Mathematics

Problem Booklet

MYP – 2
Unit-1: Numbers Change You!
Unit Title/ Time Frame Numbers Change you!

Key Concept Form

Related Concepts Representations and Quantities

Global Context & Globalization and Sustainability:

Specific Exploration Student will explore the interconnectedness of human-made systems
and communities like Market, Commodities and commercialization.

AK Strand & specific sub Economics for Development

strand Understanding the connections between economic activity and quality
of life.
Statement of Inquiry Representing numbers in different forms to quantify can help
understand the human made systems.

This assessment gives an opportunity to the students to represent

numbers in different forms like fractions, decimals and percentages to
quantify and understand the human made systems, for eg. Discounts,
offers etc
Criterion A Knowing and understanding
Criterion C Communicating
Criterion D Applying mathematics in real-life contexts
Command Terms Select – Choose from a list or group.
Apply – Use knowledge and understanding in response to a given
situation or real circumstances. Use an idea, equation, principle, theory
or law in relation to a given problem or issue.
Calculate – Obtain a numerical answer showing the relevant stages in
the working.
Explain – Give a detailed account including reasons or causes.
Organize - Put ideas and information into a proper or systematic
order,
Topics:
 Types of numbers
 Types of decimal numbers
 Four operations with integers
 Four operations with fractions
 Four operations with decimal numbers
 Order of operations
 Four operations using number line
 Convert fractions into decimal numbers
 Convert decimal numbers into fractions
 Convert fractions into percentages
 Convert percentages into fractions
 Rounding off decimal numbers to nearest tenth, hundredth and thousandth
 Inequality of numbers
 Inequality using number line
 Rate
 Ratio, equivalent ratio, proportion
 Percentages
 Convert fractions to ratio to percentage and vise versa
 Percentage increase and decrease
 Percentage Profit & Loss
 VAT, Discount & Sale
 Square numbers & Square Roots
Types of Real numbers

The main types of numbers used in school mathematics are listed below:
Natural Numbers (N): (also called positive integers, counting numbers, or natural numbers); They
are the numbers {1, 2, 3, 4, 5, …}
Whole Numbers (W): This is the set of natural numbers, plus zero, i.e., {0, 1, 2, 3, 4, 5, …}.
Integers (Z): This is the set of all whole numbers plus all the negatives (or opposites) of the natural
numbers, i.e., {… , ⁻2, ⁻1, 0, 1, 2, …}
Rational numbers (Q): This is all the fractions where the top and bottom numbers are integers; e.g.,
1/2, 3/4, 7/2, ⁻4/3, 4/1 [Note: The denominator cannot be 0, but the numerator can be].
Irrational Numbers: An irrational number is a number that cannot be written as a ratio (or fraction).
In decimal form, it never ends or repeats. The ancient Greeks discovered that not all numbers are
rational; there are equations that cannot be solved using ratios of integers.
For example,
√2 is about 1.414, which is close to 2
. But you'll never hit exactly by squaring a fraction (or terminating decimal). The square root of 2
is an irrational number, meaning its decimal equivalent goes on forever, with no repeating pattern:
√2 = 1.41421356237309...

Real numbers (R): (also called measuring numbers or measurement numbers). This includes all
numbers that can be written as a decimal. This includes fractions written in decimal form e.g., 0.5,
0.75 2.35, ⁻0.073, 0.3333, or 2.142857. It also includes all the irrational numbers such as π, √2 etc.
Every real number corresponds to a point on the number line.
Counting numbers (N): They are then introduced to 0, and this gives them the whole numbers (W).
The integers are avoided initially, even though simple subtraction could lead to negative numbers (
e.g., 3 – 4 = ⁻1).
Simple unit fractions are the next group of numbers that are met i.e., {1/2, 1/3, 1/4, 1/5 ... }, then
other fractions (e.g., 3/4, 4/9, 7/2, 3/100, ­­⁻1/2 etc.) which are known as the rational numbers (Q).
We next move onto decimal numbers (such as 0.3, 0.32, ⁻2.7). These can be called decimal
fractions, because they can be written in a fractional form (e.g., 3/10, 32/100, ⁻27/10).
These expand to the real numbers (R), which include irrational numbers such as π, √2. An
irrational number cannot be represented as a fraction (i.e., a rational number). π can be represented
with numerals, i.e., 3.14159265 ... ; however the digits go on infinitely but there is no pattern to
them.

