# Teaching for mastery in primary maths

Year 6
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## Solving problems involving ratio and proportion

• Year group: Year 6
• Term: Spring
• Topic: Ratio and proportion
• Duration: 2 weeks
• Keystage: KS2
• Age Range: 10 to 11 yrs
• Unit can be taught out of sequence: N
• Week Range: 10 - 11

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).

## Resources for this topic

### White Rose Maths

#### Ratio and proportion problems

A few problems involving ratio and proportion.

#### Reasoning - Problem Solving - Number (KS1) and Ratio (KS2) - March 7th

There are two problems for KS1 and two for KS2.

In KS1 problem students have to involve students realising they need to do a subtraction to work out the missing value and then in the second question they need to think about the numbers in a half completed number square.

At KS2 the problems both involve ratio. Although the first problem is wordy the process is relative straightforward. The second problem needs a little more thought.

Every day in March the White Rose Maths Hub is aiming to put out a question of the day.

Tweet us @WRMathsHub a picture of your children's answers for a chance to win a prize.

### Mathematics Mastery

#### Ratio and proportion

Deepening pupils’ understanding of key mathematical ideas is a core element of the Mathematics Mastery programme.

Our Key Constructs highlight the essential mathematical concepts all pupils are expected to grasp within each year group, with accompanying guidance for assessing pupil progress.

Our Key Constructs are closely aligned to the National Curriculum’s objectives. We know these can be tricky to evidence, so we’ve included an example task for each concept, as well as ideas to support slower-graspers and depth tasks to challenge higher-attaining pupils.

• Pupils should work through the tasks independently
• Teachers should incorporate the CPA approach to support pupils’ learning
• Opportunities for depth and scaffolding are built into each task

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.

### Resources shared by teachers

#### Y6 Ratio - White Rose Spring Week 10

This pack of resources covers Year 6 Ratio for week 10 of the White Rose spring term SOL.

Week 10 includes worksheets and activities on:
- What is ratio?
- Introducing ratio language
- Calculating ratio
- Simplifying ratio

In the worksheets, ratios are represented in a variety of ways and lend themselves well for use alongside concrete manipulatives and pictorial representations.

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.

We hope you find these worksheets useful and save you time planning. We aim to produce resources which are of the highest quality - we strongly believe that the visual aspects of these worksheets enable deep understanding of the areas being taught. Once you have used these resources, we would love to hear what worked particularly well and what could be improved on: we often edit our resources.

Please find Y6 Ratio Week 2 planning here: https://www.tes.com/teaching-resource/y6-ratio-white-rose-spring-week-11-11830328

Thank you for taking your time to browse this resource!

@mathsteryed

#### Y6 Ratio - White Rose Spring Week 11

This pack of resources covers Year 6 Ratio for week 11 of the White Rose spring term SOL.

Week 11 includes worksheets and activities on:
- Using scale factors
- Calculating scale factors
- Calculating scale factors problem solving
- Ratio and proportion problems
- End of unit assessment

In the worksheets, ratios are represented in a variety of ways and lend themselves well for use alongside concrete manipulatives and pictorial representations.

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.

We hope you find these worksheets useful and save you time planning. We aim to produce resources which are of the highest quality - we strongly believe that the visual aspects of these worksheets enable deep understanding of the areas being taught. Once you have used these resources, we would love to hear what worked particularly well and what could be improved on: we often edit our resources.

Thank you for taking your time to browse this resource!

@mathsteryed

#### Bob's ratio homework

This resource is intended to tackle likely misconceptions and common errors without having the students associate the teacher with the mistakes. I'd love to have comments as this is for an assignment. Thank you.

#### 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.

#### 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.

#### 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.

#### ratio & proportion

This is a good resource to help learners link the ratio and proportion concepts in real life situations… It can be given as a homework to help learners reflect on their learning and to reveal any misconceptions they might have. It is good to be used to assess each learner’s understanding of the topic. It can also be used as a main/ plenary activity where learners work on their own or with others (peer assessment)….. It can be adapted at different levels to suit and to challenge learners at all levels.

Other topics covered: Numbers

#### 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.