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# Maths Year 3/4 Autumn 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 added value for Hamilton Friends and School Subscribers.

## Unit 1 Doubling, halving and the concept of a half (suggested as 3 days)

### Objectives

Doubling, halving and the concept of a half
Unit 1: ID# 34206

Y3: Double 2-digit numbers up to 50. Halve even 2-digit numbers. Begin to halve odd numbers.
Y4: Double and halve 2-digit numbers, including odd numbers.
Double and halve 3-digit numbers. Halve odd numbers with odd tens digits, e.g. 35 and 75.

National Curriculum
Y3: Mult/Div (i) (ii)
Y4: Mult/Div (i) (ii)

Y3 Hamilton objectives
19. Multiply a 1-digit number by a 2-digit number using partitioning.
20. Partition to double and halve numbers.

Y4 Hamilton objectives
17. Know and recite times tables, including division facts, up to 12 × 12; multiply by 0 and multiply and divide by 1.
18. Use known facts, place value, factors and commutativity to multiply and divide mentally, including multiplying three numbers together.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Quick practice doubling 1-digit numbers and multiples of 10 less than 50.
Model doubling of 2-digit numbers, using a jotting to show partitioning and recombining.
Further Teaching with Y3
Further doubling of 2-digit numbers, using place value cards to support, e.g. for 34, 46 and 57.
Group Activities: T with Y4
Use the ‘Doubling forever’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
Y3 -- Doubling 2-digit numbers: either to 50, or numbers greater than 50.
Y4 -- Doubling any 2-digit number.

Day 2 Teaching
Model halving of 2-digit numbers by partitioning and recombining, including examples with odd tens digit.
Further Teaching with Y4
Revisit halving and doubling multiples of 100. Introduce doubling and halving of 3-digit numbers by partitioning and recombining.
Group Activities: T with Y3
Y3 -- Halving 2-digit numbers, including money amounts; check by doubling.
Y4 -- Doubling and halving 3-digit numbers; reasoning about strategies.

Day 3 Teaching
Quick practice halving multiples of 10 (to 90).
Model halving odd numbers (2-digts) using partitioning and recombining.
Further Teaching with Y3
Find half of 3, 5, 7, 9 then 5, 25, 45 and 65; reason about patterns.
Group Activities: T with Y4
Y3 -- Find halves, describing patterns of halves in different number sequences: 2-digit numbers.
Y4 -- Find halves, describing patterns of halves in different number sequences: 2- and 3-digit numbers.

### You Will Need

• ‘Double up’ (see resources)
• Hundreds, tens and ones place value cards
• Place value dice or number cards 0–9
• Flipchart and pens
• ‘Chocolate bars – half price sale!’ (see resources)
• Whiteboard and pens
• Cubes or counters
• ‘Halving even numbers’ (see resources)
• Interlocking cubes (including 1/2 cubes if you have them)

### Short Mental Workouts

Day 1
Doubles to Double 20

Day 2
Halve multiples of 10

Day 3
Count in 5s and 10s

### Procedural Fluency

Day 1
Y3: Identify fractions of shapes shaded.
Y4: Identify equivalent fractions (visual models).

Day 2
Y3: Compare Fractions.
Y4: Compare Fractions.

Day 3
Y3: Shade parts of circles to show mixed numbers.
Y4: Write improper fractions as mixed numbers (and vice versa).

### Mastery: Reasoning and Problem-Solving

Y3

• Start at 3 and keep doubling until your answer is close to 100 but NOT over. How many doubles did you write? Repeat, starting at 4. How many this time?
• Write the missing number(s) in these bar diagrams:
Diagram 1
 ? 36 36

Diagram 2

 52 ? ?
• Starting with 72, keep halving until you reach a 1-digit number. What is half of that number?

Y4

• Write two sentences to relate these three numbers: 37, 74 and 148.
• Use a jotting to double these numbers:
i) 216 ii) 327 iii) 438
Describe any pattern in the answers.
• Starting with 576, keep halving until you reach a 1-digit number. What is half of that number?