Types of decimal numbers

Decimal numbers are classified into three types i.e.:
Terminating Decimals: these decimals have a finite number of digits followed by the decimal
point.
For example, 0.5, 1.456, 123.456, etc.

Recurring Decimals: These consist of one or more repeating numbers or sequences of numbers
followed by the decimal point, which keeps on infinitely.
For example, 5.232323…., 21.123123…, 0.1111….

Irrational: These Decimals go on forever, are never-ending and also never form a repeating pattern.
These numbers are known as irrational numbers and cannot be written in the form of a fraction.
For example, 0.45445544…., etc.

Recurring Decimal numbers are those numbers that keep on repeating the same value after a
decimal point. These numbers are also called Repeating Decimals. For example:
1/3 = 0.33333..... (3 repeats forever)
1/7 = 0.142857142857142857....... (14285714 repeat forever)
77/600= 0.128333333...... (3 repeat forever)

To display a repeating digit in a decimal number, often we put a dot or a line over the repeating
digit as shown below:
For Example:

Non - Recurring Numbers

Non - recurring numbers are those in Mathematics that do not repeat their values after a decimal
point. They are also called non-terminating decimals and non-Repeating Decimal numbers. For
Example:
√2 = 1.41421356237309504…...
√7 = 2.647568759…...
π = 3.1415926535897932384626….....
e = 2.7182818284590452353602….....

Terminating and Recurring Decimals

When performing the conversion from fractions to decimals, you can formulate whether the
decimal will terminate or recur.
Rate, Ratio, Percentage

1. (a) Simplify the ratio 25 : 35

....................
(1)
(b) Simplify the ratio 18 : 45

....................
(1)
(c) Simplify the ratio 300 : 25

....................
(1)
2. Divide £700 in the ratio 5 : 3 : 2

£............... £............... £...............

3. Alex and Thomas share 30 sweets.
They divide them in the ratio 3:2.

How many sweets does Thomas have?

.........................
(2)

4. Sophie has 60 pencils.

The ratio of sharpened pencils to blunt pencils is 4:1

How many sharpened pencils does Sophie have?

.........................
(2)
5. The number of people who voted for the Green Party in an election was 1500.
The number of people who voted for the Blue Party was 9000.

Write the ratio of Green Party voters to Blue Party voters in its simplest form.

................................
(2)

6. A piece of carpet is 240cm long.

Mr Jones cuts it into three pieces in the ratio 1 : 2 : 5

Work out the length of the longest piece of carpet.

................................
(3)
7. Sarah has some chocolates.

24 are white chocolate.

16 are milk chocolate.
8 are dark chocolate.

(a) Write down the ratio of white chocolate to milk chocolate to dark chocolate.
Give your ratio in its simplest form.

............... : ............... : ...............

(2)

Rachel has some apples and bananas.

The ratio of apples to bananas is 2 : 3
She has 14 apples.

(b) Work out how many bananas Rachel has.

.........................
(2)
8. Chris and Molly win money in a competition.
They share the money in the ratio 2 : 3
Molly receives £240.

(a) How much money does Chris receive?

£.........................
(2)

(b) How much money did they win in the competition?

£.........................
(1)

9. Divide £945 in the ratio 2 : 5

£......................... £.........................
(2)
10. At a rugby match, the ratio of children to adults is 2 : 3
There are 80 children in the crowd.
Each adult ticket costs £8
Each child ticket costs a quarter of the adult ticket.

Work out the total money made from ticket sales.

£.........................
(4)

11. Charlene and Danielle share some money in ratio 2 : 3

Danielle gets £25 more than Charlie.

How much does each girl receive?

Charlene £.........................

Danielle £.........................
(3)
12. The ratio of boys to girls in a school is 4 : 5
There are 220 boys in the school.

How many students attend the school?

.........................
(3)

13. The ratio of girls to boys in a class is 2 : 3

What fraction of the class are girls?

.........................
(1)
What percentage of the class are boys?

.........................
(1)
14. The angles in a triangle are in the ratio 1 : 2 : 9

What is the size of the largest angle?

