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# Maths Year 5 Spring Decimals and 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.

‘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 Subtraction with decimals, e.g. money (suggested as 3 days)

### Objectives

Subtraction with decimals including money
Unit 5: ID# 5443

National Curriculum
Dec/Fr (vii) (x)

Hamilton Objectives
32. Subtract 1- and 2-place decimal numbers by counting up: 6.2 – 3.5, 13.1 – 9.45.
33. Solve problems involving decimals using known equivalences to help.

### Teaching and Group Activities for Understanding

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. Ensure children are familiar with recording on an empty number line.
Group Activities
-- Explore differences between height and stride length in younger children.
-- Investigate pairs of lengths with given differences.

Day 2 Teaching
Display a table of distances, in which the lengths can include one or two decimal places, e.g. 5.3m and 4.56m. Use Frog (counting up) to subtract pairs of numbers with different numbers of decimal places. Ensure children are comfortable with the empty number line used in this way.
Group Activities
Use the ‘Decimal differences’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Calculate height differences between 2m and 4m.
-- Investigate missing number subtractions.

Day 3 Teaching
Show children a table of prices from two bike shops. Use this to construct problems involving finding differences between amounts. Use counting up (Frog) to solve subtraction word problems.
Group Activities
-- Solve subtraction word problems, choosing an efficient strategy.
-- Rank subtractions in order of difficulty; choose a strategy to solve them.

### You Will Need

• Tape measures
• Paper clips
• Whiteboards and pens
• Flipchart
• Number cards 1–9
• ‘Word problems’ sheet (see resources)

### Mental/Oral Maths Starters

Day 1
Pairs with a total of 1 metre (pre-requisite skills)

Day 2
Subtracting numbers with one decimal place (pre-requisite skills)

Suggested for Day 3

### Procedural Fluency

Day 1
Use Frog to find the difference in tree heights.

Day 2
Find daily heights grown by a bamboo plant.
Find differences between numbers with different numbers of decimal places.

Day 3
Work in pairs to discuss, then solve, single-step and two-step word problems. These all involve subtraction, and some include another operation.

### Mastery: Reasoning and Problem-Solving

• Write the missing length in each bar model:
Diagram 1
 14.8m 7.89m

Diagram 2

 5.25m 3.58m

Diagram 3

 2.3m 1.09m
• Sunil and Zoe were meeting. They cycled 25km between them.
Zoe cycled 11.47km. How far did Sunil cycle?
• Find the differences between:
4.5 and 6.54
3.4 and 5.43
5.6 and 7.65
What’s the same? What’s different?
• If the change from £100 was as follows, how much was the total cost of the two pairs of trainers?
Pair A: change = £34.61
Pair B: change = £28.75

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

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

## Unit 2 Unit and non-unit fraction problems (suggested as 4 days)

### Objectives

Fraction problems, including unit and non-unit fractions of amounts
Unit 6: ID# 5449

National Curriculum
Dec/Fr (i) (ii)
Mult/Div (xi)

Hamilton Objectives
21. Solve problems involving multiplication and division, using knowledge of factors and multiples, as appropriate.
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.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Display a fraction wall image. Divide the class into three groups. One group writes fractions equivalent to 1/4; one writes fractions equivalent to 1/3; and one writes fractions equivalent to 1/5. Use these to compare different fractions with related denominators, e.g. 2/3 and 7/9, 7/12 and 3/4, 2/5 and 3/10.
Group Activities
Use the ‘Big triangle of fractions’ in-depth problem-solving investigation below as today’s group activity.
Or, use this activity:
-- Order pairs or trios of fractions with related denominators, using equivalence.

Day 2 Teaching
Can we split 148 children equally into three teams? Draw a bar model to represent the problem. Use a mental division strategy with jottings (vertical chunking) to find the unit fraction of this amount: 1/3 of 148. What about five teams? Six teams? Seven teams? Eight teams? Nine teams? Four teams?
Group Activities
-- Investigate divisibility, finding unit fractions of amounts.

Day 3 Teaching
Write 5/6 of 132 on the board. Talk to your partner about how we can work this out. Sketch a bar model to show 5/6 of 132. Take feedback and, together, make a class poster to agree the steps in finding non-unit fractions of amounts.
Group Activities
-- Use unit fractions as a building block to calculate non-unit fractions of amounts.
-- Create non-unit fractions problems for others to solve.

Day 4 Teaching
Display three word problems (see teaching). Ask children to read each in turn and discuss what calculation is needed to solve it. Show how sketching a bar model can sometimes help us to sort out what needs to be done. Solve together.
Group Activities
-- Create and/ or solve word problems involving finding fractions, and using multiplication and division to solve.

