Short Blocks

Maths Year 6 Spring Decimals and Fractions (B)

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

Percentages and fractions of amounts (suggested as 4 days)

Planning and Activities

Day 1 Teaching
Which fractions with denominators less than 15 can be written as 1/15s? Take feedback (1/3s and 1/5s). Show how 1/3 is 5/15 and 1/5 is 3/15. Write 2/3 and 3/5 and write these as 1/15s to compare them. Ask children to use equivalence to compare 1/2 and 3/5 then 7/10 and 3/4.
Group Activities
-- Explore fractions with an equivalent number of 1/12s.

Day 2 Teaching
Use a 1–100 bead bar. Say that each bead is one hundredth of the bar. Write 1/100. Say it is also 1% of the bar. Per cent means out of 100. Show 5 beads and write this as 5/100 or 0.05 or 5%. Show that these all mean the same thing. Repeat for other beads then discuss equivalents for 1/3 and 2/3.
Group Activities
Use the in-depth problem-solving investigation ‘Doughnut Percents’ from NRICH as today’s group activity.
Or, use this activity:
-- Use loop cards (dominoes) to explore fraction, decimal and percentage equivalents. Use online activities to consolidate.

Day 3 Teaching
Display a percentages fact web. 50% is equivalent to 1/2 so we can halve £320. Knowing 50%, we can work out 25%. How can we find 10%? It is the same as finding 1/10. Children find 10% and 1% (1/100), then discuss how to find 11%, 20%, 21% and 32%.
Group Activities
-- Explore percentages of an amount of money (£150).
-- Explore percentages of an amount of money (£328).

Day 4 Teaching
Write 1/6 of 150; ask children to discuss how to do it. Draw out dividing by 6. Children do it. Take feedback on methods, e.g. using a written method, or dividing by 3, then halving. What is 5/6 of 150? Draw out multiplying 25 by 5, or subtracting 25 from 150. Find fractions of 150 that give whole-number answers. Find unit and non-unit fractions of 150, e.g. 1/5 then 3/5, 1/15 then 7/15.
Group Activities
-- Investigate unit and non-unit fractions of 240.

Mental/Oral Maths Starters

Day 1
Write improper fractions as mixed numbers (pre-requisite skills)

Day 2
Equivalent fractions and decimals (pre-requisite skills)

Day 3
Equivalent fractions and percentages (pre-requisite skills)

Day 4
Find unit fractions of amounts within tables (pre-requisite skills)

Worksheets

Day 1

Write fractions with unrelated denominators as 1/10s, 1/6s or 1/12s, then compare.

Day 2
Fill in the missing equivalent fractions, decimals and percentages on a line.

Day 3
Use equivalence with fractions to find percentages of given amounts of money.

Day 4
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

  • Write three fractions which are equivalent to 3/4.
    Write three fractions which are equivalent to 2/5.
    Now add 3/4 and 2/5.
  • True or false?
    2/5 is the same as 20%.
    0.4 is the same as 4%.
    10% is the same as 0.1.
    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
  • Show that one fifth of 320 is 3 less than one third of 201.

In-depth Investigation: Doughnut Percents
A task involving the equivalence between fractions, percentages and decimals. Members of the group must notice the needs of others and respond. Doughnut Percents from nrich.maths.org.

Extra Support

Special People
Understanding what a percentage is

Fraction Frenzy
Finding fractions of amounts (1/4s, 1/3s, 1/5s, 1/10s)