.........................
(2)

15. Three angles are in the ratio 2 : 3 : 5

The smallest angle is 50⁰

Work out the sizes of the other two angles

............... and ...............

(2)
16. 4 schools sent students to a languages course.

One of the schools sent both French and German students.

The ratio of French to German students it sent was 1 : 3
The school sent 21 German students.

The other 3 schools sent the same number of students.

Work out the total number of students sent to the languages course.

.........................
(4)
 Division Sentence
Write the division sentence that describes each model.

1)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

2)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

3)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

4)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

5)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

6)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

=
Name: Score:

Division Sentence - Missing Numbers

Complete the divisionsentence thatdescribeseach model.

1)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

3 = 2

2)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

15 = 3

3)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

12 2 =

4)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

18 = 3

5)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

1 = 10

6)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

16 = 4
Name: Score:

Number Line Division T1S1

Indicate hops on each number line and complete the division sentences.

1) 20 5 =

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

2) 18 9 =

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

3) 12 4 =

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

4) 16 2 =

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

5) 15 3 =

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

6) 9 1 =

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Name: Score:

T1S1

Write the multiplication sentence that describes each model.

1)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

2)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

3)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

4)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

5)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

6)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

=
Name: Score:

T1S1

Complete the multiplication sentence that describes each model.

1)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

2 = 6

2)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

4 = 16

3)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

9 2 =

4)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

8 = 8

5)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

5 3 =

6)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

6 = 18
= 18
Name: Score:

T1S1

Indicate hops on each number line and complete the multiplication sentences.

1) 4 3 =

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

2) 5 2 =

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

3) 2 4 =

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

4) 3 5 =

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

5) 9 1 =

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

6) 7 2 =

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Name : Score :

0-10: S1

Complete the addition sentence that describes each model.

1)
0 1 2 3 4 5 6 7 8 9 10

0 + 2 =

2)
0 1 2 3 4 5 6 7 8 9 10

1 + = 4

3)
0 1 2 3 4 5 6 7 8 9 10

+ 2 = 7

4)
0 1 2 3 4 5 6 7 8 9 10

2 + 4 =

5)
0 1 2 3 4 5 6 7 8 9 10

+ 1 = 8

0 1 2
6) 3 4
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 5 6 7
8 9 10

3 + = 8

Printable Math Worksheets @ www.mathworksheets4kids.com

Name : Score :
Answer key

0-10: S1

Complete the addition sentence that describes each model.

1)
0 1 2 3 4 5 6 7 8 9 10

0 + 2 = 2

2)
0 1 2 3 4 5 6 7 8 9 10

1 + 3 = 4

3)
0 1 2 3 4 5 6 7 8 9 10

5 + 2 = 7

4)
0 1 2 3 4 5 6 7 8 9 10

2 + 4 = 6

5)
0 1 2 3 4 5 6 7 8 9 10

7 + 1 = 8

0 1 2
6) 3 4
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 5 6 7
8 9 10

3 + 5 = 8

Printable Math Worksheets @ www.mathworksheets4kids.com

Name : Score :

0-10: S1

Write the addition sentence that describes each model.

1)
0 1 2 3 4 5 6 7 8 9 10

+ =

2)
0 1 2 3 4 5 6 7 8 9 10

+ =

3)
0 1 2 3 4 5 6 7 8 9 10

+ =

4)
0 1 2 3 4 5 6 7 8 9 10

+ =

5)
0 1 2 3 4 5 6 7 8 9 10

+ =

0 1 2
6) 3 4
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 5 6 7
8 9 10

+ =

Printable Math Worksheets @ www.mathworksheets4kids.com

Name : Answer key Score :

0-10: S1

Write the addition sentence that describes each model.

1)
0 1 2 3 4 5 6 7 8 9 10

3 + 6 = 9

2)
0 1 2 3 4 5 6 7 8 9 10

1 + 4 = 5

3)
0 1 2 3 4 5 6 7 8 9 10

2 + 7 = 9

4)
0 1 2 3 4 5 6 7 8 9 10

5 + 3 = 8

5)
0 1 2 3 4 5 6 7 8 9 10

6 + 1 = 7

0 1 2
6) 3 4
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 5 6 7
8 9 10

4 + 5 = 9

Printable Math Worksheets @ www.mathworksheets4kids.com

Name : Score :

0-5: S1

Read each number line and solve the problem.

