Ratio - Proportion: Teaching for Mastery in Primary Maths ǀ Tes

Progression in learning explained by topic

Number and place value Addition and subtraction Multiplication and division Fractions Length, weight, area and volume Time Geometry Statistics Factors, multiples, primes Negative numbers Calculations with four operations Ratio and proportion Algebra Roman numerals Decimals Percentages Money Times tables and skip counting

Number: Ratio and proportion

Having met ratio and proportion informally as part of previous topic areas, pupils secure their understanding of the concepts.

In order to progress in these chapters, it is vital that pupils are secure in their understanding of multiplication and division, as well as fractions. Previous informal use of ratio and proportion may include knowledge of the fact that there are 100cm in 1m, and in solving problems where one quantity is twice as big as another. This work will be formalised throughout this topic.

Pupils will understand that a ratio shows the relationship between two values, describing how one is related to another. They will start by making simple comparisons between two different quantities. For example, they may compare the number of boys to girls in the class and write statements such as “for every one girl, there are two boys”. Pupils will also understand that proportion is a name given to a statement showing that two ratios are equal.

To consolidate their understanding, pupils will solve rich problems with real-life contexts, such as altering a recipe.

Ratio and proportion: 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 Resource Team

Teacher's guide: Teaching for mastery booklet

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 Resource Team

Chapter 1: Rates and scaling by fractions

In this chapter, pupils solve problems involving simple rates.

Bringing together learning from topics on multiplication, division and fractions, pupils prepare for subsequent work on solving problems involving ratio. For example, they may use inverse multiplication and division calculations to help them to multiply and divide by powers of 10 when interpreting scale drawings, or multiply and divide by powers of 1,000 in converting between units such as metres and kilometres.

Chapter 2: Solving problems involving ratio and proportion

In this chapter, pupils recognise proportionality in different contexts and solve problems linked to both ratio and proportion.

Pupils solve problems involving the relative sizes of two quantities, in which missing values can be found by using integer multiplication and division facts. They also solve problems involving similar shapes where the scale factor is known or can be found.

Further to this, pupils understand that a ratio shows how one value is related to another. They make simple comparisons between two different quantities and solve related problems, modelling this with concrete objects and pictorial representations. Pupils go on to make statements like “for every red counter, I have five blue counters” and solve problems, such as, “I have four red counters, so how many blue counters do I have?” At this stage, some pupils may begin to use formal ratio notation (a:b).

Approved resources

Ratio At Work

This powerpoint uses two scenarios: building site and office. You can choose the order in which you do them or whether to do one and not the other. These are worded ratio problems to discuss and use to establish understanding or encourage verbal explanations from students.

By Andy Lutwyche

Ratio and Proportion Match Cards

A nice visual match-up activity that links together ratio and proportion. A word document that can be adjusted to different levels and is to be printed out for students. This activity is ideal as revision for KS3 and KS4.

By MrBartonMaths

Related resources

Defuse the Bomb - Ratio and Proportion

The terrorist, ‘The Mathematician’ has left clues to how you defuse the bomb 0 you must cut the wires in the correct order. Working up from simple ratio up to proportionality via three worksheets.

By Andy Lutwyche

Simple Ratio and Proportion Worksheet

Three sections - first asks pupils to colour a set of counters in a given ratio, second asks for basic ratios (no units) to be simplified and the third leads pupils through unitary method to solve proportion problems.

By nottcl

Fractions & Ratio Worksheet (Personalised)

A consolidating activity for KS3.

Two worksheets to choose from. Edit your chosen worksheet to input the first names of the children in your class.

The children can then work out the fraction and ratio of their names that fall into certain criteria.

Worksheet 1: Relies just on the first names of the children in the class, with no other knowledge required (e.g. number of vowels in the name)

Worksheet 2: Also requires research or prior knowledge of the others in the class before successfully completing the worksheet.

This worksheet can help children to discover the link between fractions and ratio.

By Miss-Becky