move to the right 3 spaces, we are moving from a larger unit to a smaller unit, so
we multiply by
1,000.
4. Ask students what operation they used to convert from smaller units, like centimeters
to larger units, like meters. (Division)
5. Reinforce this by writing the following on the board:
500 cm = _______ m
500 cm ÷ 100 cm/m = _______m
Answer Key for More Conversions:
1. 200 centimeters is equivalent to 2 meters and 20 decimeters
2. 4,000 grams is equivalent to 400 decagrams and 40 hectograms
3. 2 liters is equivalent to 200 centiliters and 2,000 milliliters
4. 6,000 mL = 60 dL; 6,000 ÷ 100 = 60 dL
5. 40 g = 4 dag; 40 ÷ 10 = 4 dag
6. 70 km = 700 hm; 70 × 10 = 700 hm
7. Answers will vary, but students should multiply or divide accurately according to the
relationships between the units they choose

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Class 4 / D Date : / / 2021

Unit three: Concepts of measurement
Concept 2: Time and scaled measurements
LESSON 5: What Time Is It?
-------------------------------------------------------------------------------------------------------------------
Learning outcomes
In this lesson
• Students will tell time to the minute.
• Students will explain relationships between units of time.
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page 260

Resources
• Red and blue crayons or colored pencils (1 each per student)
• Analog clock with hour, minute, and second hands
• Ratio tables
• Measurement anchor chart Digital source
Video – using QR code (optional )
Vocabulary Building:
analog, decade, digital, elapsed, ratio table

ACCESS
COMMON MISCONCEPTIONS AND ERRORS
• Students may struggle to read time on an analog clock. They may confuse the hour and the
minute hands or think that the digits on the clock are in
5-minute intervals.
• Students may struggle to remember the conversions for tim e, such as how many seconds
in a minute, minutes in an hour, hours in a day, days in a week, and so on Analog and Digital
Clocks
1. Distribute (or have students take out) a red and blue crayon or colored pencils to indicate the
hour and minute hands.

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2. Direct students to work on Lesson 5 ACCESS Analog and Digital Clocks. Ask students to
record three events and the times they occur.
3. Use Calling Sticks to select 4–5 students to share their events and record on the board the
time in digital and analog formats.
4. Pose the following questions to the group and discuss:
• Why do we need to tell time?
• Why is time considered a measurement?

BUILD (40 minutes)

PRACTICE
Check Your Understanding
Write the time for each clock.
1. 3:50
2. 4:20
Fill in the blanks.
3. 5 hours 10 minutes = 310 minutes
4. 4 minutes 11 seconds = 251 seconds
5. 3 days 10 hours = 82 hours
6. 2 weeks 2 days = 16 days
7. 5 + 2 = 7; 7 × 60 = 420 minutes
Challenge: 420 × 60 = 2,520 second

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Unit three: Concepts of measurement
Concept 2: Time and scaled measurements
LESSON 6: How Long Does it take ?
-------------------------------------------------------------------------------------------------------------------
Learning outcomes
In this lesson
• Students will explain elapsed time.
• Students will solve elapsed time problems.
• Students will explain the strategies they use to solve elapsed time problems.
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page 260

Resources
• Red and blue crayons or colored pencils (1 each per student)
• Analog clock with hour, minute, and second hands
• Ratio tables
• Measurement anchor chart Digital source
Video – using QR code (optional )
Vocabulary Building:
analog, decade, digital, elapsed, ratio table

ACCESS
COMMON MISCONCEPTIONS AND ERRORS
• Students may struggle to calculate elapsed time that requires them to regroup hours and
minutes or minutes and seconds.
• Students may be unsure how to write equations with time.
• Students may not have effective strategies for converting time intervals and solving elapsed
time problems.
• Students often confuse regrouping in elapsed time problems with regrouping in the Base Ten
number system.

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BUILD (40 minutes)

PRACTICE
Direct students to Lesson 6 PRACTICE and have them
complete the problems. Address student errors and
misconceptions around elapsed time.
Check Your Understanding
Solve using two different strategies. Show your work.
Accept any strategy that yields a correct answer.
1. Ant A worked from 7:05 a.m. until 8:52 a.m. How long did Ant A work?
1 hour 47 minutes
2. Ant B started working at 11:25 a.m. and worked for
82 minutes. At what time did Ant B stop working?12:47 p.m.
3. How long did Ants A and B work all together?
3 hours 9 minutes

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Unit Four : Area And Perimeter
Concept 1: Explore Area and Perimeter
LESSON 1: Marching Ants
-------------------------------------------------------------------------------------------------------------------
Learning outcomes
In this lesson
• Students will define perimeter.
• Students will use formulas to calculate the perimeter of rectangles.
• Students will explain how to calculate perimeter.
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page331

Resources
• Large version of the Perimeter Formulas for Rectangles anchor chart
• Thinking Like a Mathematician anchor chart

Video – using QR code (optional )

Vocabulary Building:
formula, length, perimeter, quadrilateral, scale, sum, width
ACCESS
COMMON MISCONCEPTIONS AND ERRORS
• Students may confuse unit names for area and perimeter by using unit squares instead of
units.
• Students may think that perimeter is the sum of the length and the width because area is the
product of length and width.

