Short Blocks

Maths Year 6 Autumn Decimals and Fractions (B)

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 Decimals, fractions: compare, order (suggested as 4 days)

Objectives

Equivalent decimals/ fractions: compare/order; fractions of amounts
Unit 5: ID# 6211

National Curriculum
F/De (i) (ii) (vi)

Hamilton Objectives
21. Use common multiples to generate equivalent fractions, e.g. 4/8 = 1⁄2; reduce fractions to their simplest form using common factors.
22. Use knowledge of equivalence to compare/order fractions
23. Identify simple fraction/decimal/percentage equivalents: E.g. 1⁄4 = 0.25 = 25%, 1/3 = 0.33 = 33%
24. Associate a fraction with division; calculate decimal fraction equivalents, e.g. 4/5 is 0.8, 1/8 is 0.125

Planning and Activities

Day 1 Teaching
Use an interactive 1–100 square. Shade 1/100 and the 1/10. Use shading to show that 1/100 = 10/100, 1/10 = 10/100, etc. Then show that 5/10 = 50/100 = 1/2, 25/100 = 1/4, 1/5 = 2/10 = 20/100 etc. 1/8 is half 1/4 or 0.125. Find 2/8, 3/8, 4/8, 5/8, 6/8, 7/8 as decimals.
Group Activities
-- Mark halves, quarters, fifths, tenths and eighths, and the equivalent decimals on a 0 to 1 line marked in 0.1s.

Day 2 Teaching
Use a fraction wall to show equivalent fractions. Draw out that if we multiply the numerator and denominator by the same number we derive an equivalent fraction. Demonstrate how we use this to simplify fractions.
Group Activities
Use the in-depth problem-solving investigation ‘Rod Fractions’ from NRICH as today’s group activity.
Or, use these activities:
-- Use 1–12 (to 1–24) cards to make fractions, and simplify to earn points.
-- Write fractions equivalent to 1/4, then use equivalence to identify fractions less than ¼, and write fractions greater than 1/4.
Day 3 Teaching
Write 2/3 and 3/4. Which is the bigger fraction? But can children prove it? Show how we can change both to twelfths to compare. Use common multiples to compare 1/2 and 3/5, then 1/6 and 2/9.
Group Activities
-- Use a fraction wall to help write fractions as the same type of fractions in order to compare them.
-- Use cards 1 to 6 to make pairs of fractions, both less than 1. Use equivalence to compare them.
-- Equivalent fractions challenge.

Day 4 Teaching
There are 135 animals in a rescue centre. 1/5 are cats, 3/5 are dogs and the rest are ponies. How can we work out the number of cats? Suggest children use short division to find 1/5 of 135 on their whiteboards. Record: 27 cats. Find the number of dogs and ponies.
Group Activities
-- Use the bar model to help solve word problems which involve finding non-unit fractions of amounts.
-- Play fractions of amounts bingo.

You Will Need

• Mini-whiteboards and pens,
• Blank 100 square (see resources)
• ITP: Fractions
• 0 to 1 line marked in steps of 0.1 (see resources)
• Fraction wall (see resources)
• 1 to 12 cards
• Flipchart and pens
• 1 to 6 cards
• ‘Bingo – Fractions of Amounts’ from topmarks.co.uk

Mental/Oral Maths Starters

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

Suggested for Day 2
Divisibility by 2, 3 and 5 (simmering skills)

Day 3
Factors and multiples (pre-requisite skills)

Day 4
Fractions of amounts within tables (pre-requisite skills)

Worksheets

Day 1
Use equivalence to identify missing fractions and decimals on a number line.

Day 2
Find equivalent fractions.

Day 3
Write and compare pairs and trios of fractions with the same denominator.
Write and order fractions as fractions with given denominators.

Day 4
Find unit fractions and linked non-unit fractions of amounts.
Find non-unit fractions of amounts and work out fractions of numbers, e.g. ☐ /3 of 81 is 54.

Mastery: Reasoning and Problem-Solving

• Ben simplified three fractions. They all came out at ¾. Suggest what they could have been.
• True or false?
Any fraction which is simplified to give 1/3 has a numerator which is 3 × the denominator.
36/64 cannot be simplified to 4/9
1/2 is 500 × 0.001
1/4 is more than 0.2
• Write the missing numbers:
☐/6 = 4/☐
6/☐ = ☐/20
☐/10 > 1/☐
☐/32 > ☐/8
• Find 3/4 of 202:
 202
• 3/8 of biscuits are wafers, 5/8 are chocolate. How many of each?
 344

In-depth Investigation: Rod Fractions
Pick two rods of different colours. How can we work out what fraction the shorter rod is of the longer one? Rod Fractions from nrich.maths.org.

