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Maths Year 5 Autumn 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 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.

Teaching and Group Activities for Understanding

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)

Procedural Fluency

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.

Teaching and Group Activities for Understanding

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)

Procedural Fluency

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