Here are some questions that children will need to solve by the end of Key Stage 1: Q1. Bill had some cherries. He ate half of them. These are the cherries he left How many cherries did he start with? Multiplication & Division Years 1 & 2 Q2. Anna has 50 pencils. She puts 5 pencils in each party bag. How many bags does she put pencils in? Q3. Bill makes cakes with these. Ella makes double the number of cakes. Write the missing numbers. A booklet for parents Help your child with mathematics 12
Children will be learning to: Multiplication & division Targets - Year 1 Using pictures or symbols Four eggs fit in a box. How many boxes would you need to pack 20 eggs? Recognise the place value of each digit in two-digit number (tens, ones) Use knowledge of counting in twos, fives and tens to derive the multiples of 2, 5 and 10 to the tenth multiple Recall the doubles of all numbers to at least 10 Solve practical problems that involve combining groups of 2, 5 or 10, or sharing into equal groups Use the vocabulary of halves and quarters in context Solve problems involving doubling or halving in the context of numbers, measures or money, for example to 'pay' and 'give change' * Solve 1 step problems involving multiplication, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher Solve 1 step problems involving division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher Recognise, find and name a half as one of two equal parts of an object, shape or quantity Recognise, find and name a quarters one of four equal parts of an object, shape or quantity Connect halves and quarters to the equal sharing and grouping of sets of objects Using symbols to stand for unknown numbers to complete number sentences as well as using inverse operations. 2 = 4 20 = 4 = 4 * Curriculum 2014 objectives in bold for both year groups. 2 11
Year 2 Children will develop their understanding of division and use jottings to support calculation Sharing equally 6 sweets shared between 2 people, how many do they each get? Children will be learning to: Multiplication & division Targets - Year 2 Recognise the place value of each digit in two-digit number (tens, ones) Count up to 100 objects by grouping them and counting in tens, fives or twos Find one half, one quarter and three quarters of shapes and sets of objects To derive and recall all pairs of multiples of 10 with totals up to 100 Solve problems involving addition, subtraction, multiplication or division in contexts of numbers, measures or pounds and pence Understand that halving is the inverse of doubling and derive and recall doubles of all numbers to 20, and the corresponding halves Derive and recall multiplication facts for the 2, 5 and 10 times-tables and the related division facts; recognise multiples of 2, 5 and 10 Grouping or repeated subtraction There are 6 sweets, how many people can have 2 sweets each? Represent repeated addition and arrays as multiplication, and sharing and repeated subtraction (grouping) as division; use practical and informal written methods and related vocabulary to support multiplication and division, including calculations with remainders Use the symbols +, -,, and = to record and interpret number sentences involving all four operations; calculate the value of an unknown in a number sentence (e.g. 2 = 6, 30 - = 24) * Count in steps of 2, 3 and 5 from 0, and in 10s from any number, forward and backward recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers Repeated subtraction using a number line 12 3 = 4 calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication ( ), division ( ) and equals (=) signs show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts. recognise, find, name and write fractions 1 / 3, 1 / 4, 1 / 2 and 3 / 4 of a length, shape, set of objects or quantity write simple fractions for example, 1 / 2 of 6 = 3 and recognise the equivalence of 2 / 4 and 1 / 2. 10 3
Multiplication Strategies They may use symbols to represent pictures. 6 cakes shared between 2 people Year 1 Children will experience equal groups of objects and will count in 2s 5s and 10s. They will work on practical problem solving activities involving equal sets or groups. 6 cakes put into groups of 2 Example of children recording place settings. Solve practical problems that involve sharing into equal groups. Pictures or symbols How many apples in each bowl if I share 12 apples between 3 bowls? Count repeated groups of the same size (1s, 2s, 5s, 10s) Counting sets of pictures, objects, cubes or coins (2p, 5p, 10p) 3 plates, 2 cakes on each plate: 4 9
Division Strategies Or using symbols to represent objects (quicker than drawing pictures) 3 plates, 2 cakes on each plate: Year 1 Children will understand equal groups and share items out in play and problem solving. If I have 12 biscuits and share them between three children how many will we have each? Solve practical problems that involve combining groups of 2, 5 or 10 Using pictures or symbols There are three sweets in one bag. How many sweets are there in five bags? Children will share objects into equal groups and count how many in each group. They will use pictures or objects 6 cakes shared between 2 people Using number lines 3 x 2 is three groups of two 6 cakes put into groups of 2 8 5
Year 2 Children will develop their understanding of multiplication and use jottings to support calculation: Jottings 3 lots of 5 or 3 sets of 5 or 3 groups of 5 Commutativity Children should know that 3 x 5 has the same answer as 5 x 3. This can also be shown on the number line. 3 x 5 = 5 + 5 + 5 Repeated addition 3 times 5 is 5 + 5 + 5 = 15 or 3 x 5 5 x 3 = 3 + 3 + 3 + 3 + 3 Repeated addition can be shown easily on a number line: Arrays Children should be able to model a multiplication calculation using an array. This knowledge will support with the development of the grid method. Using symbols to stand for unknown numbers to complete number sentences as well as using inverse operations. x 2 = 6 2 x = 6 x = 6 6 7