Extra Support

Fraction Families
Finding equivalent fractions within fraction families, e.g. quarters and eighths, thirds and sixths, fifths and tenths, sixths and twelfths

Unit 2 Equivalent fractions: add and subtract (suggested as 3 days)

Objectives

Unit 6: ID# 6221

National Curricuum
F/De (i) (ii) (iii)

Hamilton Objectives
21. Use common multiples to generate equivalent fractions, e.g. 4/8 = 1⁄2; reduce fractions to their simplest form using common factors.
22. Use knowledge of equivalence to compare/order fractions and to add or subtract fractions and mixed numbers.

Planning and Activities

Day 1 Teaching
Compare 5/8 and 3/4 by writing both fractions as 1/8s. Then order 5/6, 2/3, 7/12 by writing all three as 1/12s. Discuss how 5/6 is bigger than 3/4 as it is only 1/6 off a whole number, as opposed to 1/4. We prove it by writing them as the same sort of fraction. List common multiples of 4 and 6. We can use this to find a denominator to use. Agree 12 is the smallest common multiple. Ask children to write both fractions as 1/12s then compare them.
Group Activities
-- Look for pairs of fractions they can write as the same sort, confirm with a fraction wall, then compare.
-- Use equivalence to sort the fractions into three groups: < 1/3, = 1/3, > 1/3.
-- Use equivalence to sort the fractions into three groups: less than 1/3, between 1/3 and 2/3, greater than 2/3.

Day 2 Teaching
Add fractions with unrelated denominators by writing 1/2 + 2/3. Point out that these are unrelated fractions. Ask children to discuss what we can do. Take feedback. Draw out changing both to 1/6s. Ask children to do this, then find the answer. Repeat for 2/3 + 2/5 and 1/2 + 2/3.
Group Activities
Use the ‘Domino Fractions’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Look for pairs of fractions with unrelated denominators to add, to give answers of less than 1, and more than 1.
-- Use equivalence to find which pairs of children ate more than a whole chocolate bar and which pairs ate less than a whole bar.

Day 3 Teaching
Write 3/4 – 1/2, 7/10 – 2/5, 3/4 – 3/8 and ask children to use the fact that these fractions are related to subtract them. Then write 3/4 – 2/3 and show that we need to change both to twelfths. Children work out 1/2 – 1/5, 2/3 – 2/5, 4/5 – 3/4.
Group Activities
-- Work out 2/3 – 1/2, 3/4 - 2/3, 4/5 – 3/4, 5/6 – 4/5 … What do children notice about the answers?
-- Work out 1/2 + 1/3, 1/2 + 1/4, 1/2 + 1/5…then 1/2 - 1/3, 1/2 - 1/4, 1/2 - 1/5 … first agreeing in pairs how to write both fractions as the same type.

You Will Need

• Mini-whiteboards and pens
• Flipchart and pens
• Fraction wall (see resources)
• Fraction cards sheet 1 (see resources)
• Sheets of paper
• Fraction cards sheet 2 (see resources)
• Sheet of fractions (see resources)
• Chocolate eater cards (see resources)

Mental/Oral Maths Starters

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

Day 2
Turn improper fractions into mixed numbers and vice versa (pre-requisite skills)

Suggested for Day 3
Equivalence (simmering skills)

Worksheets

Day 1
Compare pairs then order trios of fractions by writing them as the same sort of fraction.

Day 2
Add fractions with a total of less than 1, then more than 1.

Day 3
Subtract pairs of fractions with related and unrelated denominators.

Mastery: Reasoning and Problem-Solving

• Write the missing numbers to make each sentence true.
5/6 + 5/8 = ?/?
4/5 – ?/? = 1/4
1/6 + ?/? = 9/10
• Write an addition of two different fractions - with different denominators - which have a total of 5/8.
• How many times must I add 1/5 to 3/8 to get a total >1?
• Which is larger…
0.75 – 1/3 or 1/6 + 1/4
• Mystery fractions.
Fraction A add fraction B is one whole.
Fraction A subtract fraction B is 3/7
• Write fractions A and B in their simplest forms.

In-depth Investigation: Domino Fractions
Children use dominoes to create fractions. They explore sums of fractions using equivalent fractions and related denominators.

Extra Support

Make the Fractions Friendly