National Curriculum Resource Tool

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National Curriculum Resource Tool

Materials to support teachers and schools in embedding the National Curriculum

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National Curriculum Tool
Year 2 - Multiplication and Division

Year 2 - Multiplication and Division

New Curriculum

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).

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.

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

Connections within Mathematics

Making connections to this topic in adjacent year groups

Year 1

solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of a teacher.

Non statutory guidance:

Through grouping and sharing small quantities, pupils begin to understand: multiplication and division; doubling numbers and quantities; and finding simple fractions of objects, numbers and quantities.

They make connections between arrays, number patterns, and counting in twos, fives and tens.

Year 3

recall and use multiplication and division facts for the 3,4 and 8 times 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 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 (e.g. 4 x 12 x 5 = 4 x 5 x 12= 20 x 12 = 240) and multiplication and division facts (e.g. using 3 x 2 = 6, 6 ÷ 3 = 2 and 2 = 6 ÷3) to derive related facts (30 x 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, including measuring and scaling contexts, and correspondence problems in which m objects are connected to n objects (e.g. 3 hats and 4 coats, how many different outfits?; 12 sweets shared equally between 4 children; 4 cakes shared equally between 8 children).

Cross-curricular and real life connections

Learners will encounter multiplication and division in:

Money – shopping: finding quantities in multiple purchases, sales prices, sharing costs.

Measurement - calculating area and perimeter, finding journey distances, reading and calculating scales, adjusting recipe quantities.

Data – interpreting and evaluating data, calculating amounts from pie charts and pictograms.

Focus on: Having Fun with Function Machines, Primary and Early Years Magazine Issue 44

Lots of useful ideas about how to use a function machine, for all operations including multiplication and division.

Arrays, Multiplication and Division

Pennant, J. NRICH article.

How we can use arrays to help deepen children’s understanding of multiplication and division.

Difficulties with Division

Back, J. NRICH article.

Explores common misconceptions when learning division, and support s teachers with practical suggestions of how to overcome difficulties in teaching.

Programme of Study statements	Activity
Programme of Study statements	A	B	C	D
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 (x), 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.

Activity Set A

Multiplication tables - pelmanism style matching cards. Find the pairs of cards showing the product and multiplication fact in a timed activity.
Counting stick: using a metre stick with ten divisions use sticky notes to mark multiples of 2, 5 or 10. Practise counting on and back from different numbers. As the children become more fluent, remove more sticky notes and see how they can recall multiples starting at different points counting on and back.
BBC KS1 Bitesize: Camel Times Tables and Division Mine. These two games are a super resource for the children to practise their recall of multiplication and division facts independently.

Activity Set B

BBC KS1 Starship Number Jumbler game, a simple animation where children choose the missing operation sign in the calculation.
Write the calculation: give the children different pictures of groups of items or arrays. They then have to write the multiplication sentence to match the picture. 2p, 5p and 10p coins could be used for this activity. The children can write down how many of each coin they have and the total amount. Using coins, the children could also write division calculations to match the images.

Activity Set C

Triangle of numbers: a good activity to use as a starter or plenary, demonstrating the commutativity of multiplication. It can be used to demonstrate one number fact and the children can suggest the others.
Function box: reinforcing the relationship of division being the inverse of multiplication. To build up to this online activity, a function box could be made and used as a visual resource in class. For example, model how a number goes in and doubles, but put the number back through the machine it will halve. There are lots of different ways to use the function box in class to deepen the understanding of the relationship between multiplication and division.
Class number sentence: using digit cards and x and ÷ and = cards. Get the children to show how we can take one known fact and find others using those numbers. As the children move the digits around, they will demonstrate their understanding of using and applying their tables knowledge. What numbers can we move around in a division sentence? Can they spot the relationship between multiplication and division? Ensure they really understand the concept behind this activity, by encouraging them to show you with practical apparatus.

Activity Set D

TES word problems with differentiated questions: resources submitted by a Year 2 teacher, focusing on problem solving using multiplication.
BBC Class Clips: problem solving - how many chairs? Use multiplication facts to help the Chuckle Brothers organise their tables ready for their guests’ arrival.
Give the children a multiplication or division fact. Can they write a word problem to match it? Now swap calculations with a partner and talk about how you would solve the problem.

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 2, 5 and 10 multiplication tables, including recognising odd and even numbers

The children should be able to:

Recognise a multiple of 2, 5 or 10 and use their knowledge of multiplication facts to find corresponding division facts. They can say which numbers are odd and which are even.

e.g. 2 x 5 = 10, show me three more number facts using these numbers.

Is 34 an odd number? How do you know?

calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (x), division (÷) and equals signs

Children should be able to:

Find missing numbers or symbols in a calculation:

4 x __ = 20, __ ÷ 10 = 3

Anna has 3 boxes of cakes. Each box contains 5 cakes. How many cakes does she have altogether? Show how you worked this out.

show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot

Children should be able to:

Use their knowledge of triangles of numbers to show related number facts.

e.g. If 6 x 2 = 12 then 2 x 6 = 12 and 12 ÷ 6 = 2.

solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts

Children should be able to:

Use various methods and apparatus to help them solve word problems such as:

There are 10 lollies in a bag. Charlie needs 30 lollies for his party. How many bags does he need to buy? Show how you worked this out.

Multiple Representations of Multiplication

This video looks at the use of visual resources to develop clear conceptual understanding.

The commutative law for multiplication

This lesson, from the same collection of videos, shows children learning about commutativity using different apparatus.

BBC Learning Zone Class Clips

This video shows how a multiplication fact can be written down in different ways.

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