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# Maths Year 3 Spring Fractions

Each unit has everything you need to teach a set of related skills and concepts. 'Teaching for Understanding' provides whole-class teaching and fully differentiated adult-led group activities. ‘Problem-solving and Reasoning’ develops these skills, and includes questions to enable you to assess mastery. Practice sheets ensure procedural fluency. Extra support activities enable targeted work with children who are well below ARE.

‘UNIT PLAN’ gives you a text version of all parts of the unit to use in your school planning documentation. ‘DOWNLOAD ALL FILES’ gives you that unit plan plus all of associated documents. These bulk downloads are available to friends and School Subscribers. These bulk downloads are added value for Hamilton Friends and School Subscribers.

## Unit 1 Concept of a fraction; halving (suggested as 3 days)

### Objectives

Concept of a fraction; halving
Unit 1: ID# 3491

National Curriculum
Fr (ii) (iii)

Hamilton Objectives
23. Recognise, find and write unit fractions of ‘convenient’ amounts.
22. Recognise that 2/4 is equivalent to 1/2.
27. Solve problems involving fractions.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Using different-shaped pieces of paper. Use these to demonstrate tearing into halves, and then tearing each half in two to get quarters. Demonstrate, using different shapes, and asking how each one can be divided into thirds. Use a strip of 8 shapes to divide into halves and quarters to show 1/4 of 8 = 2.
Group Activities
-- Place counters on each half/third/quarter of strips of paper to find fractions of amounts.
-- Fold strips of 12 and 24 objects to find 1/2, 1/3 and 1/4 of 12 and 24.

Day 2 Teaching
Children fold a strip of 7 objects (see resources) in half. Point out each half. Write: 1/2 of 7 is 31/2. Children, in pairs, make a tower of 26 cubes, then break it to find 1/2 of 26. Record. Discuss a jotting. Use a similar jotting to find half of 15.
Group Activities
-- Investigation: Children use cubes to help find half of odd and even numbers, and discuss what they notice.

Day 3 Teaching
Make 46 using place value cards. Split it to show 40 and 6. Ask half the class to halve 40, and the other half to halve 6. Children take the correct place value card. Put the two cards together to show that half of 46 is 23. Repeat to halve 58 and 74.
Group Activities
-- Investigation: Pick a number to start with. If the number is even, halve it; if the number is odd, add 1. Keep going until they get to 1. Try to make the longest and shortest halving chains possible.

### You Will Need

• Large paper rectangle and circle
• ‘Strips of 6’ sheet (see resources)
• ‘Strips of 8’ sheet (see resources)
• ‘Strips of 9’ sheet (see resources)
• Strips of paper and counters
• Additional activity sheets (see resources)
• Cubes

### Mental/Oral Maths Starters

Day 1
Count in steps of 1/2 along a number line (pre-requisite skills)

Day 2
Doubles to double 15 (pre-requisite skills)

Suggested for Day 3
Sort odd and even numbers (simmering skills)

### Procedural Fluency

Day 1
Use bar models to find 1/2, 1/3 and 1/4 of amounts.

Day 2
Divide strips of odd and even numbers of objects in half. Write matching fraction statements.

Day 3
Halve odd and even 2-digit numbers by partitioning and recombining.

### Mastery: Reasoning and Problem-Solving

• Draw a symmetrical shape. Draw a line dividing it into half. Are your two halves exactly the same?
• Draw a shape that you can divide into quarters using two straight lines.
• Match each number to its half:
 14 12 32 7 64 16 24 32 102 17 34 51

In-depth Investigations:
Halving Odd and Even Numbers. See group activity Day 2 for details.
Halving Chains. See group activity Day 3 for details.

### Extra Support

Fair Fractions
Understanding what 1/2 and 1/4 are; Finding 1/2 and 1/4 of amounts (whole number answers)

## Unit 2 Finding 1/2, 1/4, 3/4, 1/3, 2/3 of amounts (suggested as 2 days)

### Objectives

Finding 1/2, 1/4, 3/4, 1/3, 2/3 of amounts
Unit 2: ID# 3499

National Curriculum
Fr (ii) (iv) (vii)

Hamilton Objectives
23. Recognise, find and write unit and non-unit fractions of convenient amounts.
27. Solve problems involving fractions.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Children fold a square paper in half in a different way to their partner. Fold it into 4 equal parts. What is each part? Children fold strips of 8 objects (see resources) in half. How many in each half? Fold it in half again, so you have 4 equal parts. How many in each quarter? How many in 2/4? In 3/4? Repeat for 16 objects.
Group Activities
-- Fold strips of objects to find 1/2 and 1/4 of numbers, then 3/4 of numbers.
-- Children have strips of objects. They are given fraction clues to guess which strip the adult is thinking of.
-- Use number facts and place value to find related fraction facts, e.g. 1/4 of 8, 1/4 of 80 and 1/4 of 800. Write answers in bar models.

