Fractions On Number Lines

Overview

Lesson 6 of 15 in Number Connections: Fractions, Decimals, Percentages. Students use open number lines to locate, sequence and justify fractions, connecting fraction magnitude with distance and measurement.

Learning intentions

• WALT locate and sequence fractions on number lines.
• WALT partition wholes and intervals into equal parts.
• WALT explain a fraction’s position using benchmarks and distance.
• WALT connect fraction size with measurement and magnitude.

Success criteria

• I can partition a whole or interval fairly.
• I can place fractions accurately on an open number line.
• I can sequence fractions from least to greatest.
• I can explain a fraction’s position using 0, 1, or another benchmark.

Curriculum links

• Number: recognise, represent, compare and order fractions, including improper fractions and mixed numbers.
• Number: connect fractions with measurement, magnitude and equivalent representations.
• Mathematical processes: use representations, justify thinking, communicate clearly and notice patterns.
• Progression: build flexible understanding of fractions as numbers, not only parts of shapes.

Lesson structure (45 minutes)

1. 0–5 min – Hook and connect Open with the fraction number-line hook. Display a strip marked only 0 and 1 and ask: “Where would you stand if you were three-quarters of the way from the start?” Students make a quick individual estimate, then discuss what evidence they used. Introduce the WALT and success criteria.

2. 5–13 min – Teacher modelling Model on the board and through the modelling slides how to partition 0–1 into equal intervals before placing one-quarter, one-half and three-quarters. Emphasise that the denominator tells how many equal intervals are needed and the numerator tells how many intervals to count. Use the MNP textbook modelling sequence: concrete or visual representation, number-line drawing, then symbolic fraction notation. Ask: “Which benchmark is this fraction closest to, and how do you know?”

3. 13–20 min – Guided practice Students work in pairs with mini-whiteboards. Give fractions such as two-fifths, four-fifths, one-third and five-sixths. Pairs draw open number lines, mark useful benchmarks and explain their choices to another pair. Pause to address common errors, especially unequal partitions and counting spaces rather than points.

4. 20–32 min – Independent practice Distribute the fractions on number lines practice worksheet. Students complete tasks involving partitioning 0–1, placing and ordering fractions, and explaining positions relative to 0, one-half and 1. Encourage students to use measurement language such as “two-thirds is two equal intervals from zero” or “five-sixths is close to one”. Circulate, question and record evidence against the success criteria.

5. 32–39 min – Flexible challenge and support Form short-term groups based on need. Students needing support use the Fractions On A Number Line Strategy Mat and movable fraction labels, focusing first on 0–1 with benchmark anchors. Other students use the Fractions On A Number Line Task Cards to locate, compare and order fractions. Challenge advanced learners to place improper fractions such as seven-fourths and eleven-sixths, and to find a fraction between two close values such as three-fifths and two-thirds.

6. 39–45 min – Plenary and exit check Return to the discussion and plenary slides. Display two fractions and ask students to decide which is further along a number line, giving a justification rather than only an answer. On the back of the worksheet, students draw a number line from 0 to 1, place three-eighths, and complete: “I know it is in this position because…”. Invite two students to share different strategies.

Resources

• the fraction number-line slide deck
• the fractions on number lines practice worksheet
• MNP textbook section and teacher model
• Mini-whiteboards, pens and erasers
• Large board number line or floor number line
• Fraction labels or sticky notes for movable placement
• the Fractions On A Number Line Strategy Mat
• the Fractions On A Number Line Task Cards

Assessment

• Observe pair explanations and board work for equal partitioning, accurate placement and benchmark reasoning.
• Use the worksheet to assess ordering, representation and written justification.
• Collect the final number-line response to identify students needing further work with intervals, benchmarks or fraction magnitude.

Differentiation

• Support: begin with 0–1 number lines, use benchmark anchors at one-half and 1, provide pre-drawn equal intervals and allow students to move labelled fraction cards before drawing.
• Support for EAL and students requiring additional scaffolding: use gestures and visual models, rehearse sentence frames such as “___ is between ___ and ___ because…”, and pair with a supportive peer.
• Core learners: vary denominators and require both a number-line representation and a verbal explanation.
• Extension: include improper fractions, mixed numbers and fractions between close values; ask students to create a fraction that fits a specified interval and defend its position.