BUILD (40 minutes)

Foraging for Formulas (20 min)
1. Ask students to look again at Problems 3 and 4. Challenge students to come up with a
formula for perimeter that uses multiplication.

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2. Give students a few minutes to explore strategies. Ask students to share what they
discovered. Record their strategies on the board. For each strategy, ask students if it
would work every time and if the strategy is efficient. Discuss.
3. Introduce the Perimeter Formulas for Rectangles anchor chart. Ask students to
compare what they discovered with the formulas on the poster.
4. Reinforce that there are several formulas to calculate perimeter for rectangles. The
last formula on the anchor chart only works on squares since the sides are all the same
length. Remind students that we can always add to calculate perimeter.
5. Direct students to complete Problems 1–4 in
Lesson 1 BUILD Foraging for Formulas. Remind students that they will need to try at
least two different formulas from the anchor chart to solve
Problems 1–3.
6. During the last 2–3 minutes of BUILD, review the answers as a class. Ask students to
discuss the efficiency of the strategies they tried.
Answer Key for Foraging for Formulas:
1. 108 centimeters
2. 176 meters
3. 160 millimeters
4. 120 centimeters
5. 346 meter
PRACTICE
Direct students to Lesson 1 PRACTICE and have them complete the problems. Address
student errors and misconceptions.
Check Your Understanding
Find the perimeter. Show your work.
1. 1,696 centimeters 2. 4,808 millimeters
3. Find the perimeter of each rectangle. Circle the larger rectangle and explain your
thinking in the box below. Note that rectangles are not drawn to scale.
1 = 386 centimeters 2 = 386 millimeters
Students should see that Rectangle 1 is the larger rectangle since it is measured in
centimeters.

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Unit Four : Area And Perimeter

Concept 1: Explore Area and Perimeter
LESSON 2: Fill The Space
-------------------------------------------------------------------------------------------------------------------
Learning outcomes
In this lesson
• Students will define area.
• Students will use formulas to calculate the area of rectangles.
• Students will explain how to calculate area.
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page338

Resources
• Large version of the Perimeter Formulas for Rectangles anchor chart
• Thinking Like a Mathematician anchor chart

Video – using QR code (optional )

Vocabulary Building:
area, length, two-dimensional, width

ACCESS
COMMON MISCONCEPTIONS AND ERRORS
• Students may confuse unit names for area and perimeter by using units instead of square
units.
• Students may confuse area and perimeter in both what the question is asking and by using an
incorrect formula.
BUILD (40 minutes)
Ask students to solve Problems 2–4.

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2. After 5–7 minutes, call on several students to share the formulas they wrote with th e
class.
3.. Display the Area Formula for Rectangles anchor chart. Ask students to compare their
formulas to the one on the anchor chart. Reinforce that the formula

used to find the area of a rectangle is A = l × w.

TEACHER NOTE: If students struggle with multiplication facts, show them how they can
draw a grid inside a rectangle to help them solve for area. Another strategy that can be
reviewed is using partial products to help break down larger numbers into numbers that
are easier to work with. For example, an 8 × 12 rectangle can be broken into an
8 × 10 rectangle and an 8 × 2 rectangle.
Answer Key for Area Review:
1. 30 square units
2. 48 square centimeters
3. Students should recognize that Area = length × width.
4. If students identified the correct formula for area, the
answer is yes.
PRACTICE
Direct students to Lesson 2 PRACTICE and have them complete the problems. Address
student errors and misconceptions.
Check Your Understanding
For each problem, find the area and perimeter. Show
your work and label your answers.
1. A = 49 square meters; P = 28 meters
2. A = 48 square centimeters; P = 32 centimeters
3. Solve the problem. Show your work and label your
answers.
Omar’s family is redecorating their dining room. The room is a rectangle that mea sures 4
meters long and 3 meters wide. How many square meters of carpet will they need for the
floor? How many meters of trim will they need to trace the border of the ceiling?
A = 12 square meters of carpet
P = 14 meters of trim

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Unit Four : Area And Perimeter

Concept 1: Explore Area and Perimeter
LESSON 3: Some Thing Is Missing
-------------------------------------------------------------------------------------------------------------------
Learning outcomes
In this lesson
• Students will use formulas to calculate unknowns when given some dimensions of
rectangles.
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page344

