5 Minute Maths Mastery - Year 6

5 Minute Maths Mastery 5

8

7 %

3

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Chief editor: Zhou Jieying Consultant: Fan Lianghuo

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Year

6 26/04/2019 15:04

CONTENTS How to use this book ...........................................................................................................................4 Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Test 7 Test 8 Test 9 Test 10 Test 11 Test 12 Test 13 Test 14 Test 15 Test 16 Test 17 Test 18 Test 19 Test 20 Test 21 Test 22 Test 23 Test 24 Test 25 Test 26 Test 27 Test 28 Test 29 Test 30 Test 31 Test 32 Test 33 Test 34 Test 35 Test 36 Test 37 Test 38 Test 39 Test 40

2

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Knowing large numbers (1) ...................................................................................................5 Knowing large numbers (2) ...................................................................................................6 Rounding of large numbers ..................................................................................................7 Multiplying four-digit numbers by one or two-digit numbers ..............................................8 Dividing four-digit numbers by a one-digit number..............................................................9 Dividing four-digit numbers by a two-digit number............................................................10 Order of operations (1) ......................................................................................................11 Order of operations (2) .......................................................................................................12 Order of operations (3) .......................................................................................................13 Numbers and operations (1) ...............................................................................................14 Numbers and operations (2) ...............................................................................................15 Geometry and measurement (1) .........................................................................................16 Geometry and measurement (2) ........................................................................................17 Geometry and measurement (3) ........................................................................................18 Fractions and division ........................................................................................................19 Basic properties of fractions (1) ........................................................................................20 Basic properties of fractions (2) ........................................................................................21 Basic properties of fractions (3) ........................................................................................22 Basic properties of fractions (4) ........................................................................................23 Basic properties of fractions (5) .........................................................................................24 Basic properties of fractions (6) ........................................................................................25 Comparison of fractions (1) ................................................................................................26 Comparison of fractions (2) ................................................................................................27 Addition and subtraction of fractions (1) ............................................................................28 Addition and subtraction of fractions (2) ............................................................................29 Addition and subtraction of fractions (3) ............................................................................30 Addition and subtraction of fractions (4) ............................................................................31 Addition and subtraction of fractions (5) ............................................................................32 Addition and subtraction of fractions (6) ............................................................................33 Multiplication of fractions (1) ..............................................................................................34 Multiplication of fractions (2) ..............................................................................................35 More fractions and division ................................................................................................36 Dividing fractions by whole numbers (1) ............................................................................37 Dividing fractions by whole numbers (2) ............................................................................38 Addition and subtraction of decimals (1)............................................................................39 Addition and subtraction of decimals (2) ...........................................................................40 Addition and subtraction of decimals (3)............................................................................41 Multiplying decimal numbers by whole numbers (1) .........................................................42 Multiplying decimal numbers by whole numbers (2) .........................................................43 Addition, subtraction and multiplication with decimals .....................................................44

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Test 41 Test 42 Test 43 Test 44 Test 45 Test 46 Test 47 Test 48 Test 49 Test 50 Test 51 Test 52 Test 53 Test 54 Test 55 Test 56 Test 57 Test 58 Test 59 Test 60 Test 61 Test 62 Test 63 Test 64 Test 65 Test 66 Test 67 Test 68 Test 69 Test 70 Test 71 Test 72 Test 73 Test 74 Test 75 Test 76 Test 77 Test 78 Test 79 Test 80

Division of decimal numbers by whole numbers (1) ..........................................................45 Division of decimal numbers by whole numbers (2) ..........................................................46 Division of decimal numbers by whole numbers (3) ...........................................................47 Division of decimal numbers by whole numbers (4) ..........................................................48 Division of decimal numbers by whole numbers (5) ..........................................................49 Multiplication and division of decimals (1) ........................................................................50 Multiplication and division of decimals (2) .........................................................................51 Operations of decimals (1) ................................................................................................52 Operations of decimals (2) .................................................................................................53 Operations of decimals (3) .................................................................................................54 Converting between fractions and decimals (1) .................................................................55 Converting between fractions and decimals (2) .................................................................56 Mixed operations of fractions and decimals (1) .................................................................57 Mixed operations of fractions and decimals (2) .................................................................58 Mixed operations of fractions, decimals and whole numbers (1).......................................59 Mixed operations of fractions, decimals and whole numbers (2).......................................60 Mixed operations of fractions, decimals and whole numbers (3).......................................61 Using letters to represent numbers (1) ...............................................................................62 Using letters to represent numbers (2) ..............................................................................63 Equations and algebra .......................................................................................................64 Simple equations (1) ...........................................................................................................65 Simple equations (2) ...........................................................................................................66 Simple equations (3) ...........................................................................................................67 Simple equations (4) ...........................................................................................................68 Simple equations (5) ..........................................................................................................69 Simple equations (6) ...........................................................................................................70 Ratio (1) ..............................................................................................................................71 Ratio (2) ..............................................................................................................................72 Ratio (3) ..............................................................................................................................73 Application of percentages (1) ...........................................................................................74 Application of percentages (2)............................................................................................75 Calculating the mean (1) .....................................................................................................76 Calculating the mean (2) ....................................................................................................77 Calculating the mean (3) ....................................................................................................78 Area of a parallelogram (1) ................................................................................................79 Area of a parallelogram (2) ................................................................................................80 Area of a triangle (1) ...........................................................................................................81 Area of a triangle (2) ...........................................................................................................82 Nets of 3-D shapes (1)........................................................................................................83 Nets of 3-D shapes (2)........................................................................................................84

