Short Blocks

Maths Year 4 Spring 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 Unit and non-unit fractions of amounts (suggested as 3 days)

Objectives

Revise fractions; find unit and non-unit fractions of amounts
Unit 1: ID# 4483

National Curriculum
Dec/Fr (iii)

Hamilton Objectives
24. Use times tables to find unit and non-unit fractions of amounts, e.g. 1/6 of 48, 3/8 of 64.

Teaching and Group Activities for Understanding

Day 1
Count in thirds along a 0-5 line marked in thirds. Point at a mark; children write the number. Repeat with a line showing 1/4s. Stress mixed numbers, e.g.one and three quarters; equivalence, e.g. one and a half is the same as one and two quarters. Repeat for tenths.
Group Activities
-- Roll a dice to generate differing lengths of a fraction counting sequence.
-- Draw number lines to count in steps of 1/8 and 1/12.

Day 2
-- Use a picture of a chocolate bar with 30 pieces to show how to find 1/5, 3/5, and 4/5 of 30, then 1/6 of 30 and 5/6 of 30. Repeat with 50 pieces to find 1/10 and subsequent non-unit fractions, e.g. 3/10.
Group Activities
-- Write fraction sentences about chocolate bars of 32 and 36 pieces.
-- Write fraction sentences about arrays of 40 and 32.

Day 3
Sketch a pizza and divide it into eight equal sections. If 16 bits of salami are distributed equally, how much on each slice? Show that 1/8 of 16 is 2 (16 ÷ 8); then derive other facts: 2/8 of 16 = 4, 3/8 of 16 = 6, etc. Show that 4/8 is 1/2. Demonstrate using a bar model and repeat with 24 pieces of tomato.
Group Activities
Use the in-depth problem-solving investigation ‘Foodie fractions’ as today’s group activity.
Or, use these activities:
-- Fold a strip of 24 pictures to explore possible unit and non-unit fractions.
-- Investigate possible unit and non-unit fractions of 24 and 36.

You Will Need

  • ‘Fraction lines’ Sheets 1 to 3 (see resources)
  • mini-whiteboards and pens
  • ‘Fraction lines’ Sheet 4 (see resources)
  • 0–9 dice
  • Squared paper
  • ‘Chocolate’ (see resources)
  • Additional activity sheets (see resources)

Mental/Oral Maths Starters

Day 1
Count 1/2s to at least 10 (pre-requisite skills)

Suggested for Day 2
Tell the time (simmering skills)

Suggested for Day 3
Find a time later (simmering skills)

Procedural Fluency

Day 1
Fill in missing fractions (in simplest form) in sequences, using fraction lines to help.

Day 2
Find unit fractions, then non-unit fractions of amounts.

Day 3
Use a bar model to help find 1/8s of 32 and 1/6s of 30. Find 1/3s and 1/5s of 30.

Mastery: Reasoning and Problem-Solving

  • Bea counts in quarters, starting at one quarter. She says five numbers then stops. What number should she say next?
  • Fill in the missing fractions:
    1¹/2, 2, 2¹/2, 3, ☐, 4, ☐, 5
    4, 3³/4, 3¹/2, ☐, 3, ☐, 2¹/2
    8/10, 9/10, ☐, ☐, 1²/10
  • Write all the fraction facts for tenths of 60.
    1/10 of 60 =
    2/10 0f 60 =
    etc. to 10/10.
  • Use this bar diagram to help find answers.
48

(i) 1/8 of 48 =
(ii) 3/8 of 48 =
(iii) 7/8 0f 48 =

  • Is 1/10 of 50 the same as 1/5 of 100?


In-depth Investigation: Foodie Fractions
Given fractions of amounts, children work out how many friends are at a picnic.