Resources
• Large version of the Perimeter Formulas for Rectangles anchor chart
• Thinking Like a Mathematician anchor chart

Video – using QR code (optional )

Vocabulary Building:
area, dimensions, formula, perimeter, unknown
ACCESS
COMMON MISCONCEPTIONS AND ERRORS
• Students may incorrectly use the area and perimeter formulas.
• Students may overgeneralize or under generalize the definition of area and/or perimeter
situations. For example, o Student interprets all “wall painting” problems as area, even if the
problem talks about the length of a striped border that is painted around the room.
o Student interprets all “fence” problems as perimeter, even if the problem talks about the
size of the garden that the fence encloses
. BUILD (40 minutes)
SCOOT (15 min)
1. Explain to students that they will use the last
10 minutes of BUILD to solve more missing dimension problems.
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2. Ask students to turn to Lesson 3 BUILD SCOOT. Introduce the SCOOT activity
(depending on how you have set up the game):
• Twelve cards, each labeled with a number and containing a perimeter or area problem,
are placed around the room (or distributed to partners).
• Students work with their partner to solve the problems. They sh ould show their work in
the box that matches their card number.
• When finished, pairs move to another card (or swap cards with another team).
• The goal is to solve as many SCOOT card problems as possible.
TEACHER NOTE: If space is limited, distribute a card to each pair of students and have
them swap cards with nearby students when finished.
As students play SCOOT, walk around the room to observe how students find the missing
dimensions. If the cards are placed around the room, take note of students who choose
to solve the Challenge cards. Identify students who may need additional support and
practice.
3. With a few minutes left in BUILD, go over the answers with students (see the SCOOT
answer key).
Answer Key for SCOOT:
1. 30 centimeters
2. 13 centimeters
3. 78 millimeters
4. 38 meters
5. 26 centimeters
6. 30 centimeters
7. 6 meters
8. 10 meters
9. 4 meters
10. 20 centimeters
11. 33 meters
12. 5 meter

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Unit Four : Area And Perimeter
Concept 1: Explore Area and Perimeter
LESSON 4: Odd Shapes
-------------------------------------------------------------------------------------------------------------------
Learning outcomes
In this lesson
• Students will calculate the area and perimeter of complex shapes.
• Students will explain their strategies for finding the area and perimeter of complex
shapes.
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page352

Resources
Unit 4 Lesson 4 Shape Cards (1 card per student)
• Scissors
• Tape
Video – using QR code (optional )
Vocabulary Building:
area, complex, perimeter

ACCESS
COMMON MISCONCEPTIONS AND ERRORS
Students may struggle to break a more complex shape into squares or rectangles in order to
calculate area and perimeter.
• Students may struggle to calculate missing side lengths in a complex shape (since not
everything is labeled).
• Students may miscalculate perimeter if there is an overlapping side in a complex shape. They
may add all sides to find perimeter but not recognize that some sides are within the irregular
shape

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. BUILD (40 minutes)

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Unit Four : Area And Perimeter

Concept 1: Explore Area and Perimeter
LESSON 5: Growing Dimensions
-------------------------------------------------------------------------------------------------------------------
Learning outcomes
In this lesson
• Students will use area and perimeter formulas to solve multiplicative comparison
problems
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page352

Resources
Cut six 10 cm × 10 cm squares out of colored construction paper (1 set for the
teacher)
• Tape

Video – using QR code (optional )

Vocabulary Building:
array, multiplicative comparison, square units
ACCESS
COMMON MISCONCEPTIONS AND ERRORS
Students may not realize that multiplicative comparisons focus on comparing two quantities
by showing that one quantity is a specified number of times larger or smaller than the other.
• Students may think that all shapes with a given perimeter have the same area or that all
shapes with a given area have the same perimeter.

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. BUILD (40 minutes)

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Unit Five : Multiplication as a Relationship

Concept 1: Multiplicative Comparisons
LESSON1: Understanding Multiplicative Comparison
-------------------------------------------------------------------------------------------------------------------

Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page385

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Resources

Video – using QR code (optional )

BUILD (40 min)

1. Tell students that so far they have used place value to compare numbers, but today they will
compare numbers using multiplication. Explain that they have already gotten a little practice doing
that by comparing their strip to your strip and estimating “how many times” their small strip could
fit onto the larger strip.
2. Tell students they will be using tape diagrams to learn how to compare using multiplication.
Explain that a tape diagram is a visual model that helps us understand number relationships.
3. Show students how to create a tape diagram. Draw two rectangles on the board, each
representing 5. Tell students that this diagram shows 5 two times.
4. Ask students to provide the answer to “How much is two 5s?” Write 10 is two times greater than
5 under the tape diagram and explain that the tape diagram helps us see that 10 is two times
greater than 5.

