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Maths Revision, Basic Rule of Math, Number System

1.
Maths Revision

2.
Number and Place Value

Use numbers from -1000 to 10 000 000

Count forwards and backwards in 4, 6, 7, 8, 9, 25, 50, steps of powers of 10

(10, 100, 1000,…)

1a) Continue the sequence by increasing each number by 25:

150, , , 225, , ,

b) Continue the sequence by decreasing each number by 100:

, 830, , , 530, ,

c) Continue the sequence by increasing each number in powers of 1000:

11 345, , , , ,

Find 10, 100 or 1000 more or less than a given number.

2a) What is 100 less than 1902? b) What is 1000 more than 3249?

c) Count forwards and backwards through zero:

3, , , , -1, , ,

Negative numbers

Use negative numbers in context and calculate intervals across zero.

3) The temperature inside is 19°C and outside is -4°C. What is the difference in

temperature between inside and outside?

Place Value

Recognise the place value of each digit in up to four-digit numbers.

4a) Underline the hundreds digit in the following numbers:

7845 689 2038

b) Underline the tens digit in the following numbers:

776 3890 1428

Page 1 of 37

Use numbers from -1000 to 10 000 000

Count forwards and backwards in 4, 6, 7, 8, 9, 25, 50, steps of powers of 10

(10, 100, 1000,…)

1a) Continue the sequence by increasing each number by 25:

150, , , 225, , ,

b) Continue the sequence by decreasing each number by 100:

, 830, , , 530, ,

c) Continue the sequence by increasing each number in powers of 1000:

11 345, , , , ,

Find 10, 100 or 1000 more or less than a given number.

2a) What is 100 less than 1902? b) What is 1000 more than 3249?

c) Count forwards and backwards through zero:

3, , , , -1, , ,

Negative numbers

Use negative numbers in context and calculate intervals across zero.

3) The temperature inside is 19°C and outside is -4°C. What is the difference in

temperature between inside and outside?

Place Value

Recognise the place value of each digit in up to four-digit numbers.

4a) Underline the hundreds digit in the following numbers:

7845 689 2038

b) Underline the tens digit in the following numbers:

776 3890 1428

Page 1 of 37

3.
Compare and Order Numbers

Compare using <, > or =

5a) 141 141 144 114 501 243 501 234

b) Organise the following from smallest to largest:

122 211 11 211 11 112 121 211 122 121

Smallest Largest

Identify, Represent and Estimate

Use models and representations of numbers.

6) Represent 2850 by colouring in the correct number of dienes:

Round numbers to the nearest 10, 100, 1000, 10 000 or 100 000 and any whole number.

(Remember 5 rounds up!)

8a) 4500 rounded to the nearest is 5000 (the rounds up).

b) 253 450 to the nearest 10 000 is (the rounds down).

c) 374 rounded to the nearest 50 is (74 is nearer to than ).

Read and Write Numbers in Numerals and Words

9) 344 285 in words is .

Roman Numerals Roman Numeral

10a) Fill in the table to

show what each b) CMXLVIII = 948

Roman numeral CCXIX =

represents:

626 =

MDCCCLXXI =

Page 2 of 37

Compare using <, > or =

5a) 141 141 144 114 501 243 501 234

b) Organise the following from smallest to largest:

122 211 11 211 11 112 121 211 122 121

Smallest Largest

Identify, Represent and Estimate

Use models and representations of numbers.

6) Represent 2850 by colouring in the correct number of dienes:

Round numbers to the nearest 10, 100, 1000, 10 000 or 100 000 and any whole number.

(Remember 5 rounds up!)

8a) 4500 rounded to the nearest is 5000 (the rounds up).

b) 253 450 to the nearest 10 000 is (the rounds down).

c) 374 rounded to the nearest 50 is (74 is nearer to than ).

Read and Write Numbers in Numerals and Words

9) 344 285 in words is .

Roman Numerals Roman Numeral

10a) Fill in the table to

show what each b) CMXLVIII = 948

Roman numeral CCXIX =

represents:

626 =

MDCCCLXXI =

Page 2 of 37

4.
Solve Problems

c) Here are 3 years written in Roman Numerals. Order the years from earliest to latest:

MMIX, MCMXCIX, MMXV

Page 3 of 37

c) Here are 3 years written in Roman Numerals. Order the years from earliest to latest:

MMIX, MCMXCIX, MMXV

Page 3 of 37

5.
Addition and Subtraction

Add and Subtract Mentally

Add and subtract three-digit numbers and ones, tens and hundreds.

1a) 376 + 3 = b) 376 + 40 = c) 376 + 200 =

Mental Methods

Add and subtract numbers mentally with larger numbers.

2) 15 672 – 3200 =

Estimate, Round, Levels of Accuracy and Inverse

Estimate by rounding to check accuracy:

3a) 54318 + 21298 ≈ + ≈ 75600

b) Inverse: check 7932 – 3457 = 4475, by + =

Multiplication Tables

Multiplication and division facts to 12 × 12.

4) Fill in the

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

missing

numbers: 1 1 2 4 5 6 8 9 10 11 12

2 2 4 6 10 12 16 18 22 24

3 6 9 12 15 21 24 27 36

4 4 8 12 16 20 24 32 36 40 44 48

5 5 15 20 30 35 40 45 50 55 65

6 6 12 24 30 36 48 54 60 72

7 21 42 56 70 77 84

8 8 16 24 40 56 64 72 96

9 9 27 36 45 54 72 81 90 108

10 10 20 40 60 70 100 110 120

11 22 33 44 55 66 88 99

12 12 24 36 48 60 72 84 96 108 120 132 144

Page 4 of 37

Add and Subtract Mentally

Add and subtract three-digit numbers and ones, tens and hundreds.

1a) 376 + 3 = b) 376 + 40 = c) 376 + 200 =

Mental Methods

Add and subtract numbers mentally with larger numbers.

2) 15 672 – 3200 =

Estimate, Round, Levels of Accuracy and Inverse

Estimate by rounding to check accuracy:

3a) 54318 + 21298 ≈ + ≈ 75600

b) Inverse: check 7932 – 3457 = 4475, by + =

Multiplication Tables

Multiplication and division facts to 12 × 12.

4) Fill in the

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

missing

numbers: 1 1 2 4 5 6 8 9 10 11 12

2 2 4 6 10 12 16 18 22 24

3 6 9 12 15 21 24 27 36

4 4 8 12 16 20 24 32 36 40 44 48

5 5 15 20 30 35 40 45 50 55 65

6 6 12 24 30 36 48 54 60 72

7 21 42 56 70 77 84

8 8 16 24 40 56 64 72 96

9 9 27 36 45 54 72 81 90 108

10 10 20 40 60 70 100 110 120

11 22 33 44 55 66 88 99

12 12 24 36 48 60 72 84 96 108 120 132 144

Page 4 of 37

6.
Multiplying and Dividing

5a) Use place value and known facts: 400 × 5 = , 630 ÷ 7 =

Multiply by 0 and 1 and divide by 1: 285 × 1 = , 285 × 0 = , 285 ÷ 1 = .

b) When multiplying the number gets and when dividing the number

gets .

c) The numbers will move in place value by the number of 0s.

