Division Learning objective We are learning to: • solve division problems.
What pupils already know • Pupils are secure with recalling and using multiplication and division facts for the 2, 3, 4, 5, 8 and 10 multiplication tables. • They have efficient mental methods using multiplication and division facts (for example, using 3 × 2 = 6, 6 ÷ 3 = 2 and 2 = 6 ÷ 3) to derive related facts (for example, 30 × 2 = 60, 60 ÷ 3 = 20 and 20 = 60 ÷ 3).
Key vocabulary multiplication, division, place value, related facts
Teaching notes • Use concrete resources to support division but move on to show how to divide a larger number by breaking up the numbers (this is called partitioning). Example 1: What is 57 ÷ 3? Break 57 up into 30 and 27. 30 ÷ 3 = 10
Example 2: A box can hold 6 eggs. How many full boxes will there be from 98 eggs? Model how to break up 98 into 60 and 38.
27 ÷ 3 = 9
60 ÷ 6 = 10
so 57 ÷ 3 = 19
38 ÷ 6 = 6 r 2 so 98 ÷ 6 = 16 r 2 However, the question asks how many full boxes there are, so we ignore the remainder and give the answer 16.
For pupils – steps to success: 1. Break up the larger number into smaller numbers so it is easier to divide. 2. Read the question carefully and, if there is a remainder, make sure it is used appropriately to answer the question.
Independent activity Refer pupils to the Year 4 Mental Arithmetic Pupil Book, pages 20–21.
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Division Use and apply Task A: Remainder word problems a) 68 children go into the school hall for a concert. There are 5 seats in each row. How many rows are needed to seat everyone? b) A box holds 4 cupcakes. How many full boxes of cupcakes will there be if the baker bakes 95 cakes? c) A minibus holds 7 passengers. How many buses will be needed to transfer 99 people to the airport? Task B: Explain how you know ÷ 7 = 13 Amy says:
The missing number is 91.
Is she correct? Yes or No? Explain how you know. Task C: Remainders A game for 2 players You will need: a dice, six coloured counters each, the ‘division playing grid’ below • Take turns to roll the dice. • Find a division fact with a remainder that matches the number shown on the dice. Cover the division fact with a counter. • The first player to place three counters in a horizontal row wins! Division playing grid
97 ÷ 8
41 ÷ 6
53 ÷ 7 94 ÷ 11 32 ÷ 5
15 ÷ 4
76 ÷ 6
50 ÷ 8
51 ÷ 9 65 ÷ 12 75 ÷ 9
28 ÷ 3
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Fractions Learning objectives We are learning to: • recognise and show (using diagrams) families of common equivalent fractions • use factors and multiples to recognise equivalent fractions and simplify where appropriate (for example, 6 = 2 or 1 = 2 ). 9
3
4
8
What pupils already know • Pupils are secure with recognising and showing (using diagrams) equivalent fractions with small denominators.
Key vocabulary equivalent fraction, numerator, denominator, equal parts
Teaching notes • • • •
Review the terms numerator and denominator. Establish that in the fraction bar below, 7 is shaded. 10 The denominator (10) tells you how many equal parts the whole is divided into. The numerator tells you the number of those equal parts that are taken.
Example: Find equivalent fractions to • Model how to use the fraction wall: find 4 and then use a ruler (dotted 12 line) to help identify fractions that are equivalent to 4 . We can see that 2 6 12 and 1 are equivalent to 4 . 3 12 • Explain that if we did not have a fraction wall, we could use factors and multiples to help find equivalent fractions: ÷2
•
2 1 4 = = 6 3 12 ÷2
×2
÷2
OR
4 8 = 12 24
÷2
×2
4 . 12
1 whole 1 2
1 2
1 3
1 3
1 4
1 4
1 5 1 6 1 8 1 10 1 12
1 4
1 5 1 6 1 8
1 5
1 8
1 1 1 10 10 10 1 1 1 1 12 12 12 12
1 4 1 5
1 6
1 6 1 8 1 10 1 12
For pupils – steps to success: 1. Find fractions that are equivalent to the fraction using, the fraction wall. 2. Use factors and multiples to find equivalent fractions.