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Unit Five : Multiplication as a Relationship

Concept 1: Multiplicative Comparisons
LESSON 2: Creating Multiplicative Comparison Equation
-------------------------------------------------------------------------------------------------------------------

Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page396

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BUILD (40 min)

Multiplying to Show
Comparisons (25 min)
1. Direct students to Lesson 2 BUILD Multiplying to Show Comparisons.
2. Read Problem 1 aloud and point out the language used to express comparisons (4 times
greater than). Explain that there is a number missing in the statement. The missing number
is represented by a blank, but we can also use letters to represent missing numbers.
3. Write on the board: 4 times greater than 3 is a. Remind students that the letter represents
an unknown or missing number. Ask students to record the information from the boa rd in
their books.
4. Ask students to think about times when they have made multiplicative comparison
statements (or heard others make them) outside of school. Share an example, such as, “I
went out to buy oranges yesterday and one market was selling them for 2 times as much
as another market,” or, “It took me 15 minutes to get to school yesterday and 3 times longer
to get home.”

.
PRACTICE
Direct students to Lesson 2 PRACTICE and have them
complete the problems. Address student errors and
misconceptions.
Check Your Understanding
Write an equation for the comparisons. Use a letter to
represent the unknown number. You do not have to
solve the equations.
1. 16 is 4 times greater than ___________
2. 4 times as many as 5 is ___________
3. Rashad’s team scored 9 goals in soccer. This is 3 times as many goals as Yaseen’s
team scored. How many goals did Yasseen’s team score?
9 = 3 ×c

Unit Five : Multiplication as a Relationship

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Concept 1: Multiplicative Comparisons
LESSON 3 : Solving Multiplicative Comparison Equations
-------------------------------------------------------------------------------------------------------------------

Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page385

BUILD (40 min)

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How Many Seats? (40 min)
1. Ask students how many times as many seats are in a car than on a bicycle. Ask
students to help you solve the problem by providing the following prompts.
• How many seats are in a typical car?
• How many seats are on a typical bicycle?
• Which has more seats?
• What multiplicative comparison statement could we use?
• What equation can we use? (Possible answer
1 × a = 4)
2. Explain to students that when they solve an equation, they say or write what the
unknown number is. Encourage students to try to solve equations from memory using
multiplication facts. However, students may also continue to use the
strategies they have learned to solve multiplication problems as needed.
3. Direct students to Lesson 3 BUILD How Many Seats? Ask students to exa mine the
information in the table. Instruct students to work with a partner to write and solve an
equation that can be used to answer each question.
4. With about 10 minutes left in BUILD, have students
share their equations and their solutions.
Answer Key for How Many Seats?:
1. 6 = 2 × a; 3
2. 36 = b × 6; 6
3. 48 = c × 4; 12
4. 48 = d × 6; 8
5. 36 = e × 4; 9
PRACTICE
Direct students to Lesson 3 PRACTICE and have them complete the problems. Address
student errors and misconceptions
Check Your Understanding
Write an equation for each of the following
comparisons, and then solve.
1. What number is 4 times as many as 8? 32; 4 × 8 = 32
2. 42 is 6 times greater than what number? 7; 6 × 7 = 42
3. A car is about 5 meters long. A bus is about 15 meters long. About how many times
longer is a bus than a car?
3; 5 × 3 = 15

Unit Five : Multiplication as a Relationship

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Concept 2 : Properties and Patterns of Multiplication
LESSON 4: Commutative Property of Multiplication
-------------------------------------------------------------------------------------------------------------------

Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page407

BUILD (40 min)

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Arrays and the Commutative Property
(30 min)
1. Direct students to Arrays and the Commutative Property in BUILD. Ask students to take
out their digit cards (1–9) and choose 2 cards.
2. Go over the directions with students to make sure they understand the learning activity.
3. Allow time for students to draw their first pair of arrays and write their first equation. As
students work, walk around, and monitor their progress. Offer support to students who are
struggling. If many students are struggling, consider having students work in pairs or small
groups.
4. At the end of BUILD, ask student volunteers to share their work on the board. Encourage
students to ask each other questions to build understanding or
clarify misconceptions.

PRACTICE
Direct students to Lesson 4 PRACTICE and have them complete the problems. Address
student errors and misconceptions.
Check Your Understanding
Apply the Commutative Property of Multiplication to complete each equation.
1. 4 × 6 = 6 × 4
2. 18 × 3 = 3 × 18
Apply the Commutative Property of Multiplication to find the unknown value.
3. 5 × a = 7 × 5 a = 7
4. 9 × 8 = 8 × b b = 9
5. Lamiaa has 40 books. Write an equation using the Commutative Property of
Multiplication to describe two ways she can arrange her books.
Accept answers that use the factors 1 and 40, 2 and
20, 4 and 10, or 5 and 8.

