• Hamilton's Flexible Maths Blocks Explained Open our sample 'Year 5 Autumn Unit 1' to find out how the blocks of units work.

• Teacher support for Maths Hamilton has a range of additional reference and advice materials for Maths.

• Free Maths Resources on Hamilton Find out which Hamilton maths units you can access for free, including our new slide presentations.

# Maths Year 5 Summer Decimals, Percentages, 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 Place value in 3-place decimals (suggested as 3 days)

### Objectives

Understanding place value in 3-place decimals
Unit 1: ID# 5743

National Curriculum
Fr (vii) (ix)

Hamilton Objectives
19. Understand the effect of multiplying/ dividing by 10, 100, 1000, including 1- and 2-place decimal answers.
29. Write decimal numbers as tenths, hundredths, thousandths, e.g. 0.71 as 71/100, 0.327 as 327/1000. Relate thousandths to tenths and hundredths.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Write on the board 3.33. Discuss what each 3 represents. Write it on a place value grid to check.
Split the class into two groups. For each team, write on the board ☐.☐☐. Using number cards 0–9, teams take turns to choose, and then place a card in their number. The aim is to make largest number possible, then the smallest number.
Group Activities
-- Complete a short investigation to revisit 2-place decimals.

Day 2 Teaching
Display a place value chart and labels. Discuss the new ‘thousandths’ label. Ask children what happens to the digit 5 as each number is multiplied or divided by 10. Circle a number on each line and record the total of the circled numbers. Repeat, this time missing out a number on one or more rows.
Group Activities
-- Write place value additions to match numbers with three decimal places.
-- Write place value additions to match numbers with three decimal places. Derive missing numbers.

Day 3 Teaching
Show a place value grid on the IWB. Write 6.426 and read it together. Give four children number cards, e.g. 1, 2, 3 and 4 to show 1.234. They stand either side of another child holding a large decimal point. Now multiply the number by 10 and children move accordingly. Repeat to multiply and divide by 10 or 100.
Group Activities
Use the in-depth problem-solving investigation ‘Greater Than or Less Than?’ from NRICH as today’s group activity.
Or, use these activities:
-- Move digit cards on a place value grid to ×/÷ by 10 and 100.
-- Multiply and divide a number by 10, 100 and 1000. Divide capacities in ml to convert to litres.

### You Will Need

• Number cards 0–9
• Whiteboards and pens
• Place value chart (see resources)
• Place value chart labels (see resources)
• Place value grid (see resources)
• Large number cards 0–9
• Flipchart and pens
• Large sheets of paper

### Mental/Oral Maths Starters

Day 1
Count in steps of 0.01 (pre-requisite skills)

Day 2
Count in steps of 0.001 (pre-requisite skills)

Day 3
Convert between m and cm (pre-requisite skills)

### Procedural Fluency

Day 1
Compare order and round numbers with 2 decimal places.

Day 2
Complete place value partitioning additions for numbers with 3 decimal places, e.g. 1.58 + 0.005 = ☐

Day 3
Work out the outputs for ×10, ÷10, ×100, ÷100, ×1000 and ÷1000 function machines.

### Mastery: Reasoning and Problem-Solving

• Write the next numbers in each sequence.
41, 4.1 ____ ____
0.009, 0.09 ____ ____
20, 2 ____ ____ ____
• Divide 65 by 10 repeatedly until you get a number that is less than 0.1. Write that number.
• True or false?
4.3 ÷ 100 = 0.43
109 = 1.009 × 100
0.005 × 100 = 0.5
71 ÷ 1000 = 0.0071
164 = 0.164 × 1000
804 ÷ 1000 = 0.084

In depth Investigation: Greater Than or Less Than?
Use numbers and symbols to make a number sentence correct. How many different ways can you find? Greater Than or Less Than? from nrich.maths.org.

