Maths Year 5/6 Autumn Fractions

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 available to friends and School Subscribers. These bulk downloads are added value for Hamilton Friends and School Subscribers.

Unit 1 Order fractions; fractions of amounts (suggested as 3 days)

Objectives

Compare and order fractions; find fractions of amounts
Unit 1: ID# 56316

Y5: Compare fractions; find fractions of amounts
Y6: Compare fractions; find fractions of amounts

National Curriculum
Y5: Fr (i), Mult/Div (v)
Y6: Fr (i) (ii) (vi)

Y5 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.
33. Solve problems involving fractions, using known equivalences to help.

Y6 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.
24. Associate a fraction with division; calculate decimal fraction equivalents, e.g. 4/5 is 0.8, 1/8 is 0.125.

Teaching and Group Activities for Understanding

Day 1 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 by dividing the numerator and denominator by their highest common factor.
Group Activities
Y5/Y6 -- Use two number cards to make a fraction, and simplify, if possible.

Day 2 Teaching
Model comparing fractions with related denominators using Fractions ITP.
Further Teaching with Y6
Challenge children to prove which of two fractions with unrelated denominators is bigger. Show how to use common multiples to write both fractions as the same sort (with the same denominator).
Group Activities
Use the ‘Fraction pictures’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
Y5 -- Write lots of fractions equivalent to 1/2, then say whether fractions > or < 1/2, then > or < 1/3.
Y6 -- Compare pairs of fractions by changing one or both so they have the same denominator.

Day 3 Teaching
Use a bar model to show sevenths of children in a school. Find the number of children in reception (1/7), KS1 (2/7) and KS2 (4/7).
Group Activities
Y5 -- Draw bar models to find unit, then non-unit fractions of amounts.
Y6 -- Play fractions of amounts bingo, or use a bar model to help solve word problems finding non-unit fractions of amounts.

You Will Need

  • ‘Fraction wall’ (see resources)
  • Whiteboards and pens
  • Number cards 1–24
  • ITP: Fractions
  • Flipchart and pens
  • ‘Fraction cards’ sheets 1 and 2 (see resources)
  • Sheets of paper
  • ‘How many children are in each key stage?’ (see resources)
  • ‘Finding fractions of amounts’ (see resources)
  • ‘Fractions of amounts: Bingo game cards and questions’ (see resources)

Short Mental Workouts

Day 1
Count in quarters and eighths along a number line

Day 2
Common multiples

Day 3
Mental division

Procedural Fluency

Day 1
Y5 Find equivalent fractions.
Y6 Find equivalent fractions.

Day 2
Y5 Compare fractions.
Y6 Write and compare pairs and trios of fractions with unrelated denominators.

Day 3
Y5 Find non-unit fractions of amounts.
Y6 Find non-unit fractions of amounts and calculate fractions of numbers, e.g. ☐/3 of 81 is 54.

Mastery: Reasoning and Problem-Solving

Y5

  • Write three fractions equivalent to 20/25. Describe any pattern in the denominators.
  • Write the missing numbers to make each sentence true.
    ☐/6 = 5/☐
    4/☐ < 5/☐
    ☐/6 > 7/10
  • Find 3/4 of 148:
148

Find 5/8 of 256:

256

Y6

  • Ben simplified three fractions. They all came out at 3/4. 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.
  • Write the missing numbers:
    ☐/6 = 4/☐
    6/☐ = ☐/20
    ☐/10 > 1/☐
    ☐/32 > ☐/8
  • Find 3/4 of 202:
202
  • 3/8 of 344 biscuits are wafers, 5/8 are chocolate. How many are there of each?

In-depth Investigation: 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.

Extra Support

Y5
Do the Splits

Finding 1/4, 3/4, 1/3 and 2/3 of numbers

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

Y6
Fraction Families
Finding equivalent fractions within fraction families, e.g. quarters and eighths, thirds and sixths, fifths and tenths, sixths and twelfths

Unit 2 Decimal/fraction equivalents (suggested as 2 days)

Objectives

Understand mixed numbers and decimal/fraction equivalents
Unit 2: ID# 56332

Y5: Mixed numbers, fraction/decimal equivalence
Y6: Mixed numbers, fraction/decimal equivalence

National Curriculum
Y5: Dec/Fr (iii)
Y6: Dec/Fr (vi)

Y5 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.

Y6 Hamilton Objectives
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.

Teaching and Group Activities for Understanding

Day 1 Teaching
Show parts of several pizzas to illustrate mixed fractions and improper fractions. Count in thirds along a counting stick past whole numbers.
Group Activities: T with Y5
Use the in-depth problem-solving investigation ‘Rod Fractions’ from NRICH as today’s group activity.
Or, use these activities:
Y5 -- Identify improper fractions which are greater than 1 or 2 and/or 3, 4 or 5.
Y6 -- Roll a 0–9 dice to create improper fractions. Write them as mixed numbers.

Day 2 Teaching
Use an interactive 100-square to show equivalence between tenths, quarters, halves, fifths and decimals. Then use Fractions ITP to show equivalent decimals for eighths.
Group Activities: T with Y5 or Y6
Y5/Y6 -- Mark halves, quarters, fifths, eighths and tenths, and the equivalent decimals on a 0–1 line marked in tenths.