Unit Five : Multiplication as a Relationship

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Concept 2 : Properties and Patterns of Multiplication
LESSON 5 : Patterns of Multiplying by 10s
-------------------------------------------------------------------------------------------------------------------

Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page407

BUILD (40 min)

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Mental Math Multiplication (15 min)
1. Ask students to turn to Lesson 5 BUILD Mental Math Multiplication. Ask students to
discuss with the whole group what they notice about the problem
and what numbers they think should go in the blanks.
2. Ask students to discuss how the problem is like the multiplicative comparison problems
they solved in previous lessons.
3. Tell students the missing information in the problem.
• The metro is 10 times as fast as walking.
• The average person walks 5 kilometers an hour.
4. Ask students what mental math strategies they would use to solve the problem. Ask
student volunteers to model their strategies for the class. .

PRACTICE
Direct students to Lesson 5 PRACTICE and have them complete the problems. Address
student errors and misconceptions.
Check Your Understanding
1. A person can walk about 5 kilometers an hour. The
average plane flies 100 times faster than that in the
air. How fast can the average plane fly?
500 kilometers an hour
2. 20 = 2 × _____
3. 8 × 100 = _____
4. 7 × _____ = 7,000

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Unit Five : Multiplication as a Relationship
Concept 2 : Properties and Patterns of Multiplication
LESSON 6-7-8 : Patterns of Multiplying
------------------------------------------------------------------------------------------------------------- ------

Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page407

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Unit Six : Factors and Multiples

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Concept 1 : understanding factors
LESSON 1 :Identifying factors for whole numbers
-------------------------------------------------------------------------------------------------------------------

Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page457

ACCESS (10 min)

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COMMON MISCONCEPTIONS AND ERRORS
• Students may only list some of the factors of a number. For example, they may forget to
include 1 and the number itself or only include one number in a factor pair
. Direct students to Problem 1. Ask students to use what they know to determine if 26 has
2, 5, and/or 10 as a factor. Discuss the answers together.
Ask students to solve Problems 2–4, and then discuss the answers together.
Answer Key for Numbers with Factors of 2, 5, and 10:
1. 26 = 2
2. 70 = 2, 5, and 10
3. 15 = 5
4. 17 = none
Finding Factor Pairs (20 min)BUILD
Finding Factor Pairs.
Explain to students there are different ways to list fact ors. In addition to the factor tree
(which they saw with 24), they can also create factor rainbows or factor T -charts.
3. Model how to create a factor rainbow for 24
Check Your Understanding
List all of the factors of each number. You may create a facto r tree, factor rainbow, or
factor T-chart.
1. 54: 1, 2, 3, 6, 9, 18, 27, 54
2. 28: 1, 2, 4, 7, 14, 28
3. Is 3 a factor of 29? Show your work and explain your reasoning.
No, 3 is not a factor of 29. Sample reasoning: I know because when I count by 3s, I s ay
27 and then 30 and 29 is not a part of the list or no, because there is no number times
3 that equals 29.
4. Is 45 a factor of 5? Show your work and explain your reasoning.
No, 45 is not a factor of 5. Sample reasoning: There is no whole number I can multiply
by 45 that will equal 5 or 45 is not a factor of 5, but 5 is a factor of 45

Unit Six : Factors and Multiples

Concept 1 : understanding factors
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LESSON 2 : Prime and Composite Numbers
-------------------------------------------------------------------------------------------------------------------

Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page407

Learning Objectives in this lesson
• Students will find all factors of a given number between 0 and 100.
• Students will explain patterns they observe in numbers that have 3, 6, or 9 as factors.
• Students will determine if a number is prime or composite.
Vocabulary Check-In composite, factors, prime
ACCESS COMMON MISCONCEPTIONS AND ERRORS
• Students may believe that all even numbers are composite numbers. However, 2 is
prime because its only factors are 1 and itself.
• Students may have difficulty identifying a number as a factor of another number if there
is no pattern for that number. For example, 4 is a factor of 24 but there is no pattern for 4
as a factor
PRACTICE
Direct students to Lesson 2 PRACTICE and have them complete the problems. Address
student errors and misconceptions.
Check Your Understanding List all the factors of each number. Then, write if the
number is prime or composite.
1. 17: 1, 17 – Prime
2. 12: 1, 2, 3, 4, 6, 12 – Composite
3. 2: 1, 2 – Prime
4. 33: 1, 3, 11, 33 – Composite
5. 51: 1, 3, 17, 51 – Composite
6. 37: 1, 37 – Prime
Unit Six : Factors and Multiples
Concept 1 : understanding factors

