Short Blocks

# Maths Year 3/4 Spring Place Value and Fractions

Each unit has everything you need to teach a set of related skills and concepts.

First time using Hamilton Maths?

The PowerPoint incorporates step-by-step teaching, key questions, an in-depth mastery investigation, problem-solving and reasoning questions - in short, everything you need to get started.

All the other resources are there to support as-and-when required. Explore at your leisure - and remember that we are always here to answer your questions.

## Unit 1 Negative numbers (suggested as 2 days)

### Objectives

Negative Numbers
Unit 1: ID# 34412

Y3: Place negative numbers on a line; order positive and negative numbers; Use negative numbers in the context of temperature.
Y4: Place negative numbers on a line; order positive and negative numbers; Use negative numbers in the context of temperature.

National Curriculum
Y3: Num/PV (vi)
Y4: Num/PV (iii)

Y3 Hamilton Objectives
5. Solve number problems and practical problems involving place value.

Y4 Hamilton Objectives
5. Recognise negative numbers in relation to number lines and temperature.

### Planning and Activities

Day 1 Teaching
Count backwards and forwards through zero using a counting stick. Order positive and negative numbers.
Group Activities: T with Y3
Y3 -- Practise ordering numbers −10 to 10; complete inequalities using < or > symbols. Some children will just practise ordering numbers −5 to 5.
Y4 -- Practise ordering numbers −10 to 10. Write three consecutive negative numbers, given the ‘middle’ number. Complete inequalities using < or > symbols. Some children will also answer and create subtractions with negative answers.

Day 2 Teaching
Model increase and decrease of temperature above/below zero using Thermometer ITP.
Group Activities: T with Y4
Use the in-depth problem-solving investigation ‘Sea Level’ from NRICH as today’s group activity.
Or, use these activities:
Y3 -- Order positive and negative numbers. Find the difference between pairs of temperatures.
Y4 -- Order positive and negative numbers. Investigate temperatures in a range of locations and solve problems relating to temperature differences.

### You Will Need

• Counting stick
• Cards/sticky notes with −5, −4, −3 … 5
• Number cards −10 to 10
• ITP Thermometer

### Short Mental Workouts

Day 1
Convert between kg and g

Day 2
Counting forwards and backwards across zero

### Procedural Fluency

Day 1
Y3: Order positive and negative numbers.
Y4: Order positive and negative numbers.

Day 2
Y3: Solve temperature problems.
Y4: Solve temperature problems

### Mastery: Reasoning and Problem-Solving

Year 3 & 4

• Put these temperatures in order, starting with the lowest:
19°C, −9°C, −18°C, 0°C, 21°C
• Estimate the number shown by the arrow on this number line:
_________________________
-10_____ ↑ ____________20
• What temperature is 10 degrees less than 4°C?
• Alfie says ‘20 degrees higher than −5°C is 25°C’. Do you agree with him?

In-depth Investigation: Sea Level
Can you calculate the depths between some of the underwater creatures?
Sea Level from nrich.maths.org.

### Extra Support

Y3 / Y4: Temperature Differences
Work together on the Y4 Day 2 group activity. Use a number line to support finding the difference between positive and negative numbers

## Unit 2 Fractions (suggested as 3 days)

### Objectives

Fractions
Unit 2: ID# 34428

Y3: Finding fractions of amounts (1/4s and 1/8s); Place fractions on a number line.
Y4: Finding fractional amounts; Fractions on a number line.

National Curriculum
Y3: Fr (ii) (iii)
Y4: Fr (i) (iii)

Y3 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.
24. Count up and down in fractional steps, e.g. counting in 1/2s, 1/4s or 1/3s; hence recognise fractions as numbers.

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.

