# Teaching for mastery in primary maths

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## Exploring multiplication and division

• Year group: Year 3
• Term: Spring
• Topic: Multiplication and division
• Duration: 3 weeks
• Keystage: KS2
• Age Range: 7 to 8 yrs
• Unit can be taught out of sequence: N
• Week Range: 1 - 3

In this chapter, pupils solve multiplication and division problems in different contexts, including missing number problems.

Problems include measuring and scaling contexts, (eg, 4 times as high, 8 times as long etc.) and correspondence problems, in which m objects are connected to n objects (eg, if there are 3 hats and 4 coats, how many different outfits are possible?).

Through problem solving, pupils develop efficient mental methods and further understand the concepts of commutativity and associativity (eg, 4 × 12 × 5 = 4 × 5 × 12 = 20 × 12 = 240), as well as multiplication and division facts (eg, using 3 × 2 = 6, 6 ÷ 3 = 2 and 2 = 6 ÷ 3) to derive related facts (eg, 30 × 2 = 60, 60 ÷ 3 = 20 and 20 = 60 ÷ 3).

Pupils continue to read, write and interpret mathematical statements involving multiplication (×), division (÷) and the equals sign (=), starting with calculations involving one and two-digit numbers for the multiplication tables they know, and progressing to the formal written methods of short multiplication and division. The development of mental methods should be encouraged at all opportunities.

## Resources for this topic

### White Rose Maths

#### Multiplying by 10 - Discover

This worksheet is aimed at Y5 and looks at the effect of multiplying by 10. The worksheet encourages place value grids. Pupils will see the effect of multiplying by 10.
Subsequent questions build on this as pupils move through the exercise. Similar concept can be used for dividing by 10, which should help pupils then generalise about multiply by 100 and 1000.

#### Division Investigation

A simple division investigation that asks pupils to show what happens when you divide.
Pupils make whole squares to represent dividing by 4. You will need to make the link to the calculation explicit. Pupils will hopefully be able to see from the investigation what it means to make the whole and what the remain represents.

Pupils can then start to reason why the remainder can never big bigger than what you are dividing by. They also look for a pattern in the remainder too.

### Mathematics Mastery

#### Exploring multiplication and division

Select ‘View more’ for an accompanying video.

Enabling teachers to continuously develop their practice is a key element of the Mathematics Mastery Programme.

This CPD video provides step-by-step guidance on exploring multiplication and division.
Our videos aim to:

• Model teaching tips, techniques and clarify how to make connections between concrete, pictorial and abstract representations
• Support the teaching of different methods and concepts, rather than focusing on one method only
• Enhance subject knowledge and support non-specialists

Like what you see?

Mathematics Mastery is a professional development programme for teachers with a mission to transform mathematics education in the UK.

This task is just a taster of the complete classroom resources we offer. We also provide in-depth development training, online CPD, specialist support and assessment tools.

We believe all elements of our programme are vital in creating lasting change – enabling every child to enjoy and succeed in mathematics.

Want to find out more? Check out our free resources and blogs or join an information session.

#### Exploring multiplication and division

Encouraging pupils to calculate flexibly is a key element of the Mathematics Mastery programme.

This practical teaching guide helps you develop your pupils to apply their number sense when problem-solving and make connections between calculation strategies.

This guide exemplifies a teaching approach for exploring multiplication and division.

• The CPA approach should be incorporated to support pupils in making connections between calculation strategies
• Teachers can use this guidance to encourage flexible mathematical thinking

Like what you see?

Mathematics Mastery is a professional development programme for teachers with a mission to transform mathematics education in the UK.

This task is just a taster of the complete classroom resources we offer. We also provide in-depth development training, online CPD, specialist support and assessment tools.

We believe all elements of our programme are vital in creating lasting change – enabling every child to enjoy and succeed in mathematics.

Want to find out more? Check out our free resources and or join an information session.

### Resources shared by teachers

#### Year 3 - Multiplication and Division - Week 1

This is pack covers Year 3: Multiplication and Division. It covers the small steps Comparing statements, Related calculations and Multiply 2-digits by 1-digits (1).

The resources aim to help children gain a deeper understanding of the concepts covered during the week. Both representations and calculations are used to see the links between multiplication and division statements and children begin to concentrate on multiplication methods.

The resources include pictorial and abstract representations as well as reasoning and problem solving activities and more open-ended problems to support and extend your whole class.

I hope you find them useful.

This pack is also part of a bundle!

