Fractions Introduction: Unit Fractions, Equivalence and Improper Fractions, Years 5–6

What a fraction is, unit fractions, equivalence and improper fractions

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About this resource

Fractions only work when the parts are equal and the whole is the same size. Half of a large pizza beats half of a small one, and some Year 5s will argue about it. This unit opens with a pizza box and its order docket.

How it runs

Three lessons of 45–60 minutes. After the 8-question pre-test, teach equal parts, the same whole and three fraction models. Students compare unit fractions with one-half and order them on number lines. Plenty think 1/10 is bigger than 1/5 because 10 is bigger than 5; one number line sorts that out. Sharing 3 pizzas between 4 people shows that a fraction is a division (3 ÷ 4 = 3/4).

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Equivalent fractions follow, with the rule "multiply or divide the numerator and the denominator by the same number". Students sort proper and improper fractions and mixed numerals, convert with diagrams and solve the Case of the Unfair Pizza.

Maths covered

MA3-RQF-01: explain the whole as 1, compare unit fractions with one-half, order unit fractions with denominators of 2, 3, 4, 5, 6, 8 and 10 on number lines, and make equivalent fractions
MA3-RQF-02: record a division as a fraction (3 ÷ 4 = 3/4) and share quantities and money equally
Extension (Stage 4): writing improper fractions as mixed numerals (Activities 7 to 9) and simplifying with the highest common factor (MA4-FRC-C-01)

Good to know

Improper fractions are Stage 3 (3 ÷ 2 = 3/2). Converting them to mixed numerals is Stage 4 in NSW, though the Australian Curriculum has it in Year 5, so keep those pages light or skip them.
Cut the fraction wall into strips.
Refreshed from my 2021 Fraction Introduction PowerPoint. Maths Detectives characters and Keynote fonts included.

What’s included

36 teacher slides with answers (editable Google Slides / PowerPoint + PDF)
16-page A4 student booklet (PDF)
Black and white booklet for low-ink printing
Editable PowerPoint copy of the booklet (colour and black and white)
Pre-test, fraction wall and a detective case file
Reflection page with a "How did I go?" self-assessment against the success criteria, and a certificate
Teacher instructions with lesson plan and answer key