### Extra Support

Understanding place value in numbers with two decimal places

Left, Right, Left, Right
Multiplying and dividing by 10 (numbers and answers to include numbers with 2 decimal places)

## Unit 2 Compare and use 3-place decimals (suggested as 2 days)

### Objectives

Compare and use decimals with 3-places, showing understanding
Unit 2: ID# 5749

National Curriculum
Fr (vii) (ix) (x)

Hamilton Objectives
29. Write decimal numbers as tenths and hundredths.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Write on the board 4.378. Ask children what each digit represents. Say both the fraction and the decimal: three tenths; zero point three. Use number cards 0–9 to play decimal number bingo to subtract the value of a digit from a 4-digit number with three decimal places. Show cans/jars with masses in grams. Convert the masses into kg. What does each digit after the decimal point represent? Show a 100g weight: Is this 0.001kg, 0.01kg or 0.1kg? Repeat for a 1g and a 10g weight. Convert millilitres to litres and kilometres to metres.
Group Activities

Use the ‘Guesstimate’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Use digits cards on a place value grid to convert between km and m, l and ml.
-- Order masses in kg with different numbers of decimal places. Convert to grams to check.

Day 2 Teaching
Write on the board ☐.☐☐☐ > ☐.☐☐☐. Use 0–9 cards. Take one. Where should we put this card to ensure that the sentence is true? Repeat until each box has a card. Children write a number in between on their whiteboards. Repeat with ☐.☐☐☐ < ☐.☐☐☐. Write numbers: 5.289, 5.974, 5.278 and 5.419. Children order the numbers on their whiteboards. Think of one number between each neighbouring pair of numbers: one with one decimal place, one with two decimal places and one with three decimal places.
Group Activities
-- Play an online game to order numbers with one and two decimal places.
-- Play a number line game to practise ordering numbers with three decimal places.
-- Choose numbers from a grid with one, two or three decimal places. Place the numbers on a number line, to try to get three in a row.

### You Will Need

• Number cards 0–9
• Cans and jars with weights (in grams) written on sticky notes
• Weights: 1g, 10g and 100g
• ‘Converting measurements’ sheet (see resources)
• A3 paper and coloured paper
• ‘Cat weights’ sheet (see resources)
• Whiteboards and pens
• Additional activity sheets (see resources)

### Mental/Oral Maths Starters

Day 1
Count on and back in steps of 0.002 (pre-requisite skills)

Day 2
Round numbers with two decimal places to the nearest whole (pre-requisite skills)

### Procedural Fluency

Day 1
Convert between km and m, l and ml.

Day 2
Locate 1-, 2- and 3-place decimals on a number line; order smallest to largest.

### Mastery: Reasoning and Problem-Solving

• Write the value of each digit as a fraction:
0.375
• Write the total of this addition as a decimal:
6/1000 + 4/10 + 3/100
• Ali’s homework needs marking. Write the correct answers for those he has wrong. Explain any mistakes Ali is making.
Write < or > or = between each pair of numbers:
(a) 0.34 < 0.099
(b) 1.075 > 1.08
(c) 6.006 < 6.06
(d) 5.264 > 5.27
(e) 9.999 > 10.001

In depth Investigation: Guesstimate
Children work out the capacity of their classroom in litres.

### Extra Support

Decimal divisions
Convert from cm to m and vice versa. Understand place value in numbers with two decimal places.

## Unit 3 Begin to understand percentages (suggested as 3 days)

### Objectives

Begin to understand percentages
Unit 3: Id# 5779

National Curriculum
Fr (xi) (xii)

Hamilton Objectives
33. Solve problems involving fractions, decimals and percentages using known equivalences to help.
28. Identify simple fraction and percentage equivalents: 1/2 ≡ 50%, 25% ≡ 1/4 and 75% ≡ 3/4, 40% ≡ 4/10 etc.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Write on the board the symbol %. Ask children where they’ve seen this. Per cent means per or out of 100. Show a blank 100-square. Each square is 1% of the whole square. Write 1%. What fraction is this? Write 1/100. Shade the top row. What fraction is shaded? In tenths? In hundredths? Continue like this.
Group Activities
-- Identify equivalent percentages, fractions and decimals shaded on 100-squares.
-- Colour some 5 × 2 rectangles according to given percentages.

Day 2 Teaching
Write on the board two headings: ‘swimming’ and ‘cycling’. Ask ten children to stand next to their favourite. What fraction prefer swimming? Show a blank 100-square, shade this number of tenths. What is this as fraction out of 100? As a percentage? Repeat with different children and different sports.
Group Activities
Use the ‘Percentage puzzles’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Apply understanding of equivalent fractions, decimals and percentages to create a display of ‘mobiles’.