#### Year 3 - Multiplication and Division - Week 2

This is pack covers Year 3: Multiplication and Division: Multiply 2-digits by 1-digits (2), Divide 2-digits by 1-digits (1), Divide 2-digits by 1-digits (2) and Divide 2-digits by 1-digits (3).

The resources aim to help children gain a deeper understanding of the concepts covered during the week. Children build on previous learning and look at multiplication and division methods with and without exchanges using concrete apparatus and images to build conceptual understanding.

The resources include pictorial and abstract representations as well as reasoning and problem solving activities and more open-ended problems to support and extend your whole class.

I hope you find them useful.

This pack is also part of a bundle!

#### Year 3 - Multiplication and Division - Week 3

This is pack covers Year 3: Multiplication and Division: Multiply 2-digits by 1-digits (1&2), Divide 2-digits by 1-digits (1, 2 & 3), Scaling and How many ways?

The resources aim to help children gain a deeper understanding of the concepts covered during the week. Children apply previous learning of multiplication and division in new contexts. They also investigate scaling problems and are given and answer to see how many ways they can get there.

The resources include pictorial and abstract representations as well as reasoning and problem solving activities and more open-ended problems to support and extend your whole class.

I hope you find them useful.

This pack is also part of a bundle!

#### Year 3 - Multiplication and Division - Weeks 1-3

This bundle of resources covers Year 3 Multiplication and Division for the first 3 weeks of the spring term. The resources support a mastery approach to teaching mathematics. CPA (Concrete-Pictorial-Abstract) is promoted throughout therefore ensuring you have appropriate concrete resources in your classroom is recommended to make full use of the packs.

#### Year 3 – Multiplication and Division – Week 9 –equal groups, multiplying by 3 and dividing by 3

This pack of resources covers Year 3 multiplication and division for week 9 of the autumn term. The resources support a mastery approach to teaching mathematics. CPA (Concrete-Pictorial-Abstract) is promoted throughout therefore ensuring you have appropriate concrete resources in your classroom is recommended to make full use of the packs.

Week 9 includes worksheets and activities on:
- Multiplication – equal groups
- Multiplying by 3
- Dividing by 3
- The 3 times-table

I hope you find the resources useful. Feedback is very welcome.

#### Year 3 – Multiplication and Division – Week 10 – Multiplying by 4, dividing by 4 and 4 times-table

This pack of resources covers Year 3 multiplication and division for week 10 of the autumn term. The resources support a mastery approach to teaching mathematics. CPA (Concrete-Pictorial-Abstract) is promoted throughout therefore ensuring you have appropriate concrete resources in your classroom is recommended to make full use of the packs.

Week 10 includes worksheets and activities on:
- Multiplying by 4
- Dividing by 4
- The 4 times-table

I hope you find the resources useful. Feedback is very welcome.

#### Year 3 – Multiplication and Division – Week 11 – Multiplying by 8, dividing by 8 & the 8 times-table

This pack of resources covers Year 3 multiplication and division for week 11 of the autumn term. The resources support a mastery approach to teaching mathematics. CPA (Concrete-Pictorial-Abstract) is promoted throughout therefore ensuring you have appropriate concrete resources in your classroom is recommended to make full use of the packs.

Week 11 includes worksheets and activities on:
- Multiplying by 8
- Dividing by 8
- The 8 times-table

I hope you find the resources useful. Feedback is very welcome.

#### Maximum product-adding and multiplying in upper KS2

This task offers learners at Upper KS2 practice in calculating, deepening of conceptual understanding of number and the opportunity to reason with number. Working with the sum and product of pairs of numbers embeds number facts and understanding of the difference between addition and multiplication.

This resource is from the publication 'Assessment in the New National Curriculum- an ATM perspective', which is available for purchase from:
https://www.atm.org.uk/Shop/Newly-Available/Assessment-in-the-New-National-Curriculum

Join ATM for as little as 4.70 per month by Direct Debit and 25% off all publications.
https://www.atm.org.uk/Membership-Types

#### Missing numbers multiplication grids

This is useful for anyone who needs to use and apply their knowledge of times tables. It is made purposefully to not be in numerical order and some lines are repeated. I have found that understanding multiplication grids can be problematic for children. This is one document but it is differentiated.

#### Multiplying by 10 - Discover

This worksheet is aimed at Y5 and looks at the effect of multiplying by 10. The worksheet encourages place value grids. Pupils will see the effect of multiplying by 10.
Subsequent questions build on this as pupils move through the exercise. Similar concept can be used for dividing by 10, which should help pupils then generalise about multiply by 100 and 1000.