Short Blocks

Maths Year 3 Summer 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 added value for Hamilton Friends and School Subscribers.

Unit 1 Fractions of amounts (suggested as 3 days)

Objectives

Using understanding of fractions to find fractions of amounts
Unit 1: ID# 3709

National Curriculum
Fr (ii) (vii)

Hamilton Objectives
23. Recognise, find and write unit and non-unit fractions of convenient amounts.
27. Solve problems involving fractions.

Teaching and Group Activities for Understanding

Day 1 Teaching
Children find different unit fractions of 12 and 16 cubes, making links to division facts.
Group Activities
-- Investigate unit fractions of different target numbers.

Day 2 Teaching
Show a bar model representing fifths of 25. How much is 1/5? Use this to find 2/5, 3/5, and 4/5 of 25.
Repeat for sixths of 24. Then find 5/6, discussing how one way is to count on 4, 8, 12, etc. but that is quicker to multiply 4 by 5. Repeat for eighths of 24. Then try 3/4 of 20 and 2/3 of 15 without a bar model.
Group Activities
Use the in-depth problem-solving investigation ‘Does it or not?’ as today’s group activity.
Or, use these activities:
-- Solve non-unit fraction questions by playing a card game.
-- Create and play non-unit fraction bingo.

You Will Need

  • Cubes
  • Mini whiteboards and pens
  • ‘Non-unit fraction cards’ sheet 1 (see resources)
  • ‘Non-unit fraction cards’ sheets 2 and 3 (see resources)
  • A5 card and counters
  • ‘Bingo boards’ (see resources)

Mental/Oral Maths Starters

Day 1
Division facts for 5 times table (pre-requisite skills)

Day 2
Division facts for 3 times table (pre-requisite skills)

Procedural Fluency

Day 1
Find unit fractions of given numbers using division/ tables facts and equipment to support.

Day 2
Find non-unit fractions of given numbers using division/ tables facts and equipment to support.

Mastery: Reasoning and Problem-Solving

  • True or false?
    -- A piece of paper folded equally in 3, then folded in half is divided into sixths when you open it out.
    -- 1/3 of a piece of paper is larger than 2/6 of the same piece.
    -- Two eighths make a quarter.
    -- 2/5 of 5 is 2.
    -- 3/8 of 16 is 5.
  • Draw a bar model to represent each question:
    (a) 3/8 of 32?
    (b) 4/5 of 40?
    (c) 5/6 of 42?
    Write the answers.
  • Write < or > or = between these two statements:
    3/5 of 40
    2/3 of 30

In-depth Investigation: Does It or Not?
Children find numbers between 50 and 100 which they can divide by 4. They halve each number twice to find out

Extra Support

On All Fours
Investigating the properties of numbers that divide by 4 to give a whole number answer

Unit 2 Fractions as operators and as numbers (suggested as 3 days)

Objectives

Understand fractions as operators and as numbers
Unit 2: ID# 3719

National Curriculum
Fr (i) (ii)

Hamilton Objectives
26. Compare and order unit fractions and fractions with the same denominator.
24. Count up and down in fractional steps, hence recognise fractions as numbers.
23. Recognise, find and write unit and non-unit fractions of convenient amounts.

Teaching and Group Activities for Understanding

Day 1 Teaching
Sketch a line 0 to 1 and mark it in tenths. Explain that the line is in 10 equal parts and each part is 1/10. Count in 1/10s along the line. Sketch a rectangle divided in 1/10s. Shade different numbers of 1/10s. Show 20 cubes. Divide into tenths by placing two cubes into each box of the rectangle. Continue with how to show tenths of 30 and 40.
Group Activities
-- Find fractions of multiples of 10.
-- Present mystery numbers to a partner by describing how much 1/10 of the number is.

Day 2 Teaching
Show some fraction number lines. Count in steps of 1/2. Ask where 3 ¹/2 is. Then ask children to find 1/2 of 200, so recognising that a fraction is both a number and an operator (used as a calculation to find a proportion of an amount). Show the line marked in 1/4s. Count in 1/4s. Find 2 ³/4. Ask children to find 1/4 of 24. Repeat with other lines/fractions, showing children that fractions are numbers on a line and also calculations, e.g. 1/4 of 8.
Group Activities
-- Find whole number unit fractions of a given amount.
-- Play fraction buzz by matching whole number unit fractions to given numbers.

Day 3 Teaching
Use a strip of paper with 24 evenly spaced items. Fold in half, then half again to find 1/4s; then half again to show 1/8s. Use this to find and compare 3/4 and 5/8 of 24. Which is bigger? Use bar models to show how we can find and compare 3/5 of 20 and 4/6 of 24.
Group Activities
Use the in-depth problem-solving investigation ‘Greedy Guzzler’ as today’s group activity.
Or, use these activities:
-- Play a card game to practise finding and comparing non-unit fraction amounts.
-- Play a card game to find non-unit fractions of amounts.

