Making Common Denominators

Overview

Lesson 7 of 19 in the unit Fractions, Decimals and Percentages. Students use fraction walls and visual models to understand why unlike denominators must be changed before adding, then apply equivalent fractions to solve and check addition problems.

Learning intentions

• WALT explain why fractions need common-sized parts before they can be added.
• WALT find equivalent fractions with a common denominator.
• WALT add fractions with unlike denominators and simplify where appropriate.
• WALT check whether an answer is reasonable using a visual model or estimation.

Success criteria

• I can explain what the denominator tells me about the size of the parts.
• I can rename fractions as equivalent fractions with a common denominator.
• I can add fractions with unlike denominators and show my working.
• I can check my answer using a model, number line or estimate.

Curriculum links

• Number: use and explain fractions, including equivalent fractions and relationships between representations.
• Number: solve addition problems involving fractions and communicate mathematical thinking.
• Mathematical practices: represent ideas, use mathematical language, reason, and justify solutions.
• Statistical and mathematical literacy: check the reasonableness of answers and identify errors in working.

Lesson structure (45 minutes)

1. 0–5 minutes – Hook and connect Open with the fraction-sharing hook. Display: “Would you rather receive (1/2) of a pizza plus (1/3) of a pizza, or (2/5) of a pizza?” Ask students to discuss why (1/2+1/3) cannot be treated as (2/5). Establish that the parts must be the same size before they are combined.

2. 5–13 minutes – Build the idea visually Give pairs the fraction wall and strip cards. Use the slides to display (1/2) and (1/3) alongside the fraction wall. Students identify a common partition: sixths. Model (1/2=3/6) and (1/3=2/6), then combine them to show (1/2+1/3=5/6). Emphasise that the whole has not changed; only the way it is partitioned has changed.

3. 13–21 minutes – Teacher modelling Use the worked-example slides to model a consistent method:

• Find a common denominator.
• Rename each fraction using equivalent fractions.
• Add the numerators, keeping the denominator.
• Simplify or check the result if possible. Work through (1/4+1/6): common denominator 12, so (1/4=3/12) and (1/6=2/12); therefore (5/12). Also model an error such as (1/4+1/6=2/10), asking students to explain why the denominators cannot simply be added.

4. 21–30 minutes – Guided practice Students solve examples with a partner, using the fraction wall or a drawing before recording number sentences. Display one question at a time from the guided-practice slides: (1/2+1/4), (2/3+1/6), and (3/5+1/10). Pause after each problem for students to show their common denominator on mini-whiteboards. Select students to explain their choices, not just their answers. Address misconceptions immediately.

5. 30–40 minutes – Independent practice Distribute the adding unlike denominators worksheet. Students complete the core questions independently, showing equivalent fractions and a check for each answer. Include visual-model questions, straightforward calculations and two word problems. Students self-check using the answer strip or self-checking prompts on the worksheet, correcting errors in a different colour. Confer with students who are still relying on adding denominators.

6. 40–45 minutes – Plenary and exit check Return to the hook on the reflection and exit slides. Ask: “Why is (1/2+1/3=5/6), not (2/5)?” Students explain to a partner using the words common denominator and equivalent fractions. Finish with a quick exit response: solve (1/3+1/4), show the equivalent fractions, and write one way to check the answer.

Resources

• the fraction addition slide deck
• the adding unlike denominators worksheet
• the fraction wall and strip cards
• Mini-whiteboards and pens
• Exercise books or maths books
• Pencils and a different-coloured checking pencil
• Prepared fraction examples on the board
• Visual timer

Assessment

• Observe pair explanations and fraction-wall use: can students identify equal-sized parts and construct equivalent fractions?
• Check mini-whiteboard responses for the common-denominator process and listen for accurate mathematical language.
• Review the worksheet and exit response for correct renaming, addition, working shown and a reasonable check.

Differentiation

• Support: begin with denominators that are multiples of one another, such as (1/2+1/4), and provide a pre-drawn fraction wall or number-line template. Allow students to build each problem before recording it.
• Support: use a worked-example prompt card: “Common denominator? Equivalent fractions? Add numerators? Check?”
• EAL and SEN: pre-teach numerator, denominator, equivalent, common and parts using gestures and labelled visuals. Accept oral explanations, drawings or sentence frames such as “I changed ___ into ___ because…”
• Extension: ask students to find two different ways to solve (1/2+1/3), create an addition problem with answer (7/8), or explain when simplifying is possible.