### Planning and Activities

Day 1 Teaching
Revise reading and writing fractions. Find simple fractional amounts.
Group Activities: T with Y3
Y3 -- Fold strips of objects to find 1/2 and 1/4 of numbers, then 3/4 of numbers. Some children will use clues to guess fraction strips.
Y4 -- 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 Teaching
Find thirds and two-thirds of numbers by folding paper into 3 equal parts and drawing smiley faces in each part.
Further Teaching with Y4
Finding fifths and tenths using a chocolate bar model.
Group Activities: T with Y4
Y3 -- Divide a box of 12 eggs into thirds to find 1/3 and 2/3 of 12; fold strips to find 1/3 and 2/3 of other numbers. Investigate which numbers from 6 to 21 (40 for Greater Depth) can be divided into thirds to give whole number answers.
Y4 -- Write fraction sentences about chocolate bars of 30 and 40 pieces.

Day 3 Teaching
Model fractions on a number line (halves and quarters to 10; eighths to 1).
Further Teaching with Y4
Understand and find tenths and fifths using a number line.
Group Activities: T with Y3
Use the in-depth problem-solving investigation ‘Fraction Bets’ as today’s group activity.
Or, use these activities:
Y3 -- Label halves and quarters on a 0–8 line. Count in halves, then quarters, then identify pairs of equivalent fractions.
Y4 -- Present mystery numbers to a partner by describing how much 1/10 of the number is.

### You Will Need

• Square sheets of paper
• Strips of 8 and 16 (see resources)
• ‘Halves and quarters’ sheet (see resources) preferably copied onto A3 paper
• ‘Finding 1/2 and 1/4 of 8, 80 and 800’ sheet (see resources)
• Chocolate bar picture (see resources)
• Dozen egg box (2 × 6) (or use picture in resources)
• ‘Fractions strips’ sheet (see resources)
• ‘Find 1/3 and 2/3 of numbers’ sheet (see resources)
• ‘Chocolate fractions’ (see resources)
• 0–10 landmarked line (see resources)
• 0–1 number lines marked in tenths (see resources)
• ‘Labelling Fractions and Finding Equivalents’ sheet (see resources)

### Short Mental Workouts

Day 1
Halve any 2-digit number

Day 2
Count in steps of 1/4

Day 3
Count in steps of 1/3

### Procedural Fluency

Day 1
Y3: Find fractions of numbers.
Y4: Find fractions of numbers.

Day 2
Y3: Find fractions of numbers.
Y4: Find tenths.

Day 3
Y3: Label fractions on a number line.
Y4: Find tenths.

### Mastery: Reasoning and Problem-Solving

Y3

• Which of these shapes are divided into quarters?
Which are divided into thirds?
[images on problem solving and reasoning sheet]
• 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.

Y4

• Bea counts in quarters, starting at one quarter. She says five numbers then stops. What number should she say next?
• Fill in the missing fractions:
1 1/2, 2, 2 1/2, 3, ☐, 4, ☐, 5
4, 3 3/4, 3 1/2, ☐, 3, ☐, 2 1/2
8/10, 9/10, ☐, ☐, 1 2/10
• Write all the fraction facts for tenths of 60.
1/10 of 60 = ☐
2/10 of 60 = ☐
etc. to 10/10.
• Is 1/10 of 50 the same as 1/5 of 100?

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

Finding 1/3 of amounts

Y4: Choccie Quarters
Counting in ¼s; Finding ½, ¼ and ¾ of amounts

## Unit 3 Equivalent fractions; +/– fractions (suggested as 4 days)

### Objectives

Equivalent Fractions; +/– Fractions
Unit 5: ID# 34476

Y3: Identify equivalent fractions using a visual image; compare fractions; Recognise and find fractions with a total of 1.
Y4: Identify equivalent fractions, writing fractions in simplest form; fraction and decimal equivalence; Add and subtract fractions with the same denominator.

National Curriculum
Y3: Fr (iv) (v)
Y4: Fr (i) (iv) (v) (vi)

Y3 Hamilton Objectives
22. Recognise and show equivalent fractions using diagrams, for 1/2, 1/4, 3/4, 1/3.
26. Add or subtract fractions with the same denominator.

Y4 Hamilton Objectives
23. Write the equivalent fraction for fractions with given denominators or numerators, e.g. 1/2 = ?/8; write a fraction in its simplest form.
25. Add and subtract fractions with the same denominator.

