Fractions on Lines

Overview

This lesson introduces fractions in a fun and interactive way. Students will explore quarters and mixed numbers using colorful fraction bars and hands-on games. Through group activities and simple real-life examples, they will learn to count in fractional steps and place these fractions on number lines with confidence and understanding.

Learning intentions

Students will be able to:

• count by quarters and identify the counting sequence (one-quarter, two-quarters, three-quarters, four-quarters)
• count by mixed numerals (for example, one and one-quarter, one and two-quarters)
• locate and represent quarters and mixed numerals on a number line using the correct order and spacing
• explain how many parts make a whole when counting fractional jumps

Success criteria

Students can:

• correctly count forward by quarters and say what number comes next
• place each quarter (and mixed numerals made from quarters) at the correct position on a number line
• show that four quarters make one whole by using a model or diagram
• justify their placement using “I can see the jumps” or “each jump is one-quarter”

Curriculum links

• Number — count by fractions including mixed numerals; locate and represent these fractions as numbers on number lines - Number — connect fractional models to counting sequences used to move along number lines (AC9M4N04 elaborations)
• Early use of number-line reasoning for fractional step patterns before linking to decimals in later lessons (supports future connections in the fractions sequence)

Lesson structure (60 minutes)

1. 0–5 min · Engaging hook with real-life examples. Show colorful fraction bars representing quarters (like a pizza or chocolate bar). Ask: “If we eat one-quarter at a time, how many pieces until the whole is gone?” Students share ideas and use fingers to count.

2. 5–15 min · Hands-on fraction bars activity. Distribute colorful fraction bars divided into quarters. Guide students step-by-step to count one-quarter, two-quarters, three-quarters, and four-quarters (one whole). Use clear, simple language and encourage questions.

3. 15–25 min · Exploring mixed numerals with fraction bars. Show how one whole bar plus extra quarters make mixed numbers (e.g., one and one-quarter). Students build these with bars and say the fractions aloud using sentence frames: “One and __-quarter is __ quarters.”

4. 25–35 min · Interactive number line introduction. Draw a large number line on the board with quarter divisions. Use a magnetic pointer to "jump" along the line, saying each fraction aloud. Students place pre-printed colorful fraction labels on mini number lines.

5. 35–48 min · Guided group stations with games and visual aids. Rotate groups through three stations:

   • Station A: Use fraction cards and counters to build and place fractions on blank number lines.
   • Station B: Fold colorful paper strips into quarters, mark mixed numerals, and discuss with peers.
   • Station C: Teacher-led table for checking understanding and addressing misconceptions. Groups record their answers collaboratively and discuss reasoning.

6. 48–55 min · Whole-class discussion and Q&A. Share group findings and common errors. Encourage students to explain their thinking using fraction language.

7. 55–60 min · Exit ticket with guided support. Students place and label two mixed numerals on a quarter-subdivided number line and write the next fraction in the sequence.

Resources

• Colorful fraction bars divided into quarters
• Fraction models: paper strips and/or circles divided into 4 equal parts
• Counters (or sticky dots) for "each jump"
• Number line templates: 0 to 1 and 0 to 2 with equal quarter subdivisions
• Pre-printed colorful fraction cards (one-quarter, two-quarters, three-quarters, one whole, one and one-quarter, one and two-quarters, etc.)
• Sentence starters: “I can see ___ jumps. Each jump is one-quarter.”
• Station materials: folded-paper strips, blank number lines, group recording sheets, fraction games materials
• Teacher pointer or magnetic arrow for number-line modelling
• Exit ticket worksheet

Assessment

• Teacher observes counting accuracy during the whole-class model (does the student say the next quarter correctly?)
• Station checks: students must correctly match a built model to its number-line position and explain using “quarter jumps”
• Exit ticket: accuracy of placements for two mixed numerals and one correct next-step in the counting sequence

Differentiation

• Support:
• Provide number lines with already-marked 0 and 1, and only subdivide the next whole into quarters for some students
• Use sentence starters and word banks (one-quarter, two-quarters, one and one-quarter)
• Offer a “model first” path at stations (build, then place, then label)
• Extension:
• Challenge students to place an additional mixed numeral (for example, 1 and three-quarters) and write an equivalent “quarters count” (for example, 1 and three-quarters = seven-quarters)
• SEN/EAL considerations:
• Keep language consistent across the lesson: “one jump is one-quarter”
• Allow oral responses for explanation, not only written sentences
• Use visuals (models and arrows) to reduce reliance on complex writing