Answers ............................................................................................................................................85

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26/04/19 3:37 PM

Date:

Knowing large numbers (1)

Day of Week:

STEP 1

1

min

1

Start the timer

Warm-up

Fill in the missing numbers. The first one has been done for you.

5 342 475 =

5 000 000

+

300 000

+

40 000

+

+

2000

400

+

70

+

3 571 596 =

+

+

+

+

+

+

9 436 034 =

+

+

+

+

+

+

6 993 905 =

+

+

+

+

+

+

2 285 439 =

+

+

+

+

+

+

STEP 2

2.5 min

5

Start the timer

Rapid calculation

Complete the table.

Description of number

Number in digits

3 millions, 4 hundred thousands, 2 ten thousands, 3 thousands, 7 hundreds and 4 ones 7 millions, 2 hundred thousands, 9 ten thousands, 3 thousands, 8 hundreds, 6 tens and 8 ones 9 millions, 3 hundred thousands, 7 ten thousands, 9 thousands and 2 tens 5 millions, 2 ten thousands, 8 thousands, 3 hundreds and 9 ones 4 millions, 6 hundred thousands, 3 thousands, 1 hundred and 8 ones 1 million, 7 thousands and 4 ones

STEP 3

1.5 min

Start the timer

Challenge

Complete the table.

Description of number

Number in digits

Read as

9 millions and 378 thousands 8 millions, 52 ten thousands and 19 ones 68 hundred thousands, 7 thousands and 39 tens

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03/05/2019 12:45

Basic properties of fractions (2)

Date: Day of Week:

STEP 1

1

min

17

Start the timer

Warm-up

Fully simplify the fractions.

4 = 8

10 = 15

8 = 12

15 = 20

6 = 15

30 = 45

20 = 60

18 = 24

STEP 2

2.5 min

Start the timer

Rapid calculation

Fully simplify the fractions.

15 = 36

28 = 42

42 = 56

9 = 15

24 = 30

10 = 30

36 = 42

20 = 35

24 = 36

19 = 38

24 = 72

12 = 20

14 = 42

18 = 20

18 = 51

18 = 12

10 = 25

16 = 24

STEP 3

1.5 min

Start the timer

Challenge

Write each division as a fraction and then simplify fully.

3÷9=

=

12 ÷ 18 =

=

35 ÷ 21 =

=

42 ÷ 36 =

=

12 ÷ 36 =

=

21 ÷ 14 =

=

36 ÷ 24 =

=

28 ÷ 35 =

=

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min

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21

26/04/19 3:38 PM

Comparison of fractions (1)

22

STEP 1

1

min

Date: Day of Week: Start the timer

Warm-up

1 , test whether the denominator is greater than twice 2 1 3 1 3 the numerator. If it is, the fraction is less than , e.g. ; if it is not, it is greater than , e.g. .

2 7 2 5 To decide whether a fraction is less than

Fill in the boxes with >, < or =.

3

12 4

4 5

5 6

3 8

5 16

1.5

3 4

1 2

0.5

10 3

13 4

2 3

2 5

3 20

1 5

STEP 2

2.5 min

Start the timer

Rapid calculation

Fill in the boxes with >, < or =.

1 3

1 4

4 5

4 7

3 8

5 8

9 16

9 25

1 2

2 3

4 9

3 7

3 10

5 12

9 11

7 12

8 9

5 6

1 3

2 7

2 5

3 10

5 8

7 10

7 8

4 5

2 5

3 8

3 7

5 12

9 10

19 25

STEP 3

1.5 min

Start the timer

Challenge

Look at the fractions in the box.

2 5

1 6

3 8

4 9

6 7

6 11

7 10

1. Write down the fractions that are less than

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Time spent:

min

3 5

2 3

3 4

5 12

1 .

2

2. Write down the fractions that are greater than

26

3 7

1 .