Day 2
Children fold A5 paper into three equal parts. Discuss how each part = 1/3. Write 1/3 on each part. Children draw 2 smiley faces on each 1/3 of their rectangles. How many smiley faces altogether? What is 1/3 of 6? Record 1/3 of 6 is 2. How many in 2/3? Record 2/3 of 6 is 4.
Group Activities
Use the ‘Fraction Clues’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities.
-- Divide a box of 12 eggs into thirds to find 1/3 and 2/3 of 12, then fold strips to find 1/3 and 2/3 of numbers.
-- Investigate which numbers from 6 to 21 (30 for greater depth) can be divided into thirds to give whole number answers. Write related fraction statements, e.g. 1/3 of 12 is 4, 2/3 of 12 is 8.

### You Will Need

• Square sheets of paper
• ‘8 objects’ sheet (see resources)
• ‘16 objects’ sheet (see resources)
• ‘Halves and quarters’ sheet (see resources)
• Scissors, flipchart and pens
• Additional activity sheets (see resources)
• A5 paper and cubes (30 for each pair)

### Mental/Oral Maths Starters

Day 1
4-times table (pre-requisite skills)

Day 2
3-times table (pre-requisite skills)

### Procedural Fluency

Day 1
Fold strips of pictures to find 1/2 and 1/4 of numbers to 28.
Find 1/2, 1/4, 2/4 and 3/4 of numbers to 40.

Day 2
Fold strips of pictures to find 1/3 and 2/3 of numbers to 24.
Find 1/3 and 2/3 of numbers using cubes or number facts.
Use number facts and place value to find 1/3 and 2/3 of 100s numbers.

### Mastery: Reasoning and Problem-Solving

• Which of these shapes are divided into quarters? Which are divided into thirds? (see download)
• Always true, sometimes true or never true?
A piece of paper folded in half twice is divided into quarters when you open it out.
1/4 of a piece of paper is larger than 1/3 of the same piece of paper.
Two quarters make a half.
1/3 of 3 is 1.

In-depth Investigation: Fraction Clues
Children use their knowledge of fractions and tables to find mystery numbers.

### Extra Support

Finding 1/3 of amounts

## Unit 3 Develop the concept of fractions (suggested as 3 days)

### Objectives

Develop the concept of fractions
Unit 3: ID# 3511

National Curriculum
Fr (iii) (iv) (vi)

Hamilton Objectives
26. Compare and order unit fractions and fractions with the same denominator.
24. Count up and down in fractional steps, hence recognise fractions as numbers.
22. Recognise and show using diagrams, equivalent fractions for 1/2, 1/4, 3/4, 1/3, e.g. 1/4 = 3/12.

### Teaching and Group Activities for Understanding

Day 1
Display, on an IWB, a 0–10 landmarked line with whole, half and quarter intervals marked (see resources). Remind children how to record 1/2. Point at the line. Repeat the activity, now marking on quarters up to 10. Point out 2/4 = 1/2; they are equivalent fractions. Mark eighths on a line.
Group Activities
-- Label halves and quarters on a 0–8 line. Count in halves, then quarters, then identify pairs of equivalent fractions.
-- Divide a paper plate ‘cake’ into quarters, then eighths. Count in eighths.
-- Draw own 0–4 line and mark and label halves, quarters and eighths.

Day 2
Display a fraction wall on an IWB (see resources). Say that each line is a fraction strip. The top line is halves; these have 2 ‘at the bottom’, the denominator. Colour 2/3. The line is split in three, so we write 3 as the denominator. I have coloured 2/3. Continue for the rest of the fraction wall.
Group Activities
Use the ‘Fraction Bets’ in-depth problem-solving investigation below as today’s group activity.
Or, use this activity.
-- Make own fraction wall, then use to compare given fractions.

