Multiplication and Divion MODELS
Multiplication groups and arrays When we put objects into rows and columns like th we call it an array. Arrays can make it easier to work out how many objects there are in a group. We can 5 use skip counting to help. 5 0 5 rows How many dots are in the arrays? a b c d row of How many dots are there? Did you count every dot or did you use a different strategy? Explain how you did it. Operations with Number C 3 53
Multiplication repeated addition One way to describe multiplication repeated addition. Look at th array. There are 3 rows. There are 5 dots in each row. We can think of th as: 5 + 5 + 5 = 5 5 5 5 3 rows How many dots are in the array? a b + = + = c d + + + = + + + = How many dogs are here? Record using repeated addition. Operations with Number C 3 54
Multiplication the symbol We know that + means add or join means subtract = means the same as What does mean? It means of. 5 Row 5 butterflies We have 5 Row 5 butterflies 5 0 altogether. We write th as 5 = 0 How many dots are in the array? Write the number facts. a b 3 4 c d Colour the right number of squares to match the facts. 5 0 5 = 0 Operations with Number C 3 55
Divion relating multiplication and divion We can use the same arrays to make multiplication and divion facts. Th array shows: 3 4 counters divided into 3 rows 4 3 AND 3 = 4 Use the arrays to finh the number statements and facts. a 5 0 divided into rows b 4 divided into rows c d Now you can only see part of the arrays. Can you still finh the facts? a 4 b 5 = Operations with Number C 4 76
Introducing multiplication 5 times table Here a skip counting pattern on a hundred grid. It shows a counting pattern of 5. 3 4 5 6 7 8 9 0 3 4 5 6 7 8 9 0 3 4 5 6 7 8 9 30 3 3 33 34 35 36 37 38 39 40 4 4 43 44 45 46 47 48 49 50 5 5 53 54 55 56 57 58 59 60 6 6 63 64 65 66 67 68 69 70 7 7 73 74 75 76 77 78 79 80 8 8 83 84 85 86 87 88 89 90 9 9 93 94 95 96 97 98 99 00 Finh each pattern by counting in 5s: a +5 +5 +5 0 5 b +5 +5 +5 45 50 Show 5 multiplication facts on each number line. a Finh labelling th number line and then show 5 jumps starting from 0: 0 5 0 30 40 Th the same as 5 = b Finh labelling th number line and then show 7 jumps starting from 0: 0 5 0 35 45 Th the same as 5 = Multiplication and Divion D 3
Multiplication facts times table Counting in s, will help you know many times table facts. Complete each pattern by counting in s: a 4 4 8 b 3 34 c 8 6 Show how many dots there are in each array by counting in s. Then write the times table fact below: c 3 twos = a 6 twos = b 8 twos = d 5 twos = e 4 twos = f 9 twos = Multiplication and Divion D 8
Multiplication facts 4 times table Practe your 4 times table. Write the multiplication fact for each array: a 3 fours b 4 fours c 5 fours d 6 fours e 7 fours f 9 fours How many cupcakes are there on: a 4 plates? b 3 plates? c 7 plates? d 9 plates? e plates? Multiplication and Divion D 0
Multiplication facts 3 times table 4 Label the number line so it goes up in 3s: 0 3 5 Write two turnaround facts for each array. The first one has been done for you. a 4 3 = b c 3 d e f Multiplication and Divion D 3
Multiplication facts square numbers A square number a number multiplied by itself. These arrays show the first 3 square numbers. = squared = = 4 squared = 4 3 3 = 9 3 squared = 9 Here another way to show square numbers. Look at the array shown on each grid and write the square number multiplication: a b c 4 squared = 6 squared = 7 squared = On th grid, shade the largest square number you can: squared = 3 Answer these: a 8 = squared b 5 = squared c 64 = squared Multiplication and Divion D 8
Divion linking multiplication and divion facts Knowing multiplication facts will help with divion facts. 6 4 6 4 4. 4 4 = 6 4 divided into 4 shares 6. Describe each of these arrays using one multiplication and one divion fact: a 4 = b 5 = 30 30 5 = c 6 6 4 = Th time, you are given part of the array. Complete the array and then write one multiplication and one divion fact that matches: a b c Multiplication and Divion D 4 30
Mental multiplication strategies doubling and halving We can change the factors of a multiplication question to make it easier. Look at 6 3. If we halve the larger factor and double the smaller factor, we make an array on the grid that the same size. Both arrays have the same amount of squares. Count the squares, are they equal to 8 6? 6 3 Halve Double 8 6 = 48 Make these problems easier by using doubling and halving. Shade an array for each: a 8 3 Halve Double b 4 4 Halve Double Multiplication and Divion E 3 0
Divion divion repeated subtraction Divion can also be thought of as repeated subtraction. Look at 30 5 =? Th question asking how many groups of 5 there are in 30. Jump in 5s along the number line and then count the jumps. 6 5 4 3 5 5 5 5 5 5 0 5 0 5 0 5 30 So, 30 5 = 6 Show these divion facts as repeated subtraction. First label the number lines and then show the jumps. a 36 6 = 0 36 b 3 = 0 Write a divion fact to match these number lines. Show the jumps. a 0 4 8 6 0 4 8 b 0 8 6 4 3 Multiplication and Divion E 4 4
Divion linking multiplication and divion facts Knowing multiplication facts will help with divion facts. Th because they are opposites. Look at how we can describe th array: 6 4 6 groups of 4 4. 4 6 = 4 4 groups of 6 4. 4 4 = 6 4 divided into 4 shares 6. 4 6 = 4 4 divided into 6 shares 4. Describe each of these arrays using two multiplication and two divion facts: a b c d Draw an array of 6 3 then describe it with multiplication and divion facts. Th also called a fact family. Multiplication and Divion E 4 5