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# Maths Year 5 Summer Fractions and Percentages

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 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 2 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 3 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.