Day 3
Display a fraction wall. Colour in 1/2. How much is coloured? How much isn’t coloured? Record as 1/2 + 1/2 = 1. Colour 2/3 on the thirds line. Record as 2/3 + 1/3 = 1. Repeat for quarters showing that we can colour 2/4 + 2/4 = 1 or 1/4 + 3/4 = 1.
Group Activities
-- Write an addition of fractions with an answer of 1 for each row of a fraction wall.
-- Use a fraction wall to say complements to 1, given a fraction. Challenge children to write pairs of fractions with different denominators that make 1, e.g. 2/4 + 1/2 = 1.

### You Will Need

• 0–10 landmarked line with whole, half and quarter intervals marked (see resources)
• ‘Labelling Fractions and Finding Equivalents’ sheet (see resources)
• Cake or pizza painted on a paper plate
• Strips of A3 paper
• Fraction wall (see resources)
• Strips of paper of identical length, seven for each pair of children
• ‘Comparing fractions’ sheet (see resources)
• Whiteboards and pens
• ITP: Tell the Time

### Mental/Oral Maths Starters

Day 1
Count in halves to at least 10 (pre-requisite skills)

Suggested for Day 2
Pairs to 60 and telling the time (simmering skills)

Suggested for Day 3
Tell the time on an analogue clock; focus on multiples of 5 minutes to the hour (simmering skills)

### Procedural Fluency

Day 1
Label halves and quarters on a 0 to 8 number line.
Label halves, quarters and eighths on a 0 to 4 number line.

Day 2
Use a fraction wall to compare pairs of fractions; then to order groups of fractions.

Day 3
Colour in a fraction of a strip and identify how much is not coloured, to total 1.
Use bar models to work out how much is needed to make 1.

### Mastery: Reasoning and Problem-Solving

• Write the missing numbers in the sequence:
1/2, ☐, 1¹/2, 2, 2¹/2, ☐, ☐
1/3, 2/3, ☐, 1¹/3, ☐, ☐
1/4, ☐, ☐, ☐, 1¹/4, ☐, 1³/4
• Draw a fraction wall of your own to show halves, thirds, quarters and fifths.
• 1/2 + 1/2 = 1
Write a similar sentence for thirds.
Write a similar sentence for quarters.
Write a similar sentence for sixths.

In-depth Investigation: Fraction Bets
Children look at fractions and make a hypothesis of which ones are closest. They then test this out by placing fractions on a line.

### Extra Support

Fair Families
Finding 1/4 of amounts by sharing objects

## Unit 4 Finding fractions of amounts (suggested as 2 days)

### Objectives

Finding fractions of amounts
Unit 4: ID# 3517

National Curriculum
Fr (ii) (vii)

Hamilton Objectives
23. Recognise, find and write unit and non-unit fractions of convenient amounts, e.g. 1/10 of 100 or 1/3 of 60.
27. Solve problems involving fractions.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Children fold strips of 16 objects (see resources) in half. How many in each half? Fold it in half again. How many in each quarter? How many in two quarters? 2/4 is the same quantity as 1/2. Fold it in half again to make eighths. How many in each eighth? Write sentences about fractions of the strip.
Group Activities
-- Fold strips of objects to find 1/2, 1/4 and 1/8 of 24.
-- Use bar models to find 1/2, 1/4 and 1/8 of 24 and 32.

Day 2 Teaching
Hand out strips of paper and ask children to fold them in thirds, then sixths. Compare thirds and sixths, agreeing that sixths are smaller. Find non-unit fractions of amounts, e.g. 5/6 of 12, etc.
Group Activities
Use the in-depth problem-solving investigation ‘Andy’s Marbles’ from NRICH as today’s group activity.
Or, use these activities:
-- Fold strips of objects to find 1/6 of 18 and 24.
-- Use folding strips then mental strategies and pattern to find sixths of multiples of 6.
-- Use bar models to find thirds and sixths of 18, 180, 24 and 240.

### You Will Need

• Sheets of A5 paper
• Strips of 16 objects (see resources)
• Strips of 24 objects (see resources)
• Flipchart and pens
• Cubes (optional)
• Strips of 12 objects (see resources)
• Additional activity sheets (see resources)

### Mental/Oral Maths Starters

Day 1
Halves of all numbers to 10 (pre-requisite skills)

Day 2
Count in 6s (pre-requisite skills)

### Procedural Fluency

Day 1
Fold strips to find halves, quarters and eighths of 24, 32 and 48.

