Multiplication Learning objective We are learning to: • develop efficient mental methods using multiplication and division facts (for example, using 3 × 4 = 12, 12 ÷ 3 = 4 and 4 = 12 ÷ 3) to derive related facts (for example, 30 × 4 = 120, 120 ÷ 3 = 40 and 30 = 120 ÷ 4).
What pupils already know • Pupils are secure with recalling and using multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers. • They can calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs.
Key vocabulary multiplication, division, place value, related facts
Teaching notes • • • •
Practise the times tables that pupils already know using a range of games, e.g. times table bingo, ping pong. Focus on teaching multiplication and division facts for 3, 4 and 8 multiplication. Use arrays to show how multiplication facts can be presented in two ways (see right): Also establish the division facts that correspond with these multiplication facts: 8 × 3 = 24 3 × 8 = 24
24 ÷ 3 = 8 24 ÷ 8 = 3
• Extend to show pupils that we can use these known facts to help multiply bigger numbers. For example: 80 × 3 = 240 30 × 8 = 240
but also, 240 ÷ 3 = 80 and 240 ÷ 8 = 30 For pupils – Steps to success: 1. Use known multiplication facts to help multiply larger numbers.
Independent activity Refer pupils to the Year 3 Mental Arithmetic Pupil Book, pages 18–19.
16
Multiplication Use and apply Task A: Multiplication search Find the pairs of numbers in Box 1 that multiply together to give an answer in Box 2. Box 1
Box 2
40
4
8
2
240
160
180
20
12
5
50
6
150
60
400
3
30
15
10
30
120
48
750
Task B: Explain how you know Mick wants to buy 30 stickers for his classmates. Each sticker costs 8p. He says:
The total price will be 24p.
Is he correct? Yes or No? Explain your answer. Task C: Multiplying larger numbers A game for two players Spinner F
You will need: a dice, Spinner F* • Take turns to roll the dice and spin Spinner F. • Multiply the number spun on the spinner by the number you have rolled. For example, if you spin 40 and you roll 3, complete the calculation 40 × 3 = 120.
• The player with the largest product scores 5 points. • The first player to score 25 points wins!
90
20
80
30
70
40 60
50
* See the Resources page for a full-sized photocopiable version © 2015 Keen Kite Books, an imprint of HarperCollinsPublishers Ltd. You may photocopy this page.
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Division Learning objective We are learning to: • recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables • develop efficient mental methods using multiplication and division facts (for example, using 3 × 4 = 12, 12 ÷ 3 = 4 and 3 = 12 ÷ 4) to derive related facts (for example, 30 × 4 = 120, 120 ÷ 3 = 40 and 30 = 120 ÷ 4).
What pupils already know • Pupils are secure with recalling and using multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers. • They can calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs.
Key vocabulary multiplication, division, divisor, place value, related facts, remainder
Teaching notes • Use concrete resources to support division by grouping. Example 1: 12 ÷ 3 =
Example 2: 17 ÷ 3 =
Display the above and establish that it shows 12 star counters divided into 3s, which gives 4 groups: 12 ÷ 3 = 4
Display the above and establish that it shows 17 star counters divided into 3s, which gives 5 groups with 2 star counters left over: 17 ÷ 3 = 5 r2
For pupils – Steps to success: 1. Divide the number into equal groups of the divisor – count how many groups there are and don’t forget the remainder.
Independent activity Refer pupils to the Year 3 Mental Arithmetic Pupil Book, pages 20–21.
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Division Use and apply Task A: Remainders Let’s investigate remainders and think about which division sentences result in remainders. • Investigate which numbers between 1 and 30 would have a remainder 1 when divided by 3. • Investigate which numbers between 1 and 40 would have a remainder 2 when divided by 4. • Are there any patterns or rules that allow us to predict the remainder for the calculation? Task B: Explain how you know Ishmal says:
Any even number divided by 3 will have a remainder of 2 because 8 ÷ 3 = 2 remainder 2 and 14 ÷ 3 = 4 remainder 2.
