# Teaching for mastery in primary maths

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## Compare, order and simplify fractions

• Year group: Year 5
• Term: Spring
• Topic: Fractions
• Duration: 1 weeks
• Keystage: KS2
• Age Range: 9 to 10 yrs
• Unit can be taught out of sequence: N
• Week Range: 4

In this chapter, pupils compare and order fractions whose denominators are all multiples of the same number.

As in previous chapters, pupils should use diagrams to explain their reasoning and understanding. This will help develop a deeper understanding of the content.

Although they have already worked with fractions greater than one whole, pupils start to explore the connection between improper fractions and mixed numbers. They recognise mixed numbers and improper fractions, convert from one form to the other and write mathematical statements greater than 1 as a mixed number (eg, 2⁄5 + 4⁄5 = 6⁄5 = 11⁄5).

The rest of this chapter explores the links between decimals and fractions. Chapter 1 of decimals, which introduces decimal notation, is therefore a necessary prerequisite for this. Explicit links are made between tenths, hundredths and thousandths in their decimal and fraction notation. Pupils read and write decimal numbers as fractions, eg, 0.71 = 71⁄100.

## Resources for this topic

### White Rose Maths

#### Reasoning - Problem Solving - Number (KS1) and Fractions (KS2) - March 4th

Today's problems are ones that involve multiplication in KS1 and fractions in KS2.

In the KS1 problem students have to find the values that a symbol represents and in the second question has to find four different ways of writing the same calculation.

At KS2 the questions are on fractions..

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.

#### Mixed numbers & improper fractions

This selection of resources will help children to embed their understanding of converting between mixed numbers and improper fractions.

### Mathematics Mastery

#### Compare, order and simplify fractions

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 comparing, ordering and simplifying fractions.

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.

#### Compare, order and simplify fractions

Mathematical discussion is a key element of the Mathematics Mastery programme.

Talk Tasks are a brilliant way of enabling pupils to develop their mathematical language, thinking, understanding and confidence.

This activity explores the concept of comparing, ordering and simplifying fractions

• Talk tasks are best completed in mixed attainment pairs, with pupils taking turns to listen and construct arguments
• Emphasis is on discussion rather than the solution, encouraging pupils to use key language and talk in full sentences
• Ask pupils to prove their answers in a variety of ways, using the CPA approach to support mathematical understanding and number sense

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

#### Year 5 Fractions Week 4

This is pack 1 of 6 on Year 5 Fractions and covers equivalent fractions and converting improper fractions to mixed numbers. The resources aim to help children gain a deeper understanding of the concepts covered in the first week. Fractions 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.

I hope you find them useful.

#### Year 5 Fractions Week 5

This is pack 2 of 6 on Year 5 Fractions and covers converting mixed numbers to improper fractions, number sequences and comparing and ordering fractions. The resources aim to help children gain a deeper understanding of the concepts covered in the second week. Fractions 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.

I hope you find them useful.

#### Year 5 Fractions Week 6

This is pack 3 of 6 on Year 5 Fractions and covers comparing and ordering fractions, investigating equivalent fractions and adding and subtracting fractions with the same denominator. The resources aim to help children gain a deeper understanding of the concepts covered in the third week. Fractions 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.

I hope you find them useful.

#### Year 5 Fractions Week 7

This is pack 4 of 6 on Year 5 Fractions and covers adding and subtracting fractions with unlike denominators. The resources aim to help children gain a deeper understanding of the concepts covered in the fourth week. Fractions 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.

I hope you find them useful.

#### Year 5 Fractions Week 8

This is pack 5 of 6 on Year 5 Fractions and covers subtracting fractions and multiplying fractions. The resources aim to help children gain a deeper understanding of the concepts covered in the fifth week. Fractions 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.

I hope you find them useful.

#### Year 5 Fractions Week 9

This is pack 6 of 6 on Year 5 Fractions and covers multiplying fractions, fractions of an amount and an end of unit assessment. The resources aim to help children gain a deeper understanding of the concepts covered in the first week. Fractions 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.

I hope you find them useful.

#### Year 5 Fractions

This is a complete bundle for Year 5 fractions covering all the Year 5 objectives for fractions. The resources aim to help children gain a deeper understanding of the concepts covered and adopt a mastery maths approach.

Fractions are represented in a variety of ways and lend themselves well for use alongside concrete manipulatives and pictorial representations.

The resources also include a range of reasoning and problem solving activities and more open ended problems to support and extend your whole class.

I hope you find them useful.

#### Number Starter - Sharing Chocolate

A Number starter activity on equivalent and comparing fractions. This pilot resource has been kindly shared by the ICCAMS project, based at Kings College, London. The project aims to raise students’ attainment and engagement in key mathematical areas. To find out more, and to access the pilot resources, please visit the link above.

#### Fraction Talk

This activity is designed to promote dialogue about fractions and allow students to justify / convince colleagues with their reasoning. I have suggested a few ways you might use this, my preferred option is to give it too the students as a paired activity (option 1). I then like to bring the whole class together to discuss.
It allows for the students to start to talk about the four operations, and allows them to recognise key concepts.
Enjoy.

#### Equivalent Fractions Game

Pupils roll dice and simplify the fractions they get on the grid, with the person with the biggest fraction getting a point. I usually play 10 rounds and then pupils move round and play someone else. They can also discuss at the end whether the game was fair and how to determine whether it was or wasn't. Sometimes if the class is small I record results on the board (like football scores) and get them to draw a up a league table! If you like this resource then please check out my other stuff on here! :)