Fraction Addition Pathways

Overview

Students build on their understanding of fractions as equal parts to add fractions with the same denominator. They use fraction strips and diagrams to explain why the denominator stays the same, then record answers as improper fractions and convert selected answers to mixed numbers.

Learning intentions

• WALT add fractions with the same denominator.
• WALT explain why only the numerators are added.
• WALT recognise when an answer is an improper fraction.
• WALT rename an improper fraction as a mixed number.

Success criteria

• I can identify the denominator and explain what it tells me.
• I can add fractions with the same denominator accurately.
• I can show my thinking with a diagram, fraction strip or number line.
• I can rename an improper fraction as a mixed number and check that it is equivalent.

Curriculum links

• Te Mātaiaho Mathematics and Statistics — Mathsteasers: higher-order thinking and challenge for advanced learners.
• Te Mātaiaho Mathematics and Statistics — Alignment: mathematical thinking is connected to relevant textbook and problem-solving content.
• Number: using fractions to represent parts of a whole and solving additive problems.
• Mathematical practices: representing, explaining, communicating and checking mathematical thinking.

Lesson structure (45 minutes)

1. 0–5 min · Hook and recall. Teacher displays the opening question in the fraction addition introduction deck: “If three friends each eat one-quarter of a pizza, how much pizza has been eaten?” Students discuss with a partner, sketch the pizza or use known fraction facts, then share answers. Elicit that the wholes must be the same size and that the denominator names the equal parts.

2. 5–12 min · Model the idea. Teacher uses the fraction wall and strip cards and the worked examples in the fraction addition introduction deck to model ( \frac{2}{6}+\frac{3}{6}=\frac{5}{6} ). Physically combine two sixths and three sixths, recording: “The denominator stays 6 because the size of each part has not changed; we add 2 + 3.” Students explain the model to a partner using the sentence frame: “I keep the denominator the same because …”

3. 12–20 min · Build to an improper fraction. Teacher models ( \frac{5}{8}+\frac{6}{8}=\frac{11}{8} ) with strips, then places the result on a number line shown in the fraction addition introduction deck. Discuss why more than one whole is possible and introduce the term improper fraction as a fraction whose numerator is equal to or greater than its denominator. Students make and record two examples with the fraction strips, including one answer greater than one whole.

4. 20–32 min · Guided partner practice. Teacher distributes the same-denominator fraction addition worksheet and directs pairs to complete the first section. Students solve examples such as ( \frac{3}{5}+\frac{1}{5} ), ( \frac{4}{7}+\frac{5}{7} ), and ( \frac{7}{10}+\frac{6}{10} ), showing at least one answer with a drawing or strip model. Teacher circulates, checking that students add numerators only and do not add denominators. Pause for a quick whole-class check using the answers on the fraction addition introduction deck.

5. 32–40 min · Rename improper fractions. Teacher demonstrates ( \frac{11}{8}=1\frac{3}{8} ): eight eighths make one whole, with three eighths remaining. Model this with strips and record both forms. Students complete the worksheet’s mixed-number section, converting appropriate answers such as ( \frac{9}{4} ), ( \frac{13}{6} ), and ( \frac{12}{5} ). Emphasise that the remainder becomes the numerator and the denominator remains unchanged. Students check by converting the mixed number back into an improper fraction.

6. 40–45 min · Plenary and exit check. Teacher displays the final prompts in the fraction addition introduction deck. Students independently answer: ( \frac{5}{6}+\frac{4}{6} ), ( \frac{7}{8}+\frac{5}{8} ), and rename the second answer as a mixed number. Invite two students to explain different representations, then collect responses for assessment.

Resources

• the fraction addition introduction deck covering the hook, models, practice instructions, discussion prompts and plenary
• the same-denominator fraction addition worksheet
• the fraction wall and strip cards
• Whiteboard and markers
• Exercise books and pencils
• Classroom display or projector
• Optional counters or paper strips for students needing additional modelling

Assessment

• During modelling, ask students to explain why the denominator stays the same; listen for “the parts are the same size”.
• While students work, check whether they add only the numerators, represent improper fractions accurately and use division or grouping to rename mixed numbers.
• Use the final independent questions as an exit check. Group students for the next lesson according to whether they need support with addition, improper fractions or mixed-number conversion.

Differentiation

• Support students with the fraction wall and strip cards, pre-drawn wholes divided into equal parts, and the sentence frames: “There are ___ equal parts” and “___ eighths make one whole.”
• Work with a small group during guided practice using denominators of 2, 3, 4 or 5 before moving to larger denominators.
• Allow students to show answers with materials, drawings and words before recording symbolic notation.
• Extend confident students by asking them to create two different same-denominator additions with the same mixed-number answer, then prove that their answers are equivalent. Provide visual examples and read instructions aloud for EAL learners or students with literacy needs.