Day 3 Teaching
Display three word problems, all of which require that children recognise percentage and fraction equivalences, e.g. that 50% is equivalent to 1/2 and 25% is equivalent to 1/4. Solve the problems using equivalences.
Group Activities

-- Use blank 100-squares to help find percentages of 200 and 300
-- Find percentages of amounts. Use conversion to percentages to compare fractions with different denominators.
-- Find any percentage of an amount by using ‘key’ percentages as a starting point.

### You Will Need

• Whiteboards and pens
• ‘Blank 100 grid’ (see resources)
• ‘Percentages’ sheet (see resources)
• Flipchart and pens
• Squared paper and coloured pencils
• ‘Mobile circles’ (see resources) printed on coloured card
• String, pens, glue and scissors
• Additional activity sheets (see resources)

### Mental/Oral Maths Starters

Day 1
Divide by 10, 100 and 1000 (pre-requisite skills)

Day 2
Percentages (pre-requisite skills)

Suggested for Day 3
Multiply three numbers together (simmering skills)

### Procedural Fluency

Day 1
Write the percentage of each 100-square that is shaded, then an equivalent vulgar and decimal fraction.

Day 2
Convert fractions to percentages.

Day 3
Find percentages of amounts: multiples of 100.
Find percentages of amounts: multiples of 10 and 100.

### Mastery: Reasoning and Problem-Solving

• Explain what 10% means. Is 10% larger or smaller than 1/5?
• Write the missing percentage in each of the bar models:
Diagram 1:
 60 Children Walk 20% Cycle 50% Drive ?

Diagram 2:

 24 Children Crisps 75% Fruit ?
• Now write the numbers of children in each category.
• Write 10% of each price:
£3.40 £5.10 £12 £9.90
Now work out 40% of each price.
• Aayush scored 13/20 on a test. Samar scored 70% on the same test. Which of them did better?

In depth Investigation: Percentage Puzzles
Children work systematically to find equivalent percentages of different amounts.

### Extra Support

Go for 100%
Understanding what a percentage is and knowing equivalent percentages for half and tenths

## Unit 4 Subtract decimal numbers by counting up (suggested as 3 days)

### Objectives

Subtract decimal numbers by counting up
Unit 4: ID# 5791

National Curriculum
Fr (x)

Hamilton Objectives
32. Subtract 1- and 2-place decimal numbers by counting up: 6.2 – 3.5, 13.1 – 9.45.
29. Write decimal numbers as tenths and hundredths.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Write on the board 23.46 and 23.64. Which is bigger? Demonstrate finding the difference using Frog. Sketch a number line from 23.46 to 23.64. Frog hops first to? (23.5). How big is that hop? And the next? (Either 23.6 or 23.64). Add hops to find the difference. Children use Frog to calculate 23.32 – 19.67. They record the answer on their whiteboards. Display a word problem for children to read and solve. A volunteer models their working.
Group Activities
-- Whole class investigation: write a number using four consecutive digits in the form: ☐☐.☐☐, e.g. 45.67. Reverse it and find the difference between the two numbers. Explain any pattern.

Day 2 Teaching
Revise using counting up (Frog) to subtract numbers with different numbers of decimal places. Start by demonstrating how to use Frog to count up to do 6.24 – 4.5. Then use Frog to help children solve subtraction word problems.
Group Activities
-- Use a landmarked number line to find the difference in side lengths of rectangles, working towards calculating with a mix of 1- and 2-place decimal numbers.
-- Solve word problems requiring subtraction of numbers with different numbers (one or two) of decimal places.

Day 3 Teaching
Use the context of buying items for their rooms to find change from £100 for amounts such as £18.49. Model representing the word problem using a bar diagram, and then using Frog to perform the calculation. Repeat, modelling several.
Group Activities
-- Play games to practise finding totals and calculating change from £100.