Independent activity Refer pupils to the Year 4 Mental Arithmetic Pupil Book, pages 22–23. 20
1 3
1 8 1 10 1 12
1 5 1 6
1 6 1 8
1 8
1 1 1 10 10 10 1 1 1 1 12 12 12 12
1 8 1 10 1 12
Fractions Use and apply Task A: True or false? For each statement write T if it is true or F if it is false. a) Three-sevenths is equivalent to b)
5 25
6 24
Create some more true statements
is equivalent to one third. 8 . 10
c) Three-fifths is equal to d)
9 . 21
is equal to one quarter.
Task B: Explain how you know Chloe has three fraction diagrams. She says:
Diagram B
Diagram A
C is the odd one out because the other two fractions are equivalent.
Diagram C
4 10
Is she correct? Yes or No? Explain how you know.
1
0
Task C: Equivalent fraction row
Spinner F
A game for 2 players You will need: Spinner F*, a set of counters, the ‘fraction grid playing board’ below, a pencil, paper clip • Each player chooses one of the fraction grid boards. • Take turns to spin Spinner F. • Look at your grid to see if there is a fraction equivalent to the fraction spun on the spinner. If there is, cover the fraction with a counter. If not, miss a turn. • The first player to place a counter on all the fractions on their grid wins!
5 15
16 20 4 12
Fraction grid playing board
Player 1
1 3
8 24
50 150
4 5
32 40
Player 2
15 20
20 60
28 84
8 10
16 30
*See the Resources pages for a full-sized photocopiable version © 2015 Keen Kite Books, an imprint of HarperCollinsPublishers Ltd. You may photocopy this page.
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Progress test 3 1 Write the smallest decimal number and then the largest decimal number. 4.5
7.5
4.7
2.8
7.8
2 2.4 × 10 =
12 Write the conversion. kg
7620 g =
13 4 hours 30 minutes =
g minutes
14 When is 8.15 a.m.? Morning, afternoon or evening?
3 9.2 ÷ 10 = 4 Answer these: 6+5= 6 + 0.5 =
15 John arrives for his dentist appointment at 1.25 p.m. He is 20 minutes early.
5 Round to the nearest whole number. 8.4
16 What change will you be given from £5 if you spend £4.35?
12.7
17 Write < , > or = to make these true.
What time is his appointment?
6 Write × or ÷ for each of these. 28.4
10 = 284
28.4
10 = 2.84
950 mm 72 cm
9 cm 5 mm 7.2 m
18 Write the total amount.
7 1.6 – 0.8 = 8 Write these in order, starting with the smallest. 20.3
70.3
77.3
70.9
20.9
9 Use the number line to help you answer these.
0
1
2
0.6 + 0.9 =
19 Jess buys a drink for £1.50 and a cake for £1.30. How much change will she get from £3?
1.4 – 0.7 = 10 Write the conversion. 85 cm =
20 Write the conversion.
mm
4 weeks =
days
11 Write the time shown on each clock. 11 12
11 12
1 2
10 9
3 8
4 7
6
5
1 2
10 9
3 8
4 7
6
5
Score 44
/ 20
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End-of-year test 11
1 Write the number at each arrow.
12
1 +3= 8 8 3 − 1 = 10 10
= =
13 What fraction is greater? 10
0
−10
7 10
of 90
7.7
500
3 Write these numbers in order, starting with the smallest. 2456
of 90 or
14 Round to the nearest whole number.
2 What is the halfway number? 300
3 9
2891
2243
4 Write the answer. 4000 + 600 + 90 + 2 =
14.2 15 Write × or ÷ for each of these. 44.5
10 = 445
44.5
10 = 4.45
16 Write these in order, starting with the lowest number.
5 Calculate these:
40.5
Subtract 150 from 800.
55.7
56.8
51.2
40.9
17 Write the time shown on each clock.
Add 70 to 455. 6 Count in 1000s and write the missing numbers.
11 12
3035
35
10
3 8
9 Write the largest fraction and then the smallest fraction. 5 9
2 9
8 9
10 Write the next equivalent fraction. 2 5
=
4 10
=
6 15
=
4 9
6
2
9
3 8
4 7
8 4800 ÷ 8 =
1
10
2
9
7 3×4×4=
1 9
11 12
1
4 7
5
6
5
18 Write the conversion. 9045 g =
kg
g
19 What change will be given from £5 if you spend £3.30? 20 Write < , > or = to make these true. 1050 mm 92 cm
10 cm 9.2 m
Score © 2015 Keen Kite Books, an imprint of HarperCollinsPublishers Ltd. You may photocopy this page.
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