### 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.