1. Explaining how we teach mathematics, and what you can do to help your child become a confident mathematician. Fawkham C.of E. Primary School Welcome to session two

2. What are we going to talk about this afternoon? Multiplication and Division Strategies Calculation methods Vocabulary: vital and constantly referred to through all our teaching. Using and applying: using the calculation methods in situations that have meaning. We use a consistent, progressive approach KS1 –Focus on mental calculation strategies KS2 -Informal written method leading to a standard written method Produced by Mrs. S. Connor Fawkham C of E Primary School

3. Starting to understand multiplication: Begin to relate addition to combining 2 groups of objects, counting all the objects. Activities: Count out 3 cakes. Now count out 3 more cakes. How many cakes are there altogether? There are 4 cars in the garage 4 more arrive. How many cars are in the garage now. The children: understand and use one-to-one correspondence when counting. know that the last number name spoken is the answer to questions such as “How many objects are there?” hold one number in their heads and count on when adding numbers. Produced by Mrs. S. Connor Fawkham C of E Primary School

4. Understanding multiplication Know by heart addition doubles of all numbers to at least 5. Begin to know: addition facts for all pairs of numbers to a total of up to at least 10 Activities: There are 6 counters in the red cup and 6 counters in the blue cup. How many counters are there altogether? Can you record this to show me what you did? What is double 4? Which two numbers would make a total of 8, 12, 14? What is double 10? What is double 4? How could we work out double 14? The children: understand that double 5 is 5 + 5 and use their knowledge of addition to find doubles. use their knowledge of doubles to 10 to find new doubles. Double and halve dart board Produced by Mrs. S. Connor Fawkham C of E Primary School

5. Understanding multiplication array Understand the operation of multiplication as repeated addition or as describing an array. Activities: How could you arrange 12 counters in equal rows? Can you record your arrangement in a number sentence using addition? Can you record it using multiplication? How can you use your knowledge of number facts to find a quicker way of working out 3 + 3 + 3 + 3 that does not involve addition? Can you use a picture to confirm that 3 x 2 = 6? Does 2 x 6 give the same answer as 6 x 2? Can you draw an array of dots to show why this is true? Explain your thinking. The children: Know that repeated addition such as 2 + 2 + 2 + 2 could be represented by 2 x 4. Are able to interpret and use images and models (e.g. sets, arrays, jumps along a number line) to carry out simple multiplication calculations. Can read and record number sentences. Produced by Mrs. S. Connor Fawkham C of E Primary School

6. I have 12 counters. How could I arrange them into equal rows? Arrays are a useful visual tool for multiplication and division Produced by Mrs. S. Connor Fawkham C of E Primary School

7. What number sentences could you write to go with this array? 2 x 6 = 126 x 2 = 12 6 + 6 = 12 2 + 2 + 2 + 2 + 2 + 2 = 12 We can also say that 12 ÷ 6 = 2 and 12 ÷ 2 = 6 Produced by Mrs. S. Connor Fawkham C of E Primary School

8. Can you think of any other ways to arrange the 12 counters? Produced by Mrs. S. Connor Fawkham C of E Primary School

9. What number sentences could you write to go with this array? 4 x 3 = 12 3 x 4 = 12 4 + 4 + 4 = 12 3 + 3 + 3 + 3 = 12 We can also say that 12 ÷ 4 = 3 and 12 ÷ 3 = 4 Produced by Mrs. S. Connor Fawkham C of E Primary School

10. Multiplication using jumps along a number line (repeated addition). 0 5 10 +5 0 2 4 6 8 10 +2 2 x 5 means jumps of 2 made 5 times or 2 jumps of 5 Produced by Mrs. S. Connor Fawkham C of E Primary School

11. 0 x 6 = 0 1 x 6 = 6 2 x 6 = 12 3 x 6 = 18 4 x 6 = 24 5 x 6 = 30 6 x 6 = 36 7 x 6 = 42 8 x 6 = 48 9 x 6 = 54 10 x 6 = 6 0 0 x 2 = 0 1 x 2 = 2 2 x 2 = 4 3 x 2 = 6 4 x 2 = 8 5 x 2 = 10 6 x 2 = 12 7 x 2 = 14 8 x 2 = 16 9 x 2 = 18 10 x 2 = 20 Multiplication facts are absolutely vital for progress with maths. The children need to know them thoroughly, so that they can use the knowledge not just in multiplication problems, but also in division, fractions, percentages, ratio etc. It is important that they learn division alongside multiplication. Multiplication can be seen as repeated addition 4 + 4 + 4 + 4 + 4 = 5 x 4 (5 lots of 4 make 20) Division can be seen as repeated subtraction. 20 – 4 – 4 – 4 – 4 – 4 = 0 (How many 4s have we taken away?) so 20 ÷ 4 = 5 Produced by Mrs. S. Connor Fawkham C of E Primary School