45 × 10 = 6.7 × 100 = 902 × 1000 =

59 ÷ 10 = 4506 ÷ 100 = 382 ÷ 1000 =

Common Multiples, Factor Pairs, Common Factors and Commutativity

6a)12 is a common multiple of and , because 12 is a multiple of and a multiple of

.

All the factor pairs of 56 are and , and , and , and .

Use this to solve:

b) 56 pencils are shared between 4 tables. How many pencils does each

table receive? .

c) The common factors of 32 and 56 are , , and because they are factors of

both 32 and 56.

d) Commutativity means changing the order of the numbers in a calculation but the

answer does not change. What other two ways can this calculation be written so that it

gives the same answer? 5 × 9 × 2 = × × = × × =

24

Prime Numbers 4 6

7a) Prime numbers only have 1 and as factors.

2 2 2 3

b) Prime factors are factors of a number that are :

c) The prime factors of 21 are and .

d) The prime factors of 24 are and .

Composite numbers are non-prime numbers: 4 is a composite number because

2 is a factor.

e) Recall the prime numbers to 19: .

Page 5 of 37

5a) Use place value and known facts: 400 × 5 = , 630 ÷ 7 =

Multiply by 0 and 1 and divide by 1: 285 × 1 = , 285 × 0 = , 285 ÷ 1 = .

b) When multiplying the number gets and when dividing the number

gets .

c) The numbers will move in place value by the number of 0s.

45 × 10 = 6.7 × 100 = 902 × 1000 =

59 ÷ 10 = 4506 ÷ 100 = 382 ÷ 1000 =

Common Multiples, Factor Pairs, Common Factors and Commutativity

6a)12 is a common multiple of and , because 12 is a multiple of and a multiple of

.

All the factor pairs of 56 are and , and , and , and .

Use this to solve:

b) 56 pencils are shared between 4 tables. How many pencils does each

table receive? .

c) The common factors of 32 and 56 are , , and because they are factors of

both 32 and 56.

d) Commutativity means changing the order of the numbers in a calculation but the

answer does not change. What other two ways can this calculation be written so that it

gives the same answer? 5 × 9 × 2 = × × = × × =

24

Prime Numbers 4 6

7a) Prime numbers only have 1 and as factors.

2 2 2 3

b) Prime factors are factors of a number that are :

c) The prime factors of 21 are and .

d) The prime factors of 24 are and .

Composite numbers are non-prime numbers: 4 is a composite number because

2 is a factor.

e) Recall the prime numbers to 19: .

Page 5 of 37

7.
Square and Cube Numbers

8a) The square numbers are 1, ,225…

e.g. 2

= × =9 2

= × = 49

b) The cube numbers are 1, , , , 125,…

e.g. 3

= × × =8 3

= × × = 125

e.g. 23 = 2 × 2 × 2 = 8 53 = 5 × 5 × 5 = 125

Order of Operations

BODMAS is a way of remembering the order in which operations are carried out.

9a) Brackets first: 3 × (4 + 5) = × =

b) Order - square or cube: 4 + 32 = + =

c) Division and Multiplication: 4 + 3 × 2 = + =

Addition and Subtraction: (as in examples above)

Division and multiplication are carried out in the order they are in the expression.

Addition and subtraction are carried out in the order they are in the expression.

Formal Methods

Use a written method to solve the following addition and subtraction calculations:

10a) 72 698 + 61 562 b) 84 935 - 12 423 c) 64 812 - 29 364

Use a written method to multiply up to 4-digit numbers by 1-digit numbers.

d) 27 × 4 e) 382 × 7 f) 2471 × 6

Page 6 of 37

8a) The square numbers are 1, ,225…

e.g. 2

= × =9 2

= × = 49

b) The cube numbers are 1, , , , 125,…

e.g. 3

= × × =8 3

= × × = 125

e.g. 23 = 2 × 2 × 2 = 8 53 = 5 × 5 × 5 = 125

Order of Operations

BODMAS is a way of remembering the order in which operations are carried out.

9a) Brackets first: 3 × (4 + 5) = × =

b) Order - square or cube: 4 + 32 = + =

c) Division and Multiplication: 4 + 3 × 2 = + =

Addition and Subtraction: (as in examples above)

Division and multiplication are carried out in the order they are in the expression.

Addition and subtraction are carried out in the order they are in the expression.

Formal Methods

Use a written method to solve the following addition and subtraction calculations:

10a) 72 698 + 61 562 b) 84 935 - 12 423 c) 64 812 - 29 364

Use a written method to multiply up to 4-digit numbers by 1-digit numbers.

d) 27 × 4 e) 382 × 7 f) 2471 × 6

Page 6 of 37

8.
Use a written method to multiply 2-digit numbers by 2-digit numbers.

g) 27 × 14 h) 14 × 23

Use short division for up to 4 digit numbers divided by one-digit numbers.

i) 76 ÷ 4 j) 487 ÷ 5

Use long division for up to 4 digit numbers divided by two-digit numbers.

Express remainders as whole numbers, fractions or decimals.

k) 516 ÷ 15

Solve Problems

Multi-step problems

11) 8451 people visit a cinema on one day. There are two films showing. 3549 adults

and 946 children see an adventure film, 1263 adults and a number of children see an

animation. How many more children see the animation than the adventure film?

a) 3549 + 1263 = adults

b) 8451 - 4812 = children

c) 3639 - 946 = children see the animation

d) 2693 - 946 = more children see the animation than the adventure film

Page 7 of 37

g) 27 × 14 h) 14 × 23

Use short division for up to 4 digit numbers divided by one-digit numbers.

i) 76 ÷ 4 j) 487 ÷ 5

Use long division for up to 4 digit numbers divided by two-digit numbers.

Express remainders as whole numbers, fractions or decimals.

k) 516 ÷ 15

Solve Problems

Multi-step problems

11) 8451 people visit a cinema on one day. There are two films showing. 3549 adults

and 946 children see an adventure film, 1263 adults and a number of children see an

animation. How many more children see the animation than the adventure film?

a) 3549 + 1263 = adults

b) 8451 - 4812 = children

c) 3639 - 946 = children see the animation

d) 2693 - 946 = more children see the animation than the adventure film

Page 7 of 37

9.
12a) Write the following numbers in each Venn Diagram:

2, 8, 5, 10, 3, 1, 9, 4, 6, 7

Prime Numbers Square Numbers Composite Numbers

b) Explain why a prime number will never be a square number.

c) Fill in the missing numbers:

× 3 = 45 or 56 ÷ = 14

Word Problems

A teacher has four new boxes of pencils, each with 12 pencils, and a tray with 37 pencils.

