Short Blocks

Maths Year 5/6 Spring Decimals and Fractions

Each unit has everything you need to teach a set of related skills and concepts.

Unit 1 Frog for decimals (suggested as 2 days)

Planning and Activities

Day 1 Teaching
Use javelin throws as a context to show how we can count up using Frog from 9.56m to 11.32m. Find other differences in throws, measured in metres, using Frog to count up.
Group Activities: T with Y5
Y5 -- Explore differences between height and stride length.
Y6 -- Investigate pairs of lengths with given differences.

Day 2 Teaching
Display a table of distances, in which the lengths can include 1 or 2 decimal places, e.g. 5.3m and 4.56m. Use Frog (counting up) to subtract pairs of numbers with different numbers of decimal places.
Group Activities: T with Y5
Use the ‘Decimal Differences’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
Y5 -- Calculate height differences between 2m and 4m. Investigate missing number subtractions.
Y6 -- Investigate missing number subtractions.

You Will Need

  • Tape measures
  • Paper clips
  • Number cards 1–9
  • Number cards 1–6
  • SATs-style questions (see download)

Short Mental Workouts

Day 1
Pairs with a total of 1 metre

Day 2
Subtracting numbers with 1 decimal place

Worksheets

Day 1
Y5/Y6: Use Frog to calculate annual tree growth.

Day 2
Y5: Find daily heights grown by a bamboo plant.
Find differences between numbers with different numbers of decimal places.
Y6: Find pairs of numbers with differences in given ranges.

Mastery: Reasoning and Problem-Solving

Y5

  • Kyla received £7.29 change from a £20 note. How much did she spend?
  • Has the shopkeeper given the correct change?

    1. Item bought: £13.45
    Paid with: £50
    Change given: £36.55

    2. Item bought: £64.79
    Paid with: £100
    Change given: £45.31
  • Write the missing digits: £75 – £24.☐6 = £☐.14
  • Write 2 amounts with a difference of £34.76.
    The larger amount has 23p.

Y6

  • Write the missing number in the bar diagram:
16.6
?4.78
  • Write two 2-place decimal numbers which add to 8.
  • Write two different 2-place decimal numbers which add to 9.7.
  • Frog counts up from a number, finishing on 11.3. He makes 3 jumps: first 0.87, then 4, then 0.3. Write the subtraction he is solving.
  • Calculate 25 – 12.64 mentally without writing anything. Check your answer using Frog.

In-depth Investigation: Decimal Differences
Children subtract pairs of numbers with consecutive digits and different numbers of decimal places, and look for patterns in their answers.

Extra Support

Y5: Frog's Teeny Hops
Finding the difference between decimal numbers on either side of a whole number, e.g. 1.8 and 2.3

Y6: Jump to Success
Counting up (using Frog) from numbers with 2 decimal places to the next whole number

Unit 2 Exploring fractions (suggested as 4 days)

Planning and Activities

Day 1 Teaching
Use a fraction wall to help children write fractions equivalent to 1/3, 1/4 and 1/5, then compare and order fractions with related denominators.
Further Teaching with Y6
Discuss which fractions with smaller denominators can be written as 1/15s. Use to compare fractions with unrelated denominators, e.g. 1/3 and 1/5.
Group Activities: T with Y6
Y5 -- Order pairs or trios of fractions with related denominators, using equivalence.
Y6 -- Explore fractions with an equivalent number of 1/12s.

Day 2 Teaching
Use a blank 100 square to show and explore equivalent fractions, decimals and percentages, particularly the 1/5s and 1/4s.
Group Activities: T with Y5
Use the ‘Big Triangle of Fractions’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
Y5 -- Create a 0–1 number line annotated with halves, quarters, fifths, tenths; some children use it to help order fractions and decimals.
Y6 -- Use loop cards (dominoes) to explore fraction, decimal and percentage equivalents. Use online activities to consolidate.