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LESSON 3 : Greatest Common Factor
-------------------------------------------------------------------------------------------------------------------

Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page471

Learning Objectives in this lesson
Students will find common factors between two whole numbers.
• Students will identify the greatest common factor between two whole numbers.
Vocabulary Check-In
common factor, factor, greatest common factor (GCF)ACCESS
COMMON MISCONCEPTIONS AND ERRORS
Once students identify one common factor, they may have difficulty finding additional
common factors, including the greatest common factor
• Find all the factors of 24. Then list out the factors of 24 from least to greatest.
• Circle all of the factors that are in both lists. These are the common factors.
18: 1, 2, 3, 6, 9, 18
24: 1, 2, 3, 4, 6, 12, 24
Common Factors: 1, 2, 3, 6
PRACTICE
Direct students to Lesson 3 PRACTICE and have them complete the problems. Address
student errors and misconceptions
Check Your Understanding
Find the greatest common factor (GCF) of the given
numbers.
1. 36 and 84: 12
2. 20 and 40: 20
3. 45 and 81: 9
Unit Six : Factors and Multiples
Concept 2 : understanding multiplies
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LESSON 4 : Identifying Multiples of Whole Numbers
-------------------------------------------------------------------------------------------------------------------
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page471

Learning Objectives in this lesson
Students will define multiples of whole numbers.
• Students will identify multiples of whole numbers.
Vocabulary Check-In
multiples, skip count
COMMON MISCONCEPTIONS AND ERRORS
Students often confuse factors and multiples. Factors are numbers multiplied together to
make a number and are finite, while multiples are the products of a given number and are
infinite.
• Students may not identify 0 or the whole number itself as a multiple. However, students
learned about the Zero Property of Multiplication and the Identity Property o f Multiplication
in the previous unit.
• When identifying multiples on a Hundreds Chart, students may believe that the multiples
of a number are in the column below it. This is only true for 2, 5, and10
.PRACTICE
Direct students to Lesson 4 PRACTICE and have them complete the problems. Address
student errors and misconceptions.
Check Your Understanding
1. Write 4 multiples of 6: Possible answers: 6, 12, 18,
24, 30, 36, 42, 48, 54, 60, 66, 600
2. Write 4 multiples of 5: Possible answers: 5, 10, 15,
20, 25, 30, 35, 40, 45, 50, 55, 60.
3. Which number is a multiple of 9? 3, 17, 45, 56, 8
Unit Six : Factors and Multiples
Concept 2 : understanding multiplies
LESSON 5 : Common Multiples
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-------------------------------------------------------------------------------------------------------------------
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page485

Learning Objectives in this lesson
Students will identify common multiples of two numbers. .
Vocabulary Check-In
Review vocabulary as needed.
COMMON MISCONCEPTIONS AND ERRORS
• Students often confuse factors and multiples. Factors are numbers multiplied together to
make a number and are finite, while multiples are the products of a given number and are
infinite.
• Students might stop at the first common multiple they ide ntify and have difficulty finding
more than one common multiple.
• Students may simply multiply two numbers together to find a common multiple and
therefore, have difficulty identifying more than one common multiple. While this is not
incorrect, there are always other multiples shared by two numbers.
BUILD
1. Assign students to work in pairs. Direct students to Lesson 5 BUILD Multiple Match.
2. Distribute the Multiple Match Blackline Master. One partner gets a Partner A set of
cards. The other partner gets a Partner B set of cards.
3. Instruct students to look at Card 1 and write 10 multiples of the number on the card
(partners have different numbers).
4. Instruct students to work with their partner to then record any multiples that are written
on both of their cards. These are called common multiples.
5. Students repeat those steps with the remaining cards. Make sure both students are
looking at their Card 2, Card 3, Card 4, and so on at the same time.
6. Go over the answers together, calling on partners to share their findings.
.PRACTICE
Direct students to Lesson 5 PRACTICE and have them complete the problems. Address
student errors and misconceptions around identifying common multiples.
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Check Your Understanding
1. Is 16 a common multiple of 8 and 4? How do you
know? Yes. Possible explanation:
8 times 2 is 16 and 4 times 4 is 16.
2. Write a common multiple of 3 and 6. Possible
answers: 6, 12, 18, 24, 60
3. Which is a common multiple of 6 and 7? 7, 14, 36, 42

Unit Six : Factors and Multiples

Concept 2 : understanding multiplies
LESSON 4 : Identifying Multiples of Whole Numbers
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-------------------------------------------------------------------------------------------------------------------
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page495