The teacher shares equally all the pencils between 5 tables. How many pencils does each

table receive?

13a) 12 × 4 = new pencils

b) 48 + 37 = pencils

c) 85 ÷ 5 = pencils per table

Solving Problems with Simple Fractions

14) 12 pizzas are cut into quarters. How many quarters of pizza will there be

altogether? .

Correspondence Problems

15) Jenna has 2 t-shirts and 4 pairs of shorts. How many possible combinations of t-shirts

and shorts does Jenna have? .

Using the Distributive Law

16) Multiplying a number by distributing it into a group of numbers added together.

For example:

39 × 7 = ×7+ × 7 = 210 + 63 = .

Page 8 of 37

2, 8, 5, 10, 3, 1, 9, 4, 6, 7

Prime Numbers Square Numbers Composite Numbers

b) Explain why a prime number will never be a square number.

c) Fill in the missing numbers:

× 3 = 45 or 56 ÷ = 14

Word Problems

A teacher has four new boxes of pencils, each with 12 pencils, and a tray with 37 pencils.

The teacher shares equally all the pencils between 5 tables. How many pencils does each

table receive?

13a) 12 × 4 = new pencils

b) 48 + 37 = pencils

c) 85 ÷ 5 = pencils per table

Solving Problems with Simple Fractions

14) 12 pizzas are cut into quarters. How many quarters of pizza will there be

altogether? .

Correspondence Problems

15) Jenna has 2 t-shirts and 4 pairs of shorts. How many possible combinations of t-shirts

and shorts does Jenna have? .

Using the Distributive Law

16) Multiplying a number by distributing it into a group of numbers added together.

For example:

39 × 7 = ×7+ × 7 = 210 + 63 = .

Page 8 of 37

10.
Fractions

1) Colour in the bar to show what fraction comes next in the sequence:

7 , 6 , 5 , 4 , ...

10 10 10 10

2) Colour in the grid to

show what fraction

comes next in

the sequence:

47 46 45 44

, , , ,

100 100 100 100 ...

Fraction of a Set of Marbles

5

3) Colour in of these marbles:

8

32 ÷ 8 = 4×5=

Equivalent Fractions

4a) Colour in the bars to represent the equivalent fractions:

3 6 12

4 = 8 = 16

Page 9 of 37

1) Colour in the bar to show what fraction comes next in the sequence:

7 , 6 , 5 , 4 , ...

10 10 10 10

2) Colour in the grid to

show what fraction

comes next in

the sequence:

47 46 45 44

, , , ,

100 100 100 100 ...

Fraction of a Set of Marbles

5

3) Colour in of these marbles:

8

32 ÷ 8 = 4×5=

Equivalent Fractions

4a) Colour in the bars to represent the equivalent fractions:

3 6 12

4 = 8 = 16

Page 9 of 37

11.
1

1 1

2 2

1 1 1 1

4 4 4 4

1 1 1 1 1 1 1 1

8 8 8 8 8 8 8 8

1

1 1 1

3 3 3

1 1 1 1 1 1

6 6 6 6 6 6

1 1 1 1 1 1 1 1 1 11 1

12 12 12 1212 12 12 12 12 12

12 12

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24

1

1 1 1 1 1

5 5 5 5 5

1 1 1 1 1 1 1 1 1 1

10 10 10 10 10 10 10 10 10 10

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20

3

b) Write 4 fractions that are equivalent to 4

=

c) Use common factors to simplify fractions:

9 3

15

= 5 9 and 15 have as a common factor.

Expressing Fractions with the Same Denominator

5) Use common multiples

4 3

5

and 8

is the smallest common multiple of 5 and 8

4 3

5

becomes 8

becomes

Page 10 of 37

1 1

2 2

1 1 1 1

4 4 4 4

1 1 1 1 1 1 1 1

8 8 8 8 8 8 8 8

1

1 1 1

3 3 3

1 1 1 1 1 1

6 6 6 6 6 6

1 1 1 1 1 1 1 1 1 11 1

12 12 12 1212 12 12 12 12 12

12 12

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24

1

1 1 1 1 1

5 5 5 5 5

1 1 1 1 1 1 1 1 1 1

10 10 10 10 10 10 10 10 10 10

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20

3

b) Write 4 fractions that are equivalent to 4

=

c) Use common factors to simplify fractions:

9 3

15

= 5 9 and 15 have as a common factor.

Expressing Fractions with the Same Denominator

5) Use common multiples

4 3

5

and 8

is the smallest common multiple of 5 and 8

4 3

5

becomes 8

becomes

Page 10 of 37

12.
Mixed Numbers and Improper Fractions

6a) Change this mixed number into an improper fraction:

2

13 =

b) Change this improper fraction into a mixed number:

14

3 =

Add and Subtract Fractions with the Same Denominator and with

Denominators that are Multiples, and with Different Denominators

and Mixed Numbers

7) Add or subtract the numerator, keeping the denominator the same. The answer can be

expressed as an equivalent fraction. Fill in the missing numbers and colour in the bar

to represent the fraction.

a) 1 3

b) 5 3

8

+ 8

= 8

= 8

- 8

= 8

=

If the denominators are different, convert the fractions to equivalent fractions with the same

denominator before adding or subtracting:

c) 1

+

3

= + =

4 8

4 3

d) 5 + 8 = + = =

Compare and Order

1 1 1 1

8a) Arrange these unit fractions from smallest to largest: 3 6 4 8

smallest largest

b) Use >, < or = to compare these fractions:

1 3 5 1

5 5 8 4

Page 11 of 37

6a) Change this mixed number into an improper fraction:

2

13 =

b) Change this improper fraction into a mixed number:

14

3 =

Add and Subtract Fractions with the Same Denominator and with

Denominators that are Multiples, and with Different Denominators

and Mixed Numbers

7) Add or subtract the numerator, keeping the denominator the same. The answer can be

expressed as an equivalent fraction. Fill in the missing numbers and colour in the bar

to represent the fraction.

a) 1 3

b) 5 3

8

+ 8

= 8

= 8

- 8

= 8

=

If the denominators are different, convert the fractions to equivalent fractions with the same

denominator before adding or subtracting:

c) 1

+

3

= + =

4 8

4 3

d) 5 + 8 = + = =

Compare and Order

1 1 1 1

8a) Arrange these unit fractions from smallest to largest: 3 6 4 8

smallest largest

b) Use >, < or = to compare these fractions:

1 3 5 1

5 5 8 4

Page 11 of 37

13.
Multiply Fractions

Multiply proper fractions and mixed numbers by whole numbers.

