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Longfield Primary School

Longfield Primary School. Maths Workshop for Year 2 Parents and Carers 26 January 2015 Mrs Claire Searle – Maths Leader. Multiplication and Division. What do you understand by: Multiplication? Division? What vocabulary can you think of that applies to each of them?

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Longfield Primary School

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  1. Longfield Primary School Maths Workshop for Year 2 Parents and Carers 26 January 2015 Mrs Claire Searle – Maths Leader

  2. Multiplication and Division • What do you understand by: • Multiplication? • Division? • What vocabulary can you think of that applies to each of them? • What equipment, pictures or images can you think of that might help children when starting multiplication and division?

  3. Multiplication • X • repeated addition eg 5 x 3 is the same as (equals) 3 + 3 + 3 + 3 + 3 • times • lots of • groups of • multiplied by • multiply • times tables • double

  4. Division • ÷ • Repeated subtraction eg 20 ÷5 = 20 – 5 – 5 – 5 - 5 • Divide • Divided by • Share • Share equally • Groups • Lots • Halve

  5. What is a maths operation?

  6. What do Year 2 pupils need to know and do using multiplication and division?

  7. Recall and use multiplication and division facts for the 2, 5 and 10 times tables including recognising odd and even numbers. • Children need to know: • Each multiplication table from • 0 x 2 to 12 x 2 • 0 x 5 to 12 x 5 • 0 x 10 to 12 x 10 • They need to be able to count in 2s, 5s and 10s, forwards and backwards – at least to the end of that table, and ideally to 100 for 2 and 5. • They need to know facts such as 2 more than 14, 5 less than 25. They also need to be able to answer questions quickly such as ‘What is 10 times 5?’ ‘Twelve lots of 10?’ ‘How many groups of 2 in 22?’ How many fives in 45? These are multiplication and division facts.

  8. Your turn! • Write the answers: 8 times 10? How many 2s in 18? What are nine groups of five? Sixteen is how many groups of two? What is 8 multiplied by 5? Divide 120 by 10. Seven twos are ... ? How many 10s in 50?

  9. Recognising odd and even numbers Children need to know whether a number is even or odd to know what will happen when it is multiplied or divided. They need to know that even numbers will ... end in 2, 4, 6, 8 or 0. And odd numbers will ... end in 1, 3, 5, 7 or 9.

  10. Calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (x), division (÷) and equals (=) signs • This means multiplication statements for up to 12 x. • Eg 10 x 5 = 50 5 x 10 = 50 • 50÷ 10 = 5 50 ÷ 5 = 10 Try this! Write the multiplication and corresponding division statements for: 8 and 5 6 and 10 8 x 5 = 40 5 x 8 = 40 40 ÷ 5 = 8 40 ÷ 8 = 5 6 x 10 = 60 10 x 6 = 60 60 ÷ 6 = 10 60 ÷ 10 = 6

  11. Calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (x), division (÷) and equals (=) signs • Use x ÷ = to make these correct • 6 5  30 • 8  2  4 • 100  10  10 • Use 5 8 and 40 to make these correct •  x  =  • ÷ =  6 x 5 = 30 8 ÷ 2 = 4 100 = 10 x 10 or 100 ÷ 10 = 10 8 x 5 = 40 or 5 x 8 = 40 40 ÷ 8 = 5 or 40 ÷ 5 = 8

  12. Show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot • Commutative – a tricky word that children in Year 2 are not expected to know – but they do need to understand the idea behind it. • Any ideas?

  13. Commutative operations • Addition and multiplication are commutative operations. This means that for these operations the numbers can be added or multiplied in any order and the answer will still be the same. (You can think of it like the word ‘commuter’ – like people the numbers can go back and forth or change place and still be the same!) • So 8 + 4 = 12 is the same as 4 + 8 = 12 • And 8 x 5 gives the same answer as 5 x 8. • But subtraction and division are not commutative. • 8 – 4 (= 4) is not the same as 4 – 8. (-4) • And 40 ÷ 5 (= 8) is not the same as 5 ÷ 40 (= 0.125) • Children need to be taught this – they don’t automatically know or recognise it, and often won’t notice or realise that they have written the calculation the wrong way round.

  14. Commutative operations • Try these calculations for yourself just to check what happens... • 8 x 10 = • 10 x 8 = • 50 ÷10 = • 10 ÷ 50 = 80 80 5 0.2

  15. Solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods and multiplication and division facts, including problems in contexts. • Problems – word problems or problems involving reasoning or working things out from known facts. • Contexts might mean using multiplication and division in other subjects, such as science, PE or history. • Could be problems involving measures, mass/weight, height/length, data.

  16. Arrays • These are examples of arrays found in the environment. What multiplications do they show?

  17. Arrays The multiplications for this array would be 2 x 4 = 8 or 4 x 2 = 8 • Oh dear! The naughty pup has chewed some of Sam’s stamps. How many stamps did Sam have to start with? What are the 2 possible multiplications for this array? What multiplication tables will help children with these questions?

