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From the NCETM ‘ACTIVITIES’ Section of the New Curriculum

Year 1 Fractions

Activities

Programme of Study statements / Activities
A / B
recognise, find and name a half as one of two equal parts of an object, shape or quantity / /
recognise, find and name a quarter as one of four equal parts of an object, shape or quantity /

Activity A - NRICH Making longer, making shorter

This activity includes doubling, halves and quarters in a very practical way using rods made from interlocking cubes. It gives children a practical context in which to explore simple multiplying and dividing, even if these particular terms are not used explicitly. It can provide a very useful context for introducing and using the vocabulary of halves and quarters.

Having multilink cubes for each child is essential.

Activity B – NRICH Happy Halving

This problem consolidates children's understanding of halving and will help them to develop their skills of visualisation.It is important pupils are clear that, in this problem, the halves must be exactly the same size as each other. A precursor to this activity might be to show the group a square and ask them to split it in half in their "mind's eye". By discussing where they have imagined the "cutting line", the children will discover that there is more than one way to do this. From this point, you can talk about whether or not the two halves are the same size each time.It may be useful for the pupils to have a sheet of the shapes. Alternatively, they could use a pegboard or geoboard to try out their ideas .

Year 2

Activities

Knowledge and understanding covered in Year 2 Fractions Programme of Study / Activities
A / B / C / D
Recognise fractions of shapes / / /
Write fractions / / /
Recognise fractions of a quantity / / / /
Recognise equivalence of 2⁄4 and 1⁄2 /
Find fractions of objects /

Activity A(i) – Halving

This problem is a wonderful way to consolidate children's understanding of halving and halves. It also gives learners experience of mathematical proof.

Activity A (ii) - Early Fraction Development

In this article, Bernard Bagnall outlines suggestions for tasks which will help young children develop the concept of fractions

Activities B – Colouring halves and quarters of shapes

E.G. Colour a half of these shapes

Year 2 continued

Colour a quarter of each shape

Activities C – What fractions is shaded?

What fraction of each of these shapes is shaded

What are two ways we could write this fraction?

Activities D

Find the number.....

What is half of 12?

A half of 12 is ______

What is a third of 15?

A third of 15 is ______

What is a Quarter of 8?

A quarter of 8 is ______

What is two thirds of 9?

Two thirds of 9 is ______

What is three quarters of 24?

Three quarters of 24 is ______

Making longer, making shorter

From nrich, brings in doubling, halves and quarters in a very practical way using rods made from interlocking cubes. It gives children a practical context in which to explore simple multiplying and dividing, even if these particular terms are not used explicitly. It can provide a very useful context for introducing and using the vocabulary of halves and quarters.

Useful Resources

Powerpoint slides – Key Stage 1 Fractions (attached)

A series of powerpoint slides which can be used as starting points to a discussion. Slides are adapable

Powerpoint slides – Key Stage 1 Fractions – Misconceptions (attached)

A series of powerpoint slides which can be used to unpick misconceptions.

Powerpoint slides – Key Stage 1 Resources (attached)

Year 3

Activities

Programme of Study statement / Activity
A / B / C / D / E / F / G
count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10 /
recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators /
recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators /
recognise and show, using diagrams, equivalent fractions with small denominators /
add and subtract fractions with the same denominator within one whole (e.g. 5/7 + 1/7 = 6/7) /
compare and order unit fractions, and fractions with the same denominators /
solve problems that involve all of the above /

Activity A – visualising fractions along a line

  • Use counting sticks and bead strings to help children visualise fractions.

If the bead string represents one whole, then each set of ten coloured beads could represent one tenth and each individual bead could represent one hundredth.