2

9a) Proper fractions: multiply the numerator by the whole number: 3

×5= =3

b) Mixed numbers: multiply the whole numbers and add the product of the fraction and

2

whole number: 2 3 × 3 = + = + =

Divide Fractions

10) Divide proper fractions by whole numbers – multiply the denominator by the

whole number:

1

4

÷2=

Decimal Equivalents

11a) Write the following fractions as decimals:

7 43

10

= 100 =

1 1 3

4 = 2 = 4 =

b) Write decimals as a fraction: 0.67 =

3

c) Calculate decimal fraction equivalents: 8 = because 3 ÷ 8 =

Decimal Place Value

Write the value of each digit in the number 0.492:

12a) 0.492 = zero ones + + +

Page 12 of 37

Multiply proper fractions and mixed numbers by whole numbers.

2

9a) Proper fractions: multiply the numerator by the whole number: 3

×5= =3

b) Mixed numbers: multiply the whole numbers and add the product of the fraction and

2

whole number: 2 3 × 3 = + = + =

Divide Fractions

10) Divide proper fractions by whole numbers – multiply the denominator by the

whole number:

1

4

÷2=

Decimal Equivalents

11a) Write the following fractions as decimals:

7 43

10

= 100 =

1 1 3

4 = 2 = 4 =

b) Write decimals as a fraction: 0.67 =

3

c) Calculate decimal fraction equivalents: 8 = because 3 ÷ 8 =

Decimal Place Value

Write the value of each digit in the number 0.492:

12a) 0.492 = zero ones + + +

Page 12 of 37

14.
Multiplication and Division

By 10, 100 and 1000:

13a) 0.2 × 10 = 2 ÷ 100 = 0.25 × 100 = 25 ÷ 1000 =

b) Multiply decimal numbers by whole numbers.

0.04 × 7 = 0.2 × 45 =

Rounding Decimals

When rounded to the nearest whole number:

14a) 0.5 rounds to

b) 2.35 rounds to

When rounded to one-decimal place:

c) 0.05 rounds to

d) 2.42 rounds to

Read, Write, Order and Compare Decimals

15a) 0.45 = ones, tenths and five .

b) Use >, < or = to compare these decimals’ to the second question in this section.

0.45 0.5 0.561 0.516

16a) % means out of .

b) 50% = = 41% =

Page 13 of 37

By 10, 100 and 1000:

13a) 0.2 × 10 = 2 ÷ 100 = 0.25 × 100 = 25 ÷ 1000 =

b) Multiply decimal numbers by whole numbers.

0.04 × 7 = 0.2 × 45 =

Rounding Decimals

When rounded to the nearest whole number:

14a) 0.5 rounds to

b) 2.35 rounds to

When rounded to one-decimal place:

c) 0.05 rounds to

d) 2.42 rounds to

Read, Write, Order and Compare Decimals

15a) 0.45 = ones, tenths and five .

b) Use >, < or = to compare these decimals’ to the second question in this section.

0.45 0.5 0.561 0.516

16a) % means out of .

b) 50% = = 41% =

Page 13 of 37

15.
Solve Problems

Adil wants to share his savings with his friends. He has £120. He gives ¼ to his friend Tommy

3

and 10 to Barney.

17a) How much money will they both receive?

b) How much money will Adil be left with?

Measure and Money Problems

18a) Ellie buys a new shirt for £4.75 and a pair of trousers for £3.50 in a sale. She pays

with a £10 note. What change will she receive?

b) A bag of potatoes weigh 2.45kg. How much will 4 bags weigh?

Decimal Problems to 3 Decimal Places

19a) A packet of sugar weighs 1.348kg. 3 kg is used to bake some cakes.

4

How much will the packet weigh now?

Knowing Percentage and Decimal Equivalents of 1 1 1 2 4 * *

, , , , , ,

2 4 5 5 5 10 25

20) Order the following from smallest to largest:

2

25%, 5 , 0.3

Page 14 of 37

Adil wants to share his savings with his friends. He has £120. He gives ¼ to his friend Tommy

3

and 10 to Barney.

17a) How much money will they both receive?

b) How much money will Adil be left with?

Measure and Money Problems

18a) Ellie buys a new shirt for £4.75 and a pair of trousers for £3.50 in a sale. She pays

with a £10 note. What change will she receive?

b) A bag of potatoes weigh 2.45kg. How much will 4 bags weigh?

Decimal Problems to 3 Decimal Places

19a) A packet of sugar weighs 1.348kg. 3 kg is used to bake some cakes.

4

How much will the packet weigh now?

Knowing Percentage and Decimal Equivalents of 1 1 1 2 4 * *

, , , , , ,

2 4 5 5 5 10 25

20) Order the following from smallest to largest:

2

25%, 5 , 0.3

Page 14 of 37

16.
Ratio and Proportion

Use Multiplication and Division Facts

1) 4 children share 6 pizzas. If 2 more children join the group and each child is to have

the same amount of pizza, how many more pizzas are needed?

2) Circle which is greater: 15% of 2 litres or 50% of 500ml

Scaled Shapes

3) The length and width of rectangle A are increased by a scale factor of 3 to make

rectangle B. What are the new dimensions of rectangle B?

4cm

A 2cm B

Use Fractions and Multiples

3

4) A child has read 50 pages of a book and has to read.

5

How many pages are there left to read?

2

a) 5

of the book has been read which is pages

1

b) of the book is pages

5

3

c) of the book is pages. There are pages left to read.

5

Page 15 of 37

Use Multiplication and Division Facts

1) 4 children share 6 pizzas. If 2 more children join the group and each child is to have

the same amount of pizza, how many more pizzas are needed?

2) Circle which is greater: 15% of 2 litres or 50% of 500ml

Scaled Shapes

3) The length and width of rectangle A are increased by a scale factor of 3 to make

rectangle B. What are the new dimensions of rectangle B?

4cm

A 2cm B

Use Fractions and Multiples

3

4) A child has read 50 pages of a book and has to read.

5

How many pages are there left to read?

2

a) 5

of the book has been read which is pages

1

b) of the book is pages

5

3

c) of the book is pages. There are pages left to read.

5

Page 15 of 37

17.
Algebra

Formulae Formulae are used in mathematics and

1a) 2s + 4 = t, if s = 5, what is t? science:

t= × + = Area of a rectangle:

a = lw (a = area, l = length and w = width)

Perimeter of a rectangle:

p = 2(l + w) (p = perimeter)

b) What is the area and perimeter of this rectangle?