In-depth Investigation: Doubling Forever
Children double numbers up to 10 (Y3) or 20 (Y4) and look for duplicate sequences.

### Extra Support

Y3: Double and Halves
Doubling multiples of 5; Halving multiples of 10

Y4: Double or Halve?
Doubling and halving 2-digit numbers using partitioning (whole number answers only)

## Unit 2 Conceptualising fractions (suggested as 3 days)

### Objectives

Conceptualising fractions
Unit 2: ID# 34222

Y3: Recognise, find and write fractions in the context of a shape; Compare fractions; Recognise and show equivalent fractions (including mixed numbers).
Y4: Fractions of shapes and equivalence; families of common equivalent fractions (including mixed numbers).

National Curriculum
Y3: Fr (iv) (vii)
Y4: Fr (including decimals) (i) (iii) (vi)

Y3 Hamilton objectives
22. Recognise and show using diagrams, equivalent fractions
27. Solve problems involving fractions.

Y4 Hamilton objectives
23. Write the equivalent fraction for fractions with given denominators or numerators.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Folding rectangles, then circles into halves and quarters, describing, identifying and writing the fractions. Fold a rectangle into thirds. Note briefly that a circle is not as straightforward to divide into thirds.
Further Teaching with Y4
Continue folding rectangles previously folded into quarters and thirds to identify eighths and sixths respectively. Recognise equivalent fractions.
Group Activities: T with Y4
Y3 -- Explore halves, quarters and thirds by folding and cutting paper shapes. Some children begin to explore equivalence.
Y4 -- Compare folded fractions of shapes to begin to identify equivalent fractions.

Day 2 Teaching
Explore the fraction wall – what it represents and how it can be used to compare non-unit fractions, e.g. 2/3 and 2/6.
Further Teaching with Y4
Extend the comparison of fractions to tenths and twelfths.
Group Activities: T with Y4
Use the ‘Best score for me!’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
Y3 -- Use a fraction wall to write equalities and inequalities.
Y4 -- Use a fraction wall to identify ‘families’ of equivalent fractions; begin to describe patterns in ‘families’ of equivalent fractions.

Day 3 Teaching
Using models of pizzas to introduce mixed numbers.
Further Teaching with Y3
Identifying equivalent fractions with mixed numbers.
Group Activities: T with Y3
Y3 -- Use ‘pizza’ images as a visual model to represent mixed numbers; compare and order fractions.
Y4 -- Play a game to create improper fractions and find equivalent mixed numbers.

### You Will Need

• Large paper rectangles and circles
• Small paper shapes: rectangles, squares and circles
• Fraction wall: one whole to eighths (see resources)
• Fraction Wall: one whole to tenths (see resources)
• Fraction wall: one whole to twelfths (see resources), including lots of reduced copies for children to shade
• 1–6 dice or spinners (2 per pair)
• 1–8 dice or spinner (2 per pair)
• 1–10 dice or spinner (2 per pair)
• Additional activity sheets (see resources)
• 1-minute timer
• Whiteboards and pens

### Short Mental Workouts

Day 1
Count in steps of 1/2 along a number line

Day 2
Doubles to double 15

Day 3
Count in 2s

### Procedural Fluency

Day 1
Y3: Count bead strings by partitioning.
Y4: Partition and make 2-digit numbers and record them as number sentences.

Day 2
Y3: Compare fractions with denominators to eighths.
Y4: Compare fractions with denominators to twelfths.

Day 3
Y3: Shade circles to show mixed numbers of wholes and halves, thirds, quarters and sixths. Convert mixed numbers to improper fractions.
Y4: Convert mixed numbers to improper fractions and vice versa.

### Mastery: Reasoning and Problem-Solving

Y3

• 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.
• Marie has written a family of fractions equivalent to 1/4. Which is the odd one out?
2/8 4/16 1/4 3/15 5/20
• Use the <, > or = symbols to complete these number sentences:
2/3 ☐ 3/4
3/5 ☐ 2/3
1¹/2 ☐ 8/6

Y4

• Write four fractions equivalent to 1/3. Now write four fractions equivalent to 2/3.
• True or false?
1/2 ≡ 100/200
If a fraction is equivalent to one quarter, the denominator is four times the numerator.
Any number of thirds can be written as an equivalent number of sixths.
Any number of sixths can be written as an equivalent number of thirds.
• Write two fractions equivalent to 2¹/4.