### Planning and Activities

Day 1 Teaching
Model equivalent fractions using visual images.
Group Activities: T with Y3
Y3 -- Use visual resources to generate ‘families’ of fractions equivalent to 1/2 and find further equivalent fractions.
Y4 -- Use visual resources to generate ‘families’ of fractions equivalent to 1/4s and/or 1/2.

Day 2 Teaching
Compare fractions using a fraction wall.
Further Teaching with Y4
Simplify fractions using a fraction wall and then by division of numerator and denominator.
Group Activities: T with Y4
Use the in-depth problem-solving investigation ‘Best Score for Me’ as today’s group activity.
Or, use these activities:
Y3 -- Make a fraction wall, then use it to compare given fractions.
Y4 -- Use the fraction wall to support identifying the simplest form of fractions.

Day 3 Teaching
Use Fractions ITP to model equivalence of tenths, fifths and halves.
Further Teaching with Y4
Fraction and decimal equivalence of tenths on a 0 to 5 number line.
Group Activities: T with Y4
Y3 -- Cut out halves, fifths and tenths from the fraction wall; match parts to create equivalent fractions. Other children find pairs of equivalent fraction cards and label them on a 0–2 line.
Y4 -- Match decimals and fractions dominoes to form a loop.

Day 4 Teaching
Use a fraction wall to identify pairs of fractions that total 1.
Further Teaching with Y4
Add and subtract fractions using pizza models and fraction number lines.
Group Activities: T with Y4
Y3 -- Write fraction additions with a total of 1, either with the same or different denominators.
Y4 -- Sort fraction addition and subtraction calculations, based on estimates; calculate answers. Some children cut fraction strips to support addition and subtraction of 1/5s and 1/6s.

### You Will Need

• ITP: ‘Fractions
• Fraction walls up to 1/8s and 1/12s (see resources)
• Strips of paper of identical length
• ‘Comparing fractions’ sheet (see resources)
• 0 to 2 line marked in tenths (see resources)
• 0 to 5 line marked in tenths (see resources)
• 1/2s, 1/5s and 1/10s fraction wall strips (see resources)
• Fraction cards (2 sheets, see resources)
• Fractions and decimals dominoes (see resources)
• Pizza (see resources)
• 0 to 2 lines (see resources)
• Fifths and sixths (see resources)
• Fraction + and - cards (see resources)

### Short Mental Workouts

Day 1
Counting in sixes

Day 2
Tell the time on an analogue clock, focus on multiples of 5 minutes

Day 3
Count in 1/4s

Day 4
Count in 1/10s to at least 2

### Procedural Fluency

Day 1
Y3: Find equivalent fractions.
Y4: Find equivalent fractions.

Day 2
Y3: Compare fractions.
Y4: Simplify fractions.

Day 3
Y3: Recognize equivalence with halves, fifths and tenths.
Y4: Recognize equivalent fractions and decimals

Day 4
Y3: Add fractions which make a whole.

### Mastery: Reasoning and Problem-Solving

Y3

• Draw a fraction wall of your own to show halves, thirds, quarters and fifths. Think carefully about how wide the ‘whole’ strip is.
Which fractions are less than 1/4?
Which fractions are greater than 1/4?
• 1/2 + 1/2 = 1
Write a similar sentence for thirds.
Write a similar sentence for quarters.
Write a similar sentence for sixths.

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.
• Add 1/2 to each of these fractions:
(i) 3/4
(ii) 1/6
(iii) 3/10
(HINT: Write 1/2 as an equivalent fraction in each case.)
• Which of these cannot be written in a simpler form?:
6/9
7/10
14/21
Why?

In-depth Investigation: Best score for me
Children find equivalent fractions to cross out numbers on a 6 × 6 square. They use strategies to find their highest score.
Y3: Support children as necessary with finding equivalents other than for ½, ¼, ¾, 1/3. A fraction wall will be a useful image.

### Extra Support

Y3: Fair Families
Finding ¼ of amounts by sharing objects

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

Wall-to-Wall Fractions
Finding fractions with a total of 1 (same denominators)