2

sec. Total:

out of 36

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Using letters to represent numbers (1)

58

STEP 1

1

min

Date: Day of Week: Start the timer

Warm-up

Simplify these expressions. The first two have been done for you. a+a=

9×z=

2a

c+c+c=

3y − y =

7s − 3s =

t+t+t+t+t=

STEP 2

2.5 min

9z

b+b=

4×d=

5r − 2r =

f×5=

Start the timer

Rapid calculation

Simplify these expressions.

1×a=

8×b=

2z + 5z + 3z =

9p − 3p =

g × 12 =

4v − 3v =

0.5r + 0.5r =

5n + 7n − 3n =

15 × e =

6y × 2 =

3x ÷ x =

12t ÷ 2 =

b + 2b =

54a ÷ 2 =

3.5b + b =

12x ÷ 12 =

STEP 3

1.5 min

Start the timer

Challenge

Simplify these expressions.

19m − 4m =

7s × 8 =

5a + 7a =

3 × 2.4p =

9.5t − 2t =

7.2a − 0.2a =

9 × 7s =

43t − t =

24x + 9x =

7.6y − 6y =

10.3t − 3.8t =

36s ÷ 3 =

5 × 1.2x =

13 × 7m =

35k − 20k =

17.6y − 6.6y =

62

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Date:

68 Ratio (2) STEP 1

Day of Week: Start the timer

Warm-up

1

min

Simplify the ratios.

4 : 12 =

24 : 28 =

32 : 48 =

64 : 56 =

10 : 20 =

34 : 30 =

75 : 25 =

96 : 54 =

STEP 2

Start the timer

Rapid calculation

2.5 min

Find the value of x.

24 : 40 = x : 60

1

x : 12.5 = 4 : 5

64 :x = 5:1

x=

x= 8.4 : 0.5 = x : 20

x=

4 : 0.6 = x : 0.9

6 : x = 5 : 1.2

x=

x= 5 4 3 : = 48 :x 8 7

x=

2

2 9 : (x + 1) = 5 : 9

5.5 : x = 3 : 12

x=

x=

STEP 3

x=

Start the timer

Challenge

1.5 min

Write these ratios. a : b = 2 : 3,

b : c = 3 : 7,

a:b:c =

a : b = 1 : 2,

b : c = 4 : 7,

a:b:c =

b : c = 4 : 5,

c : d = 5 : 9,

b:c:d =

b : c = 4 : 5,

b : d = 2 : 9,

b:c:d =

x : y = 5 : 2,

y : z = 2 : 9,

x:y:z =

x : y = 5 : 2,

y : z = 6 : 7,

x:y:z =

72

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Date:

Area of a triangle (1) 77

Day of Week:

STEP 1

1

min

Start the timer

Warm-up

Height

Base length

Use the information given about each triangle to work out its area.

Base length (cm)

12

10

25

32

45

34

75

100

10

Height (cm)

20

102

2

4

6

5

20

25

5

Area (cm2)

STEP 2

2.5 min

Start the timer

Rapid calculation

Use the information given about each triangle to work out its area.

Base length (cm)

24

12

20

20

5

12

20

80

Height (cm)

10

11

13

25

3

4

15

25

Area (cm2)

Base length (m)

54

5.4

1.2

6.8

5.8

9.3

4.8

Height (m)

30

6

5

6

5

4

4

Area (m ) 2

STEP 3

1.5 min

Start the timer

Challenge

Use the information given about each triangle to work out its area.

Base length (cm)

16

25

3.1

4.3

5.6

Height (cm)

9

4.4

8

10

7

Base length (m)

66

7.8

8.8

7.8

Height (m)

4

8

5

5

Area (cm2)

Area (m2)

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Time spent:

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sec. Total:

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81

26/04/19 12:24 PM

Date:

Nets of 3-D shapes (1) 79

Day of Week:

1

STEP 1

min

Start the timer

Warm-up

Answer these using fractions or mixed numbers.

8 ÷4= 33

7 2 × = 12 9

19 ÷ 38 = 14

7 4 − 4 11 =

3

STEP 2

2.5 min

1 1 + = 5 6

3

5 − 24 =

3

2

27 14 × = 56 45

7

8 9 + 12 18 =

Start the timer

Rapid calculation

Tick the nets that will form a cube.

1.

2.

3.

4.

5.

6.

7.

8.

9.

STEP 3

1.5 min

Start the timer

Challenge

These nets all form a cube when folded. Number each face so that the faces that will be opposite each other have the same number.

1.

2.

3 1

2

3.

1

1

3

3

2

4.

3

2

5. 2

6.

1

1 1

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Time spent:

min

sec. Total:

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83

26/04/19 12:25 PM