Day 3 Teaching
Investigate what numbers of equally-sized teams 148 children can be placed in, using mental division with jottings to find unit fractions of 148.
Further Teaching with Y6
Use key percentages of amounts (e.g. 50%, 10%, 1%) to find other percentages of the same amounts.
Group Activities: T with Y6
Y5 -- Investigate divisibility; finding unit fractions of amounts between 100 and 200.
Y6 -- Explore percentages of an amount of money.

Day 4 Teaching
Sketch a bar model to show 5/6 of 132. Make a class poster to agree the steps in finding non-unit fractions of amounts. Find unit, then linked non-unit fractions of other amounts, e.g. 120, 150.
Group Activities: T with Y5
Y5 -- Use unit fractions as a building block to calculate non-unit fractions of amounts; some children create problems for others to solve.
Y6 -- Investigate unit and non-unit fractions of 240.

You Will Need

  • Fraction wall (see resources)
  • Fractions cards (1) & (2) (see resources)
  • Blank 100-square (see resources)
  • ITP: Fractions
  • IWB calculator
  • >40cm strips of paper
  • Ordering fractions (see resources)
  • Number line 0–1 (see resources)
  • Fractions, decimals and percentages equivalence dominoes (see resources)
  • 100-bead bar (or use 0–100 beaded line in resources)
  • Percentages ‘Fact web’ Sheets 1, 2 and 3 (see resources)
  • Find fractions of amounts (see resources)
  • Find unit and non-unit fractions of 240 (see resources)
  • SATs-style questions (see download)

Short Mental Workouts

Day 1
Write improper fractions as mixed numbers

Day 2
Factor bugs

Day 3
Division facts

Day 4
Find unit fractions of amounts

Worksheets

Day 1
Y5: Use equivalence to compare and order pairs or trios of fractions.
Y6: Write fractions with unrelated denominators as 1/10s, 1/6s or 1/12s, then compare.

Day 2
Y5: Identify equivalent fractions and decimals using a shaded 100-square.
Y6: Fill in the missing equivalent fractions, decimals and percentages on a 0 - 1 line.

Day 3
Y5: Find unit fractions of amounts (3-digit numbers).
Y6: Use equivalence with fractions to find percentages of given amounts of money.

Day 4
Y5: Use bar models to help find unit fractions and then non-unit fractions of amounts.
Y6: Use, then draw bar models to find unit and related non-unit fractions of amounts.
Find non-unit fractions of amounts, then answer word problems.


Mastery: Reasoning and Problem-Solving

Y5

  • Write 3 fractions equivalent to 18/30. Explain how you did this.
  • Which of these is not equivalent to 12/20:
    24/40, 22/30, 72/120, 3/5?
  • Write the missing numbers to make each sentence true.
    ☐ /5 = 15/25
    4/6 = ☐ /15
    ☐ /7 > 8/10
  • Find 3/5 of 130:
130
1/51/51/51/51/5
  • 3/8 of a number is 99. What is the number?
?
//////

Y6

  • Write 3 fractions equivalent to 8/15. Explain how you did this.
  • Which of these is not equivalent to 60%:
    0.6, 15/25, 1/6, 6/10, 3/5, 0.06?
  • True or false?
    -- 2/5 is the same as 20%.
    -- 1.4 is the same as 14%.
    -- 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
  • Is the missing symbol <, > or =:
    20% of 320 ☐ 4/9 of 144?

In-depth investigation: Big Triangle of Fractions
Children add fractions with related denominators and find equivalent fractions to identify patterns.

Extra Support

Y5: Fraction Facts
Finding simple unit and related non-unit fractions of amounts (1/3s, 1/4s and 1/5s)

Decimal Pictures
Finding equivalent fractions and decimals (halves, quarters and tenths)

Y6: Special People
Understanding what a percentage is

Fraction Frenzy
Finding fractions of amounts (1/4s, 1/3s, 1/5s, 1/10s)

Unit 3 Multiply and divide fractions (suggested as 3 days)

Planning and Activities

Day 1 Teaching
Use hops on fraction lines to multiply unit fractions by whole numbers. Convert improper fractions to mixed numbers in simplest form.
Further Teaching with Y6
Use a garden context to find fractions of fractions, i.e. multiply fractions.
Group Activities: T with Y6
Y5 -- Explore multiplication of unit fractions and non-unit fractions by whole numbers.
Y6 -- Derive a rule for multiplying pairs of fractions, using supporting images.