Is he correct? Yes or No? Explain how you know. Task C: Divide and move
Spinner G
A game for two players You will need: a paper clip, Spinner G*, a pencil, a different coloured counter per player, the ‘divide and move game board’ below • Both players put their counters on start. • Take turns to spin Spinner G. • If the number on the spinner divides into the number that the counter is on without a remainder, then move your counter on one space. • Continue taking turns. The first player to reach finish wins!
8
3
5
4
Divide and move game board
START 16
30
24
15
12
16
20
24
20
40
30
12
FINISH
* See the Resources page 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
Copy and shade
3 4
of the rectangle.
11 A glass holds 500 ml. How many glasses can be filled using 3 litres of water? 12 A purse contains eight tokens each worth 30p. What is the total value of the tokens in the purse? 13 How much does it cost to buy 8 chocolates which cost 40p each? 14 Read the weight on each of these measuring scales.
2
Write the next equivalent fraction. 2 3
=
6 9
=
3
What is
1 2
of 80?
4
Copy and complete by writing < or >. 2 3
5
=
4 6
4 10
of 60
kg
of 70
Write these fractions in order, starting with the smallest.
kg
15 Write <, > or = for each of these. 50 cm
5m 7 kg
8000 g 1 8
6
1 2
3 4
7 10
What fraction of this circle is shaded?
16 Choose from the options below to write the time that shows five past six in the evening. 5.06 a.m.
6.05 a.m.
6.05 p.m.
5.06 p.m.
17 Convert the following: 4 m 70 cm = 60 cubes are sorted by colour. Write how many coloured cubes there are in questions 7â&#x20AC;&#x201C;8. 7 8 9
1 3 2 6
18 Which three of these coins can be used to make 26p?
white = grey =
Write 0.8 as a common fraction.
10 Use the fraction grid to help you answer the sum below.
19 Write the time shown on this clock. 11 12
1
10
2
9
3 8 7
4 12
+
7 12
6
5
4
= 20 Write the time half an hour later than in question 19.
Score 44
cm
/ 20
Š 2015 Keen Kite Books, an imprint of HarperCollinsPublishers Ltd. You may photocopy this page.
End-of-year test
2 Use the number line to answer this: 16 – 9 =
0
2
6
4
11 All the buttons are used to make three baby coats each with the same number of buttons. How many buttons are on each coat? 12 There are nine different colours of buttons; red, blue, green, purple, yellow, orange, pink, silver and gold. There is the same number of buttons of each colour on each coat. How many green buttons will there be?
Ones
Tens
Hundreds
1 Write the number shown on the abacus in numerals.
8
10 12 14 16 18 20
13 Four baby coats are made using all the buttons. One coat has two more buttons than the others. How many buttons are there on each of the four coats?
3 Subtract 40 from 99.
14 A wrist-watch costs £135. In a sale it is reduced by £32. How much will the watch cost now?
4 159 + 8 =
15 What fraction of this rectangle is shaded?
5 Two numbers have a difference of 30. One of the numbers is 60. What could the other number be? 6 Do these calculations and then write the answer that is an even number.
16 What is
3 4
17 What is the time shown on each clock? 11 12
442 + 4
2
402 + 71
9 8
7 Write these weights in order, starting with the heaviest. 412 g 364 g
469 g
3 8 7
6
5
4
18 Convert the following: 2 1 kg =
g
2
6m =
cm
404 g
8 Do these calculations and then write the answer that is an odd number. 56 ÷ 7
2
9
4
5
6
1
10 3
7
324 g
11 12
1
10
12 – 7 18 – 5
of £100?
3 × 10 8×2
Look at the text book and pen to help you answer questions 19–20. Ma
th
s
36 ÷ 6 49 ÷ 7 £7 Text book
£1 Pen
9 What is the remainder when 35 is divided by 6? 10 5 × 4 × 5 = Here are 18 buttons. Use these to answer questions 11–13.
19 How much will it cost in total for six students to buy one text book each? 20 How much change would you get from £30 if you bought three text books and one pen?
Score © 2015 Keen Kite Books, an imprint of HarperCollinsPublishers Ltd. You may photocopy this page.
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