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National Curriculum Resource Tool

Materials to support teachers and schools in embedding the National Curriculum

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Year 3 - Multiplication and Division

New Curriculum

  • recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables
  • write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods
  • solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects.

Non-Statutory Guidance

Pupils continue to practise their mental recall of multiplication tables when they are calculating mathematical statements in order to improve fluency. Through doubling, they connect the 2, 4 and 8 multiplication tables.

Pupils develop efficient mental methods, for example, using commutativity and associativity (for example,4 × 12 × 5 = 4 × 5 × 12 = 20 × 12 = 240) and multiplication and division facts(for example, using 3 × 2 = 6, 6 ÷ 3 = 2 and 2 = 6 ÷ 3) to derive related facts(for example,30 × 2 = 60, 60 ÷ 3 = 20 and 20 = 60 ÷ 3).

Pupils develop reliable written methods for multiplication and division, starting with calculations of two - digit numbers by one - digit numbers and progressing to the formal written methods of short multiplication and division.

Pupils solve simple problems in contexts, deciding which of the four operations to use and why. These include measuring and scaling contexts, (for example, four times ashigh, eight times as long etc.) and correspondence problems in which m objects are connected to n objects (for example, 3 hats and 4 coats, how many different outfits?; 12 sweets shared equally between 4 children; 4 cakes shared equally between 8 children).

Links and Resources

Teachers should use every relevant subject to develop pupils’ mathematical fluency. Confidence in numeracy and other mathematical skills is a precondition of success across the national curriculum.
Teachers should develop pupils’ numeracy and mathematical reasoning in all subjects so that they understand and appreciate the importance of mathematics.

– National Curriculum in England Framework Document, September 2013, p10

Connections within Mathematics

Making connections to other topics within this year group

When focusing on aspects of ‘Number and Place Value’ in Year 3, in particular when counting in steps of 4, 8, 50 and 100, children will have the opportunity to link with work on multiplication and division.

When interpreting and presenting data using bar charts, pictograms and tables in Year 3, children can use their knowledge of multiplication facts when creating and reading scales and data sets.

Making connections to this topic in adjacent year groups

Year 2

  • recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers
  • 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.

Non-Statutory Guidance

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, to arrays and to repeated addition. They begin to relate these to fractions and measures (for example, 40 ÷ 2 = 20, 20 is a half of 40). They use commutativity and inverse relations to develop multiplicative reasoning (for example, 4 × 5 = 20 and 20 ÷ 5 = 4).

Year 4

  • recall multiplication and division facts for multiplication tables up to 12 × 12
  • use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together three numbers
  • recognise and use factor pairs and commutativity in mental calculations
  • multiply two-digit and three-digit numbers by a one-digit number using formal written layout
  • solve problems involving multiplying and adding, including using the distributive law to multiply two digit numbers by one digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects.

Non-Statutory Guidance

Pupils continue to practise recalling and using multiplication tables and related division facts to aid fluency.

Pupils practise mental methods and extend this to three-digit numbers to derive facts, (for example 600 ÷ 3 = 200 can be derived from 2 x 3 = 6).

Pupils practise to become fluent in the formal written method of short multiplication and short division with exact answers (see Mathematics Appendix 1).

Pupils write statements about the equality of expressions (for example, use the distributive law 39 × 7 = 30 × 7 + 9 × 7 and associative law (2 × 3) × 4 = 2 × (3 × 4)). They combine their knowledge of number facts and rules of arithmetic to solve mental and written calculations for example, 2 x 6 x 5 = 10 x 6 = 60.

Pupils solve two-step problems in contexts, choosing the appropriate operation, working with increasingly harder numbers. This should include correspondence questions such as the numbers of choices of a meal on a menu, or three cakes shared equally between 10 children.

Cross-curricular and real life connections

Learners will encounter aspects of multiplication and division when working on area, relating to arrays. Problem solving work involving finding all possibilities and combinations also draws on knowledge of multiplication tables facts.

Fractions work within other curriculum areas and in real life links naturally to multiplication and division work.

The notion of equal groups can emerge in many different activities and contexts, e.g. when packing boxes, purchasing quantities of items for several people etc.

A useful article that discusses the ways in which arrays can be used to represent the concept of multiplication and division, extending to the use of open arrays to represent properties of larger numbers and calculations with larger numbers.

An article on how one school developed a whole school approach to teaching times tables through songs that the children wrote themselves. Explores research into alternatives to traditional rote learning and ideas surrounding application.

  • Anghileri, J. (2008). Uses of counting in multiplication and division. In: Thompson, I Teaching and Learning Early Number. 2nd ed. Maidenhead: Oxford University Press. 110-123.

An interesting chapter about the role of and progression in counting for children to develop understanding and fluency in calculating in this strand of mathematics.

Here Jenni Back offers advice on the possible difficulties that arise when teaching division and offers links to NRICH activities that can support children’s understanding in these difficult areas.

Programme of Study statement Activity
A B C D E
recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables
write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods    
solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects.      

Activity A – Always, Sometimes, Never

A wonderful, generic resource that can be adapted to suit learners of different abilities as well as different aspects of the curriculum. Versatile resource to use to spark discussion and gain a deep insight into pupils’ understanding of a concept. This set is specifically for division and multiplication.

Activity B – Using pendulum to count in equal steps

Children choose their individual target table and count in steps of their chosen multiple silently in their head in time to pendulum / counting stick etc. Teacher stops and children give the number they have reached and times table facts for that multiple.

Activity C – Arrays for TU x U

Interactive website that gives the array model for the calculation and children input the missing numbers. Also provides an empty numberline representation of the calculation to support children’s developing mental strategies. Arrays can be printed / matched to word problems or children can write their own word problems for the arrays/ calculations.

Activity D – Multiplication involving multiples of 10 and 100, describing effects and moving onto modelling multiplication of 2 digit numbers

Year 3 lessons 131 – 140 from the Centre for Innovation in Mathematics Teaching: MEP

These activities are quite challenging and are based around whole class interactive teaching with pupils having regular opportunity to explain, self correct and reason. There are a number of shorter tasks in each lesson, giving the children chance to engage with a concept in different ways.

Activity E – Andy’s Marbles

A challenging problem that requires children to link multiplication, division and fractions to find the number of marbles Andy started with. A perfect example for the use of the Bar Model.

Useful Resources

  • Counters
  • Hundred squares
  • Times table squares
  • Counting stick
  • Cuisenaire rods
  • Place value discs

Examples of what children should be able to do, in relation to each (boxed) Programme of Study statement

recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables
  • multiply seven by three; what is four multiplied by nine? Etc.
  • Circle three numbers that add to make a multiple of 4

    11 12 13 14 15 16 17 18 19
     
  • Leila puts 4 seeds in each of her pots. She uses 6 pots and has 1 seed left over. How many seeds did she start with?
  • At Christmas, there are 49 chocolates in a tin and Tim shares them between himself and 7 other members of the family. How many chocolates will each person get?
write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods
  • One orange costs nineteen pence. How much will three oranges cost?
  • Mark drives 19 miles to work every day and 19 miles back. He does this on Mondays, Tuesdays, Wednesdays, Thursdays and Fridays. How many miles does he travel to work and back in one week?
solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects

Miss West needs 28 paper cups. She has to buy them in packs of 6

How many packs does she have to buy?

Times Tables in Ten Minutes

A wonderful video from the ATM YouTube Channel where Jill Mansbergh shows a way of using a counting stick to learn times tables facts and the relationships between them. Can be adapted for any times table.