### You Will Need

• Fraction wall (see resources)
• Fractions cards (1) (see resources)
• Fractions cards (2) (see resources)
• Large sheets of paper
• Find fractions of amounts (see resources)
• Solving word problems (see resources)
• Flipchart and pens
• Whiteboards and pens
• A4 paper

### Mental/Oral Maths Starters

Day 1
Find unit fractions of amounts - within tables (pre-requisite skills)
'
Fractions of amounts bingo' from http://topmarks.co.uk

Day 2
Division facts (pre-requisite skills)

Day 3
Find unit fractions of amounts (pre-requisite skills)

Suggested for Day 4
Mental division with remainders (simmering skills)

### Procedural Fluency

Day 1
Use equivalence to compare and order pairs or trios of fractions.

Day 2
Find unit fractions of amounts (3-digit numbers).

Day 3
Use bar models to help find unit fractions and then non-unit fractions of amounts.

Day 4
Find fractions, multiply and divide to solve word problems.

### Mastery: Reasoning and Problem-Solving

• Write three fractions equivalent to 3/5.
Look at the pattern in the denominators.
Then write three fractions equivalent to 2/3 and do the same. What can you predict about the pattern in the denominators of fractions equivalent to 5/6?
• Write the missing numbers to make each sentence true.
?/6 > 7/12
?/6 = 5/?
4/? < 5/?
• Draw a bar model to represent each problem. Then find the answer.
(i) 1/3 of 153
(ii) 1/6 of 612
(iii) 7/12 of 144
• Find 3/5 of each of:
(a) 105 (b) 205 (c) 305
Use the pattern to predict the answer to 3/5 of 405.

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

### Extra Support

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

## Unit 3 Multiply fractions; decimal equivalences (suggested as 3 days)

### Objectives

Decimal/fraction equivalences; multiplying fractions by whole numbers
Unit 7: ID# 5471

National Curriculum
Dec/Fr (ii) (iii) (v) (vi) (xii)

Hamilton Objectives
21. Solve problems involving multiplication and division, using knowledge of factors and multiples, as appropriate.
27. Multiply proper fractions and mixed numbers by whole numbers supported by materials and diagrams.
28. Identify simple fraction and decimal equivalents.
33. Solve problems involving fractions.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Display a blank 100-square (see resources). Use this to show that one little square is 0.01, which is ≡ 1/100. Shade one row to show that to 0.1 ≡ 10/100 ≡ 1/10. Use shaded parts of the 100-square to show decimal equivalents for halves, quarters and fifths.
Group Activities
-- Create a 0–1 number line annotated with halves, quarters, fifths and tenths.
-- Mark a 0–1 number line with halves, quarters, fifths and tenths; use it to help order fractions and decimals.

Day 2 Teaching
Show a 0–3 line marked in quarters (see resources). Write 6 × 1/4. Draw six hops of 1/4. Six lots of one quarter is six quarters! How else can we write this? Agree that we can write this as 1²/4, or 1¹/2.
Repeat for 9 × 1/4, 6 × 1/8 and 10 × 1/8.
Group Activities
-- Explore multiplication of unit fractions by whole numbers.
-- Explore multiplication of non-unit fractions by whole numbers.

Day 3 Teaching
Sketch two identical pizzas. Two children are eating pizza. They are copycats, if one eats 3/8 of a pizza, so does the other! Divide each pizza into eighths, and cross out 3/8 of each pizza. What is double 3/8? 6/8! Simplify this. Repeat the process to show 2 × 5/8. Derive the ‘rule’ for multiplying fractions by a whole number. 2 × 2/5 = 4/10. What has the person done wrong?
Group Activities
Use the ‘Fraction frenzy’ in-depth problem-solving investigation below as today’s group activity.
Or, use this activity:
-- Investigate patterns when multiplying non-unit fractions by whole numbers.

### You Will Need

• Blank 100-square (see resources)
• ITP: Fractions
• >40cm strips of paper
• Ordering fractions (see resources)
• 0–3 line marked in quarters (see resources)
• 0–2 line marked in eighths (see resources)
• Sticky notes
• 1–9 dice
• Additional activity sheets (see resources)

### Mental/Oral Maths Starters

Suggested for Day 1

Suggested for Day 2
Find the lowest common multiple (simmering skills)

Suggested for Day 3
Units of time (simmering skills)

### Procedural Fluency

Day 1
Identify equivalent fractions and decimals using a shaded 100-square.

Day 2
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.

Day 3
Multiply non-unit fractions by 2, 3, 4 and 5.

### Mastery: Reasoning and Problem-Solving

• Write the missing decimal numbers to make each sentence true. Some can have more than one answer!
☐ = 4¹/2
☐ = 5³/4
13/100 > ☐
7/10 < ☐
☐ = 2/5
• 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.
• Five 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

In-depth investigation: Fraction frenzy
Children multiply proper fractions by whole numbers in a multiplication grid and look for patterns.

### Extra Support

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

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