1)
0 1 2 3 4 5

0 + 3 =

2)
0 1 2 3 4 5

3 + 2 =

3)
0 1 2 3 4 5

1 + 4 =

4)
0 1 2 3 4 5

2 + 2 =

5)
0 1 2 3 4 5

4 + 1 =

6)
0 1 2 3 4 5

1 + 2 =

Printable Math Worksheets @ www.mathworksheets4kids.com

Name : Answer key Score :

0-5: S1

Read each number line and solve the problem.

1)
0 1 2 3 4 5

0 + 3 = 3

2)
0 1 2 3 4 5

3 + 2 = 5

3)
0 1 2 3 4 5

1 + 4 = 5

4)
0 1 2 3 4 5

2 + 2 = 4

5)
0 1 2 3 4 5

4 + 1 = 5

6)
0 1 2 3 4 5

1 + 2 = 3

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Name : Score :

0-10: S1

Complete the subtraction sentence that describes each model.

1)
0 1 2 3 4 5 6 7 8 9 10

9 – = 8

2)
0 1 2 3 4 5 6 7 8 9 10

– 5 = 0

3)
0 1 2 3 4 5 6 7 8 9 10

3 – 2 =

4)
0 1 2 3 4 5 6 7 8 9 10

– 4 = 6

5)
0 1 2 3 4 5 6 7 8 9 10

8 – = 2

6) 0 1 2 3
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 4 5 6
7 8 9 10

6 – 3 =

Printable Math Worksheets @ www.mathworksheets4kids.com

Name : Answer key Score :

0-10: S1

Complete the subtraction sentence that describes each model.

1)
0 1 2 3 4 5 6 7 8 9 10

9 – 1 = 8

2)
0 1 2 3 4 5 6 7 8 9 10

5 – 5 = 0

3)
0 1 2 3 4 5 6 7 8 9 10

3 – 2 = 1

4)
0 1 2 3 4 5 6 7 8 9 10

10 – 4 = 6

5)
0 1 2 3 4 5 6 7 8 9 10

8 – 6 = 2

6) 0 1 2 3
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 4 5 6
7 8 9 10

6 – 3 = 3

Printable Math Worksheets @ www.mathworksheets4kids.com

Name : Score :

0-5: S1

Indicate hops on each number line and complete the subtraction sentences.

1) 3 – 2 =

0 1 2 3 4 5

2) 4 – 1 =

0 1 2 3 4 5

3) 5 – 2 =

0 1 2 3 4 5

4) 1 – 1 =

0 1 2 3 4 5

5) 4 – 3 =

0 1 2 3 4 5

6) 5 – 5 =

0 1 2 3 4 5

Printable Math Worksheets @ www.mathworksheets4kids.com

Name : Answer key Score :

0-5: S1

Indicate hops on each number line and complete the subtraction sentences.

1) 3 – 2 = 1

0 1 2 3 4 5

2) 4 – 1 = 3

0 1 2 3 4 5

3) 5 – 2 = 3

0 1 2 3 4 5

4) 1 – 1 = 0

0 1 2 3 4 5

5) 4 – 3 = 1

0 1 2 3 4 5

6) 5 – 5 = 0

0 1 2 3 4 5

Printable Math Worksheets @ www.mathworksheets4kids.com

Name : Score :

0-5: S1

Read each number line and solve the problem.

1)
0 1 2 3 4 5

5 – 4 =

2)
0 1 2 3 4 5

4 – 2 =

3)
0 1 2 3 4 5

1 – 1 =

4)
0 1 2 3 4 5

5 – 3 =

5)
0 1 2 3 4 5

3 – 1 =

6)
0 1 2 3 4 5

2 – 1 =

Printable Math Worksheets @ www.mathworksheets4kids.com

Name : Answer key Score :

0-5: S1

Read each number line and solve the problem.

1)
0 1 2 3 4 5

5 – 4 = 1

2)
0 1 2 3 4 5

4 – 2 = 2

3)
0 1 2 3 4 5

1 – 1 = 0

4)
0 1 2 3 4 5

5 – 3 = 2

5)
0 1 2 3 4 5

3 – 1 = 2

6)
0 1 2 3 4 5

2 – 1 = 1

Printable Math Worksheets @ www.mathworksheets4kids.com

Name : Score :

Number Line - Integers ES1

A) Mark the integers on the number line.