  1. Label the two ends of the bead string as 0 and 1. Give students tags to place each tenth on the bead string. You could use a 1-10 bead string instead of a 1-100 bead string.
  2. Join several bead strings together to create fraction lines that extend over one. For example, five bead strings allow fractional numbers from 0 to 5. Label simultaneously in mixed numbers (2 ½) and improper fractions (5/2).
  3. Ask the pupils to represent each tenth with a variety of manipulatives, for example, Numicon, Dienes (Big Base) and coins.
  4. Extend pupils’ understanding to include the equivalence of fractions, decimals and percentages. For example, ½ = 0.5 = 50% or 2 2/10 = 2.2 = 220%

Activity B

  • Fractional Triangles

This problem could be used as part of a lesson on finding fractions of various shapes. It should help develop an understanding of the relationship between the part and the whole. It allows children to explore fractions in a non-threatening, open-ended way and yet it does contain some real challenge. This practical activity develops an understanding of the part and the whole,

  • Understanding unit fractions: A Hungarian Approach (pdf downloaded)

A series of lessons on finding fractions of amounts from Lesson 11, page 9 onwards based on an alternative, Hungarian approach, to teaching maths. There are linked resources and activities, although the site is slightly tricky to navigate.

Activity C

  • Trains (downloaded as a word document)

An activity from New Zealand that involves using number rods to develop children’s understanding that fractions can extend beyond 1.

  • Children can make number lines for display around the classroom, that demonstrate counting in different fractional steps. For example counting in steps of ½ an apple, 1/4s of pizza, 1/10 of a £1 (steps of 10p)
  • Daily practice of counting forwards and backwards in 1/2s, 1/4s, 1/10s and 1/3s, including extending to below zero

Activity D – equivalent fractions

  • Fractional Walls

An activity based on Cuisenaire / number rods.

  • Matching Fractions

A ‘pelmanism’ style matching activity based on fractions.

  • Use equivalence circles, for example pizza or cake slices in a variety of activities for pupils to explore equivalence.

Activity E – adding fractions

Addition, subtraction and equivalent fractions

A series of activities based on deepening students’ understanding of adding and subtracting fractions with the same denominator.

  • Use a variety of representations, for example, number rods, paper strips and equivalence circles to model what happens when you add or subtract fractions with the same denominator. This will help children understand why the denominator doesn’t change.

Activity F

  • Fractions interactive teaching programme

(ITP available electronically)

NB This resource was produced for the Primary National Strategy, which was formally discontinued in 2011. However, the resource has the potential to complement teaching in line with the new 2014 mathematics curriculum)

This ITP allows you to divide a green strip into a number of equal parts and colour the individual parts in yellow, clearly showing any comparison.

  • Smartie Fractions

Use mini packets of smarties for children to find the fraction of each colour in a packet. This is useful for comparing fractions with the same denominator and for adding and subtracting fractions

More wonderful ‘Maths and Smarties’ ideas. http://webcache.googleusercontent.com/search?q=cache:PvjwLerUHg8J:www.education.nt.gov.au/__data/assets/pdf_file/0016/5290/maths_with_smarties.pdf+&cd=11&hl=en&ct=clnk&gl=uk

Activity G – solving problems

  • Use the Bar Model to solve problems

Use the ‘Thinking blocks on the maths playground’ website to model word problems involving fractions and to model adding and subtracting unit fractions. There are video demonstrations, guided problems and the ability to use the blocks to solve your own problems.

Fair Feast

Assess and develop children’s understanding of equal sharing with this picnic problem. In this problem, the familiar context of sharing provides an opportunity in which to explore fractions in a variety of ways. The task involves finding fractional quantities of whole numbers as well as dividing a unit into equal pieces.

Useful Resources

Mental Images for Fractions, Decimals, Percentages, Ratio and Proportion (FDPRP)

A list of models and images to support the development of children’s understanding of fractions.Includes ideas on how to use them in the classroom.