  18. Your turn! Draw arrays to show these multiplications: 2 x 6 6 x 5 3 x 10

  19. Anything else? • Pupils use a variety of language to describe multiplication and division. • Pupils are introduced to the multiplication tables. They practise to become fluent in the 2, 5 and 10 multiplication tables and connect them to each other. They connect the 10 multiplication table to place value, and the 5 multiplication table to the divisions on the clock face. They begin to use other multiplication tables and recall multiplication facts, including using related division facts to perform written and mental calculations. • Pupils work with a range of materials and contexts in which multiplication and division relate to grouping and sharingdiscrete and continuous quantities, and relating these to fractions and measures (e.g. 40 ÷ 2 = 20, 20 is a half of 40). They use commutativity and inverse relations to develop multiplicative reasoning (e.g. 4 × 5 = 20 and 20 ÷ 5 = 4).

  20. Models and Images 2 + 2 + 2 + 2 + 2 = 10 5 groups of 2 or 5 x 2 = 10 2 multiplied by 5 or 5 multiplied by 2 5 pairs 5 hops of 2 5 + 5 + 5 + 5 + 5 + 5 = 30 6 groups of 5 or 6 x 5 = 30 5 multiplied by 6 or 6 multiplied by 5 6 groups of 5 6 hops of 5

  21. Models and images 10p + 10p + 10p +10p + 10p = 50p 5 times 10p = 50p 5 hops of 10p 5 x 10p = 50p On an empty numberline, draw the hops for this calculation and write the different ways you could work this out: 5p + 5p + 5p + 5p + 5p + 5p + 5p = 35p 7 times 5p = 35p 7 hops of 5p 7 x 5p = 35p

  22. Inverse operations • Multiplication and division are inverse operations. This means they are the reverse of each other. • Addition and subtraction are also inverse operations. • So an answer can always be checked by carrying out the calculation the other way round. 8 x 10 = 80 • 80 ÷ 10 = 8 or 80 ÷ 8 = 10

  23. Division by sharing One for you, and you and you and you and me. Keep going until they have all been used up. If there are any objects left over they are called the ‘remainder’.

  24. Division by sharing You can use any objects to represent the cakes, but ask a child to do this practically first – using concrete objects helps make the connection between real objects and the symbols we use in maths.

  25. Division by grouping Keep taking out groups of the same number. How many groups are there? Any left over that won’t make another group of the same number are the remainder.

  26. Questions for the end of KS1 • There are 4 apples in each pack. Mrs Pullen buys 3 packs of apples. How many apples does she buy? KS1 2001 level 2b Encourage your child to draw their answer. Have a go at drawing an answer to one of these questions now.

  27. Questions for the end of KS1 • There are 35 children. They get into teams of 5. How many teams are there altogether? • KS1 2003 level 3

  28. What is a fraction? • Talk to someone else – what do you think?

  29. What do Year 2 Pupils need to know and do with fractions?

  30. Talking Maths Which thought bubble shows the cake being shared equally? What are two parts that are equal called? What about the parts of the cake cut in 4? What are they called?

  31. What do you think?

  32. Exploring equivalence using a tangram What fraction is each part of the whole? What other fractions can you make? What equivalences can you find?

  33. Numerators and Denominators • A fraction is made up of 2 numbers. The top number is called the NUMERATOR and the bottom number is called the DENOMINATOR. In the fraction ¾, 3 is the numerator and 4 is the denominator. • DENOMINATOR • This number shows how many equal ‘pieces’ something has been divided into. In the fraction ¾, 4 is the denominator showing that there are 4 equal pieces making up the whole. • NUMERATOR • This number shows how many of those pieces there are. In the fraction ¾ there are 3 pieces out of the total of 4.

  34. Recognise, find, name and write fractions 1/3, ¼, 2/4 and ¾ of a length, shape, set of objects or quantity. How many stars make up 1/3 of the group? What is half of 12?

  35. Write simple fractions eg1/2 of 6 = 3 and recognise the equivalence of 2/4 = 1/2

  36. Equivalent fractions ½ = 2/4 = 3/6 = 4/8 = 5/10 = 6/12 = ... ¼ = 2/8 = 3/12 = 4/16 = 5/20 = ... 1/3 = 2/6 = 3/9 = 4/12 = 5/15 = ... ¾ = 6/8 = 9/12 = 12/16 ... Make fraction strips showing quarters, thirds, sixths,

  37. Questions for end of KS1

  38. Websites • http://www.bbc.co.uk/bitesize/ks1/maths/ • http://www.topmarks.co.uk/maths-games/5-7-years/multiplication-and-division • http://www.maths-games.org/times-tables-games.html • http://www.maths-games.org/fraction-games.html • http://primarygamesarena.com/Key-Stage-1

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