1) a) –2 b) 7 c) –5 d) 1

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10

2) a) 9 b) –4 c) 3 d) –8

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10

B) Answer the questions using the number line below.

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10

1) 2 units to the left of 3 is

2) 6 units to the right of –1 is

3) 4 units to the left of –4 is

4) 3 units to the right of 7 is

5) 1 unit to the left of 10 is

6) 5 units to the right of –6 is

Printable Math Worksheets @ www.mathworksheets4kids.com

 7) 8 units to the left of 5 is

Printable Math Worksheets @ www.mathworksheets4kids.com

Name : Score :
Answer key
ES1
Number Line - Integers

A) Mark the integers on the number line.

1) a) –2 b) 7 c) –5 d) 1

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10

2) a) 9 b) –4 c) 3 d) –8

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10

B) Answer the questions using the number line below.

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10

1) 2 units to the left of 3 is 1

2) 6 units to the right of –1 is 5

3) 4 units to the left of –4 is –8

4) 3 units to the right of 7 is 10

5) 1 unit to the left of 10 is 9

6) 5 units to the right of –6 is –1

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 7) 8 units to the left of 5 is –3

Printable Math Worksheets @ www.mathworksheets4kids.com

 ES1

Integers on a Number Line

A) Locate the integers on the number line.
1) a) –8 b) 3 c) –5 d) 4

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10

2) a) 2 b) –6 c) 7 d) –1

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10

B) Observe the number line and answer the questions.

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10

1) What integer is 2 units to the left of 1 ?

2) What integer is 7 units to the left of 9 ?

3) What integer is 9 units to the left of –1 ?

4) What integer is 5 units to the right of 5 ?

5) What integer is 1 unit to the right of –9 ?

6) What integer is 4 units to the left of 8 ?

7) What integer is 3 units to the right of –6 ?
 S1

Writing Algebraic Inequalities

Translate each verbal phrase into an inequality.

1) y is not more than 15.

2) x is greater than 7.

3) The value of a is at least 1.

4) The value of n is greater than 5.

5) 4 is less than m.

6) The value of s is less than or equal to 10.

7) 6 is not less than b.

8) The value of d is less than 13.

9) p is more than 9.

10) The value of r is at most 12.

Name:

BSI

Translate each verbal phrase into an inequality.

1 ) 5 is not more than x. 2) The value of x is greater than or equal

to 14.

3) x is greater than or equal to 12. 4) 6 is not le5s than x.

5) The value of x is greater than 7. 6) x is greater than 15.

7) x is not more than 13. 8) 9 is less than or equal to x.

9) The value of x is at least 1. 10) The value of x is less than 14.

11) 10 is less than or equal to x. 12 x is more than 3.

13) 16 is less than x. 14) The value of x is at most 8.

15) The value of x is not greater than 18. 16) 2 is more than x.
Convert Decimal numbers to percentage and vice versa

1. Write 0.4 as a percentage.

.........................%
(1)

2. Write 0.72 as a percentage.

.........................%
(1)

3. Write 28% as a decimal.

.........................
(1)

4. Write 0.02 as a percentage.

.........................%
(1)

5. Write 5% as a decimal.

.........................
(1)
6. Write 90% as a decimal.

.........................
(1)

7. Write 49% as a decimal.

.........................
(1)

8. Write 0.8 as a percentage.

.........................%
(1)

9. Write 8.5% as a decimal.

.........................
(1)

10. Write 0.215 as a percentage.

.........................%

(1)
11. Match each decimal and percentage.

(2)

12. Arrange the following numbers in order, from smallest to largest

0.61 59% 0.6 62%

...................................................................
(2)
13. Arrange the following numbers in order, from smallest to largest

0.6 11% 0.1 8%

...................................................................
(2)

14. 14.

(a) Write down the percentage of the grid that is shaded.

.........................%
(1)

(b) Write your answer to (a) as a decimal.

.........................
(1)
15. 15.

Explain why James is incorrect.

(2)

16. Over a season, a football team won 55% of their matches and drew 32%.

(a) Work out what percentage of games were lost.

.........................
(1)
(b) Write 32% as a decimal.

