Use repeated addition to find the total number of fingers. Find the total of each group by using repeated addition. Multiplication and Division
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1 Introducing multiplication groups of 5 Use repeated addition to find the total number of fingers = 5 groups of 5 is equal to 5. Find the total of each group by using repeated addition. a How many pencils? = 0 groups of 5 is equal to 0 b How many eggs? = 0 6 groups of 5 is equal to 0 c How many beads? = 5 5 groups of 5 is equal to 5 D
2 Introducing multiplication groups of 5 This is a multiplication symbol and it means groups of. So instead of repeated addition, we can use a multiplication symbol = = 5 Find the total of each group by using repeated addition: a groups of 5 is equal to 0 5 = 0 b 6 rows of 5 is equal to = 0 Ring the shapes in groups of 5. One group is ringed for you. Then complete the multiplication fact. a groups of 5 is equal to 5 5 = 5 b groups of 5 is equal to 0 5 = 0 D
3 Introducing multiplication 5 times table Here is a skip counting pattern on a hundred grid. It shows a counting pattern of Finish each pattern by counting in 5s: a b Show 5 multiplication facts on each number line. a Finish labelling this number line and then show 5 jumps starting from 0: This is the same as 5 5 = 5 b Finish labelling this number line and then show 7 jumps starting from 0: This is the same as 7 5 = 5 D
4 Introducing multiplication 5 times table Write a 5 times table fact for each set of 5 cent coins. The first one has been done for you. a b c 5 = = = 5 Times tables are a set of multiplication facts from to 0 based on multiplying by the same number each time. Write the answers for the 5 times table. 5 Now answer the mixed up 5 times table. a 5 = 0 b 8 5 = c 9 5 = 5 d 0 5 = = 5 e 5 = 5 f 6 5 = 0 5 = 0 g 7 5 = 5 h 5 5 = 5 5 = 5 = 5 0 i 5 = 5 j 5 = = 5 6 Write the missing number in each 5 times table fact. 6 5 = 7 5 = 0 5 a 7 5 = 5 b 5 = = 0 c 0 5 = 50 d 5 = = 5 e 8 5 = 0 f 5 = = 50 g 6 5 = 0 h 9 5 = 5 D
5 Introducing multiplication 0 times table If you can skip count in 0s, you know your 0 times table. Complete this sequence by counting in 0s: Count the longs and then complete the multiplication fact: a b c 6 0 = 60 0 = = 80 Complete the 0 times table: 0 = 0 0 = 0 0 = 0 0 = 0 Write the missing number in each 0 times table fact: a 5 0 = 50 b 8 0 = 80 c 7 0 = = 6 0 = 7 0 = 8 0 = 9 0 = Complete this 0 wheel: = D 5
6 Introducing multiplication multiplying any number by 0 When we multiply any number by 0, a zero goes in the units column and the digits all move Hundreds Tens Units one space along to the left. 0 0 = 0 Show how the digits all move along when they are multiplied by 0 and write the answers below: a Hundreds Tens Units b Hundreds Tens Units = 70 0 = 0 c Hundreds Tens Units d Hundreds Tens Units = 50 0 = 0 Connect these 0 facts to the answers: D
7 Introducing multiplication multiplying numbers by 0 and Any number multiplied by always equals the same number. Any number multiplied by 0 always equals zero. Practise multiplying by : a b 8 groups of are equal to 8 6 groups of are equal to 6 8 = 8 6 = 6 c d 5 groups of are equal to 5 groups of are equal to 5 = 5 = Practise multiplying by and 0: a 0 = 0 b 6 = 6 c 0 = 0 d = e 8 0 = 0 f 0 = 0 Complete this grid: D 7
8 Multiplication facts times table Counting in s, will help you know many times table facts. Complete each pattern by counting in s: a b c Show how many dots there are in each array by counting in s. Then write the times table fact below: c twos = 6 a 6 twos 6 = b 8 twos 8 = 6 d 5 twos e twos f 9 twos 5 = 0 = 8 9 = 8 8 D
9 Multiplication facts times table How many straws are in: a drinks? = 6 c 5 drinks? 5 = 0 b 0 drinks? 0 = 0 d drinks? = How many wheels have: a bikes? = 8 b 9 bikes? 9 = 8 c 7 bikes? 7 = d bikes? = 6 5 Double each number: a 6 = b 9 = 8 Multiplying by is the same as doubling. c 8 = 6 d 7 = 6 Complete this doubling wheel. These facts are not in the times table, but they are facts that are useful to know Double D 9
10 Multiplication facts times table Practise your times table. Write the multiplication fact for each array: a fours = b fours = 6 c 5 fours 5 = 0 d 6 fours 6 = e 7 fours 7 = 8 f 9 fours 9 = 6 How many cupcakes are there on: a plates? b plates? = 6 = c 7 plates? d 9 plates? e plates? 7 = 8 9 = 6 = 8 0 D
11 Multiplication facts times table Here is a half of a hundred grid: a Circle the counting pattern of s. Cross the counting pattern of s. b What do you notice? The counting pattern of s is in the s counting pattern. Complete the matching and facts: a 6 = and = Can you see that the arrays have half the rows and double the columns of the? This means there is the same total, but the array is arranged differently. So, 6 = b = 8 and = 8 So, = c 8 = d 0 = 5 D