Day 2 Teaching
Divide fractions of pizzas into 2, then 3 and 4 equal parts to model division of fractions by whole numbers.
Further Teaching with Y5
Double fractions of pizza, then multiply fractions by 3.
Group Activities: T with Y5
Y5 -- Investigate patterns when multiplying non-unit fractions by whole numbers.
Y6 -- Divide fractions by whole numbers using supporting images.

Day 3 Teaching
Roll a 1-6 dice. Children work in pairs to choose 1 of a given set of fractions to multiply by the number on the dice, aiming to reach a whole number answer.
Further Teaching with Y6
Remind children how we multiply fractions, then use a cake image to revise how to divide fractions by whole numbers.
Group Activities: T with Y6
Y5 -- Write the 2/3 times table, or the 3/4 times table, exploring whole number answers.
Y6 -- Investigate sequences of fraction calculations and a general statement.

You Will Need

  • 0–3 and 0–2 lines (see resources)
  • 1–9 dice
  • Multiplying fractions (1) & (2) (see resources)
  • Multiplying fractions using images (see resources)
  • Finding 1⁄4s of 1⁄5s (see resources)
  • Pictures of pizzas to display (see resources)
  • Multiplying fractions (1) number lines (see resources)
  • Dividing fractions 1 & 2 (see resources)
  • Large 1-6 dice
  • SATs-style questions (see download)

Short Mental Workouts

Day 1
Counting in 1/8s

Day 2
Find the lowest common multiple

Day 3
Units of time

Worksheets

Day 1
Y5: Use number lines to help multiply 1/3, 1/4 and 1/5 by whole numbers, writing answers as mixed numbers if greater than 1.
Multiply unit fractions by whole numbers, simplifying answers where possible. Predict where answers will be greater than 1.
Y6: Find unit fractions of 1/2, 1/3 and 1/4, using an image. Use an image to begin with to multiply unit, then non-unit, fractions; then use the ‘short’ strategy to multiply numerators and denominators.

Day 2
Y5: Multiply non-unit fractions by 2, 3, 4 and 5.
Y6: Divide fractions by whole numbers using a supporting image.

Day 3
Y5: Find pairs of fractions and whole numbers with products between 2 and 3.
Y6: Multiply pairs of fractions and divide fractions by whole numbers.

Mastery: Reasoning and Problem-Solving

Y5

  • Draw a 0–5 number line. Mark quarters: 1/4, 1/2, 3/4, 1¹/4, etc.
    Draw the hops to show seven lots of 1/4.
    Draw the hops to show five lots of 3/4.
  • 5 children each eat 4/5 of their lunches. How many lunches did they eat altogether?
  • True or false?
    6 × 3/4 = 4¹/2
    12 × 1/5 = 25
    9 × 2/3 = 6
    7 × 1/4 < 2

Y6

  • Find one quarter of
    (a) 1/3
    (b) 2/5
    (c) 3/8
  • A large cake is divided into 10 equal pieces. 1 piece is split into thirds. What fraction is each piece? Another piece is split into quarters. What fraction is each piece?
  • We divide a quarter of a pie into 5 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 ☐

Y5 In-depth investigation
Use the Day 2 or 3 group activity as this unit’s in-depth investigation.

Y6 In-depth Investigation
Use the Day 3 group activity as this unit’s in-depth investigation.

Extra Support

Y5: Tiny Steps
Counting in steps of 1/2, 1/3, and 1/4

Y6 Folding Fractions
Finding half of fractions using supporting paper-folding images