Fractions are the topic that quietly decides how confident a student feels about the rest of secondary mathematics. Get the conceptual foundation right in Years 7–9 and everything from ratios to algebra becomes easier. This walkthrough gives New South Wales teachers a single, structured lesson on adding and subtracting fractions, built to sit inside the NSW syllabuses and the way the NSW Education Standards Authority (NESA) frames working mathematically across Stage 4–5 (and Stage 6 for seniors). You get objectives, a warm-up, an I-do/we-do/you-do sequence, guided practice and a plenary exit check, anchored to Fractions Complete – Grades 6 to 7.
Learning objectives and syllabus links
By the end of the lesson, students will be able to add and subtract fractions with unlike denominators by finding a common denominator, and explain why a common denominator is necessary. This targets the Fractions, Decimals and Percentages content in the NSW Mathematics syllabus and the Working Mathematically processes of communicating and reasoning. It also builds the Numeracy general capability that NESA threads across learning areas. Note in your programming that fluency here underpins later Stage 5 algebra.
Warm-up (7 minutes)
Put up a deliberately wrong worked example: one-half plus one-third equals two-fifths. Ask, "Is this right? Convince me using a diagram." Students sketch fraction bars or a shared pizza to test it. This surfaces the core misconception — adding numerators and denominators — before you teach anything, and it frames the lesson as fixing a genuine problem. Take a couple of responses and let the class arrive at "the pieces are different sizes, so we can't just add them."
Explicit teaching: I-do, we-do, you-do
Use gradual release so the procedure is grounded in the concept.
- I-do: model one-half plus one-third, showing the fraction bars first, then converting both to sixths, narrating each step.
- We-do: work a second example together, students prompting you for the next move.
- You-do: students complete two problems independently with the diagram alongside the numbers.
- Support and stretch: provide a fraction wall for those who need it and improper-fraction problems for those ready.
The graduated problem sets in Fractions Complete – Grades 6 to 7 line up directly with this sequence, so you can pull examples straight into each phase.
Guided practice
Move students into paired practice with a mix of unlike-denominator problems, including one word problem — "a recipe needs three-quarters of a cup of flour and two-thirds of a cup of sugar; how much dry ingredient in total?" Circulate with diagnostic questions: "What's your common denominator and how did you find it? Does your answer make sense?" Keep a visual model available so reasoning stays connected to meaning rather than becoming a memorised rule. This is the fluency-with-understanding balance NESA expects.
Plenary and exit check (6 minutes)
Close with an exit ticket of one calculation and one explanation: "Solve five-sixths minus one-fourth, and explain in a sentence why you needed a common denominator." Collect these for a fast formative read on who has the concept versus who has only the steps. This feeds directly into your ongoing NESA assessment and reporting. Looking ahead, the same reasoning underpins later NSW topics such as Quadratic Functions and Parabolas and the sample-space work in Probability – Fundamentals and Tree Diagrams, where fraction fluency is assumed all the way to the HSC.
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