# Teaching for mastery in primary maths

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## Introduction to decimals

• Year group: Year 4
• Term: Summer
• Topic: Decimals
• Duration: 2 weeks
• Keystage: KS2
• Age Range: 8 to 9 yrs
• Unit can be taught out of sequence: N
• Week Range: 1 - 2

In this chapter, pupils are formally introduced to decimal notation.

To start, pupils are introduced to tenths and hundredths of a whole and relate decimal notation to the division of whole number by 10 and 100. Pupils make connections between fraction and decimal representations, realising that a given number or proportion may be expressed either way. They also find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths.

Pupils learn decimal notation and the language associated with it, including in the context of measurements, and recognise and write decimal equivalents of any number with tenths or hundredths. They go on to order decimal amounts and quantities expressed to the same number of decimal places and make comparisons between them. Additionally, they represent numbers with one or two decimal places in several ways, such as on number lines.

By working with concrete manipulatives and pictorial representations of tenths and hundredths, pupils come to recognise and write decimal equivalents to 14, 12 and 34. They use fractions-related language and concepts to help them make connections between fraction and decimal notation.

Later, pupils round decimals with one decimal place to the nearest whole number and compare numbers with up to two decimal places. Pupils connect hundredths to tenths and place value and decimal measure. They build on their understanding of place value and decimal notation to record metric measures, including money and solve simple measure and money problems involving fractions and decimals to two decimal places. They also estimate, compare and calculate different measures, including money in pounds and pence.

## Resources for this topic

### White Rose Maths

#### KS2 Reasoning and Problem Solving Questions - 25th April 2016

Following our March twitter problems we have been inundated with requests for a few more new ones in the run up to SATS. We are not sure how often we will put them up, but here are five problems you can use with your Y6 group.

We hope you like them. Feel free to tweet us your solutions to @WRMathsHub

#### Reasoning - Problem Solving - Number Problems Galore - March 16th

Here are today's questions. There are two problems for KS1 and two for KS2.

In KS1 problem children have to find missing numbers in an addition pyramid and see if they can reason to find a missing number in a different one. They then have to solve a multi-step problem, which initially looks easier than it actually is.

At KS2 children have to be able to adding fractions and decimals together and convert between fraction and decimal. For the second question children have to adding and subtract decimals after converting to the same unit of measure.

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.

#### Place value - decimals

Here are a set of problem cards to get children thinking about place value with decimals.

### Mathematics Mastery

#### Introduction to decimals

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 introduction to decimals.

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.

#### Introduction to decimals

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 decimals

• 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 4 Decimals – White Rose Summer Block Week 1

This pack of resources covers Year 4 decimals for week 1 of the summer term.

Week 1 includes worksheets and activities on:

• Making a whole
• Write decimals
• Compare decimals

In the worksheets, decimals 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 Y4 Decimals Week 2 here: https://www.tes.com/teaching-resource/year-4-decimals-white-rose-summer-block-week-2-11862919

Thank you for taking your time to browse this resource!

@mathsteryed

#### Year 4 Decimals – White Rose Summer Block Week 2

This pack of resources covers Year 4 decimals for week 2 of the summer term.

Week 2 includes worksheets and activities on:

• Order decimals
• Round decimals
• Halves and quarters

In the worksheets, decimals 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

#### Decimal number lines

Decimal number lines to complete. Two differentiated sheets.

#### Position of the Digits (Place Value)

A lesson on deepening the understanding of place value for year 7's.

#### Introduction to decimals

This is a set of resources I designed for a low ability year 7 group I teach to introduce the concept of decimals and their size and different ways of displaying them. I focus mainly on one and two decimal place numbers. It could lead to work on ordering decimals.
The student sheet is designed for them to fill in with place value and examples. There is then a shading sheet for tenths and one for hundredths. Finally there are some cards which contain 9 different 1 and 2 decimal place numbers where pupils have to sort into their groups - decimal number version, shaded version (using a 10x10 grid), number line version and a version where the decimal is spelled. This could develop into understanding that, say, 0.4 is larger than 0.18 - a common misconception.
There is a powerpoint attached that works through all this.
Happy to send powerpoint in earlier version or the worksheets in word to allow editing if you want.
Let me know how you get on with them.
I have a website, mrchadburn.co.uk which I'm hoping to upload this and other resources. Please keep visiting as it develops and comments, criticisms keenly accepted.

#### Place value - decimal puzzle

Match the decimals given in words to the number given in digits. Devices within the puzzle allow students to self monitor their work and correct errors. Students like to finish a puzzle, but they don’t always like the jokes they decode! Each puzzle also supports literacy. Students have to split the string of letters into recognisable words to read the punchline. (answers included). If you like this, search for: Place Value - A pack of decimal and fraction puzzles.

Keywords: place value, decimals, units, tenths, hundredths, thousandths, puzzle, joke, number system, practice, math, maths joke, mathematics, unlock untangle understand.

#### Ordering Decimals Worksheet

A short differentiated worksheet for pupils to rewrite the decimlas they have been given in ascending order

#### Rounding and decimal places

Answer sheet included. Code activity using rounding with some foundation understanding and a couple of tougher thinking questions. Used for year 8 and year 9. Solution is 'Maths is totally fabulous' because I use the word fabulous lots but should work well for some other teachers. Based and extended from original idea by another teacher: http://www.tes.co.uk/teaching-resource/Rounding-Code-Breaker-to-nearest-10-100-1000-6363634/

#### Rounding & Ordering Decimals Bingo

KS3 / GCSE Place value and ordering. Rounding and ordering decimals bingo - no more need to be said. Enjoy!