Short Blocks

# Maths Year 5 Autumn Decimals and Fractions (B)

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

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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 Mixed numbers and fractions of amounts (suggested as 3 days)

### Objectives

Mixed numbers and fractions of amounts
Unit 5: ID# 5273

National Curriculum
Dec/Fr (iii) (xii)

Hamilton Objectives
25. Recognise mixed numbers and improper fractions and convert from one to the other, writing mathematical statements.
33. Solve problems involving fractions, using known equivalences to help.

### Planning and Activities

Day 1 Teaching
Divide 3 pizzas into quarters. Shade five quarters.. How much have I shaded? We say/write this as 5/4, an improper fraction, or 1 1/4 pizzas, a mixed number. Repeat with 10 quarters, 7 thirds and 3 2/3.
Group Activities
Use the in-depth problem-solving investigation ‘Balance of Halves’ from NRICH as today’s group activity.
Or, use these activities:
-- Identify improper fractions which are greater than 1 or 2.
-- Identify improper fractions which are greater than 2, 3, 4 or 5.

Day 2 Teaching
Count in 1/3s along counting stick, until 3 1/3s. What are three thirds? Label 3/3 and 1. Continue saying four thirds, five thirds until six thirds. What is this? Point to 12/3, 21/3. Children write different ways of writing these numbers. Ask children to show other improper fractions.
Group Activities
-- Roll a 1–9 dice to create improper fractions, write them as mixed numbers.
-- Draw diagrams to show improper fractions and mixed numbers.
-- Place improper fractions and mixed numbers on a number line.

Day 3 Teaching
Say that in a school of 105 children, 1/7 are in Reception. 2/7 are in Key Stage 1 and 4/7 are in Key Stage 2. Show a bar model diagram to show this. Model finding each of these fractions. Repeat for other examples.
Group Activities
-- Draw bar models to find unit, then non-unit fractions of amounts.

### You Will Need

• 1–9 dice
• Counting stick
• 2–9 cards
• Bar model pictures (see resources)
• Whole class practice (see practice sheets Day 3)

### Mental/Oral Maths Starters

Day 1
Count in 1/4s and 1/8s along a number line (pre-requisite skills)

Suggested for Day 2
Mental multiplication (simmering skills)

Day 3
Mental division (pre-requisite skills)

### Worksheets

Day 1
Write improper fractions as mixed numbers and vice versa using images of pizzas.

Day 2
Convert improper fractions to mixed numbers and vice versa.
Write sequences of mixed numbers according to a given rule.

Day 3
Find non-unit fractions of amounts.

### Mastery: Reasoning and Problem-Solving

• Count in fifths from 0 to 10.
How many numbers have you said?
• How many thirds in three whole pizzas?
How many quarters in four whole pizzas?
What are 25 fifths equivalent to?
• Suggest missing numbers to make these sentences true:
☐/6 = 2 ¹/6
1 ☐/10 > ☐/10
☐/8 > 3 ¹/☐
• Find 3/4 of 148:
 148 1/4 1/4 1/4 1/4
• Find 5/8 of 256:
 256

In-depth Investigation: Balance of Halves
Can you hang weights in the right place to make the scale balance? Balance of Halves from nrich.maths.org.

### Extra Support

Do the Splits
Finding 1/4, 3/4, 1/3 and 2/3 of numbers

## Unit 2 Add/subtract equivalent fractions (suggested as 5 days)

### Objectives

Unit 6: ID# 5281

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

Hamilton Objectives
23. Identify, name and write equivalent fractions; reduce fractions to simplest form, including tenths to fifths, hundredths to tenths, e.g. 40/100 = 4/10 = 2/5.
24. Compare and order fractions where the denominators are multiples of the same number.
26. Add and subtract fractions where the denominators are multiples of the same number.

### Planning and Activities

Day 1 Teaching
Show a fraction wall. Children find fractions equivalent to 1/4. Children write fractions not on the wall which are equal to 1/4. Write 3/12 and explain it is more simply written as 1/4. This is called writing the fraction in its simplest form. Call out other fractions for children to write in simplest form.
Group Activities
-- Use two cards to make a fraction and simplify.

Day 2 Teaching
Which is greater, 3/5 or 7/10? Model comparing fractions with related denominators using ITP Fractions: two bars - 1/10s and 1/5s. Click to highlight 3/5 and 7/10. Repeat to compare other fractions.
Group Activities
-- Write lots of fractions equivalent to 1/2, then say whether fractions are less than 1/2, then greater or less than 1/3.
-- Compare fractions with unrelated denominators by writing them as fractions with the same denominator.

Day 3 Teaching
Write 3/8 and 1/4. Which is greater? Model comparing by writing both as eighths. Write 3/8 > 2/8. Repeat with 2/5 and 3/10. Order 5/6, 2/3, 7/12 by writing them as twelfths.
Group Activities
Use the ‘Fraction Pictures’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Order groups of fractions with related denominators by writing them as fractions with the same denominator.

Day 4 Teaching
Model adding fractions with related denominators. Write 1/2 + 3/4 and model how we can add these fractions by making them both quarters. Repeat to show 2/3 + 1/6 and 1/2 + 5/8.
Group Activities
Use the ‘Oddly Friendly Fractions’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Add unit fractions with related denominators.
-- Identify and add pairs of fractions with a total greater than, and with a total less than 1.

Day 5 Teaching
Write: 3/4 – 1/2, 7/10 – 2/5, 3/4 – 3/8. Show how we write each pair as same type of fraction. This is because each pair is the same fraction family.
Group Activities
-- Subtract fractions with related denominators.
-- Subtract fractions with unrelated denominators.

### You Will Need

• Fraction wall (see resources)
• Mini-whiteboards and pens
• 1–12 cards
• ITP: Fractions
• Flipchart and pen
• Comparing and ordering fractions sheet (see resources)
• Adding fractions sheet (see resources)
• Cards 1–16

### Mental/Oral Maths Starters

Day 1
Divisibility by 2, 3, and 5 (pre-requisite skills)

Day 2
Factors (pre-requisite skills)

Day 3
Count in 1/4s and 1/8s along a number line (pre-requisite skills)

Day 4
Improper fractions (pre-requisite skills)

Suggested for Day 5

or
Times tables (simmering skills)

### Worksheets

Day 1
None for this day

Day 2
Children compare pairs of fractions by first writing them with the same denominator.

Day 3
Compare and order fractions (2 versions: one for Working at ARE/greater depth and one for working towards ARE.
Day 4
Add pairs of fractions, first with a total of less than 1, then with a total of more than 1.

Day 5
Subtract pairs of related fractions

### Mastery: Reasoning and Problem-Solving

• Write three fractions equivalent to 20/25.
Look at the pattern in the denominators.
Then write three fractions equivalent to 7/21 and do the same.
What can you predict about the pattern in the denominators of fractions equivalent to 3/4?
• Write the missing numbers to make each sentence true.
?/6 = 8/24
4/? < 5/?
?/6 > 7/10
• How many times must I add 1/5 to 1/10 to get a total over 1?
• Mystery fractions.
Fraction A is half fraction B
Fraction B is added to 6/8 to give one whole.
Write fractions A and B in their simplest forms.

In-depth Investigation 1: Fraction Pictures
Children use knowledge of equivalent fractions to work out what fraction each shape is as part of the whole picture, and which shapes are the same size.

In-depth Investigation 2: Oddly Friendly Fractions
Children explore patterns when adding fractions. They create fractions with related denominators and then add these, turning improper fractions into mixed numbers.

### Extra Support

Fraction Families
Finding equivalent fractions to 1/2, 1/3 and 1/4

Pete’s Pies