### You Will Need

• Mini-whiteboards and pens
• ‘0 to 4m lines’ (see resources)
• Flipchart and pens
• ‘Subtracting decimals’ word problems (see resources)
• Number cards 0–9

### Mental/Oral Maths Starters

Day 1
Find the complement to the next whole (pre-requisite skills)

Day 2
Find the change from £10 (pre-requisite skills)

Suggested for Day 3
Subtract any pair of 2-digit numbers mentally (simmering skills)

### Procedural Fluency

Day 1
Use Frog (counting up) to subtract pairs of numbers, with one or two decimal places.

Day 2
-- Solve word problems requiring subtraction of numbers with the same number (one or two) of decimal places.
-- Solve word problems requiring subtraction of numbers with one and two decimal places.

Day 3
-- Find change from £100.
-- Find the difference between prices.

### Mastery: Reasoning and Problem-Solving

• Choose two numbers and find the difference between them:
14.45 16.12 13.57 8.87
Repeat this twice.
• Write the missing numbers.
(a) 23.4 – ☐ = 18.67
(b) 15.5 = ☐ + 8.78
(c) 32.4 – 18.55 = ☐
• Find change from £100 when buying:
-- chair £56.89
-- table £75.37
-- rug £20.08

In-depth Investigation
Use Day 1’s Group Activity as this unit’s investigation.

### Extra Support

Mini minuses
Using Frog to subtract numbers with one decimal place

## Unit 5 Add/subt fractions with related denominators (suggested as 3 days)

### Objectives

Add and subtract fractions with related denominators
Unit 5: ID# 5801

National Curriculum
Fr (ii) (iv) (iii)

Hamilton Objectives
25. Recognise mixed numbers and improper fractions and convert from one to the other, writing mathematical statements.
26. Add and subtract fractions where the denominators are multiples of the same number.
23. Identify, name and write equivalent fractions.

### Teaching and Group Activities for Understanding

Day 1 Teaching
In a school, 1/4 of children voted for cycling as their favourite sport, 3/8 voted for swimming, the rest voted for football. Which was the most popular? Model how to use fraction equivalences (fraction families) to solve this. Repeat for comparing other pairs of fractions, e.g. 7/10 and 3/5, 5/9 and 2/3.
Group Activities
-- Use a fraction wall to help compare two fractions with related denominators. Convert improper fractions to mixed numbers.
-- Play a game comparing fractions that have related denominators.

Day 2 Teaching
Display ‘Adding and subtracting fractions’ (see resources). Children work in pairs to add two fractions with the same denominator. Then find two fractions with different, but related, denominators to add by converting one so they have the same denominator. Model a strategy for 4/5 + 7/10 (total >1), converting the resulting improper fraction to a mixed number. Children try 3/4 + 5/8. Perform subtractions using similar strategies.
Group Activities
Use the in-depth problem-solving investigation ‘A4 Fraction Addition’ and/or ‘A4 Fraction Subtraction’ from NRICH as today’s group activity.
Or, use this activity:
-- Whole class activity: Find the total of, and difference between, two fractions with related denominators.

Day 3 Teaching
Write 3¹/2 + 2¹/4. We add the 3 and 2, then add the fractions, then combine the answers. Ask children to do this and agree the answer 5³/4. Repeat for 2³/4 + 1¹/2. This time we’ve got another whole to add from adding the fractions. Repeat to subtract mixed numbers: 3⁷/8 – 2¹/4.
Group Activities
-- Add and subtract mixed numbers (fractions in some additions total >1).
-- Subtracting mixed numbers which need converting to improper fractions first, e.g. 3¹/2 – 2³/4.

### You Will Need

• Mini-whiteboards and pens
• Fraction wall (see resources)
• flipchart and pens
• Number cards 1–9
• Adding and subtracting fractions (see resources)
• Adding and subtracting mixed numbers (see resources)

### Mental/Oral Maths Starters

Day 1
Equivalent fractions (pre-requisite skills)

Day 2
Count in steps of eighths (pre-requisite skills)

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

### Procedural Fluency

Day 1
Practise comparing, then ordering groups of proper fractions; compare mixed numbers and improper fractions by converting them all to mixed numbers.

Day 2
Practise adding and subtracting fractions with related denominators, some totals > 1.