12 Multiplication facts times table Practise your times table. Use this array = to complete the times table: = 6 Now try them mixed up: a = 9 b 8 = = = 9 c 7 = d 0 = 0 5 = 5 e = 6 f = 6 = 7 = 8 g 5 = 5 h 6 = 8 8 = i 9 = 7 j = 9 = 7 0 = 0 Alfred is an alien from the Planet Trampolon. The surface of Planet Trampolon is like walking on a trampoline. That s why Alfred and all his race of aliens need legs for extra balance. They also have fingers on each hand and eyes. a How many legs for: 6 aliens? aliens? 6 = 8 = b How many eyes for: aliens? 0 aliens? = 9 0 = 0 c How many fingers on one hand for: 9 aliens? 5 aliens? 9 = 7 5 = 5 D
13 Multiplication facts times table Label the number line so it goes up in s: Write two turnaround facts for each array. The first one has been done for you. a = b = 6 c 5 = 5 = = 6 5 = 5 d 6 = 8 6 = 8 e 7 = f 9 = 7 7 = 9 = 7 D
14 Multiplication facts 6 times table Practise your 6 times table. Did you know that we can use 6 for short? So 6 just means 6 times table, just as means times table. Use this array to 6 = 6 complete the 6 times table: 6 = Fill in the missing numbers: a 9 6 = 5 6 = 6 = 5 6 = 6 6 = 7 6 = 8 6 = 9 6 = 0 6 = b 6 6 = 6 c 6 = 8 d 6 = e 0 6 = 60 f 6 = g 8 6 = 8 Complete this table by recalling the times table. Then complete the 6 times table. Can you see how the times table helps with the 6? Solve these problems. a I saved $7 every week over 6 weeks. How much did I save in total? b 8 pencil cases had blue pens in each. How many blue pens are there in total? c 9 classes each baked 6 cakes for the school fundraiser. How many cakes were baked in total? $7 6 = $ 8 = 9 6 = 5 D
15 Multiplication facts 6 times table You know more times tables facts than you + realise. For example, knowing your 5 can help with your 6. + The array shows rows of 5. If we add another + dot to each row we can change rows of 5 to rows of 6. This is called building up. 5 = = 8 5 Change these 5 arrays into 6 arrays. a = = b = = 6 Complete this table to show how to change a 5 array to a 6 array by building up. The first one has been done for you. 5 Build up by 6 a 5 = 5 6 = 8 b 5 = 0 c 7 5 = 5 d 5 = 0 e 6 5 = 0 f 9 5 = 5 6 = = 6 = = = 5 D 5
16 Multiplication facts 9 times table Practise your 9 times table. Use this array to complete the 9 times table: 9 = 9 9 = 8 9 = 7 9 = = = = = = = 90 Complete these 9 facts. Look out for turnarounds. a 9 = d 9 = 7 b 9 = 6 c 6 9 = 5 8 e 9 5 = 5 f 9 = 9 Find the cost of these items: a 6 fruit salads = $5 b banana splits = $ Mango juice $ c mango juices = $9 d 5 fruit salads = $5 Banana split $6 e banana splits = $8 f 7 mango juices = $ Fruit salad $9 6 D
17 Multiplication facts 9 times table 9 =? If you get stuck on a 9, remember the 0 fact and build down. 0 = 0 9 = 7 Change this 0 array into a 9 array: 0 = 0 9 = 6 5 Complete this table to show how to change a 0 array to a 9 array by taking from each row. 0 Build down by 9 0 = 0 9 = = = = 60 0 = 0 0 = = = = = = 5 9 = 6 9 = = = 6 D 7
18 Multiplication facts square numbers A square number is a number multiplied by itself. These arrays show the first square numbers. = squared = = squared = = 9 squared = 9 Here is another way to show square numbers. Look at the array shown on each grid and write the square number multiplication: a b c = = = 9 squared = 6 6 squared = 6 7 squared = 9 On this grid, shade the largest square number you can: 0 0 = 00 0 squared = 00 Answer these: a 8 = 9 squared b 5 = 5 squared c 6 = 8 squared 8 D
19 Multiplication facts multiples When two numbers are multiplied together, the answer is called a multiple. For example, the first multiples of 5 are 5, 0, 5. 5 = 5 5 = 0 5 = 5 Complete the list of multiples for each number in the circle: a b c d In each group of multiples, cross out the number that does not belong. You will need to look carefully, because they are not in order. a Multiples of b Multiples of c Multiples of Use the clues to work out the multiples: a This number is a multiple of both 9 and and is less than 0 but greater than 0. b This number is a multiple of 5. It is greater than 5 but less than c This number is a multiple of both and 8 and is the next squared number after 9. 6 D 9
20 Mental multiplication strategies doubling strategy There are many double facts that you should know. This includes numbers outside the times tables that we have been working on. Here are double facts that are handy to know: double 0 is 0 double 5 is 0 Can you think of more? List all the double facts outside of the times table that you know in the space below. Here are two to start you off: double is double 50 is 00 Answers will vary. Complete these doubling wheels: Double Double Doubling digit numbers is easy if you split the digits and double each part. Complete this doubling grid. The first one has been done for you. a Double 6 = = 60 + = 7 b Double = 0 + = = 6 c Double 9 d Double = = = 8 = 0 + = 80 + = 8 0 D