You Will Need

  • Counting stick and sticky notes
  • Whiteboards and pens
  • Flipchart and pen
  • 0–9 dice or number cards 2–9
  • ‘100-square’ (see resources)
  • Fractions ITP (see resources)
  • ‘0–1 line marked in steps of 0.1’ (see resources)

Short Mental Workouts

Day 1
Count in quarters and eighths along a number line

Day 2
Reading scales

Procedural Fluency

Day 1
Y5: Write improper fractions as mixed numbers and vice versa using images of pizzas.
Y6: Problems with mixed numbers and improper fractions.

Day 2
Y5: Use equivalence to identify missing fractions and decimals on a number line (supporting images of 1/10s and 1/4s)
Y5/6: Use equivalence to identify missing 1/10s and 1/4s as fractions and decimals on a number line
Y6: Use equivalence to identify missing fractions and decimals on a number line.

Mastery: Reasoning and Problem-Solving

Y5/Y6

  • Count in thirds from zero to 5.
    How many numbers have you said?
  • Count in fifths from zero to 10.
    How many numbers have you said?
  • How many thirds in three whole pizzas?
    How many quarters in four whole pizzas?
    How many eighths in two and a half pizzas?
  • What whole number are 25 fifths equivalent to?
  • Write the following as fractions:
    0.4 0.75 0.125 0.07
  • Suggest missing numbers to make these sentences true:
    ☐/6 = 2 1⁄6
    1☐/10 > ☐/10
    ☐/8 > 3 1⁄☐

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

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

Unit 3 Add/subtract fractions, using equivalence (suggested as 3 days)

Objectives

Add and subtract fractions, using equivalence
Unit 3: ID# 56340

Y5: Compare, add and subtract fractions with related denominators
Y6: Compare, add and subtract fractions with unrelated denominators

National Curriculum
Y5: Fr (i) (iv)
Y6: Fr (i) (ii) (iii)

Y5 Hamilton Objectives
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.

Y6 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.

Teaching and Group Activities for Understanding

Day 1 Teaching
Compare fractions with related denominators by writing them as fractions with the same denominator.
Further Teaching with Y6
Compare fractions with unrelated denominators, spotting common multiples of the denominators.
Group Activities: T with Y6
Y5 -- Order groups of three fractions with related denominators by writing them as fractions with the same denominator.
Y6 -- Compare pairs of fractions with unrelated denominators by changing one or both so they have the same denominator. Order fractions with unrelated denominators.

Day 2 Teaching
Add fractions with related then unrelated denominators by writing them as fractions with the same denominator.
Group Activities: T with Y5
Use the ‘Oddly friendly fractions’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
Y5 -- Add unit fractions with related denominators, or add pairs of fractions with a total >1 or <1.
Y6 -- Use equivalence to add pairs of fractions with unrelated denominators.

Day 3 Teaching
Subtract fractions with related denominators by writing them as fractions with a common denominator.
Further Teaching with Y6
Subtract fractions with unrelated denominators by writing them as fractions with a common denominator.
Group Activities: T with Y6
Y5 -- Subtract fractions with related or unrelated denominators.
Y6 -- Define common denominators to add and subtract unrelated fractions in patterned sequences.

You Will Need

  • Whiteboards and pens
  • ‘Fraction wall’ sheet 1 and 2 (see resources)
  • ‘Comparing and ordering fractions’ (see resources)
  • ‘Fraction cards’ sheets 1 and 2 (see resources)
  • Flipchart and pen
  • Additional activity sheets (see resources)
  • ITP: Fractions
  • Number cards 1–16: one set per pair

Short Mental Workouts

Day 1
Factors

Day 2
Turn improper fractions into mixed numbers and vice versa

Day 3
Common multiples

Procedural Fluency

Day 1
Y5: Compare pairs, then order trios of fractions.
Y6: Compare pairs, then order trios of fractions.

Day 2
Y5: Add pairs of fractions (related denominators), first with a total <1, then with a total >1.
Y6: Add pairs of fractions, first with a total <1, then with a total >1.

Day 3
Y5: Subtract pairs of related fractions. Subtract fractions with unrelated denominators.
Y6: Subtract pairs of fractions with related and unrelated denominators.

Mastery: Reasoning and Problem-Solving

Y5

  • Write the missing numbers to make each sentence true:
    1/4 + 5/8 = /
    4/5 – /10 = 3/10
    5/6 = 1/6 + /3
  • Write an addition of two different fractions to give a total of 11/12.
  • How many times must I add 1/4 to 3/8 to get a total over 1?
  • Which is larger:
    8/15 – 1/3 or 1/6 + 1/12 ?

Y6

  • 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 which have a total of 5/8.
  • How many times must I add 1/5 to 3/8 to get a total over 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: Oddly Friendly Fractions
Children create fractions with related denominators (Y5) or unrelated denominators. (Y6) and then add these, turning improper fractions into mixed numbers.

Extra Support

Y5
Fraction Families

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

and

Pete’s Pies
Adding fractions with same denominator, including answers greater than 1

Y6
Make the Fractions Friendly

Adding fractions with related denominators

and

Teeny Subtractions
Subtracting fractions with related denominators