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Maths · Ages 8–9 · 50 minutes

Finding fractions of amounts

Children find unit and non-unit fractions of amounts by dividing by the denominator and multiplying by the numerator, and explain each step with a bar model.

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Success criteria

  • I can find a unit fraction by dividing
  • I can find a non-unit fraction by dividing then multiplying
  • I can draw a bar model to show it

Key vocabulary

  • fraction
  • numerator
  • denominator
  • unit fraction
  • non-unit fraction
  • bar model
  • of

You will need

  • strips of paper for bar models
  • counters
  • mini whiteboards
  • a bag of 24 sweets or cubes

Curriculum links

  • Year 4· England
  • Grade 3· United States
  • Primary 4· Nigeria
  • Class 4· India

Practice sheets

Generated fresh each time you press a button, and marked instantly on screen.

The lesson at a glance

50 minutes in all. Timings are a guide: follow your class.

  1. Step 1: Starter

    Quick division recall on whiteboards: 20 ÷ 4, 18 ÷ 3, 35 ÷ 5, 24 ÷ 6.
    8 minutes

  2. Step 2: Teach

    Draw a long bar and write 24 above it.
    14 minutes

  3. Step 3: Guided practice

    On whiteboards, children draw a bar for each and show both steps.
    10 minutes

  4. Step 4: Independent practice

    Use the practice buttons above.
    14 minutes

  5. Step 5: Plenary

    Write two answers on the board: "2/3 of 18 = 6" and "2/3 of 18 = 12".
    4 minutes

  6. Step 6: Assessment for learning

    Look for children who: divide by the denominator first without prompting; remember to multiply by the numerator for non-unit fractions; draw a bar with the right number of equal parts.

  7. Step 7: Differentiation

    Children who need support can use counters on a drawn bar, sharing into the parts before counting one part.

  8. Step 8: Common misconceptions

    Dividing by the numerator (2/5 of 30 = 15).

  9. Step 9: Home link

    When cooking or sharing snacks, ask fraction questions such as "What is a quarter of these 12 strawberries?

1.Starter

8 minutes

Quick division recall on whiteboards: 20 ÷ 4, 18 ÷ 3, 35 ÷ 5, 24 ÷ 6. Then ask: "What is half of 30? How did you work it out?" Someone will say "divide by 2". Write it up: half of 30 = 30 ÷ 2 = 15. "Today, every fraction will work like that."

2.Teach

14 minutes

Draw a long bar and write 24 above it. "This bar is all 24 sweets. I want to find one third of 24."

Split the bar into 3 equal parts. "The denominator, 3, tells me how many equal parts. 24 ÷ 3 = 8, so each part is 8." Write 8 in each part. "One third of 24 is 8."

"Now two thirds. That's two of those parts." Shade two parts. "8 + 8 = 16, or 2 × 8 = 16. Two thirds of 24 is 16."

Step by step

  1. Divide by the denominatorThat finds the size of one part.
  2. Multiply by the numeratorThat's how many parts you want.
  3. Check with the barDo the parts add up to the whole?

Try 3/4 of 20 together. Bar in 4 parts; 20 ÷ 4 = 5; three parts is 15. Ask: "What is the other quarter? What do 15 and 5 make?" This shows the parts always rebuild the whole.

"A short way to remember it: divide by the bottom, times by the top."

The rest of the plan

Guided and independent practice, the plenary, assessment for learning, differentiation, common misconceptions and the home link are free with a Crayonbird account.

  1. Guided practice10 minutes
  2. Independent practice14 minutes
  3. Plenary4 minutes
  4. Assessment for learning
  5. Differentiation
  6. Common misconceptions
  7. Home link
See the whole plan, free

Learning Wiki

Fractions

A fraction is part of a whole that has been split into equal parts. In ¾, the bottom number says how many equal parts and the top says how many you have.

Equivalent fractions

Equivalent fractions look different but are the same size, like 1/2, 2/4 and 4/8. You make them by multiplying or dividing the top and bottom by the same number.

Division

Division is sharing into equal groups, or finding how many groups fit. The sign is ÷, so 12 ÷ 3 = 4. The answer is called the quotient.

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