5cm

2cm

Express missing number problems algebraically:

2a) If a number (g) is 12 more than a number (h):

g= + or h = –

a) A locksmith charges £15 callout and £20 per hour for any work. What formulae would

calculate his charge for h number of hours?

.

This linear sequence starts with 3 and each step is 4: 3, 7, 11, 15…

3) The 1st term is 4 × 1 – 1 = 3, the 2nd term is 4 × 2 – 1 = 7, the 3rd is 4 × 3 – 1 = 11…

therefore the nth term is .

4) Find possible pairs of numbers for a and b in 3a + b = 12.

5) The total of two numbers is 15. Both numbers are between 5 and 10.

Find all the possible combinations.

Page 16 of 37

Formulae Formulae are used in mathematics and

1a) 2s + 4 = t, if s = 5, what is t? science:

t= × + = Area of a rectangle:

a = lw (a = area, l = length and w = width)

Perimeter of a rectangle:

p = 2(l + w) (p = perimeter)

b) What is the area and perimeter of this rectangle?

5cm

2cm

Express missing number problems algebraically:

2a) If a number (g) is 12 more than a number (h):

g= + or h = –

a) A locksmith charges £15 callout and £20 per hour for any work. What formulae would

calculate his charge for h number of hours?

.

This linear sequence starts with 3 and each step is 4: 3, 7, 11, 15…

3) The 1st term is 4 × 1 – 1 = 3, the 2nd term is 4 × 2 – 1 = 7, the 3rd is 4 × 3 – 1 = 11…

therefore the nth term is .

4) Find possible pairs of numbers for a and b in 3a + b = 12.

5) The total of two numbers is 15. Both numbers are between 5 and 10.

Find all the possible combinations.

Page 16 of 37

18.
Measurement

Estimate, Measure, Compare, Add and Subtract

Measure and draw lines using a ruler in centimetres (cm) or millimetres (mm).

Lengths (mm/cm/m)

1a) Measure this line in cm.

b) Draw a line that is 12.5mm long.

Mass (g/kg)

Measure the mass of objects using different scales.

4a) 3 apples weigh 435g. One is eaten, and the 2 remaining apples weigh 285g.

b) What is the mass of the eaten apple?

Capacity (ml/l)

5) Circle which jug has more water.

250ml 0.3l

Convert between units

6a) Length: 1 km = m, 1m = cm or mm, 1cm = mm

b) Mass: 1kg = g

e)

c) Capacity/ Volume: 1l = ml days hath September,

April, June and November.

d) Time: 1 year = days

(leap year days), All the rest have ,

1 week = days, Excepting February alone

1 day = hours, Which only has but days clear

1 hour = minutes,

And in each leap year.

1 minute = seconds.

Page 17 of 37

Estimate, Measure, Compare, Add and Subtract

Measure and draw lines using a ruler in centimetres (cm) or millimetres (mm).

Lengths (mm/cm/m)

1a) Measure this line in cm.

b) Draw a line that is 12.5mm long.

Mass (g/kg)

Measure the mass of objects using different scales.

4a) 3 apples weigh 435g. One is eaten, and the 2 remaining apples weigh 285g.

b) What is the mass of the eaten apple?

Capacity (ml/l)

5) Circle which jug has more water.

250ml 0.3l

Convert between units

6a) Length: 1 km = m, 1m = cm or mm, 1cm = mm

b) Mass: 1kg = g

e)

c) Capacity/ Volume: 1l = ml days hath September,

April, June and November.

d) Time: 1 year = days

(leap year days), All the rest have ,

1 week = days, Excepting February alone

1 day = hours, Which only has but days clear

1 hour = minutes,

And in each leap year.

1 minute = seconds.

Page 17 of 37

19.
Convert between metric and imperial units

7a) 1 inch ≈ cm 5 miles ≈ km

1kg ≈ (pounds) 1 litre ≈ pints

b) A road sign says Sheffield 45 miles. How many kilometres is it to Sheffield?

km

Perimeter, Area and Volume

The perimeter is the measurement around the edge of a shape.

8a) The sides of this rectangle are 8cm and 3cm, so the perimeter is cm.

b) Measure and calculate the perimeter of rectilinear shapes (including squares).

12cm

3cm

Perimeter = cm.

6cm

5cm

Page 18 of 37

7a) 1 inch ≈ cm 5 miles ≈ km

1kg ≈ (pounds) 1 litre ≈ pints

b) A road sign says Sheffield 45 miles. How many kilometres is it to Sheffield?

km

Perimeter, Area and Volume

The perimeter is the measurement around the edge of a shape.

8a) The sides of this rectangle are 8cm and 3cm, so the perimeter is cm.

b) Measure and calculate the perimeter of rectilinear shapes (including squares).

12cm

3cm

Perimeter = cm.

6cm

5cm

Page 18 of 37

20.
9a) Find the area of rectilinear shapes by counting squares.

Area = cm2

b) Calculate the area of rectangles: multiply the length of two adjacent sides.

3cm Area = 8cm × 3cm = cm2

8cm

c) Estimate the area of irregular shapes by counting the whole squares and the squares

with more than half included in the shape:

1 square = 1cm2 Area = cm2

Page 19 of 37

Area = cm2

b) Calculate the area of rectangles: multiply the length of two adjacent sides.

3cm Area = 8cm × 3cm = cm2

8cm

c) Estimate the area of irregular shapes by counting the whole squares and the squares

with more than half included in the shape:

1 square = 1cm2 Area = cm2

Page 19 of 37

21.
Shapes with the same area can have different perimeters.

4cm

6cm

A 3cm B 2cm

d) Find the area and perimeter of these rectangles. What do you notice?

The area of a triangle is based on it being half of a rectangle that includes the triangle.

h

b

e) The area of a triangle is of the base (b) × the height (h) or bh

A similar idea is used to find the area of a parallelogram. Cut a triangle off one end

and move to the other and the parallelogram becomes a rectangle.

f) The area of a parallelogram is the × the height (h) or .

Add and subtract giving change.

10) Jude buys a bag of apples for £1.25 and a bag of oranges for £2.15. He pays with a £5

note. How much change will he be given?

Page 20 of 37

4cm

6cm

A 3cm B 2cm

d) Find the area and perimeter of these rectangles. What do you notice?

The area of a triangle is based on it being half of a rectangle that includes the triangle.

h

b

e) The area of a triangle is of the base (b) × the height (h) or bh

A similar idea is used to find the area of a parallelogram. Cut a triangle off one end

and move to the other and the parallelogram becomes a rectangle.

f) The area of a parallelogram is the × the height (h) or .

Add and subtract giving change.

10) Jude buys a bag of apples for £1.25 and a bag of oranges for £2.15. He pays with a £5

note. How much change will he be given?