Extra Support

Choccie Quarters
Counting in 1/4s; Finding 1/2, 1/4 and 3/4 of amounts

Unit 2 Equivalent fractions; simplest form; +/- (suggested as 3 days)

Objectives

Identify equivalent fractions; reduce to simplest form; add and subtract fractions
Unit 2: ID# 4493

National Curriculum
Dec/Fr (i) (iv) (vi)

Hamilton Objectives
23. Write the equivalent fraction for fractions with given denominators or numerators, e.g. 1/2 ≡ ?/8; write a fraction in its simplest form, e.g. 6/12 ≡ 1/2.
25. Add and subtract fractions with the same denominator.

Teaching and Group Activities for Understanding

Day 1
Use the ITP ‘Fractions’ to show 1/2s, 1/4s and 1/8s. Discuss how many 1/4s and 1/8s are equivalent to 1/2. Model writing equivalence statements, 1/2 ≡ 4/8. Find a sequence of other fractions equivalent to 1/2.
Group Activities
Use the in-depth problem-solving investigation ‘Best score for me!’ as today’s group activity.
Or, use these activities:
-- Use visual resources to generate ‘families’ of fractions equivalent to 1/4s.
-- Use visual resources to generate ‘families’ of fractions equivalent to 1/2.

Day 2
Show children a fraction wall (see resources). Children revise fractions equivalent to one half. Discuss the relationship between the denominator and the numerator. Show how to reduce to simplest form visually (on fraction wall); then by dividing the numerator and denominator by the same number. Use 6/12, then 2/6, then 6/8 as examples. Note how we can make fractions equivalent to 1/3 by multiplying the numerator and denominator by the same number.
Group Activities
-- Use the fraction wall to support identifying the simplest form of fractions.

Day 3
Show a picture of two pizzas, each divided in 1/4s. Three quarters are eaten. Cross these out. Then another two quarters are eaten. Cross out two more quarters. How many quarters have been eaten? Record 3/4 + 2/4 = 5/4. Write the mixed number equivalent: 3/4 + 2/4 = 1¹/4.
Repeat to show other additions and subtractions of fractions with same denominator, e.g. 4/5 + 3/5, 1³/5 – 4/5.
Group Activities
-- Sort fraction addition and subtraction calculations, based on estimates; calculate answers.
-- Cut fraction strips to support addition and subtraction of 1/5s and 1/6s.

You Will Need

  • ITP ‘Fractions’ (see resources)
  • Mini-whiteboards and pens
  • Fraction walls (see resources)
  • ‘Pizzas’ sheet (see resources)
  • ‘Fifths and sixths’ sheet (see resources
  • Scissors
  • ‘0 to 2 lines’ sheet (see resources)
  • Fraction addition cards (see resources)
  • Fraction subtraction cards (see resources)

Mental/Oral Maths Starters

Day 1
Count in steps of ¼ (pre-requisite skills)

Day 2
Count in steps of 1/3 (pre-requisite skills)

Day 3
Fractions with total of 1 (pre-requisite skills)

Procedural Fluency

Day 1
Identify fractions equivalent to 1/2 and 1/4.

Day 2
Use a fraction wall to identify equivalent fractions, including 1/8s, 1/9s and 1/12s.

Day 3
Add and subtract pairs of fractions with the same denominators using fraction lines to help.

Mastery: Reasoning and Problem-Solving

  • Write four fractions equivalent to 1/3.
    Now write four fractions equivalent to 2/3.
  • True or false?
    1/2 ≡ 100/200
    If a fraction is equivalent to one quarter, the denominator is four times the numerator.
    Any number of thirds can be written as an equivalent number of sixths.
    Any number of sixths can be written as an equivalent number of thirds.
  • Add 1/2 to each of these fractions:
    (i) 3/4
    (ii) 1/6
    (iii) 3/10
    (HINT: Write 1/2 as an equivalent fraction in each case.)
  • Which of these cannot be written in a simpler form: 6/9 7/10 14/21? Why?


In-depth Investigation: Best score for me!
Children find equivalent fractions to cross numbers on a 6 x 6 square. They use strategies to find their highest score.

Extra Support

The Half Family (1)
Finding fractions which are equivalent to one half

Wall-to-wall Fractions (2)
Finding fractions with a total of 1 (same denominators)