Fraction Number-Line Walk

Overview

In this second lesson of Rational Numbers in Action, students connect familiar sharing experiences with the position of simple fractions on a number line from 0 to 1. They use their bodies, floor markers and fraction strips to locate and compare one-quarter, one-half, three-quarters and one whole.

Learning intentions

• WALT place simple fractions on a picture or number line from 0 to 1.
• WALT use fraction strips to identify equal parts of a whole.
• WALT describe fraction positions using before, after, more and less.
• WALT explain why two quarters are equal to one-half.

Success criteria

• I can place 0, one-quarter, one-half, three-quarters and one whole.
• I can use the words before, after, more and less to compare positions.
• I can use a fraction strip to show where a fraction belongs.
• I can explain why two quarters equal one-half.

Curriculum links

• Mathematics and Statistics — rational numbers and fractions in meaningful representations.
• Mathematics and Statistics — communicating mathematical thinking using words, diagrams and concrete materials.
• Mathematics and Statistics — reasoning, comparing and explaining relationships between quantities.
• Mathsteasers — developing higher-order thinking through challenge, justification and multiple representations.

Lesson structure (45 minutes)

1. 0–5 min · Hook and connect. Display a picture of a chocolate bar divided into four equal parts using the opening fraction picture and ask, “If I eat one piece, where could I show that on a line from none to all?” Students turn and talk, then share what they remember about halves and wholes from Lesson 1.

2. 5–12 min · Model the benchmarks. Use the 0-to-1 number-line model to show a floor line marked 0 and 1 whole, then place the one-half card halfway between them. Teacher models the language: “One-half is after 0, before 1, and less than one whole.” Students gesture to show before, after, more and less, and help check whether the spacing is equal.

3. 12–22 min · Human number line. Give selected students large cards labelled 0, one-half and one whole; invite the class to position them on a floor number line. Add quarter cards and ask, “Where might one-quarter go? How do you know?” Students use movement and discussion to place one-quarter and three-quarters, then physically stand in order from 0 to 1. Teacher questions individuals: “Which fraction is closer to 0? Which is more: one-quarter or one-half?”

4. 22–32 min · Fraction-strip investigation. In pairs, students use prepared strips divided into halves and quarters to match pieces to the human number line. Teacher demonstrates that two quarter pieces cover the same length as one half. Students place one-quarter, two-quarters, one-half and three-quarters on a desk number line, explaining their choices to a partner.

5. 32–40 min · Partner placement task. Distribute the fraction number-line partner task. One partner chooses or draws a fraction card and places it on the 0-to-1 line; the other checks using a fraction strip and asks, “Is it before or after one-half? Is it more or less?” Partners swap roles and record at least four placements. Circulate and question students individually.

6. 40–45 min · Share and exit check. Return to the discussion and closing slides and revisit the question, “Why do two quarters equal one-half?” Invite two pairs to demonstrate with strips. Students complete the final worksheet prompt by drawing or explaining the position of one-quarter and three-quarters before handing it in.

Resources

• One slide deck, the fraction number-line slide deck
• One worksheet, the fraction number-line partner task
• Floor tape or chalk for a 0-to-1 number line
• Large cards labelled 0, one-quarter, one-half, three-quarters and one whole
• Prepared fraction strips showing halves and quarters
• Small fraction cards for partner placement
• Pencils, crayons and clipboards
• Open floor space for 25 students

Assessment

• Observe whether students place the benchmark cards in the correct positions and whether the intervals are equal.
• Use questioning during the human number line and partner task: “How do you know?”, “What is before one-half?” and “How could the strip prove it?”
• Check the worksheet and closing response for accurate placement, comparative language and the explanation that two quarters equal one-half.

Differentiation

• Support learners with labelled floor benchmarks, coloured quarter markers, pre-drawn worksheet number lines, repeated modelling and sentence starters such as “___ is before ___ because…”.
• Provide movement, concrete strips and partner support before expecting students to draw or record independently. Allow students to point, place or verbally explain their thinking.
• For EAL learners and students needing language support, pair each word with a gesture or picture and repeatedly model “before”, “after”, “more”, “less”, “quarter” and “half”.
• Extend advanced learners by giving mixed fraction cards to order, including two-quarters, and asking them to explain why two quarters equal one-half using both a strip and a number line.

Extension

• Ask students to create a 0-to-1 number line and place all the fraction cards without using the floor model.
• Challenge students to find another way to prove that two quarters and one-half represent the same amount, then explain it to a peer.