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.

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

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