Maths Year 5/6 Summer Fractions and Percentages

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

Calculating with fractions(suggested as 5 days)

Planning and Activities

Day 1
In a school, ¹/4 of children voted cycling as their favourite sport, 3/8 voted swimming, the rest voted football. Which was most popular? Model how to use fraction equivalences to solve this. Compare other pairs of fractions, e.g. 31/4 and 15/4, then 11/3 and 31/3.
Group Activities: T with Y5
Y5 -- Use a fraction wall to compare pairs of fractions with related denominators; convert improper fractions to mixed numbers.
Y5/Y6 -- Play a game comparing fractions with related denominators.

Day 2
Display ‘Adding and subtracting fractions’. Pairs of children add two fractions with the same denominator; then two fractions with different, but related, denominators, converting one so they have the same denominator. Repeat for subtraction. Discuss how to use equivalence to add pairs of fractions with unrelated denominators.
Group Activities: T with Y5
Y5/Y6 -- Whole class activity: Find the total of, and difference between, pairs of fractions with related (Y5) or unrelated (Y6) denominators.

Day 3
Write 3¹/2 + 2¹/4. We can add the 3 and 2, then add the fractions, then combine the answers. Relate to partitioning and recombining used to add pairs of 2-digit numbers. Agree the answer as 5³/4. Repeat for 2³/4 + 1¹/2. This time we have got another whole to add from adding the fractions. Repeat for 22/3 + 15/6. Repeat to subtract: 3⁷/8 – 2¹/4.
Further Teaching with Y6
Discuss how to calculate 31/2 + 22/3 and 22/3 - 11/4.
Group Activities: T with Y6
Y5 -- Add and subtract mixed numbers (fractions in some additions total greater than 1).
-- Subtract mixed numbers which need converting to improper fractions first, e.g. 31/2 – 23/4.
Y6 -- Find pairs of mixed numbers with a total greater than 6, then a difference less than 1.
-- Subtract mixed numbers which need converting to improper fractions first, e.g. 31/2 – 22/3.

Day 4
Sketch two cakes, dividing each into fifths. Two children eat 2/5 of a cake each. Record: 2 × 2/5 = 4/5. Repeat for 2 × 4/5 = 8/5 = 1³/5, and 2 × 2/3. Pairs of children double other fractions less than 1, finding answers less than 1 and greater than 1. Discuss: ‘Sometimes/Always/Never: A multiplication produces a bigger answer than both of the numbers in the calculation.’
Further Teaching with Y6
Write 1/2 × 3/4 on the board. Remind children of the strategy we can use to multiply fractions (multiply the numerators and then multiply the denominators). Demonstrate by sketching a cake on the board, shading 3/4 and asking children how much is half of the shaded section. Repeat for 1/2 × 4/5, then find 2/3 × 6/7.
Group Activities: T with Y6
Y5 – Use circles divided into thirds to help create the 3/4 times table.
– Use three number cards 2–6 or 2–12 to create ‘whole number × fraction’ calculations.
Y6 -- Investigate pairs of fractions with products less than/greater than 1/2.

Day 5
Write on the board 3 × 2³/4. Say that three children ate 2³/4 rounds of sandwiches each. Children discuss how to calculate how much has been eaten in total. Take feedback. Use brackets to show how we can calculate the multiplication by partitioning the mixed number.
Group Activities: T with Y5
Y5 -- 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.
Y6 -- Investigate a sequence of ‘mixed number × whole number’ multiplications.

You Will Need

• Mini-whiteboards and pens
• ‘Fraction wall’ (see resources)
• Flipchart and pens
• Number cards 1–9, 2–9, 2–6 and 2–12
• ‘Adding and subtracting fractions’ (see resources)
• ‘Adding and subtracting mixed numbers’ (see resources)
• ‘3/4 times table’ (see resources)
• 1–10 and 1–12 dice
• ‘Fraction multiplication Bingo: 3/4’ (cut sheet into four separate cards, see resources)
• Several sets of digit cards 2–5

Short Mental Workouts

Day 1
Equivalent fractions

Day 2
Count in steps of eighths

Day 3
Fractions with a total of 1

Day 4
Convert improper fractions to mixed numbers

Day 5
Count in steps of 11/4

Worksheets

Day 1
Y5/Y6: Compare, then order groups of proper fractions; compare mixed numbers and improper fractions by converting them all to mixed numbers.

Day 2
Y5: Add and subtract fractions with related denominators, some totals greater than 1.
Y6: Add and subtract fractions with related and unrelated denominators, some totals greater than 1. Carry out an investigation.

Day 3
Y5: Add and subtract fractions with related denominators.
Y6: Add and subtract fractions with unrelated denominators.

Mastery: Reasoning and Problem-Solving

Y5

• 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?
Now add each pair:
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.
• 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

Y6

• Write the missing numbers to make each sentence true.
5/6 + 5/8 = ?/?
4/5 – ?/? = 1/4
1/6 + ?/? = 9/10
• Write an addition of two different fractions, with different denominators, which have a total of 5/8.
• How many times must I add 1/5 to 3/8 to get a total greater than 1?
• Which is larger:
0.75 – 1/3 or 1/6 + 1/4
• Mystery fractions.
Fraction A add fraction B is one whole.
Fraction A subtract fraction B is 3/7.
Write fractions A and B in their simplest forms.
• Find one quarter of
(a) 1/3
(b) 2/5
(c) 3/8.
• A large cake is divided into ten equal pieces. One piece is split into thirds. What fraction is each smaller piece? Another piece is split into quarters. What fraction is each of these smaller pieces?
• We divide a quarter of a pie into five pieces. What fraction is each piece?
• Fill in the missing numbers:
1/4 of ☐ is 1/12.
☐ of 1/2 is 1/6.
1/5 of 2/3 is ☐.

In-depth investigation
Complete Day 5’s Group Activities

Extra Support

Y5
Pete’s Pizza Passion
Adding and subtracting fractions with the same denominator.

Mini multiplications
Counting in unit fraction steps on a number line. Writing mixed numbers.

Y6
Make the Fractions Friendly

Adding fractions with related denominators.

Teeny Subtractions
Subtracting fractions with related denominators.

Folding Fractions
Finding half of fractions using supporting paper-folding images.