Day 3
Further practise adding and subtracting fractions with related denominators.
Practise adding and subtracting mixed numbers.

### Mastery: Reasoning and Problem-Solving

• Sunil and Zoe have picked 36 cherries in total. Sunil has 1/3 of the cherries and Zoe has 1/2. How many cherries are left for Sunil’s little brother?
• Which of these additions will have a total less than 1 whole?
2/3 + 5/6
3/4 + 3/8
1/5 + 3/10
1/3 + 5/12
• The total of each pair of fractions is 11/12. Write the missing fraction in each pair.
1/4 and ☐
☐ and 1/6
1/2 and ☐
Write each fraction in its simplest form.

In-depth Investigation: A4 Fraction Addition and/or A4 Fraction Subtraction
Explore calculating with fractions using A4 paper to model wholes and related parts. A4 Fraction Addition and/or A4 Fraction Subtraction from nrich.maths.org.

### Extra Support

Pete’s Pizza Passion
Adding and subtracting fractions with the same denominator

## Unit 6 Multiply fractions by whole numbers (suggested as 2 days)

### Objectives

Multiply fractions and mixed numbers by whole numbers
Unit 6: ID# 5807

National Curriculum
Fr (iii) (v)

Hamilton Objectives
21. Solve problems involving multiplication and division.
25. Recognise mixed numbers and improper fractions and convert from one to the other, writing mathematical statements.
33. Solve problems involving fractions.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Sketch two cakes, dividing each into fifths. Two children eat 2/5 of a cake each. How much do they eat altogether? Record: 2 × 2/5 = 4/5. Two other children eat 4/5 of a cake. How much is this? Shade 4/5 of the first cake in one colour, then last 1/5 and 3/5 of the other cake in a different colour. Record 2 × 4/5 = 8/5 = 1³/5. Repeat for 2 × 2/3. Challenge children to work in pairs to double other fractions less than 1, finding answers less than one and more than 1.
Group Activities
-- Use circles divided into thirds to help write the 2/3 times table.
-- Use three 2 to 6 or 2 to 12 number cards to create whole number × fraction calculations.

Day 2 Teaching
Write on the board 3 × 2³/4. Say that three hungry children ate 2³/4 rounds of sandwiches each! Children discuss how to work out how much has been eaten all together. Take feedback. Use brackets to show how we can work out the multiplication in stages.
Group Activities
Use the ‘Fraction fireworks’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Play a Bingo game, multiplying numbers 2 to 10 by 3/4.
-- Investigate using the digits 2, 3, 4 and 5 to make as many different multiplications of mixed numbers and whole numbers as possible.
-- Investigate a sequence of mixed number by whole number multiplications.

### You Will Need

• Mini-whiteboards and pens
• ‘2/3 times table’ activity sheet (see resources)
• Number cards 2–12
• 1–10 dice
• Fraction multiplication Bingo: 3/4 (cut sheet into four separate cards - see resources)

### Mental/Oral Maths Starters

Day 1
Convert improper fraction to mixed numbers (pre-requisite skills)

Suggested for Day 2
Equivalent fractions, decimals and percentages (simmering skills)

### Procedural Fluency

Day 1
Write the 2/5 times table using a supporting image.
Practise multiplying fractions by whole numbers.

Day 2
Further practise multiplying fractions by whole numbers.
Write the 1³/4 times table.
Practise multiplying mixed numbers by whole numbers.

### Mastery: Reasoning and Problem-Solving

• Count in steps of 4/5, starting from 4/5. What is the first number you say which is not a mixed number? What is the second number you say which is not a mixed number?
Stop counting here!
• Six children each say they want 2/3 of a pizza for a party tea. How many pizzas will Dad need to buy?
Four dogs each eat 3/5 of a tin of dog food every day. How many tins must Mum buy for a week?
• True or false?
6 × 1³/4 = 10¹/2
12 × 2¹/5 = 22²/5
9 × 3²/3 = 33¹/3
7 × 4¹/4 < 30

In-depth Investigation: Fraction Fireworks
Children find the answers to a sequence of fraction multiplications and look for patterns in the answers.

### Extra Support

Mini multiplications
Count in unit fraction steps on a number line. Write mixed numbers.