12. Times table awards By the time the children come into year 3 they should already be confident with the 2, 5 and 10 times tables. To help motivate the children to learn their times tables in class 2 we have times table awards. For being able to recite the times table they earn a bronze sticker. For being able to answer random questions from the times table they earn a silver sticker. For being able to answer division questions, word problems, fraction questions using that times table they earn a certificate with a gold sticker that is presented in front of the school. 0 x 2 = 0 1 x 2 = 2 2 x 2 = 4 3 x 2 = 6 4 x 2 = 8 5 x 2 = 10 6 x 2 = 12 7 x 2 = 14 8 x 2 = 16 9 x 2 = 18 10 x 2 = 20 0 x 2 = 0 1 x 2 = 2 2 x 2 = 4 3 x 2 = 6 4 x 2 = 8 5 x 2 = 10 6 x 2 = 12 7 x 2 = 14 8 x 2 = 16 9 x 2 = 18 10 x 2 = 20 0 x 6 = 0 1 x 6 = 6 2 x 6 = 12 3 x 6 = 18 4 x 6 = 24 5 x 6 = 30 6 x 6 = 36 7 x 6 = 42 8 x 6 = 48 9 x 6 = 54 10 x 6 = 6 0 Produced by Mrs. S. Connor Fawkham C of E Primary School

13. Speed races By the time the children leave year 2 they should know their number bonds (as listed last week), doubles etc. In Class 2 we revise these, then move onto ensuring that they can recall mixed up times tables with the added pressure of time. They answer 50 questions in 3 minutes, if they get them all right they move onto the next list next time. If they get less than 48 correct they get the same list again next time. They are rewarded with merit marks when they improve their best score. Produced by Mrs. S. Connor Fawkham C of E Primary School

14. Know by heart the 2, 3, 4, 5 and 10 multiplication tables Use these facts to derive new facts Two numbers multiplied together make 20. What could the two numbers be? A baker puts 5 buns in each of 10 rows. How many buns are there? How would you write 25 + 25 + 25 + 25 as a multiplication calculation? Using the numbers 2, 4, 15, 30 and 50. Work out six different multiplication calculations. How do you work out 4 x 30? 40 x 30? The children: can use their knowledge of multiplication to check calculations and solve problems respond rapidly to oral or written questions and, where appropriate, explain the strategy used, e.g. 7 times 4 (known off by heart); what is the product of 15 x 4 (they explain strategy)? are able to work out e.g. the 6 times table by adding the 2 times table facts to the 4 times table facts or doubling the 3 times table facts. Place value Darts Hit the button Tables wheel Produced by Mrs. S. Connor Fawkham C of E Primary School

15. Multiplying and dividing by 10 and 100 We learn how to move the digits. The bully 10 or 100 pushes the digits over. Multiply by 10 move the digits one place to the left Multiply by 100 move the digits two places to the left Divide by 10 move the digits one place to the right Divide by 100 move the digits two places to the right. Moving the digits over demonstration 10 Produced by Mrs. S. Connor Fawkham C of E Primary School

16. Know by heart all multiplication facts up to 10 x 10 Extend written methods Work out 47 x 5 by partitioning 47, e.g. (40 x 5) + (7 x 5) = 200 + 35 = 235 and by the grid method. 72 x 38 = ? What is the approximate answer? Use the grid method to work out the exact answer. Look at these multiplications. 43 63 64 46 x6 x4 x3 x6 Which gives the biggest answer? Can you explain why? The children: use pencil and paper methods to support, record or explain calculations, achieving consistent accuracy approximate first and explain orally how their method works know that when calculations are set out in columns units should line up under units, tens under tens, etc. X with arrow cards Produced by Mrs. S. Connor Fawkham C of E Primary School

17. Using and applying This is when the problem appears in a story that is, or could be real. How can we use multiplication to help us solve this word problem? Sam had 6 packets of balloons for his party. Each packet contained 38 balloons. How many balloons would Sam blow up altogether? The first problem is to identify the sum needed. Produced by Mrs. S. Connor Fawkham C of E Primary School

