# Maths Year 3/4 Spring Place Value, Decimals, Fractions

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

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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 x and ÷ with money and 1-place decimals (suggested as 3 days)

### Objectives

x and ÷ with Money and 1-Place Decimals
Unit 3: ID# 34444

Y3: Multiply and divide by 10 and 100 including with money.
Y4: Divide numbers by 10 to give tenths (one place decimal). Multiply 1-place decimals to give whole numbers; Multiply and divide by 10 and 100 (one place decimals).

National Curriculum
Y3: Num/PV (ii); Mult/Div (iii)
Y4: Dec/Fr (vii)

Y3 Hamilton Objectives
18. Multiply 2-digit numbers by 10 or 1-digit numbers by 100; divide multiples of 10 or 100 by 10 or 100. Understand the effect of x or ÷ by 10 or 100.

Y4 Hamilton Objectives
26. Know that one-place decimal numbers represent ones and tenths.
29. 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.

### Planning and Activities

Day 1 Teaching
Model multiplying and dividing by 10 using a place value grid.
Further Teaching with Y4
Divide by 10 to give tenths using decimal place value grid.
Group Activities: T with Y4
Y3 -- Create 2-digit numbers and multiply and divide them by 10. Record these calculations. Some children challenge others to guess a starting number by giving the answer to × 10 questions.
Y4 -- Move digit cards on a place value grid to divide 2-digit numbers by 10. Write a generalisation.

Day 2 Teaching
Model multiplying and dividing by 10 and 100 using a place value grid.
Further Teaching with Y4
Multiply 1 place decimals by 10, moving digits across the decimal point. Use function machine to x10 and ÷10.
Group Activities: T with Y3
Use the in-depth problem-solving investigation ‘Testing 10s’ as today’s group activity.
Or, use these activities:
Y3 -- Play a divide and multiply card game.
Y4 -- Use a function machine or play bingo to practise multiplying and dividing numbers by 10.

Day 3 Teaching
Model multiplying and dividing by 10 and 100 (one-place decimals) using ITP ‘Moving digits’.
Further Teaching with Y3
Multiplying and dividing by 10 and 100 using money.
Group Activities: T with Y3
Y3 -- Multiply and divide shop prices by 10 and 100.
Y4 -- Find different routes through a maze (× 10, ÷ 10, × 100, ÷ 100) where the same number will come out exactly as it was entered.

### You Will Need

• 100s, 10s 1s place value grid (see resources)
• 10s, 1s, 0.1s place value grid (see resources)
• Cardboard box with two slots
• Sticky notes labelled ÷ 10 and × 10
• ÷ and × card game function cards and number cards (see resources)
• ‘Party bag toy shop’ sheet (see resources)
• Money place value grid (see resources)
• ‘Multiplying by 10 and 100’ sheets 1 and 2 (see resources)
• ITP: ‘Moving digits
• Real money
• ‘Multiplication and division maze’ (see resources)

### Short Mental Workouts

Day 1
Division facts for 10 times table

Day 2
Division facts for 5 times table

Day 3
£ and p notation

### Procedural Fluency

Day 1
Y3: Multiply and divide by 10.
Y4: Divide by 10 with decimals.

Day 2
Y3: Multiply and divide by 10 and 100.
Y4: Multiply and divide by 10 with decimals.

Day 3
Y3: Multiply and divide money by 10 and 100.
Y4: Multiply and divide by 10 and 100 with decimals.

### Mastery: Reasoning and Problem-Solving

Y3

• Describe in words what happens to a number when we multiply by 10. Now explain why it happens. You may draw a picture if it helps.
• Write the missing numbers:
(a) ☐ × 10 = 550
(b) 100 × 39 = ☐
(c) ☐ ÷ 10 = 60
(d) 17 × ☐ = 170
(e) 500 ÷ ☐ = 5
(f) ☐ × 10 = 990
• Write the result number in each chain:
5 × 100 ÷ 10 × 10 ÷ 100 = ?
300 ÷ 10 ÷ 10 × 10 × 10 = ?
40 × 10 ÷ 100 × 10 = ?
Invent your own chain where you finish with the starting number.
• Write the missing numbers
£3.40 × 10 = ☐ ☐ ÷ 10 = £5.50
100 × 9p = ☐ £7 ÷ ☐ = 7p

Y4

• Complete each sentence:
3.4 × 10 = ☐ 65 ÷ 10 = ☐
☐ ÷ 10 = 12.3 ☐ × 10 = 81
• Write the value of one tenth of each number:
57 84 6 13
• Use this fact 56 = 7 × 8 to find the answer to each calculation:
7 × 80 7 × 0.8 7 × 800 560 ÷ 8

In-depth Investigation: Testing 10s
Children multiply (Y3) or divide (Y4) numbers by 10, carry out a given procedure and look for patterns in their answer.

### Extra Support

Y3: Treasure or Trap
Multiplying and dividing by 10

Zeros Matter
Writing amounts of money in pounds and pence, including amounts with 0 in the 10ps or 1ps column

Y4: Moving Digits
Multiplying and dividing by 10 (whole number answers)

Digit Dance
Multiplying and dividing by 10 (including numbers and answers with one decimal place)

## Unit 4 Decimals and money on a line (suggested as 3 days)

### Objectives

Decimals and Money on a Line
Unit 4: ID# 34460

Y3: Placing and ordering 3-digit numbers and money on a number line; rounding them to the nearest 10.
Y4: Placing and ordering 1-place decimals on a line and rounding.

National Curriculum
Y3: PV (iii)
Y4: Fr (viii) (ix)

Y3 Hamilton Objectives
1. Read, write and locate any 3-digit number on a landmarked line from 0–1000 and use this to order and compare numbers.
6. Round to the nearest ten and hundred.

Y4 Hamilton Objectives
26. Know that one-place decimal numbers represent ones and tenths.
27. Round decimals with one decimal place to the nearest whole number.

### Planning and Activities

Day 1 Teaching
Model placing numbers on a number line and rounding.
Further Teaching with Y4
Relate one place decimals to cm and mm, and round decimals.
Group Activities: T with Y3
Y3 -- Locate 3-digit numbers on landmarked lines.
Y4 -- Position 1-place decimals accurately on landmarked 0–10 lines and round to the nearest whole. Some children will measure items less than 10cm to the nearest mm.

Day 2 Teaching
Order decimals on a number line.
Further Teaching with Y3
Order money on a number line and round to the nearest pound.
Group Activities: T with Y3
Y3 -- Create amounts of money using number cards and round to the nearest pound.
Y4 -- Position 1-place decimals accurately on number lines; some children will round to the nearest whole.

Day 3 Teaching
Compare decimal numbers using a number line.
Further Teaching with Y3
Compare and order amounts money using a number line.
Group Activities: T with Y4
Use the in-depth problem-solving investigation ‘Counter Place Value’ as today’s group activity.
Or, use these activities:
Y3 -- Investigation: How many amounts of money from £1 to £10 have the digit 9?
Y4 -- Roll a dice to make numbers with 1 decimal place. Play ‘Higher or lower’ using the rolled digits. Some children write 1-place decimal numbers in a given range then order the group of numbers.

### You Will Need

• Rulers marked in cm and mm
• Blank landmarked line (see resources)
• Small sticky notes
• ‘Placing 3-digit numbers on a landmarked line’ sheet (see resources)
• Items less than 10cm long
• 0–9 digit cards
• 0–10 lines (see resources)
• Blank cards
• £0 to £10 number line (see resources)
• 1–6 and 0–9 dice
• Squared paper
• Calculators

### Short Mental Workouts

Day 1
Place 2-digit numbers on a 0–100 line

Day 2
Count on and back in 1s and 10s

Day 3
Tell the time to the nearest 5 minutes

### Procedural Fluency

Day 1
Y3: Place 3-digit numbers between hundreds.
Y4: Place decimals on lines.

Day 2
Y3: Place money on a line.
Y4: More placing decimals on lines.

Day 3
Y3: Find ‘in between’ amounts.
Y4: Compare numbers with 1 decimal place.

### Mastery: Reasoning and Problem-Solving

Y3

• Sketch a 0–1000 line. Mark 500. Now mark 350, 700 and 990. How can you demonstrate that you have marked these accurately?
• True or false?
- Between any pair of next-door multiples of 100, there are always 98 whole numbers.
- The middle of a 500–1000 line is 800.
- There are ten numbers ending in 3 between 300 and 400.
- The digit 0 is used 18 times between 600 and 700.
• Write numbers to make the sentences true:
100 < ☐ < 110
304 > ☐ > 302
999 > ☐ > 888
0 < 101 < ☐
459 < ☐ < 461
• Write the value of the 5 digit in these numbers:
652
591
905

Y4

• Write each number as a decimal:
(i) One and four tenths
(ii) 6/10
(iii) 102/10
(iv) One half
(v) One fifth
• Billy measured his mobile phone. These were its dimensions:
Length: 12cm and 8mm
Width: 64mm
Thickness: 8mm.
Write these as numbers of centimetres, with a decimal place if necessary.
• Write <, > or = between each pair of numbers:
4.5 5.4
0.6 1/2
7.1 7.8
0.3 3/10
2/5 0.5

In-depth Investigation: Counter place value
Children place counters on a place value grid to make 3-digit numbers and then use logic to ensure they have made all combinations.
Y3 make whole numbers.
Y4 make numbers with 1 decimal place.

### Extra Support

Y3: In-betweenies
Placing numbers on a 0–100 landmarked line

Make the number
Knowing the value of each digit in 3-digit numbers

Y4: Decimals are a snip
Understanding place value in numbers with 1 decimal place and how we can write tenths as fractions or decimals

## Unit 5 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)