## Multiplication & Division Solve simple multiplication & division with apparatus & arrays. (Y1)

Hunters Hall Primary –Maths Planning Guidance Multiplication & Division Solve simple multiplication & division with apparatus & arrays. (Y1) Multipli...
Author: Bryce Williams
Hunters Hall Primary –Maths Planning Guidance

Multiplication & Division Solve simple multiplication & division with apparatus & arrays. (Y1) Multiplication: Finding patterns of numbers using a 100 square I can recognise some of the 2, 5 and 10 times-tables and can explain the patterns I see

Making sets of objects of the same size and counting objects in repeated sets.

Counting in twos, fives, tens and threes and using a number line.

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Arrays and repeated addition     4 x 2 or 4 + 4     2 x 4 or 2 + 2 + 2 + 2 Using Numicon and Cuisenaire rods to aid multiplication.

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How many socks are there altogether in these eight pairs? How many fingers are there altogether on six hands? There are 10 crayons in each box.

How many crayons are there altogether?

Hunters Hall Primary –Maths Planning Guidance  How many 2p coins make 20p? Count five hops of 2 along this number line. What number will you reach?  Put these coins in this box. How much have you put in the box altogether?

Division: I can share objects into equal groups and tell you how many there are in one group  How do you know you need to put the 20 animals in groups of 5? What clues are there? How many groups did you make?  Here are 20 counters. Arrange them in equal rows. Is there a different way to arrange them in equal rows?

Calculate & write multiplication & division calculations using multiplication tables. (Y2) Multiplication: Children to practice using arrays to represent and record number sentences and to explore the commutative law of multiplication: I know how to write number sentences for multiplication I can explain what my number sentences mean I can use arrays to help me work out multiplication  Explain how you work out how many dots there are without counting them all.  Here are 20 counters. How could you arrange them in equal rows?  How could you use a number sentence to show your arrangement? 4 + 4 + 4 + 4 + 4 = 20  Write this addition fact as a multiplication fact.  ×=

Is 5 × 3 the same as 3 × 5? How do you know?

Division: I can use sharing to work out divisions and can explain what I did I can use a number line to do multiplication and division and can work out remainders if there are any

Children to use arrays to explore division as well as multiplication. For example, an image for 56 ÷ 7 = 8 Either:  How many lots of 7 counters can I find? (grouping) Or  If I put these into 7 groups, how many will there be in each group?

Hunters Hall Primary –Maths Planning Guidance

As well as using arrays to explore multiplication relate children’s understanding of counting and times tables facts to help them with multiplication and division facts: I can count in steps of 2, 5 or 10  What is the multiple of 10 before 70?  What three numbers come next: 35, 40, 45, …?  What is the next even number after 24? I can recognise some of the 2, 5 and 10 times-tables and can explain the patterns I see I can use these patterns to see if other numbers belong to the sequence  Look at the numbers in the 5 times-table. What do you notice? If we carried on, what do you think the next number would be? If we carried on, do you think the pattern would continue? How do you know? Think of a number bigger than 100 that would be in the 5 times-table if we carried on. Why do you think that number would be in the table? I know some of my times-tables for 2, 5 and 10 I can use counting or other strategies for those I don’t know I know that multiples of 5 end in 5 or 0  What tips would you give someone who had forgotten the 10 times-table?  How could you use a 10 times-table fact such as 10 × 6 = 60 to work out a 5 times-table fact such as 5 × 6 = 30? I know my 2, 5 and 10 times-tables and can work out the division facts that go with them I can tell if a number is a multiple of 2, 5 or 10  Write the missing numbers in the boxes. 5 × 4 = 10 ×   × 5 = 50 45 ÷ 5 =   Draw rings around all the multiples of 5. 45 20 54 17 40 I can use a number line/arrays to do multiplication and division and can work out remainders if there are any  Harriet knows that 2 × 10 = 20. What is 2 × 11? How do you know?  Show me using a number line/arrays how you could show:

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Hunters Hall Primary –Maths Planning Guidance 3×4 2×6 Show me on a number line how you could do: 14 ÷ 2 15 ÷ 3 20 ÷ 5 Look at these diagrams:

Is 2 × 4 the same as 4 × 2? How do you know? I can use sharing to work out divisions and can explain what I did  Suppose 15 pencils were to be shared out between three children. How many pencils would each child get? Explain to me how you could work it out.  Explain to me how you would work out 20p divided equally among five people. How could you write it down?  What about 18 sweets between two people? How many more sweets would you need to give them 10 sweets each?  How many £2 coins do you get for £20? How do you know? I can use arrays to help me work out multiplication and division I can do multiplication and division in different ways and show how I do them  Explain how you work out how many dots there are without counting them all.  Here are 20 counters. How could you arrange them in equal rows?  How could you use a number sentence to show your arrangement?  4 + 4 + 4 + 4 + 4 = 20  Write this addition fact as a multiplication fact.  ×=

Recognise & use inverse. (Y2) Allow children to explore the relationship between multiplication and division through creating arrays.

What number sentences can you create from this array? 8 x 7 = 56 7 x 8 = 56 56 ÷ 7 = 8 56 ÷ 8 = 7 Can you make four number sentences using 3, 4 & 12 using either the x or ÷ symbols?

