Fractions Beyond One

Overview

Students build on their understanding of fractions as equal parts of a whole. They use fraction strips, diagrams and equations to add and subtract fractions with the same denominator, including totals greater than one whole.

Learning intentions

• WALT add fractions with the same denominator.
• WALT subtract fractions with the same denominator.
• WALT recognise when a fraction is greater than one whole.
• WALT rename an improper fraction as a mixed number.

Success criteria

• I can keep the denominator the same when adding or subtracting like fractions.
• I can add or subtract the numerators and explain what the answer means.
• I can show fractions beyond one whole using a model or number line.
• I can rename an improper fraction, such as 9/8, as a mixed number: 1 1/8.

Curriculum links

• Te Mātaiaho Mathematics and Statistics — Mathsteasers: higher-order thinking questions that deepen mathematical understanding.
• Te Mātaiaho Mathematics and Statistics — Mathsteasers / Additional resources for advanced learners: reasoning, explaining and justifying mathematical ideas.
• Te Mātaiaho Mathematics and Statistics — Mathsteasers / Alignment: challenging tasks connected to familiar mathematical content.
• Mathematical competencies: communicating mathematical thinking, using representations, and justifying a strategy.

Lesson structure (40 minutes)

1. 0–5 min · Hook and prior knowledge. Teacher displays a rectangle divided into eight equal parts and asks, “If I add 3/8 three times, can my answer be more than one whole?” Open with the fraction hook slide and invite students to make a quiet estimate before sharing with a partner. Students identify the denominator, numerator and whole, then explain whether they think 3/8 + 3/8 + 3/8 is less than, equal to or greater than one.

2. 5–12 min · Build the idea. Teacher uses the fraction wall and strip cards to model three eighth strips placed end to end: 3/8 + 3/8 + 3/8 = 9/8. Emphasise that the denominator stays eight because the size of the parts has not changed; only the number of eighths changes. Students physically combine strips, count eighths, and connect 8/8 with one whole and 9/8 with 1 1/8. Teacher records both forms and models the language “nine eighths is one whole and one eighth”.

3. 12–18 min · Direct teaching and discussion. Teacher returns to the worked-example slides and models like-denominator addition and subtraction: 2/6 + 3/6 = 5/6, 4/8 + 5/8 = 9/8 = 1 1/8, and 7/10 − 3/10 = 4/10. Ask, “What changes? What stays the same?” Students explain the rule in their own words: combine or separate the numerators, while keeping the denominator the same. Address the misconception that denominators should also be added or subtracted.

4. 18–29 min · Supported practice. Teacher distributes the fraction addition and subtraction worksheet. Complete the first two questions together, requiring a drawing, equation and answer. Circulate and ask, “How many equal parts are in one whole?” and “How do you know your answer is greater than one?” Students solve the remaining questions independently, then compare one answer with a partner. They include examples both below and beyond one whole, such as 5/8 + 6/8 and 11/12 − 4/12.

5. 29–36 min · Reasoning challenge. Teacher displays the challenge from the partner reasoning slides: “I added two fractions with denominator 8 and got 12/8. What could the two fractions have been? Find at least two possibilities.” Encourage students to use strips, drawings or equations and to justify whether their possibilities are correct. Students work in pairs, find possible solutions such as 5/8 + 7/8 or 6/8 + 6/8, and explain how they know. Invite two pairs to share different strategies.

6. 36–40 min · Plenary and assessment. Teacher revisits the final reflection slide and asks students to complete the sentence, “When adding or subtracting fractions with the same denominator, I…” Finish with the final reflection question as an individual response. Students state the rule, solve 3/8 + 6/8, and rename the result as a mixed number. Share one clear explanation before packing away.

Resources

• the fraction reasoning slide deck
• the fraction addition and subtraction worksheet
• the fraction wall and strip cards
• Whiteboard and markers
• Pencils and coloured pencils
• Board space for worked examples
• Optional document camera for modelling

Assessment

• Listen during the hook and modelling for accurate use of numerator, denominator and whole.
• Check worksheet representations and explanations, not only answers; conference with students who change the denominator.
• Use the final question, 3/8 + 6/8, to identify who can add beyond one whole and rename 9/8 as 1 1/8.

Differentiation

• Support students with fraction strips, pre-drawn equal-part diagrams and the sentence stem: “The denominator stays the same because…”
• Pair students strategically and rehearse explanations orally before requiring written reasoning.
• For students needing additional challenge, ask them to find all pairs of eighths that total 12/8 and explain how they know their list is complete.
• For EAL learners and students requiring SEN support, use the visual models consistently, read questions aloud, reduce the number of worksheet items and accept oral or drawn explanations.