Learning Objectives in this lesson
Students will define multiples of whole numbers.
• Students will identify multiples of whole numbers.
Vocabulary Check-In
multiples, skip count
COMMON MISCONCEPTIONS AND ERRORS
Students often confuse factors and multiples. Factors are numbers multiplied together to
make a number and are finite, while multiples are the products of a given number and are
infinite.
• Students may not identify 0 or the whole number itself as a multiple. However, students
learned about the Zero Property of Multiplication and the Identity Property o f Multiplication
in the previous unit.
• When identifying multiples on a Hundreds Chart, students may believe that the multiples
of a number are in the column below it. This is only true for 2, 5, and10
.PRACTICE
Direct students to Lesson 4 PRACTICE and have them complete the problems. Address
student errors and misconceptions.
Check Your Understanding
1. Write 4 multiples of 6: Possible answers: 6, 12, 18,
24, 30, 36, 42, 48, 54, 60, 66, 600
2. Write 4 multiples of 5: Possible answers: 5, 10, 15,
20, 25, 30, 35, 40, 45, 50, 55, 60.
3. Which number is a multiple of 9? 3, 17, 45, 56, 8
Unit Six : Factors and Multiples
Concept 2 : understanding multiplies
LESSON 6 : Relationships between Factors and Multiples

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-------------------------------------------------------------------------------------------------------------------
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page500

Learning Objectives in this lesson
• Students will explain the relationship between factors and multiples.
• Students will determine if a number is a factor or a multiple of another number
Vocabulary Check-In
common multiple, factor, multiples, product
COMMON MISCONCEPTIONS AND ERRORS
Students often confuse factors and multiples. Factors are numbers multiplied together to
make a number, while multiples are the numbers said when counting by a number.
• Students may have difficulty describing the relationship between factors and multiples
in words. However, they should be able to describe the relationship using a pair of
numbers as an example.
BUILD
1. Ask students to turn to Lesson 6 BUILD Making Connections Problem 1.
2. Ask students to write two sentences explaining how the numbers are related.
Encourage students to think about factors and multiples.
3. Call on students to share out.
4. Direct students to complete the remaining problems.
5. Ask students to discuss their answers with a partner.
6. Invite students to share their thinking on how factors and multiples are related with the
class.

.PRACTICE
PRACTICE

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Direct students to Lesson 6 PRACTICE and have them comp lete the problems. Address
student errors and misconceptions.
Check Your Understanding
1. Is 7 a factor of 21 or a multiple of 21? Factor
2. Write a sentence explaining the relationship between 6, 4, and 24. Use the vocabulary
factor and multiple. 6 and 4 are factors of 24. 24 is a multiple of 6. 24 is a multiple of 4.
3. Which of the following are factors of 12? 24, 6, 48, 4, 104. Which of the following is a
multiple of 10? 5, 30, 2, 15,1

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Unit Seven multiplication and division
Unit 7 : multiplication and division
Concept 1 : Multiplying by 1-Digit and 2-Digit Factors
LESSON 1 : The Area Model Strategy
-------------------------------------------------------------------------------------------------------------------
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page527

Learning Objectives
• Students will use area models to represent two-digit by one-digit multiplication.
• Students will explain how they use place value to multiply.
Vocabulary Check-In
area model, decompos
COMMON MISCONCEPTIONS AND ERRORS
While there are multiple ways to decompose a number, students should decompose
numbers using place value when using the area model for multiplication. For example, it
is possible to decompose 23 in many different ways including
17 and 6, 10 and 13, or 14 and 9. However, 23 should be decomp osed into 20 and 3
when using an area model for multiplication.
• Students may incorrectly decompose the factors according to their digits rather than
according to the value of their digits. They may decompose 45 as 4 and 5 rather than 40
and 5..

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Unit Seven multiplication and division
Unit 7 : multiplication and division
Concept 1 : Multiplying by 1-Digit and 2-Digit Factors
LESSON 2 : The Distributive Property
-------------------------------------------------------------------------------------------------------------------
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page527

Learning Objectives
will use an area model to multiply a one digit number by a whole number with up to four
digits.
• Students will explain the Distributive Property of Multiplication.
• Students will apply the Distributive Property of Multiplication to multiply a one-digit
number by a whole number with up to four digits.
Vocabulary Check-In
area model, decompose, Distributive Property of Multiplication
Decomposing Numbers
1. Direct students to Lesson 2 ACCESS Decomposing Numbers.
2. Ask students to fill in the blanks to decompose each number using place value.
3. When they are finished, read each problem aloud and instruct students to call out the
answers when prompted.
Answer Key for Decomposing Numbers:
1. 536 = 500 + 30 + 6
2. 1,275 = 1,000 + 200 + 70 + 5
3. 264 = 60 + 4 + 200
4. 7,625 = 5 + 7,000 + 20 + 600