21 Mental multiplication strategies doubling strategy The double-double strategy is when you multiply by. Look at double-double : double once is and double twice is 8. Practise using the double-double strategy with these tables. The first one is done for you. a 7 = 8 b 5 = 60 Double 7 once Double 7 twice 8 Double 5 once Double 5 twice 0 60 c = 8 d = 8 Double once Double once Double twice 8 Double twice 8 e = f = 56 Double once Double once 8 Double twice Double twice 56 5 Play this game with a partner. You will need this page each and a die to share. The aim is to be the first to place a tick above all the numbers. Double or double-double the number rolled on the die, then tick the answer on the grid. For example, Player rolls a. They can either double it in order to tick 8 OR double-double it to tick 6. You must apply one of the strategies to the number rolled. If you can t tick a box, you miss a turn! Answers will vary. D
22 Mental multiplication strategies split strategy The split strategy is when we multiply numbers in parts. Let s use the split strategy for 5. Split into 0 and. Next multiply each part by 5, then add: What is 5? 0 5 = 50 5 = = 60 So, 5 = 60 Try the split strategy with these. Use the arrays if you get stuck. a What is 7? 0 7 = 70 7 = 70 + = 8 So, 7 = 8 b What is 9? 0 9 = 90 9 = = 08 So, 9 = 08 D
23 Mental multiplication strategies split strategy Practise the split strategy again, this time without an array to look at. a What is? 0 = 0 = = 6 So, = 6 b What is 6? 0 6 = 60 6 = 60 + = 7 So, 6 = 7 c What is 8? 0 8 = 80 8 = = 96 So, 8 = 96 Use the split strategy to multiply by. is 0 + a 8 = 0 b 9 = 7 c 7 = 9 d 5 = 65 D
24 Mental multiplication strategies compensation strategy Remember how we learned the 9 by building down from the 0? 0 = 0 9 = 7 This is the compensation strategy. Look at 9. 9 is close to 0, so we can multiply by the next multiple of ten which is 0. Then we build down because we have an extra group of. 9 0 = 60 So, 9 = 57 When you are multiplying by a multiple of ten, look for a fact you know then put a zero on the end. These patterns show you how to do this: a = 6 b 5 = 5 0 = = 50 c 7 = d = = 0 0 = 60 The steps for the compensation strategy are set out for you here. Practise multiplying by the next multiple of ten and then build down. a = 50 5 So, 5 9 = 5 b 9 0 = 60 So, 9 = 57 c 9 0 = 80 So, 9 = 78 D
25 Mental multiplication strategies compensation strategy Use the compensation strategy. This time you have to think of the next multiple of ten and what you have to build down by. The first one has been done for you. a 9 0 = 0 So, 9 = 7 b 9 0 = 0 So, 9 = 6 c = 0 6 So, 6 9 = d = 00 5 So, 5 59 = 95 Roll a die to make your own multiplication questions. Choose the compensation strategy for one column and the split strategy for the other. a 9 = b 9 = c 9 = a = b = c = Which strategy did you use and why? Which strategy did you use and why? Answers will vary. Answers will vary. D 5
26 Division sharing and grouping Division is when we make fair shares. If we share these 6 cakes equally between kids, they each get cakes. We call these fair shares because each share is equal. 6 Share the items equally in each picture by drawing lines to connect them. Write how many are in each share. a Share these 6 ice creams between kids. equal shares = each b Share these 8 pencils between 6 pots. each 6 equal shares = c Share these 9 eggs between baskets. each equal shares = D
27 Division sharing and grouping Division is also when we make equal groups. Here are 0 candy apples. How many bags do we need if we put in each bag? If we circle candy apples in each group, we can make 5 groups. So, we need 5 bags. Circle equal groups in each picture and write how many are in each share: a b Out of 9 strawberries, how many groups are there if there are in each group? Out of 6 paper clips, how many groups are there if there are in each group? c d Out of 6 fish, how many groups are there if there are 6 in each group? Out of flowers, how many groups are there if there are in each group? 6 6 Draw a picture to show 7 groups with 5 in each share. How many in total? 5 D 7