Page 20 of 37

22.
11a) Match the analogue clock to the digital clock that is showing the same time:

04 50

08 45

1 2 1 0

03 20

06 1 5

b) A film lasts 136 minutes. How long is the film in hours and minutes?

hours and minutes

c) Convert the following times from 12-hour to 24-hour clock and vice versa:

3:45 p.m. = 11:20 a.m. =

15:55 = 06:10 =

Solve Problems

12a) 2 equal bottles of water contain 500ml of drink. How many litres will 7 bottles hold?

b) A 6.5kg bag of soil is divided into 20 pots equally. Each pot needs 0.5kg. How much

more does each pot need?

÷ =

– = kg is needed by each pot

Page 21 of 37

04 50

08 45

1 2 1 0

03 20

06 1 5

b) A film lasts 136 minutes. How long is the film in hours and minutes?

hours and minutes

c) Convert the following times from 12-hour to 24-hour clock and vice versa:

3:45 p.m. = 11:20 a.m. =

15:55 = 06:10 =

Solve Problems

12a) 2 equal bottles of water contain 500ml of drink. How many litres will 7 bottles hold?

b) A 6.5kg bag of soil is divided into 20 pots equally. Each pot needs 0.5kg. How much

more does each pot need?

÷ =

– = kg is needed by each pot

Page 21 of 37

23.
Geometry – Shape

2D Shapes

1a) Main shapes: circle, triangle, quadrilateral, square, rectangle, rhombus, parallelogram,

pentagon, hexagon, octagon, decagon. Identify each one:

Draw 2D shapes using given dimensions and angles.

b) Draw a square with sides 5cm.

c) Draw an isosceles triangle with one side of 5cm and 2 sides of 7cm.

Page 22 of 37

2D Shapes

1a) Main shapes: circle, triangle, quadrilateral, square, rectangle, rhombus, parallelogram,

pentagon, hexagon, octagon, decagon. Identify each one:

Draw 2D shapes using given dimensions and angles.

b) Draw a square with sides 5cm.

c) Draw an isosceles triangle with one side of 5cm and 2 sides of 7cm.

Page 22 of 37

24.
Compare and classify shapes

2a) Draw the shapes that belong within the venn diagram:

Has at least one

Has 4 sides

right angle

Draw a line to the triangle being described:

b) Equilateral (all sides and angles equal)

c) Isosceles (2 sides and angles equal)

d) Scalene (no sides and angles equal)

e) Right-angled triangle (one angle a right angle)

Page 23 of 37

2a) Draw the shapes that belong within the venn diagram:

Has at least one

Has 4 sides

right angle

Draw a line to the triangle being described:

b) Equilateral (all sides and angles equal)

c) Isosceles (2 sides and angles equal)

d) Scalene (no sides and angles equal)

e) Right-angled triangle (one angle a right angle)

Page 23 of 37

25.
3D Shapes

3a) Main shapes: sphere, cylinder, cube, cuboid, tetrahedron, square-based pyramid,

triangular prism, pentagonal prism, hexagonal prism. Identify each one:

Recognise, describe and build simple 3D shapes, including making nets.

b) What shape is made from this net?

4a) An angle measures a . d) An angle is less than

a right angle (90°).

b) A angle is the corner

of a square.

e) An angle is between a

right angle and a straight line.

c) 2 right angles make a line.

Page 24 of 37

3a) Main shapes: sphere, cylinder, cube, cuboid, tetrahedron, square-based pyramid,

triangular prism, pentagonal prism, hexagonal prism. Identify each one:

Recognise, describe and build simple 3D shapes, including making nets.

b) What shape is made from this net?

4a) An angle measures a . d) An angle is less than

a right angle (90°).

b) A angle is the corner

of a square.

e) An angle is between a

right angle and a straight line.

c) 2 right angles make a line.

Page 24 of 37

26.
Draw and Measure Angles

Read the scale

One of the

on the other line

lines must

round from 0.

be on the 0.

5a) The angle is: .

The angles at a point and whole turn total 360° (four right angles).

b) Fill in the missing numbers: c) Angles at a point on a line total 180°.

105°

110° 105°

°

° 25°

d) One right angle = °

e) Two right angles = °

f) Three right angles = °

Page 25 of 37

Read the scale

One of the

on the other line

lines must

round from 0.

be on the 0.

5a) The angle is: .

The angles at a point and whole turn total 360° (four right angles).

b) Fill in the missing numbers: c) Angles at a point on a line total 180°.

105°

110° 105°

°

° 25°

d) One right angle = °

e) Two right angles = °

f) Three right angles = °

Page 25 of 37

27.
Angles in a triangle add up to 180°.

a

35°

6a) What is the size of angle a? . 80°

Angles in a quadrilateral add up to 360°.

105° b

b) What is the size of angle b, c and d?

, , .

d c

7) Draw the following lines:

a) Horizontal

b) Vertical

c) Parallel Lines

d) Perpendicular lines (at a right angle)

Page 26 of 37

a

35°

6a) What is the size of angle a? . 80°

Angles in a quadrilateral add up to 360°.

105° b

b) What is the size of angle b, c and d?

, , .

d c

7) Draw the following lines:

a) Horizontal

b) Vertical

c) Parallel Lines

d) Perpendicular lines (at a right angle)

Page 26 of 37

28.
8) Identify the lines of symmetry with a dotted line:

9) Complete two examples of a symmetrical figure:

Page 27 of 37

9) Complete two examples of a symmetrical figure:

Page 27 of 37

29.
Regular and Irregular Polygons

Regular polygons have equal sides and equal angles.

10a) Identify the following:

Irregular polygons do

not have equal sides and

angles. They may have

equal angles or equal

sides but not both.

A rhombus has equal

sides and a rectangle has

equal angles but they are

not regular (unless they

are a square).

b) Explain why these shapes are regular polygons.

72° 60° 45°

11a) Identify the main parts of a circle:

b) The is the distance around the perimeter of the circle.

c) The is the distance from the centre to the circumference.

d) The is the distance from the circumference to the circumference

on the other side through the centre of the circle.

e) The is double the radius.

Page 28 of 37

Regular polygons have equal sides and equal angles.

10a) Identify the following:

Irregular polygons do

not have equal sides and

angles. They may have

equal angles or equal

sides but not both.

A rhombus has equal

sides and a rectangle has

equal angles but they are

not regular (unless they

are a square).

b) Explain why these shapes are regular polygons.

72° 60° 45°

11a) Identify the main parts of a circle:

b) The is the distance around the perimeter of the circle.

c) The is the distance from the centre to the circumference.

d) The is the distance from the circumference to the circumference

on the other side through the centre of the circle.

e) The is double the radius.

