Number: Calculations with four operations

Throughout these chapters, pupils explore the importance of using operations in the correct order.

Previously, pupils will have used all four operations, sometimes in combination, to solve problems.

In this topic, they will start to understand the importance of the order in which calculations are performed and the impact that this has on the answer.

Calculations with four operations: Teaching for mastery booklet

Brought to you by Tes in partnership with experts at Mathematics Mastery and the White Rose Maths Hub, this PDF provides teachers with the progression of learning for the topic, broken down into digestible chapters.

It is an ideal starting point for primary teachers looking to brush up on their subject knowledge, or adopt the mastery approach to maths in their classroom.

Check out the Teaching for mastery site, which contains schemes of work accompanied by quality-assured classroom resources.

Download resources to match this topic in the planning and lesson resources pages of the new primary maths section.

By Tes Resources Team

Teacher's guide: Teaching for mastery booklet

Brought to you by Tes in partnership with experts at Mathematics Mastery and the White Rose Maths Hub, this PDF provides teachers with the progression of learning for the topic, broken down into digestible chapters.

It is an ideal starting point for primary teachers looking to brush up on their subject knowledge, or adopt the mastery approach to maths in their classroom.

Check out the Teaching for mastery site, which contains schemes of work accompanied by quality-assured classroom resources.

Download resources for all primary maths topics in the planning and lesson resources pages of the new primary maths section.

By Tes Resources Team

Chapter 1: Combining addition, subtraction, multiplication and division

In this chapter, pupils solve problems using all four operations.

Pupils continue to solve problems involving addition, subtraction, multiplication and division, and demonstrate their understanding of the meaning of the equals sign. As they begin to solve problems combining all four operations, they appreciate the importance of the order in which operations are used.

Take this problem, for example: “If 3 boxes each contain 5 counters and 4 boxes each contain 10 counters, how many counters are there is total?” Here, pupils recognise the importance of multiplying before adding the resulting answers.

Chapter 2: Calculations with four operations

In this chapter, pupils use their knowledge of the order of operations to carry out calculations and solve problems.

When given a long calculation, pupils often work from left to right. This frequently leads to the incorrect answer. Experience of this error, particularly in meaningful contexts, helps pupils to understand the importance of calculation order. 

In time, pupils know that calculations in brackets should be completed first, before moving onto powers, addition and subtraction, and multiplication and division. Pupils continue to use mental methods to calculate and estimate answers to problems. 

Approved resources

Word Problems in context - Sammy's Sports Shop

Word problems using all four operations, including single and multi-step problems and an open-ended extension activity (to keep even the brightest occupied!) Encourages children to use their own reliable methods of working out, but also to record and show working out accurately.
By tp_1986

Mixed Word Problems Year 3 / 4

Mixed word problems using all four operations. Children tick the operations that they will use. These are in word so you can adapt.
By natashacordwell

New York Budgeting Activity

Adapted this from a format I saw on another website. I planned it for a group of high level 4 year 5 children for an NQT assessment lesson. The children were absolutely hooked by it and really enjoyed themselves. Took about 3-4 lessons to actually complete in the end. Requires the children to be able to use all operations securely, and have a good knowledge of fractions, decimals and percentages.
By kj226

2 step word problems for year 4/5, all operations

Using the Dexter and Dood superhero range of resources, the children can read these puzzle, access the key information and then write a number sentence using written methods. There are colourful and in most cases require more than one calculation to find the answer.
By hilly100m

Arrays and repeated addition as multiplication

Here is a worksheet which looks at arrays and repeated addition as multiplication. It has a focus on pirates as this is what my class have been looking at.
By Maximus26

Related resources

100 Mental Maths starters

Designed to jump start Maths lessons. Each slide has three questions when run as a slide show (so there's actually 300 questions). Each question is progressively harder as it goes along (in built differentiation!). Intended as 1 a day starter before leaping into the full lesson but could be used as a 'filler' for rainy days. Based on several other excellent resources I found, combined and added to!
By theautisticteacher

BIDMAS Worksheet

Using BIDMAS Putting in brackets Puuting in correct operations

By ems21

Written Methods Game

Board game in which students practise their written methods of addition/subtraction/multiplication/division. Students play the game in pairs. They must throw a dice to know how many squares to move and then use a written method to answer the calculation on the square that they land on. Their partner will peer assess and check that what they have done is right.
By fionajones88