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Class 4 / D Date : / / 2021

Unit Seven multiplication and division
Unit 7 : multiplication and division
Concept 1 : Multiplying by 1-Digit and 2-Digit Factors
LESSON 3 and 4 and 5 : The Partial Products Algorithm- The Standard Multiplication Algorithm
-------------------------------------------------------------------------------------------------------------------
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page541

Learning Objectives
In this lesson
• Students will use the partial products algorithm to multiply a one-digit number by a
whole number with up to four digits
Vocabulary Check-In
No new vocabulary

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Unit Seven multiplication and division

Unit 7 : multiplication and division
Concept 1 : Multiplying by 1-Digit and 2-Digit Factors
LESSON 6 : Two digit multiplication
-------------------------------------------------------------------------------------------------------------------
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page541

Learning Objectives
In this lesson
n • Students will identify patterns when multiplying two multiples of 10. • Students w ill multiply a
two-digit number by a multiple of 10.
• Students will assess the reasonableness of an answer using estimation and mental math.
Vocabulary Check-In
Distributive Property of Multiplication

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Unit Seven multiplication and division

Unit 7 : Dividing by 1 digit
Concept 2 : Multiplying by 1-Digit and 2-Digit Factors
LESSON 10 : Exploring Remainders
-------------------------------------------------------------------------------------------------------------------
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page541

Learning Objectives
Students will identify the dividend, divisor, and quotient of a division problem.
• Students will solve division problems.
• Students will explain what a remainder represents in a division problem.
Vocabulary Check-In
dividend, divisor, quotient, remainder

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Unit Seven multiplication and division

Unit 7 : Dividing by 1 digit
Concept 2 : Multiplying by 1-Digit and 2-Digit Factors
LESSON 12 : Patterns and Place Value in Division
-------------------------------------------------------------------------------------------------------------------
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page541

Learning Objectives
In this lesson • Students will use place value, multiplication facts, and patterns with zeros to
divide multiples of 10, 100, and 1,000 by one-digit divisors

Vocabulary Check-In
dividend, divisor, quotient, remainder

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Unit Seven multiplication and division

Unit 7 : Dividing by 1 digit
Concept 2 : Multiplying by 1-Digit and 2-Digit Factors
LESSON 12: The Area Model and Division
-------------------------------------------------------------------------------------------------------------------
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page541

Learning Objectives
In this lesson • Students will use area models to represent and solve division problems
Vocabulary Check-In
area model, dividend, divisor, quotient, remainder

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Unit Seven multiplication and division

Unit 7 : Dividing by 1 digit
Concept 2 : Multiplying by 1-Digit and 2-Digit Factors
LESSON 13: The Partial Quotients Algorithm
-------------------------------------------------------------------------------------------------------------------
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page541

Learning Objectives
In this lesson
• Students will use the partial quotients algorithm to divide dividends with up to four digits by one -digit
divisors
Vocabulary Check-In
partial quotients algorithm

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Unit Seven multiplication and division

Unit 7 : Dividing by 1 digit
Concept 2 : Multiplying by 1-Digit and 2-Digit Factors
LESSON 14: The Standard Division Algorithm
-------------------------------------------------------------------------------------------------------------------
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page541

Learning Objectives
In this lesson
• Students will estimate quotients using properties of place value and patterns in multiplication
and division.
• Students will use the standard algorithm to solve division problems.

Vocabulary Check-In
The Standard Division Algorithm

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Unit Seven multiplication and division

Unit 7 : Dividing by 1 digit
Concept 2 : Multiplying by 1-Digit and 2-Digit Factors
LESSON 15: Division and multiplication
-------------------------------------------------------------------------------------------------------------------
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page541

Learning Objectives
In this lesson
• Students will use properties of place value to accurately record quotients.
• Students will use the relationship between multiplication and division to check the accuracy of
quotients. .

Vocabulary Check-In
The Standard Division Algorithm

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Unit Seven multiplication and division

Unit 7 : Dividing by 1 digit
Concept 2 : Multiplying by 1-Digit and 2-Digit Factors
LESSON 16 : Solving Challenging Story Problems
-------------------------------------------------------------------------------------------------------------------
Teaching Strategies
Lean and whisper
Model
One stay one stray
Popcorn
Relay Race
Shake It Share It High Five

Shoulder Partners
Think Aloud
Snowball Fight

Teachers Guide : Page541

Learning Objectives
In this lesson
• Students will organize information in story problems to determine when to add, subtract, multiply, or
divide.
• Students will solve story problems using addition, subtraction, multiplication, and division.

Vocabulary Check-In
No new vocabulary

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