Short Blocks

Maths Year 3 Spring Fractions (B)

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.

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Unit 1 Finding fractions of amounts (suggested as 2 days)

Objectives

Finding fractions of amounts
Unit 4: ID# 3517

National Curriculum
Fr (ii) (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
Children fold strips of 16 objects (see resources) in half. How many in each half? Fold it in half again. How many in each quarter? How many in two quarters? 2/4 is the same quantity as 1/2. Fold it in half again to make eighths. How many in each eighth? Write sentences about fractions of the strip.
Group Activities
-- Fold strips of objects to find 1/2, 1/4 and 1/8 of 24.
-- Use bar models to find 1/2, 1/4 and 1/8 of 24 and 32.

Day 2 Teaching
Hand out strips of paper and ask children to fold them in thirds, then sixths. Compare thirds and sixths, agreeing that sixths are smaller. Find non-unit fractions of amounts, e.g. 5/6 of 12, etc.
Group Activities
Use the in-depth problem-solving investigation ‘Andy’s Marbles’ from NRICH as today’s group activity.
Or, use these activities:
-- Fold strips of objects to find 1/6 of 18 and 24.
-- Use folding strips then mental strategies and pattern to find sixths of multiples of 6.
-- Use bar models to find thirds and sixths of 18, 180, 24 and 240.

You Will Need

  • Sheets of A5 paper
  • Strips of 16 objects (see resources)
  • Strips of 24 objects (see resources)
  • Flipchart and pens
  • Cubes (optional)
  • Strips of 12 objects (see resources)
  • Additional activity sheets (see resources)

Mental/Oral Maths Starters

Day 1
Halves of all numbers to 10 (pre-requisite skills)

Day 2
Count in 6s (pre-requisite skills)

Procedural Fluency

Day 1
Fold strips to find halves, quarters and eighths of 24, 32 and 48.

Day 2
Use bar models to find thirds and sixths of numbers 18 to 36.

Mastery: Reasoning and Problem-Solving

  • Find 1/8, then 3/8 and then 5/8 of 24.
  • Write the missing numbers.
    ___ of 15 is 5
    2/3 of ___ = 14
    3/5 of 20 = ____
    ___ of 10 = 4
  • Which is bigger, 2/5 of 35 or 3/8 of 32?

In-depth Investigation: Andy's Marbles
Calculate fractions of numbers to help Andy work out how many of his marbles have been lost or given away. Andy's Marbles from nrich.maths.org.

Extra Support

Fruit Strips
Finding 1/4 of numbers by folding strips

Unit 2 Find unit/non-unit fractions using division (suggested as 3 days)

Objectives

Find unit and non-unit fractions using division
Unit 5: ID# 3527

National Curriculum
Fr (ii) (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
Use a strip with 12 objects pictures on it. Demonstrate how we find 1/4, 3/4 and 1/3 and 2/3 of this quantity by folding the strip into quarters and then thirds.
Group Activities
-- Find 1/4 of numbers in the 4-times table. See link with division facts.
-- Children find unit fractions (1/2, 1/4, 1/3, 1/5, 1/8, 1/10) using their knowledge of times tables. Make links with arrays.
-- Find 1/8 of numbers in the 8-times table. See link with division facts.

Day 2
Children find 1/2 of 24 by dividing 24 by 2. Repeat with 1/3 of 18. Draw the corresponding array (3 rows of 6 stars) to model 1/3 is 6. If we know that 1/3 is 6, what would 2/3 of 18 be? Use the same method to find other non-unit fractions.
Group Activities
-- Use the in-depth problem-solving investigation ‘Fractions in a Box’ from NRICH as today’s group activity.
Or, use these activities:
-- Use a bar models to help find unit fractions and related non-unit fractions of numbers.
-- Write multiplications, divisions then fraction sentences about arrays.
-- Write fraction sentences to go with multiplication sentences for 24 and 40.

Day 3
Use a bar model to show fifths of 20. Find 2/5, 3/5, 4/5 of 20. Use a bar model to represent eighths of 24. Find 1/8 and then 3/8, 5/8 and 7/8. Children make a poster to show how we use arrays or bar models to help us find non-unit fractions.
Group Activities
-- Use bar models and coins to answer word problems about fractions of money.
-- Solve word problems involving non-unit fractions.

You Will Need

  • Strips of 12 objects (see resources)
  • Bar models (see resources)
  • Cubes
  • ‘Unit fractions of numbers’ sheet (see resources)
  • Whiteboards and pens
  • ‘Find non-unit fractions’ sheet 1
  • Additional activity sheets (see resources)
  • Flipchart and pens
  • Large sheets of paper
  • 10p and 2p coins

Mental/Oral Maths Starters

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

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

Day 3
8-times table (pre-requisite skills)

Procedural Fluency

Day 1
Use cubes, times-tables knowledge and bar models to help find unit fractions (1/2, 1/4, 1/5, 1/8, 1/10) of numbers.

Day 2
Find unit and related non-unit fractions of numbers.

Day 3
Find unit and non-unit fractions of numbers. Answer word problems.

Mastery: Reasoning and Problem-Solving

  • Complete each sentence.
    1/3 of 15 = ☐ so 2/3 of 15 = ☐
    1/5 of 40 = ☐ so 4/5 of 40 = ☐
    1/6 of 24 = ☐ so 5/6 of 24 = ☐
  • Draw an array of 8 rows of 5 stars to help you find 3/8 of 40.
  • Draw three bar models, one to represent each of these fraction problems.
    2/3 of 24
    5/8 of 24
    3/5 of 30

In-depth Investigation: Fractions in a Box
Find fractions of numbers to work out the number of counters in a box. Fractions in a Box from nrich.maths.org.

Extra Support

This unit has no separate Extra Support activities.