.........................
(1)
17. Complete this table.

(3)
1. Complete the table.

(3)

2. (a) Write 0.1 as a fraction.

.........................
(1)

(b) Write 0.1 as a percentage.

.........................
(1)

3. (a) Write ¼ as a percentage.

.........................
(1)

(b) Write ¼ as a decimal.

.........................
(1)
4.

(a) Write down the fraction of this shape that is shaded.

Give your fraction in its simplest form.

.........................
(2)

(b) Write as a decimal.

.........................
(1)

(c) Samuel says that 25% is greater than 0.3.

Is he correct?
Explain your answer.

..........................................................................................................................

..........................................................................................................................

..........................................................................................................................
(1)
5. The table shows the percentage of votes each party obtains in an election.

(a) Work out what percentage voted for Labour.

.........................
(1)

(b) Write 35% as a fraction.

Give your answer in its simplest form.

.........................
(2)

(c) Write 11% as a decimal.

.........................
(1)

8000 people voted in the election.

(d) Work out 25% of 8000

.........................
(1)
6. (a) Write 20% as a decimal.

.........................
(1)

(b) Write 9% as a fraction.

.........................
(1)

7. A train is late arriving into a station.

It should arrive at 5 pm
It arrives at 5.15 pm.

(a) How many minutes late is the train?

.........................
(1)

(b) Write your answer as a fraction of an hour.

.........................
(1)

8. (a) Write 0.9 as a percentage.

.........................
(1)

(b) Write 0.9 as a fraction.

Give your answer in its simplest form.

.........................
(2)
9. Complete the table.

(3)

10. For every £200 that Mrs Wallace earns, she saves £34.

(a) Work out £34 as a percentage of £200.

.........................%
(2)

(b) Last month Mrs Wallace earns £1000.

How much of this does she save?

£.........................
(2)
11. Alannah has 300 scarves that she takes to a market to sell.

Alannah sells of the scarves.

(a) How many scarves does Alannah sell?

.........................
(2)

(b) Write as a percentage.

.........................
(1)
(c) Write as a decimal.

.........................
(1)

Of the 300 scarves, 200 are not blue.

(d) Write the number of scarves which are blue as a fraction of the total number
of scarves.

.........................
(1)
12. (a) What fraction of this shape is shaded?

.........................
(1)

(b) Shade 0.4 of this shape.

(1)

(c) What percentage of this shape is shaded?

.........................
(1)
13. Penny gets £8 pocket money.
She is given an increase of £1.

(a) Write down £1 as a fraction of £8

.........................
(1)

(b) Write your answer as a percentage

.........................
(1)

14. Complete the table.

(4)

15. Convert 0.124 to a fraction.

Give your answer in its simplest form.

.........................
(2)
15. Convert to a decimal.

.........................
(2)

16. Convert to a percentage.

.........................
(2)
17. Convert to a decimal.

.........................
(2)
Square Numbers & Square Roots

Solve the problems given in the exercise below:

Square root of fraction:

Solve the following problems on patterns using square numbers:
 Instructions:
1) All the questions are compulsory.
2) Show your working as marks are not necessarily awarded for a correct answer with no working.
3) You need to present your work neatly.
______________________________________________________________________________________
_

Q1(a) Which of the following shows how to calculate 33 % of 70?

33 100 70 33 70 33 100 70 100
(i)   (ii)  (iii)  (iv) 
1 1 1 100 1 70 1 30 1

Answer: _______

(b) About 65% of the mass of an adult human is water. Ollie weighs 64 kg. How much
of Ollie’s mass is water, to the nearest kilogram?

Q2. Solve the following expression and shade the given figure to indicate the answer.

Q3: Select an appropriate sign (=, < or >) to fill in the blanks:
3
a) _____ 40%
5
6
b) ______ 1.5
5
c) 2.08 _______ 2.5

Q4: Evaluate:

a)
 b)

Q5: John loads his shopping trolley with several items priced as shown.
$ 1.25
Per
pack

each
$ 8.35
$ each
13.50
each
a) Calculate the total cost of John’s purchases.

John has $50 with him. He is not very sure if he has enough money to buy these items.
At the cash counter, he got to know that there is a flat 10% discount going on for
Christmas.
b) Assuming that there is no VAT to be paid, Calculate and show if he would be
able to buy all these items with the amount he has with him.
Q6: These are the scores for a dancing competition.
Children needed to score more than half to get
into the final which would be on T.V.

