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.

First time using Hamilton Maths?

The PowerPoint incorporates step-by-step teaching, key questions, an in-depth mastery investigation, problem-solving and reasoning questions - in short, everything you need to get started.

All the other resources are there to support as-and-when required. Explore at your leisure - and remember that we are always here to answer your questions.

## Unit 1 Frog for decimals (suggested as 2 days)

### Objectives

Using Frog to find the difference
Unit 1: ID# 56476

Y5: Subtract pairs of numbers with 1 or 2 decimal places.
Y6: Subtract pairs of numbers with 1 or 2 decimal places.

National Curriculum
Y5: Dec/Fr (x)
Y6: Dec/Fr (vii)

Y5 Hamilton Objectives
32. Subtract 1 and 2 place decimal numbers by counting up: 6.2 – 3.5, 13.1 – 9.45.

Y6 Hamilton Objectives
31. Subtract decimal numbers using mental strategies or written counting up.
29. Find the complement to 1, or to next whole number, for a number <10 with up to 3 decimal places.

### 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

### 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

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

## Unit 2 Exploring fractions (suggested as 4 days)

### Objectives

Fractions: comparing, equivalence, fractions of amounts
Unit 2: ID# 56492

Y5: Equivalent fractions, decimal equivalence; fractions of amounts.
Y6: Equivalent fractions, decimals and %s; fractions and %s of amounts.

National Curriculum
Y5: Dec/Fr (i) (ii) (vi)
Y6: Dec/Fr (i) (ii) (vi) (xi)

Y5 Hamilton Objectives
23. Identify, name and write equivalent fractions; reduce fractions to simplest form.
24. Compare and order fractions where the denominators are multiples of the same number.
33. Solve problems involving fractions.

Y6 Hamilton Objectives
21. Use common multiples to generate equivalent fractions.
22. Use knowledge of equivalence to compare/order fractions.
23. Identify simple fraction and decimal equivalents.
24. Associate a fraction with division. Calculate decimal fraction equivalents, e.g. 4/5 is 0.8, 1/8 is 0.125.
33. Calculate simple percentages of whole numbers. Solve problems involving use of percentages for comparisons.

### 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)
• 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)

### 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 1/5 1/5 1/5 1/5 1/5
• 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)

### Objectives

Multiply and divide fractions
Unit 3: ID# 56500

Y5: Multiply fractions by whole numbers.
Y6: Multiply and divide fractions.

National Curriculum
Y5: Dec/Fr (v)
Y6: Dec/Fr (iv) (v)

Y5 Hamilton Objectives
27. Multiply proper fractions and mixed numbers by whole numbers supported by materials and diagrams.

Y6 Hamilton Objectives
25. Understand that if 2 numbers less than 1 are multiplied, the answer is smaller than either of them.
26. Multiply simple pairs of proper fractions, writing the answer in its simplest form.
27. Divide proper fractions by whole numbers, recognising that 3⁄4 ÷ by 2 is equivalent to 3⁄4 × 1⁄2.

### 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

### 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