Maths Year 5/6 Summer Division, Fractions and Percentages

Day 1
Model short division to find 2381 ÷ 3 using sticky notes and base-10 equipment, or the ‘Short division 1’ presentation. Repeat with 1381 ÷ 6 and 1281 ÷ 5 using just the sticky notes.
Group Activities: T with Y5
Y5 -- Investigate short division of given 3-digit numbers. Explain a pattern in the remainders.
-- Investigate short division of given 4-digit numbers. Explain a pattern in the remainders.
Y6 -- Division investigation (square a prime number, add 14, divide by 12, note the remainder).

Day 2
Use the ‘bus shelter’ short division layout to model 5466 ÷ 4. Agree that we can divide the remainder 2 by 4 to give 2/4. How can we simplify this? Agree the answer as 1366¹/2. Repeat for 5120 ÷ 6. Write 5118 ÷ 6. What do you think will be the answer to this? Can you suggest other divisions by 6 that will not have a remainder? A division that will have 1/6 in the answer?
Group Activities: T with Y5/6 activity
Y5 -- Make a 3-digit number; divide by a fourth number. Score the remainder.
Y5/Y6 -- Divide 4-digit numbers by 1-digit numbers, investigating largest possible fraction remainders.
Y6 -- Divide 4-digit numbers by 1-digit numbers, investigating largest possible fraction remainders.

Day 3
Write: 472 ÷ 4, 3958 ÷ 3, 2786 ÷ 4, 7975 ÷ 4. Children agree an estimate for each. Take feedback on strategies. Model finding 2786 ÷ 4; express the remainder as fraction and simplify. Children calculate 2054 ÷ 3, then write a division with an answer >1000 and one with an answer <1000.
Further Teaching with Y6
Write 555, pointing out that this 3-digit number has all digits the same. Ask children to add the three digits, then calculate 555 ÷ 15, estimating first. Show, using long division.
Group Activities: T with Y6
Y5 -- Use the ‘Remainder runners’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Practise short division of 3- and 4-digit numbers, creating calculations with number cards.
Y6 -- Use short or long division to investigate properties of divisibility.

• ‘Short division 1’ presentation (see resources)
• 1000s, 100s, 10s and 1s base-10 equipment
• Sticky notes, 0–9 digit cards
• Mini-whiteboards and pens
• ‘Short division 2’ presentation (see resources)
• ‘Short division 3’ presentation (see resources)
• ‘Amazing 6720’ (see resources)

Day 1
Division facts for the 6 times table

Day 2
Division loop cards

Day 3
Division facts

Day 1
Y5: Practise short division of 3-digit by 1-digit numbers, with remainders.
Practise short division of 4-digit by 1-digit numbers, with remainders.
Y6: Complete a division investigation involving prime numbers.

Day 2
Y5: Calculate multiplications; use them to choose 3-digit numbers to divide by 3, 4 and 5 to give answers within given ranges.
Practise dividing 4-digit numbers, expressing remainders as fractions.
Y6: Use short division to divide 4-digit numbers by 1-digit numbers.

Day 3
Y5: Use short division to divide 3-digit and 4-digit numbers by 1-digit numbers.
Y6: Complete one of two division investigations. Make observations, generalise, explore proofs.

Y5

• Find:
  581 ÷ 7 = ☐
  3456 ÷ 5 = ☐
  5400 ÷ 9 = ☐
• A farmer is packing eggs. Each box holds six eggs. The farmer has 890 eggs to pack. How many boxes will the farmer fill?
• Fill the missing boxes to give an answer with fraction remainders as follows:
  187 ÷ ☐ = ____1/2
  331 ÷ ☐ = ____3/4
  ☐ ÷ 10 = ____2/5

Y6
This unit has no separate problem-solving activities for Y6.

Y5 In-depth investigation: Remainder runners
Children divide 1234, 2345, 3456 by 3, 4, 5 … 12 and look for patterns in the remainders.

Y6 Complete Group Activity from Day 1, Day 2 or Day 3.

Y5
Chunking Champs
Using chunking to divide, answers between 10 and 30, with remainders.

Y6
This unit has no separate Extra Support activities for Y6

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.

• 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

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

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.

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

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.

Day 1
Write %. Ask children where they have 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. Model how to use division on a calculator to convert fractions to decimals.
Group Activities: T with Y5
Y5 -- Identify equivalent percentages, fractions and decimals shaded on 100 squares.
-- Colour 5 × 2 rectangles according to given percentages.
Y6 -- Use a calculator to convert fractions to decimals by division and place the fractions on a 0–1 (or 0–2) line.
-- Given the answer 1.181818 (13 ÷ 11), use a calculator to calculate the ‘mystery’ division.

Day 2
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: T with Y5 or Y6
Use the in-depth problem-solving investigation ‘Percentage puzzles’ as today’s group activity.
Or, use these activities:
Y5 -- Apply understanding of equivalent fractions, decimals and percentages to make a display of mobiles.
Y6 -- Create a 0–1 line showing equivalent fractions, decimals and percentages.

Day 3
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: T with Y5 or Y6
Y5 -- 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.
Y6 -- Find any percentage of an amount by using ‘key’ percentages as a starting point.

• Mini-whiteboards and pens
• ‘Blank 100-square’ (see resources)
• Interactive whiteboard calculator
• ‘Percentages’ (see resources)
• Flipchart and pens
• Squared paper
• ‘Three in a row’ Sheets 1 and 2 (see resources)
• Calculators
• Cards
• ‘Mobile circles’ (see resources, printed on coloured card), string, pens, glue
• Large piece of paper, marker pens, sticky notes, A3 paper
• ‘Comparing percentages’ (see resources)
• Coloured pencils

Day 1
Divide by 10, 100 and 1000

Day 2
Percentages

Day 3
Find non-unit fractions of amounts

Day 1
Y5: Write equivalent percentage, decimal and fraction for shaded portions of a 100-grid.
Y6: Play a calculator game, converting fractions to decimals using division.

Day 2
Y5 Explore common fraction-percentage equivalents.
Y6: Write equivalent decimals, fractions and percentages.

Day 3
Y5: Calculate %s of multiples of 100.
Calculate %s of 3-digit multiples of 10.
Y6: Use equivalence with fractions and key percentages to calculate percentages of amounts.

Y5

• Explain what 10% means. Is 10% larger or smaller than 1/5?
• Write the missing percentage in each of the bar models (see download).
  Now write the numbers of children in each category.
• Write 10% of each price:
  £3.40; £5.10; £12; £9.90
  Now calculate 40% of each price.
• Aayush scored 13/20 on a test. Samar scored 70% on the same test. Which of them did better?

Y6

• True or false?
  2/5 is the same as 20%.
  0.4 is the same as 4%.
  10% is the same as 0.1.
  30% is the same as 1/3.
• Find 10% of these prices. Use that to find 20%.
  (a) £14.20
  (b) £1.50
  (c) £99

In-depth investigation: Percentage puzzles
Children work systematically to find equivalent percentages of different amounts.

Y5
Go for 100%
Understanding what a percentage is and knowing equivalent percentages for half and tenths

Y6
Special People
Understanding what a percentage is