Children to apply their understanding to missing number sentences: I can work out the missing numbers in number sentences  Explain how you worked out the missing number in this number sentence: 24 ÷  = 6  What are the missing numbers? How do you know?  × 2 = 16 10 ×  = 40  ×  = 20 5 × 4 = 10 ×   × 5 = 50 45 ÷ 5 =   Make up some ‘missing-number’ problems for others to solve

Hunters Hall Primary –Maths Planning Guidance When I think I have the answer, I can put it in the number sentence and check whether it is correct

Multiply 2-digit by 1-digit (Y3) Arrays can be used to give a visual representation of the grid method of multiplication:

60 + 42 = 102 17 x 6 = 102 Progress to column method of multiplication:

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What is 4 × 2? What is 10 × 2? How could we use these facts to work out 14 × 2? Tell me two multiplication facts we could use to work out 16 × 2. What is the answer?

Mental methods: 13 x 2 = (10 x 2) + (3 x 2)

Multiply: o 2-digit by 1-digit o 3-digit by 1-digit (Y4)

Hunters Hall Primary –Maths Planning Guidance

Progressing to:

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What is 4 × 2? What is 10 × 2? How could we use these facts to work out 14 × 2? Tell me two multiplication facts we could use to work out 16 × 2. What is the answer? A square pool has sides 12 m long. If you walked around the edge of it, how far would you walk? What calculation did you do? How did you work it out? Altogether the four sides of a square picture frame are 60 cm long. How long is each side? What calculation did you do? How did you work it out? What two multiplication facts could you use to work out 13 × 3? Meg drew this number line. What calculation did she work out? 10 × 4 = 40 and 3 × 4 = 12. What is 13 × 4? How would partitioning help you to calculate 27 × 6? Give me an example of a two-digit by one-digit multiplication you could do mentally. Give me an example of a similar multiplication where you would use a written method. One length of the swimming pool is 25 metres. Jane swims 5 lengths of the pool. How far does Jane swim altogether?

Divide: 3-digit by 1-digit (Y4) Chunking method:

: Short division:

Hunters Hall Primary –Maths Planning Guidance

Model short division using counters:

Multiply: o 4-digits by 1-digit/ 2-digit (Y5) Grid method: 4567 x 6 is approx 5000 x 6 = 30000 4567 x 6 4000

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Extend to short standard method:

4567 x

6 42 (6 x 7) 360 (6 x 60) 3000 (6 x 500)

24000 (6 x 4000) 27404

Hunters Hall Primary –Maths Planning Guidance

Chunking:

Divide: o 4-digits by 1-digit (Y5) Long division:

Short division:

Multiply & divide: Whole numbers & decimals by 10, 100 & 1000 (Y5) I can multiply and divide by 10 and 100. I can explain what happens to the digits when I do this I can multiply or divide a whole number by 10, 100 or 1000 I can multiply and divide whole numbers and decimals by 10, 100 and 1000

Show children how multiplying a number by 10 moves the digits one place to the left, and multiplying by 100 moves the digits two places to the left.

Demonstrate the effect of dividing a number by 10. Show children how the digits move one place to the right, and when dividing by 100 the digits move two places to the right.

Hunters Hall Primary –Maths Planning Guidance

Extend to x and ÷ by 1000 and x and ÷ decimals by 10, 100 & 1000 Use a calculator or the Moving digits ITP to model how it is the digits and not the decimal point that move when we multiply or divide by powers of 10.

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Why do 6 × 100 and 60 × 10 give the same answer? I have 37 on my calculator display. How can I change it to 3700 in one operation? Is there another way to do it?  What number is 10 times smaller than 2450? What number is 100 times bigger than 36?  I divide a four-digit number by 100. The answer is between 70 and 75. What could the four-digit number be?  Change 4527 pence into pounds. Change £10.39 to pence.  Explain the calculation you would use to change 25 to 2500.  How many tens are there in 200? How many hundreds in 2000?  If 4 × 6 = 24, what is 40 × 6 and 400 × 6? How could you quickly work out the answers to these calculations: 3 × 80, 120 ÷ 4?  The product of two numbers is 2000. What could the two numbers be?  This calculator display shows 0.1. Tell me what will happen when I multiply by 100. What will the display show?  What number is ten times as big as 0.01? How do you know that it is ten times 0.01?  I divide a number by 10, and then again by 10. The answer is 0.3. What number did I start with? How do you know?  How would you explain to someone how to multiply a decimal by 10?  What is a quick way to multiply by 1000? To divide by 100?  How many hundreds are there in one thousand?  Divide 9300 by 100.  Write in the missing number: 3400 ÷  = 100  Write what the four missing digits could be:  ÷ 10 = 3  What number is ten times as big as 0.05? How do you know that it is ten times 0.05?  Divide 31.5 by 10.  I divide a number by 10, and then again by 10. The answer is 0.3. What number did I start with? How do you know? How would you explain to someone how to multiply a decimal by 10?

Multiply: o 4-digit by 2-digit (Y6) I can multiply a 3-digit number by a 2-digit number using a written method. I can explain each step of my calculation I can multiply a 4-digit number by a 2-digit number using a written method. I can explain each step of my calculation Practice multiplying 3-digit by 2-digit before moving on to 4-digit by 2-digit

Hunters Hall Primary –Maths Planning Guidance 286  29 4000 1600 120 1800 720 54 8294

200  20  4000 80  20  1600 6  20  120 200  9  1800 80  9  720 6  9  54

extend to

286  29 5720 2574 8294

286  20 286  9

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Extend to multiplying 4-digit by 2-digit using an efficient method

Divide: 4-digit by 2-digit (Y6) Chunking method for 3-digit by 2-digit: 560 ÷ 24 24 560 20  480 24  20 80 3 72 24  3 8 Answer: 23 R 8

Extend to 4-digit by 2-digit Long division: