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# Maths Year 4 Spring Decimals and 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 Unit and non-unit fractions of amounts (suggested as 3 days)

### Objectives

Revise fractions; find unit and non-unit fractions of amounts
Unit 1: ID# 4483

National Curriculum
Dec/Fr (iii)

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
Count in thirds along a 0-5 line marked in thirds. Point at a mark; children write the number. Repeat with a line showing 1/4s. Stress mixed numbers, e.g.one and three quarters; equivalence, e.g. one and a half is the same as one and two quarters. Repeat for tenths.
Group Activities
-- Roll a dice to generate differing lengths of a fraction counting sequence.
-- Draw number lines to count in steps of 1/8 and 1/12.

Day 2
-- Use a picture of a chocolate bar with 30 pieces to show how to find 1/5, 3/5, and 4/5 of 30, then 1/6 of 30 and 5/6 of 30. Repeat with 50 pieces to find 1/10 and subsequent non-unit fractions, e.g. 3/10.
Group Activities
-- Write fraction sentences about chocolate bars of 32 and 36 pieces.
-- Write fraction sentences about arrays of 40 and 32.

Day 3
Sketch a pizza and divide it into eight equal sections. If 16 bits of salami are distributed equally, how much on each slice? Show that 1/8 of 16 is 2 (16 ÷ 8); then derive other facts: 2/8 of 16 = 4, 3/8 of 16 = 6, etc. Show that 4/8 is 1/2. Demonstrate using a bar model and repeat with 24 pieces of tomato.
Group Activities
Use the in-depth problem-solving investigation ‘Foodie fractions’ as today’s group activity.
Or, use these activities:
-- Fold a strip of 24 pictures to explore possible unit and non-unit fractions.
-- Investigate possible unit and non-unit fractions of 24 and 36.

### You Will Need

• ‘Fraction lines’ Sheets 1 to 3 (see resources)
• mini-whiteboards and pens
• ‘Fraction lines’ Sheet 4 (see resources)
• 0–9 dice
• Squared paper
• ‘Chocolate’ (see resources)
• Additional activity sheets (see resources)

### Mental/Oral Maths Starters

Day 1
Count 1/2s to at least 10 (pre-requisite skills)

Suggested for Day 2
Tell the time (simmering skills)

Suggested for Day 3
Find a time later (simmering skills)

### Procedural Fluency

Day 1
Fill in missing fractions (in simplest form) in sequences, using fraction lines to help.

Day 2
Find unit fractions, then non-unit fractions of amounts.

Day 3
Use a bar model to help find 1/8s of 32 and 1/6s of 30. Find 1/3s and 1/5s of 30.

### Mastery: Reasoning and Problem-Solving

• 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:
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 answers.
 48

(i) 1/8 of 48 =
(ii) 3/8 of 48 =
(iii) 7/8 0f 48 =

• Is 1/10 of 50 the same as 1/5 of 100?

In-depth Investigation: Foodie Fractions
Given fractions of amounts, children work out how many friends are at a picnic.

### Extra Support

Choccie Quarters
Counting in 1/4s; Finding 1/2, 1/4 and 3/4 of amounts

## Unit 2 Equivalent fractions; simplest form; +/- (suggested as 3 days)

### Objectives

Identify equivalent fractions; reduce to simplest form; add and subtract fractions
Unit 2: ID# 4493

National Curriculum
Dec/Fr (i) (iv) (vi)

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, e.g. 6/12 ≡ 1/2.
25. Add and subtract fractions with the same denominator.

### Teaching and Group Activities for Understanding

Day 1
Use the ITP ‘Fractions’ to show 1/2s, 1/4s and 1/8s. Discuss how many 1/4s and 1/8s are equivalent to 1/2. Model writing equivalence statements, 1/2 ≡ 4/8. Find a sequence of other fractions equivalent to 1/2.
Group Activities
Use the in-depth problem-solving investigation ‘Best score for me!’ as today’s group activity.
Or, use these activities:
-- Use visual resources to generate ‘families’ of fractions equivalent to 1/4s.
-- Use visual resources to generate ‘families’ of fractions equivalent to 1/2.

Day 2
Show children a fraction wall (see resources). Children revise fractions equivalent to one half. Discuss the relationship between the denominator and the numerator. Show how to reduce to simplest form visually (on fraction wall); then by dividing the numerator and denominator by the same number. Use 6/12, then 2/6, then 6/8 as examples. Note how we can make fractions equivalent to 1/3 by multiplying the numerator and denominator by the same number.
Group Activities
-- Use the fraction wall to support identifying the simplest form of fractions.

Day 3
Show a picture of two pizzas, each divided in 1/4s. Three quarters are eaten. Cross these out. Then another two quarters are eaten. Cross out two more quarters. How many quarters have been eaten? Record 3/4 + 2/4 = 5/4. Write the mixed number equivalent: 3/4 + 2/4 = 1¹/4.
Repeat to show other additions and subtractions of fractions with same denominator, e.g. 4/5 + 3/5, 1³/5 – 4/5.
Group Activities
-- Sort fraction addition and subtraction calculations, based on estimates; calculate answers.
-- Cut fraction strips to support addition and subtraction of 1/5s and 1/6s.

### You Will Need

• ITP ‘Fractions’ (see resources)
• Mini-whiteboards and pens
• Fraction walls (see resources)
• ‘Pizzas’ sheet (see resources)
• ‘Fifths and sixths’ sheet (see resources
• Scissors
• ‘0 to 2 lines’ sheet (see resources)
• Fraction addition cards (see resources)
• Fraction subtraction cards (see resources)

### Mental/Oral Maths Starters

Day 1
Count in steps of ¼ (pre-requisite skills)

Day 2
Count in steps of 1/3 (pre-requisite skills)

Day 3
Fractions with total of 1 (pre-requisite skills)

### Procedural Fluency

Day 1
Identify fractions equivalent to 1/2 and 1/4.

Day 2
Use a fraction wall to identify equivalent fractions, including 1/8s, 1/9s and 1/12s.

Day 3
Add and subtract pairs of fractions with the same denominators using fraction lines to help.

### Mastery: Reasoning and Problem-Solving

• 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 numbers on a 6 x 6 square. They use strategies to find their highest score.

### Extra Support

The Half Family (1)
Finding fractions which are equivalent to one half

Wall-to-wall Fractions (2)
Finding fractions with a total of 1 (same denominators)

## Unit 3 Introduction to one place decimals (suggested as 3 days)

### Objectives

Introduction to one place decimals
Unit 3: ID# 4513

National Curriculum
Dec/Fr (v) (vii)

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, identifying the value of the digits in the answer as ones and tenths.

### Teaching and Group Activities for Understanding

Day 1
Use large pieces of A1 paper, with one cut into 10 equal strips to model 1s and 0.1s. Demonstrate that if a child is holding 1 strip, they have one tenth or 0.1. Repeat for 4 strips and 8 strips. Show that if a child is holding one whole piece of paper and 3 strips or tenths, they have 1.3, etc. Record different decimal numbers.
Group Activities
-- Cut paper to make tenths. Use to play a game counting on in tenths to make 1s and 0.1s.

Day 2
Launch the ITP ‘Moving digits’. Click, then drag cards to make the number 56. Click on ÷ 10. Discuss the place value of each digit, explaining that the 6 is now ‘six tenths’. Point out that we can also write this as zero point 6, 0.6. Repeat, dividing other numbers by 10 to derive 1-place decimals, e.g. 27, 49, 435, 409, 40, 4.
Group Activities
Use the in-depth problem-solving investigation ‘Magical square decimals’ as today’s group activity.
Or, use these activities:
-- Move digit cards on a place value grid to divide 2-digit numbers by 10.
-- Create 2-digit numbers and divide them by 10. Write a generalisation.

Day 3
Draw a large decimal point on a flipchart. Ask 2 children to stand either side holding large digit cards, e.g. 2 and 5 to show 2.5. Ask children to discuss in pairs what each child will need to do if we multiply 2.5 by 10. Model this, showing that 2.5 × 10 = 25 as both digits move one place value column to the left. Repeat for other numbers.
Group Activities
-- Use a ‘function machine’ to multiply and divide numbers by 10.
-- Play bingo to practise multiplication and division of numbers by 10.

### You Will Need

• Three pieces of A1 paper (one should be folded into ten strips, ready to be cut)
• Scissors
• Lots of A4 paper, trimmed to 28cm × 20cm, then cut into quarters (14cm × 10cm) and 1–6 dice
• ITP: Moving digits
• Place value grids (see resources) laminated
• 1–9 digit cards
• Large 0–9 digit cards, flipchart and pens
• Mini-whiteboards and pens and sticky notes labelled ÷10 and × 10
• Cards and cardboard box with two slots

### Mental/Oral Maths Starters

Suggested for Day 1
Count in 1/4s (simmering skills)

Day 2
Divide multiples of 10 by 10 (pre-requisite skills)

Day 3
Count in 1/10s to at least 2 (pre-requisite skills)

### Procedural Fluency

Day 1
Write decimals to go with pictures of wholes and tenths.

Day 2
Divide 2-digit numbers by 10, then find which numbers have been divided by 10.

Day 3
Identify result of multiplying by 10, including some inverse calculations.
Identify result of multiplying and dividing by 10, including some inverse calculations.

### Mastery: Reasoning and Problem-Solving

• Complete each number sentence:
(a) 3.4 × 10 = ☐
(b) 65 ÷ 10 = ☐
(c) ☐ ÷ 10 = 12.3
(d) ☐ × 10 = 81
• Draw a function machine which divides by 10.
Write the output for these three numbers: 13, 5, 92.
Write the input if 0.6 is the output.
Write the input if 2.2 is the output.
• Write each fraction as a decimal number.
One whole and six tenths
2²/10
Five wholes and one tenth
4/10

In-depth Investigation: Magical Square Decimals
Children use the arrangement of digits on a magic square to create one place decimals. They try to demonstrate that they have found all the possibilities.

### Extra Support

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

## Unit 4 Consolidate one-place decimal numbers (suggested as 3 days)

### Objectives

Consolidate understanding of one-place decimal numbers
Unit 4: ID# 4519

National Curriculum
Dec/Fr (v) (ix) (x)

Hamilton Objectives
26. Know that one-place decimal numbers represent ones and tenths.
28. Recognise and write decimal equivalents of any number of tenths and decimal equivalents to 1/2 and 1/5.
31. Compare numbers with the same number of decimal places up to two decimal places.
32. Solve simple measure/money problems involving fractions and decimals to two decimal places.

### Teaching and Group Activities for Understanding

Day 1
Point to 2/10 on counting stick. How else can we say this? (1/5) Launch ITP ‘Fractions’. Show 1/5 and 2/10 on two separate bars to show equivalence. Show both written as fractions and decimals. Repeat for other fifths and tenths.
Group Activities
-- Move elastic bands along strips of card to show tenths, given as fractions and decimals.
-- Mark tenths and fifths on a number line as fractions and as decimals. Play Decimal Bingo.

Day 2
Give each child a ruler marked in cm and mm. Children measure their finger nails in cm. Show that we can use tenths to give an accurate measurement, e.g. 1cm and 3 tenths (mm) which we write as 13mm or 1.3cm.Repeat for other amounts.
Group Activities
-- Measure items less than 10cm to the nearest mm. Record in cm, e.g. 5.7cm. Round to nearest cm.
-- Position 1-place decimals accurately on landmarked 0–10 lines and round to the nearest whole.
-- Position 1-place decimals accurately on sketched 0–7 lines.

Day 3
Ask which is more, 1.2 or 2.1? What whole number lies between? Confirm by placing both a on a 0–10 number line.
Write ☐.☐ > ☐.☐ on the board and roll a dice to create numbers to compare. Repeat for ☐.☐ < ☐.☐. Children agree in pairs a whole number between the two.
Group Activities
Use the in-depth problem-solving investigation ‘Round the Dice Decimals 1’ from NRICH as today’s group activity.
Or, use these activities:
-- Write 1-place decimal numbers in a given range then order the group of numbers.
-- Roll a dice to make numbers with 1 decimal place. Play ‘Higher or lower’ using the rolled digits.

### You Will Need

• Counting stick
• ITP: Fractions
• ITP: Tell the time
• Squared paper and 1 - 6 dice
• Flipchart and pens
• Strips of scrap card, elastic bands which fit snugly round the strips of card
• Items less than 10cm long
• Rulers marked in cm and mm
• 0–10 number lines (see resources)
• 0–9 dice
• Mini-whiteboards and pens
• 1–9 digit cards and coloured pencils

### Mental/Oral Maths Starters

Day 1
Count in 1/10s between two numbers (pre-requisite skills)

Day 2
Count on/back in steps of 10 to/from 4-digit numbers (pre-requisite skills)

Suggested for Day 3
Tell the time to the nearest 5 minutes (simmering skills)

### Procedural Fluency

Day 1
Recognise tenths of shaded diagrams, as decimals, fractions and an equivalent number of fifths.

Day 2
Place or identify numbers with one decimal place on a number line. Round to nearest whole number.

Day 3
Write < or > between numbers with one decimal place. Use digits to create accurate inequalities. Create accurately ordered sets of numbers.

### Mastery: Reasoning and Problem-Solving

• Write each number as a decimal.
(i) One and four tenths
(ii) 6/10
(iii) 10 ²/10 (ten and two tenths)
(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 > 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: Round the Dice Decimals
Use two dice to generate two numbers with 1 decimal place. What happens when you round these numbers to the nearest whole number? Round the Dice Decimals from nrich.maths.org.

### Extra Support

Decimals are a Snip
Understanding place value in numbers with one decimal place and how we can write tenths as fractions or decimals

## Unit 5 Rehearse equivalence: fractions/decimals (suggested as 2 days)

### Objectives

Rehearse equivalence in fractions and decimals
Unit 5: ID# 4547

National Curriculum
Dec/Fr (i) (v)

Hamilton Objectives
23. Write the equivalent fraction for fractions with given denominators or numerators.
28. Recognise and write decimal equivalents of any number of tenths and decimal equivalents to 1⁄2, 1/5 etc.

### Teaching and Group Activities for Understanding

Day 1
Use the ‘Fractions’ ITP to show 1/2s, 1/5s and 1/10s. Find pairs of equivalent fractions and record. Say that we can write 2/10 in a simpler form as 1/5. Ask children to write 4/10 in its simplest form. Show a line from 0 to 2 marked in tenths (see resources). Mark fifths and halves. How can 1 4/10 be simplified?
Group Activities
-- Cut out halves, fifths and tenths from the fraction wall. Match parts to create equivalent fractions.
-- Find pairs of equivalent fraction cards and label them on a 0 to 2 line.

Day 2
Display a 0 to 5 line marked in tenths (see resources). Count along the line in 0.1s. Point to various places on the line, children write the decimal. Point to 0.1. How else can we write and say this decimal? Record 0.1 ≡ 1/10. Repeat for other points. Record equivalences.
Callie wrote 3 3/5 and her partner wrote 3.6. Do they agree with each other?
Group Activities
-- Match decimals and fractions dominoes to form a loop.

### You Will Need

• ITP: Fractions
• Mini-whiteboards and pens
• Fraction wall (see resources)
• Fraction cards (see resources)
• 0 to 2 line marked in tenths (see resources)
• 0 to 5 line marked in tenths (see resources)
• Fractions and decimals dominoes (see resources)
• Scissors
• 0–5 line marked in tenths (see resources, copy onto A3 paper)

### Mental/Oral Maths Starters

Day 1
Count on and back in steps of 0.1 (pre-requisite skills)

Suggested for Day 2
Count in steps of 1/3 (simmering skills)

### Procedural Fluency

Day 1
Mark 1/10s on a 0 to 2 line; simplify to 1/5s or 1/2s where possible.

