Add Fractions Precisely

Overview

This 30-minute one-to-one lesson develops Year 6 understanding of adding fractions with the same and related denominators. The student uses fraction representations, equivalent fractions and written strategies to explain why denominators must be considered before adding.

Learning intentions

• WALT add fractions with the same denominator.
• WALT rename fractions with related denominators so they can be added.
• WALT use diagrams and equations to explain our thinking.
• WALT check whether an answer is reasonable.

Success criteria

• I can explain what the numerator and denominator represent.
• I can add fractions with the same denominator and keep the denominator unchanged.
• I can find equivalent fractions before adding fractions with different but related denominators.
• I can simplify or check my answer and explain my strategy.

Curriculum links

• Mathematics and Statistics — Number: using fractions, equivalence and additive reasoning.
• Mathematics and Statistics — communicating mathematical thinking using diagrams, symbols and explanation.
• Mathsteasers: applying higher-order thinking to deepen understanding.
• Mathsteasers / Alignment: connecting challenge questions with relevant mathematical learning.

Lesson structure (30 minutes)

1. 0–4 min · Hook and diagnostic. Teacher opens with the fraction sharing hook and asks, “Ari eats ( \frac{1}{2} ) of a pizza and Moana eats ( \frac{1}{4} ). How much pizza has been eaten?” The student sketches or uses a fraction strip, gives an estimate, and explains their first idea.

2. 4–9 min · Build the concept. Teacher uses the visual fraction model and worked example to model ( \frac{2}{8}+\frac{3}{8} ), emphasising that the eighths are equal-sized parts, so the numerators are added while the denominator stays 8. The student builds the calculation with a drawn bar or fraction strip and explains why ( \frac{5}{8} ) is sensible.

3. 9–15 min · Related denominators. Teacher models ( \frac{1}{2}+\frac{1}{4} ), partitioning halves into quarters and renaming ( \frac{1}{2} ) as ( \frac{2}{4} ), then demonstrates ( \frac{2}{4}+\frac{1}{4}=\frac{3}{4} ). The student records the steps and identifies the common denominator, using the prompt: “What must the parts have in common before we combine them?”

4. 15–23 min · Guided practice. Teacher distributes the adding fractions practice sheet and works through the first question with the student. The student completes examples such as ( \frac{3}{10}+\frac{4}{10} ), ( \frac{1}{3}+\frac{1}{6} ), ( \frac{3}{4}+\frac{1}{8} ), and one word problem, drawing a model for at least two questions.

5. 23–27 min · Explain and challenge. Teacher returns to the reasoning challenge and discussion prompt and asks, “Is ( \frac{2}{3}+\frac{1}{6}=\frac{3}{9} ) correct? Convince me.” The student identifies the error, solves the problem correctly, and explains why simply adding denominators does not work.

6. 27–30 min · Plenary and exit check. Teacher asks the student to complete the final question on the reflection and exit question: ( \frac{5}{6}+\frac{1}{12} ), including one sentence explaining the denominator choice. The student shares the strategy verbally and states one rule for adding fractions.

Resources

• the adding fractions slide deck
• the adding fractions practice sheet
• Fraction strips or fraction circles
• Whiteboard and marker
• Pencil and ruler
• Coloured pencils
• One-to-one teacher questioning prompts

Assessment

• Listen for whether the student explains that fractions must refer to equal-sized parts before they are combined.
• Check the worksheet for accurate equivalent fractions, correct addition of numerators and reasonable answers.
• Use the final question to assess independent transfer: the student should rename ( \frac{5}{6} ) as ( \frac{10}{12} ), then find ( \frac{11}{12} ).

Differentiation

• Support with fraction strips, bar models, squared paper and the sentence frame: “I renamed ___ as ___ because both fractions are divided into ___ equal parts.”
• If the student is unsure, return to concrete representations and use denominators of 2, 4, 8 or 10 before attempting less familiar examples.
• Provide challenge by asking the student to create two different addition equations with the same answer, or to explain why ( \frac{1}{3}+\frac{1}{6} ) can be solved without using twelfths.
• For EAL learners or students needing language support, use labelled visuals for numerator, denominator, equal parts and equivalent, and accept oral explanation alongside written working.