Which children got into the final?

Who got the final score?

Q7: An advertisement for a brand of bread claims that it now has ‘20% more fibre!’
The nutritional information table on the package shows that a 40g serve of bread
contains 3.4 g of fibre. Before the improvement was made, the same 40g serving
contained 2.8 g of fibre.
a) Write the increase in the amount of fibre as a fraction of the original amount in the
simplest form.

b) Convert this fraction to a percentage, rounding your answer to 2 decimal places.

c) Is the bread manufacturer’s claim of ‘20% more fibre’ justified? Explain your
answer.
 Criterion A (Knowing and understanding)

Achievement Level descriptor

level

0 The student does not reach a standard described by any of the

descriptors below.
1-2 The student is able to:

i. select appropriate mathematics when solving simple problems in

familiar situations
ii. apply the selected mathematics successfully when solving these
problems
iii. generally solve these problems correctly in a variety of context

3-4 The student is able to:

i. select appropriate mathematics when solving more complex

problems in familiar situations
ii. apply the selected mathematics successfully when solving these
problems
iii. generally solve these problems correctly in a variety of context.

5-6 The student is able to:

i. select appropriate mathematics when solving challenging

problems in familiar situations
ii. apply the selected mathematics successfully when solving these
problems
iii. generally solve these problems correctly in a variety of context.

7-8 The student is able to:

i. select appropriate mathematics when solving challenging

problems in both familiar and unfamiliar situations
ii. apply the selected mathematics successfully when solving these
problems.
iii. generally solve these problems correctly in a variety of context.
 Criterion C (Communicating)

Achievement Level descriptor

level
0 The student does not reach a standard described by any of the
descriptors below.
1-2 The student is able to:

i. use limited mathematical language

ii. use limited forms of mathematical representation to present
information

3-4 The student is able to:

i. use some appropriate mathematical language

ii. use appropriate forms of mathematical representation to present
information adequately

5-6 The student is able to:

i. usually use appropriate mathematical language

ii. usually use appropriate forms of mathematical representation to
present information correctly
iii. move between different forms of mathematical representation with
some success.

7-8 The student is able to:

i. i. consistently use appropriate mathematical language

ii. use appropriate forms of mathematical representation to
consistently present information correctly
iii. move effectively between different forms of mathematical
representation.
 Party Time!
Diya is planning to invite her friends for her birthday party. She decides to keep it a low budget party, so,
she decides to do it at her home. She plans to order the food from outside, however wants to bake
something at home on her own.
She looks for the recipe and finalizes the following two.

She has finalized her list of guests and there are total 35 people including her family members. Now she
wants to buy the ingredients using the above two recipes.
Task 1: Use your mathematical knowledge to help her create the list of ingredients required for any one.

Task 2: Explain the degree of accuracy of your solution.

Task 3: Due to hike in fuel prices, the cost of eggs has now increased by 30%, from BDT 160 per dozen.
By how much will the cost of ingredients increase for the recipe chosen by you in task 1.

You need to show all your working clearly.

 Criterion D: Applying mathematics in real-life contexts
Achievement
Level descriptor
level
0 The student does not reach a standard described by any of the descriptors below.
The student is able to:
i. identify some of the elements of the authentic real-life situation
1–2
ii. apply mathematical strategies to find a solution to the authentic real-life
situation, with limited success.
The student is able to:
i. identify the relevant elements of the authentic real-life situation
ii select, with some success, adequate mathematical strategies to model the
3–4
authentic real-life situation
ii. apply mathematical strategies to reach a solution to the authentic real-life
situation
The student is able to:
i. identify the relevant elements of the authentic real-life situation
ii. select adequate mathematical strategies to model the authentic real-life
5–6 situation
iii. apply the selected mathematical strategies to reach a valid solution to the
authentic real-life situation
iv. describe the degree of accuracy of the solution
The student is able to:
i. identify the relevant elements of the authentic real-life situation
ii. select appropriate mathematical strategies to model the authentic real-life
7–8
situation
iii. apply the selected mathematical strategies to reach a correct solution
iv. explain the degree of accuracy of the solution