18. What would the calculation look like? 6 x 38 = What would the approximate answer be? 6 x 40 = 240 We know that 38 rounds to 40 6 x 4 = 24 so…… Produced by Mrs. S. Connor Fawkham C of E Primary School

19. 38 x 6 = 30 6 8 228 180 48+ 120 (80 + 40) 100 (100 + 0) 228 18048 8 (0+ 8) Grid multiplication Grid method TU x U Having worked out an approximate answer does this answer look likely to be correct? Produced by Mrs. S. Connor Fawkham C of E Primary School

20. Use written methods of multiplication of numbers including decimals What two numbers multiplied together result in the answer 370? Give the children some worked examples that are incorrect. Are they correct? How do you know? How could we put them right? If we know 357 x 27 = 9639, what other multiplication and division facts can we derive? e.g. 357 x 2.7 = 963.9 What is the approximate answer to 4.96 x 3? What is the exact answer? Which of these calculations do you think will give the larger answer: 13.7 x 8 or 13.8 x 7? Carry out the calculation to confirm your answer. The children: are aware that approximating first enables checking whether the answer is realistic. understand that an appropriate written method should be chosen according to the numbers involved. are secure in using mental jottings, informal methods or standard written methods appropriate to the problem. Increasingly complex contexts should be used including multiplication and division by TU and U.t Produced by Mrs. S. Connor Fawkham C of E Primary School

21. Pupils learn to multiplyTU by TU; for example; 23 x 14 = (20 x 10) + (20 x 4) + (3 x 10) + (3 x 4) This is set out in the grid method. x 20 3 10 200 30 = 230 4 80 12 = 92 322 1 23 x 14 = Produced by Mrs. S. Connor Fawkham C of E Primary School

22. 23 x 14 12 (4 x 3) 80 (4 x 20) 30 (10 x 3) 200 (10 x 20) 322 23 x 14 92 (4 x 23) 230 (10 x 23) 322 Then pupils will then be taught a more traditional method. For example: leading to: They will progress to using bigger numbers and decimals. Produced by Mrs. S. Connor Fawkham C of E Primary School

23. Division goes alongside multiplication Division as sharing To start with the children learn to share objects into equal groups Then write the number sentence; 6 shared between 2 is 3 each, 6 ÷ 2 = 3 We use visual images, record jottings and use number sentences for division. Division as grouping or chunking (repeated subtraction) 20 spots in groups of 5 (columns). 20 spots in groups of 4 (rows). Using a number line 20 ÷ 5 = 4 20 divided into groups of 5 equals 4 05101520 The family of sums 4 x 5 = 20 5 x 4 = 20 20 ÷ 4 = 5 20 ÷ 5 = 4 Using arrays Division on a number line Produced by Mrs. S. Connor Fawkham C of E Primary School

24. Learn to divide a two digit number by a single digit, including with remainders. We do this by ‘chunking’ Taking away chunks of the number. 78 ÷ 6 78 take away 60 (10 lots of 6) Leaving 18 (3 lots of 6) So we can see that 78 ÷ 6 is 13 52 ÷ 3 Take away 30 (10 lots of 3) Leaving 22 Take away 21 (7 lots of 3) Leaving 1 remainder So we can see that 52 ÷ 3 is 17 r 1 Produced by Mrs. S. Connor Fawkham C of E Primary School

25. 12 remainder 3 or 7 86 -70(10 x 7) 16 -14( 2 x 7) 2 2727 chunking Produced by Mrs. S. Connor Fawkham C of E Primary School

26. Useful tricks: Knowing that the two times table is also the doubles number bonds that they should already know (all answers are even numbers). 4 times table is double the two times table (all answers are even numbers). 8 times table is double the four times table (if they can double two digit numbers quickly in their head this is a useful skill) (all answers are even numbers). 6 times table is double the 3 times table (all answers are even numbers). 6 times table is the 4 times table plus the 2 times table, or 5 times table + 6. Multiples of the 5 times table always end in 0 or 5. Little rhymes that help with some of the trickiest multiplication facts: I ate and I ate till I was sick on the floor 8 times 8 is 64. 5, 6, 7, 8 56 is 7 x 8 Produced by Mrs. S. Connor Fawkham C of E Primary School

27. These are some of the activities that we carry out, trying to make learning tables fun and keep the children motivated. Number grids Function machines Matching pairs Produced by Mrs. S. Connor Fawkham C of E Primary School

28. Thank you for attending Questions? Please look at some of the resources we use. Don’t forget the next sessions Tuesday 2:30-3:00 24 th November 1 st December Produced by Mrs. S. Connor Fawkham C of E Primary School