Maths Workshop for Year 2 Parents and Carers 7 December 2015 Mrs Claire Searle Maths Leader 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? X repeated addition eg 5 x 3 is the same as (equals) times lots of groups of multiplied by multiply times tables double Repeated subtraction eg 20 5 = 20 5 5 Divide Divided by Share Share equally Groups Lots Halve 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. 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? 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. 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 = 5 = 8 40 8 = 5 6 x 10 = x 6 = 6 = 10 = 6 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 = = 8 x 5 = 40 or 5 x 8 = 8 = 5 or 40 5 = 8 6 x 5 = 30 8 2 = = 10 x 10 or 100 10 = 10 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? 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 = 12 is the same as = 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 dont automatically know or recognise it, and often wont notice or realise that they have written the calculation the wrong way round. Try these calculations for yourself just to check what happens... 8 x 10 = 10 x 8 = 50 10 = 10 50 = 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. These are examples of arrays found in the environment. What multiplications do they show? The multiplications for this array would be 2 x 4 = 8 or 4 x 2 = 8 What are the 2 possible multiplications for this array? What multiplication tables will help children with these questions? Oh dear! The naughty pup has chewed some of Sams stamps. How many stamps did Sam have to start with? Draw arrays to show these multiplications: 2 x 6 6 x 5 3 x 10 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 sharing discrete 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). = 10 5 groups of 2 or 5 x 2 = 10 2 multiplied by 5 or 5 multiplied by 2 5 pairs 5 hops of = 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 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 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 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. 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. Keep taking out groups of the same number. How many groups are there? Any left over that wont make another group of the same number are the remainder. There are 4 apples in each pack. Mrs Pullen buys 3 packs of apples. How many apples does she buy? KS level 2b Encourage your child to draw their answer. Have a go at drawing an answer to one of these questions now. There are 35 children. They get into teams of 5. How many teams are there altogether? KS level 3 8 x 5 = 24 2 = stickers Talk to someone else what do you think? 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? Exploring equivalence using a tangram What fraction is each part of the whole? What other fractions can you make? What equivalences can you find? 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 , 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 , 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 there are 3 pieces out of the total of 4. How many stars make up 1/3 of the group? What is half of 12? Write simple fractions eg 1 / 2 of 6 = 3 and recognise the equivalence of 2 / 4 = 1 / 2 Equivalent fractions = 2 / 4 = 3 / 6 = 4 / 8 = 5 / 10 = 6 / 12 =... = 2 / 8 = 3 /12 = 4 / 16 = 5 / 20 =... 1 / 3 = 2 / 6 = 3 / 9 = 4 / 12 = 5 / 15 =... = 6 / 8 = 9 / 12 = 12 / 16 =... Make fraction strips showing quarters, thirds, sixths, Questions for end of KS1 Questions for end KS1 2016 SATs of 16 = of 40 = games/5-7-years/multiplication-and- divisiongames/5-7-years/multiplication-and- division games.htmlgames.html games.htmlgames.html