9780008161361

Decimal calculations Learning objective We are learning to: • use a range of mental strategies to solve decimal calculations.

What pupils already know • Pupils are secure with identifying tenths, using multiplication facts for up to 12 × 12.

• Pupils have a good range of mental calculation strategies for adding and subtracting whole numbers.

Key vocabulary strategy, method, partition, count on, count back

Teaching notes • Model how to use a range of strategies to solve mental calculations involving decimals.

Use near doubles Example: What is 4.2 + 4.3?

4.2 + 4.2 = 8.4 So 4.2 + 4.3 = 8.5

Count on or back in different jumps Example: What is 7.4 − 5.6?

1.4

0.4

5.6

6

7 7.4 – 5.6 = 1.8

Partition, or break numbers up Example: What is 3.8 × 6?

3 × 6 = 18 0.8 × 6 = 4.8 So 3.8 × 6 = 18 + 4.8 = 22.8

Use the facts you know Example: What is 0.8 × 8?

8 × 8 = 64 So 0.8 × 8 = 6.4

For pupils – Steps to success: 1. Read the calculation.

2. Choose one of the strategies to help solve the calculation.

Independent activity Refer pupils to the Year 5 Mental Arithmetic Pupil Book, pages 34–35.

30

7.4

Decimal calculations Use and apply Task A: Target 3.6 Use the signs +, – and × to make the target 3.6 Example: 1.3 + 2.3 = 3.6 How many possible ways can you find?

Task B: Explain how you know Suraj says:

The difference between 6.7 and 8.4 is the same as 3.3 – 1.6 Is he correct? Yes or No? Explain how you know.

Task C: The greatest product!

A game for 2 players You will need: Spinner E*, a dice, a pencil, a paper clip • Player 1 spins Spinner E twice to generate a decimal number. For example, if the player spins the numbers 4 and 3 they can make the decimal number 4.3 • Player 1 rolls the dice and multiplies the decimal number by the number rolled.

• For example, if you roll 5 then you have to do the following calculation: Spinner E 4.3 × 5 = 4 × 5 = 20 0.3 × 5 = 1.5 So 4.3 × 5 = 21.5 • Player 2 now has a turn.

• The player who has the greatest product scores 5 points.

• The first player to score 25 points wins.

9

1

8

2

7

3 6 5

*

4

See the Resources pages for a full-sized photocopiable version

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31

Area and perimeter Learning objectives We are learning to: • measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres • compare the areas of rectangles (including squares), and include using standard units: square centimetres (cm2) and square metres (m2) • estimate the area of irregular shapes.

What pupils already know • Pupils are secure in finding the area of rectangles and squares by counting squares.

• They can measure and calculate the perimeter of a rectangle and square using centimetres and metres.

Key vocabulary rectilinear shape, composite rectilinear shape, area, perimeter

Teaching notes • Remind pupils of the definitions of the terms area and perimeter and distinguish between the two.

• The units for perimeter can be cm or m and the units for area are cm2 or m2.

Example: What is the area and perimeter of this shape? 4 cm • Establish that in order to find the area and perimeter we first need to split this composite shape into two rectangles.

• Area of composite = shape = = =

9 cm

15 cm 3 cm

area of rectangle A + area of rectangle B. 4 cm × 9 cm + 3 cm × 15 cm 2 + 45 cm2 36 cm 2 81 cm

• Perimeter of composite shape: explain that if we found the perimeter of rectangle A and then the perimeter of rectangle B, this would include lengths that are not included in the composite shape. Model how to use the information given to find the length of each side: Perimeter = 15 cm + 3 cm + 19 cm + 9 cm + 4 cm + 6 cm = 56 cm

A B

4 cm 9 cm

6 cm = (9 cm – 3 cm) 15 cm 3 cm 19 cm = (15 cm + 4 cm)

For pupils – Steps to success: 1. Area: length × width. Units = cm2. Perimeter: 2 × (length + width). Units = cm.

2. If you are finding the perimeter of a composite shape, be careful to not add on the sides of the rectilinear that are not included!

Independent activity Refer pupils to the Year 5 Mental Arithmetic Pupil Book, pages 38–39.