You Will Need

  • Cubes
  • ‘Finding tenths’ resource sheet and lots of copies of the ‘Finding tenths’ grid (see resources)
  • Counters
  • ‘Fraction number lines’ sheet (see resources)
  • ‘Finding 1/3 of 12’ bar model (see resources)
  • Number cards
  • Additional activity sheets (see resources)
  • Counters
  • Mini whiteboards and pens
  • Calculators

Mental/Oral Maths Starters

Day 1
Multiply and divide by 10 (pre-requisite skills)

Day 2
Counting in steps of 3 (pre-requisite skills)

Suggested for Day 3
Halve even numbers to 100 (simmering skills)

Procedural Fluency

Day 1
Work out tenths of numbers and solve missing number challenges.

Day 2
Investigate the fractions that numbers <30 can be split into
Investigate the fractions that numbers <60 can be split into.

Day 3
Find non-unit fractions using multiplication and division facts.

Mastery: Reasoning and Problem-Solving

  • Shade 3/10 of this shape in one colour. Shade 1/2 in another colour. How many tenths are unshaded?
  • Write the missing numbers in each sequence:
    3/4, 1, ☐, ☐, ☐, 2, 2¹/4, ☐
    3²/3, 3¹/3, ☐, ☐, ☐, 2, 1²/3
    1³/5, 1⁴/5, ☐, ☐, ☐, 2³/5, ☐
  • Use the 1/18s fraction strip (see download) to find 1/3 of 18 and 2/3 of 18. Now find 5/6 of 18.
  • 1/3 + 2/3 = 1. Write similar number sentences for fifths, eighths and tenths.

In-depth Investigation: Greedy Guzzler
Children explore which is the greater fraction of a set amount. They also fold strips to look at the fractions.

Extra Support

Treasure Trove
Finding 1/2, 1/4 and 3/4 of amounts

Unit 3 Add/subt same denominator fractions (suggested as 2 days)

Objectives

Equivalent fractions; add/subtract with same denominator
Unit 3: ID# 3727

National Curriculum
Fr (iv) (v) (vi) (vii)

Hamilton Objectives
23. Recognise, find and write unit and non-unit fractions of convenient amounts, e.g. 1/10 of 100 or 1/3 of 60.
27. Solve problems involving fractions.

Teaching and Group Activities for Understanding

Day 1 Teaching
Use Fractions ITP to show 1/2s, 1/4s, 1/6s, 1/8s and 1/10s. Click to change 1/2 of the first bar to yellow. Children write how many of each fraction are the same as 1/2. Confirm by clicking on that number of parts to turn them yellow. Repeat to show other equivalences, e.g. 2/8 = 1/4.
Group Activities
-- Find equivalent fractions using a fraction wall.
-- Suggest fractions equivalent to 1/2 and 1/4.

Day 2 Teaching
Display the pizza divided into 1/8s. Say that a child ate 2 slices and another child ate 3 slices. Cross these out. How much of the pizza have they eaten altogether? Write 2/8 + 3/8 = 5/8. Repeat for 3/8 + 4/8. Notice how we can just add the numerators - we can do this when the denominator is the same, because the numerators show how many equal-sized parts (slices) of the whole there are. How much is left? Repeat to show other additions/subtractions using 1/8s and 1/6s on one pizza.
Group Activities
Use the in-depth problem-solving investigation ‘Fraction Match’ from NRICH as today’s group activity.
Or, use these activities:
-- Add and subtract fractions with the same denominator.
-- Play fraction pairs by adding or subtracting fractions with the same denominator.

You Will Need

  • ITP: Fractions
  • Fraction wall (see resources)
  • Scissors and counters
  • Mini whiteboards and pens
  • Cards that show 1/2, 1/4 3/4, 1/3 and 2/3
  • ‘Adding and subtracting fractions’ sheets (see resources)
  • Additional activity sheets (see resources)

Mental/Oral Maths Starters

Day 1
Place fractions on a line (pre-requisite skills)

Day 2
Fractions with a total of 1 (pre-requisite skills)

Mastery: Reasoning and Problem-Solving

  • True or false?
    1/2 is the same as 2/5.
    3/5 is the same as 6/10.
    2/3 is the same as 5/6.
    3/4 is the same as 9/12.
  • Write < or > or = between each pair of fractions.
1/25/6
9/103/5
1/26/10
1/43/12
  • Some pizzas are divided into sixths. Write the fraction of a pizza that each child ate.
    Edward: 2 slices
    Bella: 3 slices
    Jake: 5 slices
    Charlie: 1 slice
    Charlie and Bella shared a pizza, so what fraction was left?
    Jake and Edward shared 2 pizzas, so what fraction was left?

In-depth Investigation: Fraction Match
Work together as a team to make sure each person in the group has 4 cards which relate to each other. Fraction Match from nrich.maths.org.