Page 28 of 37

30.
Geometry – Position and Direction

Coordinates in all four quadrants.

y

1a) The coordinates are: 8

7 A

A( , )

6

B( , ) 5

4

C( , )

3

B 2

1

x

-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

-1

-2

-3

-4

-5

-6

C -7

-8

Some coordinates grids are drawn without squares.

b) Work out the coordinates of points a and b.

c) Compare the coordinates of the 2 triangles to find the answer.

y

a

a=( , )

b (0,4) b=( , )

x

(-4,-2)

(-6,-5) (-2,-5)

* not to scale

Page 29 of 37

Coordinates in all four quadrants.

y

1a) The coordinates are: 8

7 A

A( , )

6

B( , ) 5

4

C( , )

3

B 2

1

x

-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

-1

-2

-3

-4

-5

-6

C -7

-8

Some coordinates grids are drawn without squares.

b) Work out the coordinates of points a and b.

c) Compare the coordinates of the 2 triangles to find the answer.

y

a

a=( , )

b (0,4) b=( , )

x

(-4,-2)

(-6,-5) (-2,-5)

* not to scale

Page 29 of 37

31.
Translate shapes on a coordinates grid.

2) Translate this triangle so point A translates to point B.

y

8

7 B

6

5

4

3

2

1

x

-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

-1

A -2

-3

-4

-5

-6

-7

-8

Translations can also be on blank grids as in the coordinates section above.

Page 30 of 37

2) Translate this triangle so point A translates to point B.

y

8

7 B

6

5

4

3

2

1

x

-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

-1

A -2

-3

-4

-5

-6

-7

-8

Translations can also be on blank grids as in the coordinates section above.

Page 30 of 37

32.
Reflection

Reflect shapes on a coordinates grid.

3a) Reflect this triangle about the y-axis.

8

7

6

5

4

3

2

1

x

-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

-1

-2

-3

-4

-5

-6

-7

-8

y

Reflections can also be on blank grids as in the coordinates section above.

Page 31 of 37

Reflect shapes on a coordinates grid.

3a) Reflect this triangle about the y-axis.

8

7

6

5

4

3

2

1

x

-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

-1

-2

-3

-4

-5

-6

-7

-8

y

Reflections can also be on blank grids as in the coordinates section above.

Page 31 of 37

33.
Statistics

Present data in these graphs and tables and solve problems:

Favourite Colour

1) How many children were asked to vote for their favourite colour?

Bar Charts

2a) How many more children chose cheese and onion as their favourite crisps than ready

salted?

Page 32 of 37

Present data in these graphs and tables and solve problems:

Favourite Colour

1) How many children were asked to vote for their favourite colour?

Bar Charts

2a) How many more children chose cheese and onion as their favourite crisps than ready

salted?

Page 32 of 37

34.
Continuous data can have any value – usually a measurement.

25

The Height of Children

20

Number of children

15

10

5

0

80cm -89cm

90cm -99cm

110cm -119cm

120cm -129cm

100cm -109cm

Height in cm

b) How many children are 1m or taller?

Here is a table showing the number of chocolate bars sold to customers in a shop over 4 days.

Monday Tuesday Wednesday Thursday

Saturn 2 1 3 4

Twin 0 2 2 3

Stars 5 3 2 0

Cluster 2 2 2 2

Treasure 1 3 5 0

Tiger 6 3 4 1

Plimmy 1 3 2 2

3) Which chocolate bar is the most popular?

Page 33 of 37

25

The Height of Children

20

Number of children

15

10

5

0

80cm -89cm

90cm -99cm

110cm -119cm

120cm -129cm

100cm -109cm

Height in cm

b) How many children are 1m or taller?

Here is a table showing the number of chocolate bars sold to customers in a shop over 4 days.

Monday Tuesday Wednesday Thursday

Saturn 2 1 3 4

Twin 0 2 2 3

Stars 5 3 2 0

Cluster 2 2 2 2

Treasure 1 3 5 0

Tiger 6 3 4 1

Plimmy 1 3 2 2

3) Which chocolate bar is the most popular?

Page 33 of 37

35.
Time Graphs

Time graphs show the changing of data over time. These often take the form of line graphs

but can also be a bar chart.

Number of Children Who Have a School Meal

4) How many school meals were served during the week?

Line Graphs

Length of a Shadow

09:00 10:00 11:00 12:00 13:00 14:00 15:00

5a) At which time of day was the shadow at its shortest?

b) How long was the shadow at 15:00?

Page 34 of 37

Time graphs show the changing of data over time. These often take the form of line graphs

but can also be a bar chart.

Number of Children Who Have a School Meal

4) How many school meals were served during the week?

Line Graphs

Length of a Shadow

09:00 10:00 11:00 12:00 13:00 14:00 15:00

5a) At which time of day was the shadow at its shortest?

b) How long was the shadow at 15:00?

Page 34 of 37

36.
Train timetable from London to Newcastle

Destination Journey A Journey B Journey C

London 10:20 11:30 16:40

Derby 12:20 18:00

Sheffield 12:40 13:10 18:30

Hull 13:20 13:55 19:15

Newcastle 14:25 14:40

6) Which train takes the least time to get from London to Hull?

Pie Charts

Pie charts show data by dividing a circle to represent the different proportions of the data.

A class of children chose their favourite flavour of crisps. Here is a pie chart of the results.

Salt and Vinegar

Cheese and Onion

Ready Salted

In questions about pie charts children have to use the proportion of

the pie to work out answers.

In this pie chart, 20 children are asked how they travel to school.

7) Estimate how many children travelled by bus.

8a) The mean of a set of data is equivalent to sharing the data out .

b) If 4 test scores are 3, 5, 6, 8, the mean is found by adding the data (3 + 5 + 6 + 8 = )

and then sharing between the 4 scores by dividing by 4 ( ÷4= ).

c) What is the mean of 15, 17, 20, 24, 24?

Page 35 of 37

Destination Journey A Journey B Journey C

London 10:20 11:30 16:40

Derby 12:20 18:00

Sheffield 12:40 13:10 18:30

Hull 13:20 13:55 19:15

Newcastle 14:25 14:40

6) Which train takes the least time to get from London to Hull?

Pie Charts

Pie charts show data by dividing a circle to represent the different proportions of the data.

A class of children chose their favourite flavour of crisps. Here is a pie chart of the results.

Salt and Vinegar

Cheese and Onion

Ready Salted

In questions about pie charts children have to use the proportion of

the pie to work out answers.

In this pie chart, 20 children are asked how they travel to school.

7) Estimate how many children travelled by bus.