  • Overcoming Barriers in Fractions

All the Overcoming Barriers materials from level 1 to level 5 linked to fractions, decimals and percentages contain useful assessment questions and a range of models and images

Year 4

Activities

Programme of Study statement / Activity
A / B / C / D / E / F / G
Recognise and show, using diagrams, families of common equivalent fractions. /
Count up and down in hundredths; recognise that hundredths arise when dividing an object by a hundred and dividing tenths by ten. /
Solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number /
Add and subtract fractions with the same denominator. /
Recognise and write decimal equivalents of any number of tenths or hundredths. / /
Recognise and write decimal equivalents to ¼; ½; ¾. /
Round decimals with one decimal place to the nearest whole number. /
Compare numbers with the same number of decimal places up to two decimal places. /

A range of web based interactive programmes, aimed at providing practice and consolidation for pupils exploring equivalent fractions.

Of course, concrete materials and activities are the best way to teach children about fractions and enable them to build strong concepts.

Activity A – interactive programmes

  1. Game matching pictures and equivalent fractions

Activity B – Tenths and Hundredths

  1. A resource pack of materials:https://hwb.wales.gov.uk/cms/hwbcontent/Shared%20Documents/vtc/phase4_20030829/Mathematics/Keystage2/Numbers/Tenthsandhundre/Introduction/default.htm

Including an interactive place value grid to teach tenths and hundredths, activities on key vocabulary and terms, reference material and animations and three differentiated worksheets on tenths and hundredths

  1. A series of activities to introduce and use hundredths

Make a hundred square of pennies in the classroom and talk about one hundredth of a pound and a tenth of a pound. Consider how, for example, 23p is written as a decimal. How would we write four pound and eighty-two pence? What would it look like in our coins?

  1. Interactive matching of decimal notation to a shaded 10x10 grid representation

Activity C – fractions to calculate quantities

  1. Game for one or two players required to match the answer to the unit fraction of amount requested

Activity D – adding and subtracting fractions

  1. Game practising adding two or more fractions with the same denominator
  2. Online adding and subtracting fractions activities written as word problems. Some useful ideas.

Activity E – decimal equivalents

  1. Excellent ‘splat’ game accessible at several different levels, requiring children to match the fraction (in tenths or hundredths) to the decimal representation

2.‘The Decifractor’. A flexible resource demonstrating equivalences between fractions and decimals.

3.Pelmanism-style game , matching fractions to decimals. 4.Arcade type game, where ‘Fraction Man’ has to defeat the decimals (by matching them). Note – this does get challenging! 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 units, tenths and hundredths

Activity F – dividing by 10 and 100

  1. Interactive Teaching Program – ‘Moving Digits’. A good modelling program to show how digits move when multiplied or divided by 10 or 100. (Downloaded)
  2. Interactive game where children are required to find the calculation that matches the answer given… to help them cross the river.

Activity G – rounding and comparing decimals

  1. Rounding decimals activity – uses one and two decimal places.
  2. Practise rounding numbers to one decimal place.
  3. Spreadsheets ‘Rounding’ and ‘Rounding Decimals’
  1. Ordering numbers with up to two decimal places. https://hwb.wales.gov.uk/cms/hwbcontent/Shared%20Documents/VTC/phase4_20030829/Mathematics/Keystage2/Numbers/Anintroductiont/Introduction/MainSessionPart1.htm
  2. Arrange the decimals in order from lowest to highest.
  3. Order the decimal number cards (select number of decimal places) from lowest to highest.

Activity H – solve problems involving fractions and decimals

  1. Pelmanism-style game. Match the coin pictures to the correct fraction of amount.
  2. BBC skillswise activity focusing on money amounts as fractions.
  3. Fractions of amounts interactive word problems.These are Strategy Excel sheets – also can be found in the ‘Existing Assets’ folders for ITPs