28 Division left overs Sometimes when we make equal groups there are some left over. Here are bananas. If we make equal groups of 6, there is banana left over. Make groups of each of the following items and show the left overs: a Here are butterflies: b Here are 6 apples: If we make equal groups of there is left over. If we make equal groups of 7 there are left over. c Here are paper planes: d Here are 9 match sticks: If we make equal groups of 6 there are left over. If we make equal groups of 5 there are left over. Draw a picture to show groups of with left over. How many are there in total? 5 8 D
29 Division the division symbol This is a division symbol So instead of saying Share tennis balls fairly between tennis players. How many balls do they each get? We can write: = 6 This says divided by is 6. It means that there are groups of 6. Write the division facts using the division symbol for each picture: a 0 divided by = b 8 divided by 8 = 6 c divided by = 6 Solve each of these division problems: a Share 5 lollies between bowls. How many lollies are in each bowl? 5 = 5 b Share 0 oranges between 5 baskets. How many are in each basket? 0 5 = c Out of a pile of 6 coloured pencils, 6 go into each pot. How many pots are needed? 6 6 = 6 D 9
30 Division linking multiplication and division facts Knowing multiplication facts will help with division facts. 6 = 6 rows of is. = 6 divided into shares is 6. Describe each of these arrays using one multiplication and one division fact: a = b 6 5 = 0 = 0 5 = 6 c = 6 6 = This time, you are given part of the array. Complete the array and then write one multiplication and one division fact that matches: a 7 = 7 = b 0 = = c 7 = = 0 D
31 Division linking multiplication and division facts Play this memory game with a partner. The aim of this game is to find pairs of matching multiplication and division facts. Each player needs a copy of this page and to cut out their cards. Players join their cards together, shuffle and lay them face down. Take turns in turning over a pair of cards. If they match the player keeps the pair, if they don t match, they must be placed back in the same position. The winner is the player with the most pairs. copy D
32 Highest product apply Getting ready This is a game for two players. You will need a pack of playing cards but just the cards with numbers on them. You will also need a copy of this page so you can use the table to keep score. copy What to do Shuffle the cards well and deal them evenly so you each get 8 cards. Player turns over two cards and finds the product by multiplying these together. Player does the same. The highest answer wins the round and scores a point. Use the table below to keep track of your scores. Player Player D 5
33 Mystery numbers solve What to do Read the clues to find out the mystery number: I am a multiple of 6. I am also a multiple of. I am greater than 0, but less than 0. I am greater than 5 6. I am less than 0. I am a square number. 6 I am smaller than 6 7. I am bigger than 6 squared. The sum of my digits is. 9 When I am multiplied by a die number, I make 0. I am less than 5. I am bigger than 7 9. I am less than 7. I am divisible by I am a factor of 8. I am bigger than squared. I am smaller than 5 squared. D 5
34 Multiplication concentration apply Getting ready This is a game for two players. Copy this page and page 5, and then cut out all the cards. copy What to do Shuffle the cards well and lay them out face down in an array in two groups. The rectangles are the questions, the squares are the answers. Players take turns turning over one of each card. If they can make a multiplication fact, the player keeps the pair. Keep playing until there are no cards left. The winner is the player with the most matching pairs D 5
35 Multiplication concentration apply 7 0 copy = = 8 = 5 = = 7 = 0 = 0 = = 5 = = 6 = 8 = 5 = 8 = = 7 = 56 = 0 = 5 = 6 = 9 = 50 = 6 = 6 = 6 D 5 5
36 Product bingo apply Getting ready This is a game for four players. Each player needs a copy of this page and 5 counters. The group needs dice. Make extra copies of this page so you can play again. copy What to do Choose one player to be the caller. The other players fill their grid with numbers from this list:,,,, 5, 6, 8, 9, 0,, 5, 6, 8, 0,, 5, 0 and 6. The caller rolls the dice and calls out a times table fact based on the numbers rolled. For example, if they roll a 6 and a 5, they would say 6 5. If a player has 0 in their grid, they place a counter on the number. The winner is the first player to get rid of all their counters. 6 D 5
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Series Student Multiplication and Division My name D Copyright 009 3P Learning. All rights reserved. First edition printed 009 in Australia. A catalogue record for this book is available from 3P Learning
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