8a) The mean of a set of data is equivalent to sharing the data out .

b) If 4 test scores are 3, 5, 6, 8, the mean is found by adding the data (3 + 5 + 6 + 8 = )

and then sharing between the 4 scores by dividing by 4 ( ÷4= ).

c) What is the mean of 15, 17, 20, 24, 24?

Page 35 of 37

37.
Important Vocabulary

Some vocabulary is also described within the booklet. Fill in the missing information:

Vocabulary Meaning

Flat shapes with no thickness. In theory a 2D shape cannot be picked up,

2D shapes but in practice shapes made of paper are counted as 2D.

(A list of shapes is included in the section on shape.)

A shape with 3 dimensions that can be picked up.

3D shapes

(A list of shapes is included in the section on shape.)

Algebra

Analogue

Area The amount of space taken up by a shape.

The working out of an answer using addition, subtraction, multiplication

or division.

Capacity

The answer is the same no matter which way the calculation is

Commutativity

completed: e.g. 2 + 4 = 4 + 2 or 2 × 4 = 4 × 2.

A number that has more than 2 factors.

(1 is not a composite number because it only has 1 factor.)

Cube number The result of multiplying a whole number by itself twice: e.g. 2 × 2 × 2 = 8

Denominator

A single symbol used to make a numeral: 7

(All numbers are made from the ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0.)

Digital A clock using digits to tell the time.

Discrete

A statement where the value of each mathematical expression is equal:

e.g. 3 + 4 = 7

Equivalent A fraction which has the same value but is divided into a different

1 2

fraction number of parts: e.g. 2 = 4

A factor of a number is a number into which the number can be divided

Factor

with no remainders: e.g. the factors of 8 are 1, 2, 4, and 8.

Factor pairs are 2 factors that are multiplied together to make the

number: e.g. the factor pairs of 8 are 1 and 8, 2 and 4.

A number expressed as the number of parts into which the whole has

Fraction 3

been divided: e.g 4 represents 3 parts out of 4.

Page 36 of 37

Some vocabulary is also described within the booklet. Fill in the missing information:

Vocabulary Meaning

Flat shapes with no thickness. In theory a 2D shape cannot be picked up,

2D shapes but in practice shapes made of paper are counted as 2D.

(A list of shapes is included in the section on shape.)

A shape with 3 dimensions that can be picked up.

3D shapes

(A list of shapes is included in the section on shape.)

Algebra

Analogue

Area The amount of space taken up by a shape.

The working out of an answer using addition, subtraction, multiplication

or division.

Capacity

The answer is the same no matter which way the calculation is

Commutativity

completed: e.g. 2 + 4 = 4 + 2 or 2 × 4 = 4 × 2.

A number that has more than 2 factors.

(1 is not a composite number because it only has 1 factor.)

Cube number The result of multiplying a whole number by itself twice: e.g. 2 × 2 × 2 = 8

Denominator

A single symbol used to make a numeral: 7

(All numbers are made from the ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0.)

Digital A clock using digits to tell the time.

Discrete

A statement where the value of each mathematical expression is equal:

e.g. 3 + 4 = 7

Equivalent A fraction which has the same value but is divided into a different

1 2

fraction number of parts: e.g. 2 = 4

A factor of a number is a number into which the number can be divided

Factor

with no remainders: e.g. the factors of 8 are 1, 2, 4, and 8.

Factor pairs are 2 factors that are multiplied together to make the

number: e.g. the factor pairs of 8 are 1 and 8, 2 and 4.

A number expressed as the number of parts into which the whole has

Fraction 3

been divided: e.g 4 represents 3 parts out of 4.

Page 36 of 37

38.
9

A fraction where the numerator is larger than the denominator: e.g 2

A whole number with no parts: e.g. 5, 18, 109.

A whole number with no fraction or decimal part: e.g. 6 or 57.

An inverse operation is the opposite or reverse of an operation: e.g. the

Inverse

inverse of 6 – 4 = 2 is 2 + 4 = 6 or the inverse of 6 ÷ 3 = 2 is 2 × 3 = 6.

Often known as weight – how much matter is in an object.

1

Mixed number A whole number and a proper fraction: e.g. 4 2

A symbol, symbols, word or words that stand for a number: 37 or thirty-

Numeral

seven.

Numerator The top part of a fraction.

Perimeter

Place value The value of each digit in any number: In 27 the 2 represents 2 tens.

A 2D shape with any number of sides.

Prime factor A factor which is a prime number: e.g. 3 is a prime factor of 12.

Prime Number

1

Proper fraction A fraction where the numerator is smaller than the denominator: e.g 2

A quarter of the space represented by coordinates, bordered by

the x and y axes.

Quadrilateral Any four sided shape.

A shape with all angles as right angles

Rectilinear

(the right angle can be inside or outside the shape).

The mathematical relationship between different measurements or

Scale

number of objects.

Square number The result of multiplying a whole number by itself: e.g. 2 × 2 = 4

Multiplying 2 numbers by a number and adding, gives the same answer

as multiplying the sum of the 2 numbers by the other number:

e.g. 4 × (3 + 2) = 4 × 3 + 4 × 2.

The movement of a shape without rotation or reflection.

Volume

Mass is measured by how much something weighs, but this can change

in different locations.

Page 37 of 37

A fraction where the numerator is larger than the denominator: e.g 2

A whole number with no parts: e.g. 5, 18, 109.

A whole number with no fraction or decimal part: e.g. 6 or 57.

An inverse operation is the opposite or reverse of an operation: e.g. the

Inverse

inverse of 6 – 4 = 2 is 2 + 4 = 6 or the inverse of 6 ÷ 3 = 2 is 2 × 3 = 6.

Often known as weight – how much matter is in an object.

1

Mixed number A whole number and a proper fraction: e.g. 4 2

A symbol, symbols, word or words that stand for a number: 37 or thirty-

Numeral

seven.

Numerator The top part of a fraction.

Perimeter

Place value The value of each digit in any number: In 27 the 2 represents 2 tens.

A 2D shape with any number of sides.

Prime factor A factor which is a prime number: e.g. 3 is a prime factor of 12.

Prime Number

1

Proper fraction A fraction where the numerator is smaller than the denominator: e.g 2

A quarter of the space represented by coordinates, bordered by

the x and y axes.

Quadrilateral Any four sided shape.

A shape with all angles as right angles

Rectilinear

(the right angle can be inside or outside the shape).

The mathematical relationship between different measurements or

Scale

number of objects.

Square number The result of multiplying a whole number by itself: e.g. 2 × 2 = 4

Multiplying 2 numbers by a number and adding, gives the same answer

as multiplying the sum of the 2 numbers by the other number:

e.g. 4 × (3 + 2) = 4 × 3 + 4 × 2.

The movement of a shape without rotation or reflection.

Volume

Mass is measured by how much something weighs, but this can change

in different locations.

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