Year 5

Activities

Programme of Study statements / Activities
A / B / C / D / E / F
compare and order fractions whose denominators are all multiples of the same number / / / /
recognise mixed numbers and improper fractions and convert from one form to the other /
add and subtract fractions with the same denominator and related fractions / /
multiply proper fractions and mixed numbers by whole numbers / / /
read and write decimal numbers as fractions (e.g. 0.71 = 71/100) / / / /
recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents /
read, write, order and compare numbers with up to three decimal places / / /
Solve problems involving numbers with up to three decimal places
recognise the per cent symbol (%) and understand that per cent relates to “number of parts per hundred” and write percentages as a fraction with denominator 100, and as a decimal / /
write percentages as a fraction with denominator 100, and as a decimal / / /

Activity A - Fractions ITP (in ‘Existing assets’ Maths ITP or

An interactive program that allows you to model part-whole relationships using a strip divided in to equal parts. Relationships can be shown as fractions, decimals (to three places) or percentages.

Activity B - Fractions Jigsaw (sheet downloaded)A jigsaw-based activity that requires children to add and subtract fractions with the same and different denominators. Pieces must be matched to an answer that may be expressed in equivalent forms. It also includes multiplying fractions by a whole number.

Activity C - Peaches today, Peaches tomorrow…

(pdf downloaded)

A problem solving activity that requires children to find fractions of whole numbers. It provides plenty of practice and has many extension opportunities.

Activity D - Metre sticks and metre strips

Use classroom metre sticks/rulers and I metre long strips of paper to model relationships between a whole, tenths, hundreds and thousandths. Children can explore the size of 1, 2 and 3 decimal places and how they link to units of measurement. Labelling points with decimal, fraction and percentage equivalents can help to reinforce links between all three.

Activity E - Matching fractions, decimals and percentages

A pelmanism-style activity matching pairs of equivalent fractions, decimals and percentages. Points are awarded for correct answers and deducted for turning over cards without success.

Activity F - Using blank hundred squares

Use blank hundred squares to model and explore percentages, tenths and hundredths. Decimals, fractions and percentages can be represented by colouring in blank hundred squares which children can use to support addition and subtraction.

Useful Resources (All in Maths ITPs ‘Existing Assets’)

  • Moving digits ITP
  • Maths rods
  • Clock faces to model different fractions
  • Area ITP
  • Fractions ITP

Year 6

Activities

Programme of Study statements / Activities
A / B / C / D / E / F / G
Use common factors to simplify fractions; use common multiples to express fractions in the same denomination /
Compare and order fractions, including fractions >1 /
Associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [ for example, 3⁄8 ] /
Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions /
Multiply simple pairs of proper fractions, writing the answer in its simplest form [ for example, ¼ × ½ = 1⁄8 ] / /
Divide proper fractions by whole numbers [ for example, ⅓ ÷ 2 = 1⁄6 ] /
Identify the value of each digit to three decimal places and multiply and divide numbers by 10, 100 and 1000 where the answers are up to three decimal places /

Activity A : Factors and Multiples Game

This game from Nrich could replace standard practice exercises on finding factors and multiples. In order to play strategically, pupils must start to think of numbers in terms of their factors (pdf notes downloaded)

Activity B(i) : Rod Fractions

Compare a series of coloured rods and the relationships between them with this clearly presented Nrich activity

Activity B(ii) : Laundry Line

This activity features a laundry line with ‘fraction washing.’ The aim is to hang the fractions on the line in the right order between 0 and 1. Once a game has been completed, you can raise the level of difficulty.

Activity B(iii) : Chocolate

Using chocolate bars to compare fractions – a context guaranteed to keep them focused! (Like Fraction Action)

Activity C : Fraction strips

The ‘Fractions’ Interactive Teaching Programme, allows the user to divide a strip into equal parts and colour them as needed. Strips can be labelled as a fraction, decimal or percentage. The ratio of parts can also be displayed. Multiple strips can be created to demonstrate equivalence.( In ‘Existing Assets ‘Maths ITPs)

Activity D(i) : Clock Faces

Give children the chance to explore clock faces as a way of representing time. Talk about 5 minute sectors of the clock being equivalent to twelfths, ten minute sectors to sixths, fifteen minute chunks to quarters etc…