In-depth Investigation: Best Score For Me!
Children find equivalent fractions, then (Y3) keep a tally of the numbers used, or (Y4) cross out numbers used on a 1-36 grid. They develop strategies to achieve their highest score.

### Extra Support

Y3 and Y4: The Half Family
Finding fractions which are equivalent to one half

## Unit 3 Finding fractions of amounts (suggested as 2 days)

### Objectives

Finding fractions of amounts
Unit 3: ID# 34238

Y3: Finding 1/4 and 3/4 of quantities; Finding 1/3 and 2/3 of quantities.
Y4: Find unit and non-unit fractions of amounts.

National Curriculum
Y3: Fr (ii) (iii) (vii)
Y4: Fr (including decimals) (iii)

Y3 Hamilton objectives
22. Recognise and show using diagrams, equivalent fractions
23. Recognise, find and write unit and non-unit fractions of convenient amounts
27. Solve problems involving fractions.

Y4 Hamilton objectives
24. Use times tables to find unit and non-unit fractions of amounts, e.g. 1/6 of 48, 3/8 of 64.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Folding strips of 8 and then 16 objects to determine halves, quarters and three-quarters of amounts.
Further Teaching with Y4
Finding unit and non-unit fractions of 30, then 50 using a chocolate bar image, then by calculating with division and multiplication.
Group Activities: T with Y4
Y3 -- Fold paper strips of objects to find unit fractions of amounts; begin to find three-quarters of quantities. Some children use number facts to find fractions of amounts.
Y4 -- Use a chocolate bar model to find quarters, thirds, sixths and eighths of 24 … OR … Use a chocolate bar model to find unit and non-unit fractions of 32 and 36.

Day 2 Teaching
Fold A5 paper into three equal parts. Use as a model to support finding one-third and two-thirds of different amounts.
Further Teaching with Y4
Use a pizza model to find eighths of 16. Use the more abstract bar model to represent eighths of 16 and 24.
Group Activities: T with Y4
Use the ‘Fraction clues’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
Y3 -- Use strips of images and/or number facts to help find one-third and two-thirds or other fractions of quantities.
Y4 -- Find unit and non-unit fractions of a strip of 24 objects. Other children will use division and tables facts to find unit and non-unit fractions of 40, then 60.

### You Will Need

• 8 objects (see resources – cut into strips)
• 16 objects (see resources – cut into strips)
• Chocolate sheet (see resources)
• Whiteboards and pens
• Additional activity sheets (see resources)
• A5 pieces of paper – pre-marked to aid folding into thirds
• Cubes or counters

### Short Mental Workouts

Day 1
Sort odd and even numbers

Day 2
Tell the time

### Procedural Fluency

Day 1
Y3: Find halves, quarters and eighths using paper strip models.
Y4: Link division and fractions. Find fractions using number facts.

Day 2
Y3: Find thirds and sixths using a bar model.
Y4: Find unit and non-unit fractions using a bar model.

### Mastery: Reasoning and Problem-Solving

Y3

• 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.
A quarter of a piece of paper is larger than a third of the same piece of paper.
Two quarters make a half.
One-third of 3 is 1.

Y4

• Fill in the missing fractions:
1¹/2, 2, 2¹/2, 3, ☐, 4, ☐, 5
4, 3³/4, 3¹/2, ☐, 3, ☐, 2¹/2
8/10, 9/10, ☐, ☐, 1²/10
• Write all the fraction facts for tenths of 60.
1/10 of 60 = ☐
2/10 0f 60 = ☐ etc. to 10/10.
• Use this bar diagram to help find:
(i) 1/8 of 48 = ☐
(ii) 3/8 of 48 =☐
(iii) 7/8 0f 48 = ☐
 48
• Is 1/10 of 50 the same as 1/5 of 100?

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

### Extra Support

Y3
Fair Fractions

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