Day 2
Place fractions and decimals on a 0 to 2 line, writing each equivalent decimal and fraction.

### Mastery: Reasoning and Problem-Solving

Always true, sometimes true or false?
-- One half is zero point five.
-- A number of fifths can be written as an equivalent number of tenths.
-- A number of tenths can be written as an equivalent number of fifths.
-- 4/5 is less than 4/10.
-- Counting in tenths is the same as counting in 0.1s.
-- If I count on in steps of 0.1, the number after zero point nine is zero point ten.

In-depth Investigation
Use the Whole class activity on Day 2.

### Extra Support

Sticky Tenths
Consolidating understanding of tenths as fractions and as decimals

## Unit 6 Decimals: x/÷ by 10/100; +/- 0.1 (suggested as 2 days)

### Objectives

Multiply/divide by 10/100; add/subtract 0.1 to/from decimals
Unit 6: ID# 4561

National Curriculum
Dec/Fr (v) (vii)

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.

### Teaching and Group Activities for Understanding

Day 1
Display a blank 100 grid. Write 0.1, 0.2, 0.3 in first 3 squares. Ask what steps we are counting in. Take feedback and count in steps of 0.1 to end of row. Fill in the missing numbers. Ask children to write the first 3 numbers in the next row. Discuss what is added as we move down/up/left/right on the grid. Children record on their whiteboards. Ring three empty squares on the grid. Children work in pairs to agree each of the numbers.
Group Activities
-- Fill in a partially completed 0.1 to 10 grid. Explore +/– 0.1 or 1 calculations.
-- Play a dice game to practise adding and subtracting 0.1 and 1 to/from any number 0.1 to 10.

Day 2
Launch the ITP ‘Moving digits’. Click, then drag cards to make the number 24. Click on × 100. Discuss the results.
Click on the ÷ 10 button twice. Point out that dividing by 10 twice is the same as dividing by 100. Make 4.9 and multiply by 100. How could we get back to 4.9? Repeat for 800 ÷ 100, 80 ÷ 100, 280 ÷ 100. Discuss place value changes and the inverse nature of multiplication and division.
Group Activities
-- 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

• Blank 100 grid (see resources)
• Partly filled in 0.1 to 10 grid (see resources)
• A series of ‘slidy box cards’ showing additions and subtractions of 0.1 and 1
• Large blank 100 grid (see resources, copy onto A3 paper)
• 1–6 dice and coloured pens
• Interactive Whiteboard calculator
• ITP: Moving Digits
• Multiplication and division maze (see resources)
• Calculators

### Mental/Oral Maths Starters

Day 1
Place decimals on a 0.1 line (pre-requisite skills)

Day 2
Convert cm to mm (pre-requisite skills)

or

Suggested for Day 2
Convert between kg and g, km and m, l and ml (simmering skills)

### Procedural Fluency

Day 1
Fill in missing numbers on shapes taken from the 0.1 to 10 grid.

Day 2
Practise multiplying and dividing by 10 and 100 (whole answers or numbers with 1dp).
Balance equalities using multiplication or division by 10 or 100.

### Mastery: Reasoning and Problem-Solving

• Complete each sequence of numbers.
3.7, 3.8, 3.9, ☐, ☐
1.3, 1.2, ☐, 1, ☐, 0.8
0.8, 1.8, ☐, ☐, 4.8, ☐
9.3, 9.2, ☐, ☐, ☐, 8.8
☐, ☐, 10.6, 9.6, ☐
• Write the value of ten times each number.
(a) 3.4
(b) 6.2
(c) 0.8
(d) 1.1
• Write the value of one tenth of each number.
(a) 57
(b) 84
(c) 6
(d) 13
• Use this fact 56 = 7 × 8 to find the answer to each calculation.
(i) 7 × 80
(ii) 7 × 0.8
(iii) 7 × 800
(iv) 560 ÷ 8

In-depth Investigation
Use the Whole class activity on Day 2.

### Extra Support

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