Day 2
Use bar models to find thirds and sixths of numbers 18 to 36.

### Mastery: Reasoning and Problem-Solving

• Find 1/8, then 3/8 and then 5/8 of 24.
• Write the missing numbers.
___ of 15 is 5
2/3 of ___ = 14
3/5 of 20 = ____
___ of 10 = 4
• Which is bigger, 2/5 of 35 or 3/8 of 32?

In-depth Investigation: Andy's Marbles
Calculate fractions of numbers to help Andy work out how many of his marbles have been lost or given away. Andy's Marbles from nrich.maths.org.

### Extra Support

Fruit Strips
Finding 1/4 of numbers by folding strips

## Unit 5 Find unit/non-unit fractions using division (suggested as 3 days)

### Objectives

Find unit and non-unit fractions using division
Unit 5: ID# 3527

National Curriculum
Fr (ii) (vii)

Hamilton Objectives
23. Recognise, find and write unit and non-unit fractions of convenient amounts, e.g. 1/10 of 100 or 1/3 of 60.
27. Solve problems involving fractions.

### Teaching and Group Activities for Understanding

Day 1
Use a strip with 12 objects pictures on it. Demonstrate how we find 1/4, 3/4 and 1/3 and 2/3 of this quantity by folding the strip into quarters and then thirds.
Group Activities
-- Find 1/4 of numbers in the 4-times table. See link with division facts.
-- Children find unit fractions (1/2, 1/4, 1/3, 1/5, 1/8, 1/10) using their knowledge of times tables. Make links with arrays.
-- Find 1/8 of numbers in the 8-times table. See link with division facts.

Day 2
Children find 1/2 of 24 by dividing 24 by 2. Repeat with 1/3 of 18. Draw the corresponding array (3 rows of 6 stars) to model 1/3 is 6. If we know that 1/3 is 6, what would 2/3 of 18 be? Use the same method to find other non-unit fractions.
Group Activities
-- Use the in-depth problem-solving investigation ‘Fractions in a Box’ from NRICH as today’s group activity.
Or, use these activities:
-- Use a bar models to help find unit fractions and related non-unit fractions of numbers.
-- Write multiplications, divisions then fraction sentences about arrays.
-- Write fraction sentences to go with multiplication sentences for 24 and 40.

Day 3
Use a bar model to show fifths of 20. Find 2/5, 3/5, 4/5 of 20. Use a bar model to represent eighths of 24. Find 1/8 and then 3/8, 5/8 and 7/8. Children make a poster to show how we use arrays or bar models to help us find non-unit fractions.
Group Activities
-- Use bar models and coins to answer word problems about fractions of money.
-- Solve word problems involving non-unit fractions.

### You Will Need

• Strips of 12 objects (see resources)
• Bar models (see resources)
• Cubes
• ‘Unit fractions of numbers’ sheet (see resources)
• Whiteboards and pens
• ‘Find non-unit fractions’ sheet 1
• Additional activity sheets (see resources)
• Flipchart and pens
• Large sheets of paper
• 10p and 2p coins

### Mental/Oral Maths Starters

Day 1
Division facts for the 5-times table (pre-requisite skills)

Day 2
Division facts for the 3-times table (pre-requisite skills)

Day 3
8-times table (pre-requisite skills)

### Procedural Fluency

Day 1
Use cubes, times-tables knowledge and bar models to help find unit fractions (1/2, 1/4, 1/5, 1/8, 1/10) of numbers.

Day 2
Find unit and related non-unit fractions of numbers.

Day 3
Find unit and non-unit fractions of numbers. Answer word problems.

### Mastery: Reasoning and Problem-Solving

• Complete each sentence.
1/3 of 15 = ☐ so 2/3 of 15 = ☐
1/5 of 40 = ☐ so 4/5 of 40 = ☐
1/6 of 24 = ☐ so 5/6 of 24 = ☐
• Draw an array of 8 rows of 5 stars to help you find 3/8 of 40.
• Draw three bar models, one to represent each of these fraction problems.
2/3 of 24
5/8 of 24
3/5 of 30

In-depth Investigation: Fractions in a Box
Find fractions of numbers to work out the number of counters in a box. Fractions in a Box from nrich.maths.org.

### Extra Support

This unit has no separate Extra Support activities.