34

Area and perimeter Use and apply Task A: Crazy paving patio Mr Jones is having a new crazy paving patio built. He would like to have a range of designs to present to his builder. Each patio design should have: a) a rectilinear shape. b) a perimeter of 36 m.

How many different designs can you construct?

Task B: Explain how you know Karmal says: The perimeter of a rectangle can be written as: 2(a + b) a+b+a+b 2a + 2b Is he correct? Yes or No? Explain how you know.

Task C: Composite perimeter

A game for 2 players You will need: a dice, a ruler, some paper, a pencil • Player 1 rolls the dice twice. Draw a rectangle with a ruler using the numbers rolled.

For example: if you roll a 3 and 4 you can draw rectangle A: 3 cm

A

• Player 1 repeats, but this time draws the new rectangle next to rectangle A so that one of the sides joins.

For example: if you roll a 6 and 2 you can draw rectangle B:

2 cm

3 cm

A

B 6 cm

4 cm • Player 1 now finds the perimeter of this composite shape.

For example: 2 cm + 6 cm + 2 cm + 4 cm + 3 cm + 4 cm + 3 cm = 24 cm • Now, it’s Player 2’s turn.

• The player with the greatest perimeter scores 2 points.

• The first player to score 6 points wins

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Progress test 3 1 6.6 × 2 = 2 Write the smallest and then the largest fraction or percentage in this set.

12 50

7 25

25%

36 100

2 50

33%

3 Write 60% as a fraction, in its simplest form.

12 A film starts at 9.15 p.m. and finishes at 10.50 p.m. How long is the film?

13 82 = 14 What is the perimeter of a rectangle with sides 45 cm wide and 20 cm long?

15 The area of a square is 81 cm2. What is the length of each side?

4 26 ÷ 100 = 5 Round each decimal to the nearest tenth.

16 How long is 75 minutes and 35 minutes in total?

5.27 5.127 Use these library opening and closing times to answer questions 17–19.

6 Write the missing digits.

75% = 0.

=

4

Monday

Tuesday

Opens

9.15 a.m.

10.05 a.m.

Closes

12.05 p.m.

12.50 p.m.

7 Write the greatest height and then the

smallest height.

3.27 m

1.42 m

4.141 m

4.233 m

3.4 m

8 Write < or > to make this true.

80%

17 How long is the library open for on Tuesdays?

18 On which day is the library open for the longest?

7 10

9 5.007 × 100 = 10 Use this number line to help you work out this subtraction.

5.4 – 3.7 = 5.4

3.7

19 The time is 8.25 on Monday morning and Mark wants to visit the library.

How long does he have to wait to visit the library?

20 What is next square number in this series?

16

25

36

11 9 cm 3 cm Area = Perimeter =

cm2 cm

Score 44

/ 20

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End-of-year test 12 How much is

1 Multiply both numbers by 100.

5 6

of £12?

13 Write the smallest fraction and then the largest fraction.

625 8315 2 Write in words the value of the underlined digit.

11 3

423 513

14 3

22 3

31

3 Make the smallest possible number from these digit cards.

8 3

3

14 Write two fractions that total 8.

2

4 9

3 1

6

21

31

2

41

2

2

61 2

4 What is the total of these three numbers?

2156

1105

15 Round each decimal to the nearest tenth.

4510

5 274 ml of water is poured from a 1000 ml jug.

How much water is left in the jug?

6 Write two numbers that have a difference of 3200.

7.52 5.678 16 Write the heaviest weight and then the lightest weight.

5.73 kg

5300

6900 3300

2.52 kg

5700

8.663 kg

2100

4.141 kg 8.5 kg

17 Write < or > to make this true 7 Write < or > to make this correct.

3 × 52

6 × 21

8 Write down a multiple of 9.

9 Write down a factor of 45.

10 Multiply these three numbers.

4

2

9

11 Write this as an improper fraction and as a mixed number.

40%

3 5

18 The area of a square is 121 cm2. What is the length of each side?

19 The time is 9.25 on Saturday morning and Joe wants to go to the gym. The gym opens at 11.15 a.m. How long does he have to wait to attend the gym?

20 What is the area and perimeter of a rectangular shape 8 cm long and 12 cm wide?

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