Shearing-Shed Fraction Race

Overview

Lesson 6 of 10 in Fraction Detectives in Action. Students use rural shearing-shed and paddock contexts to compare and order non-unit fractions with the same denominator, moving from equal-sized physical parts to pictures, number lines and symbols. Planned for 18 students; use pairs or six teams if 22 students attend.

Learning intentions

• WALT compare fractions with the same denominator.
• WALT explain why the numerator matters when the parts are equal-sized.
• WALT order fractions such as one-eighth, three-eighths and six-eighths.
• WALT use fraction strips, shaded models and number lines to show our thinking.

Success criteria

• I can identify equal-sized parts in a fraction model.
• I can compare numerators when the denominators are the same.
• I can order same-denominator fractions from smallest to largest.
• I can explain my answer using a model, number line or words.

Curriculum links

• Recognising and representing fractions as equal parts of a whole.
• Comparing and ordering fractions in familiar contexts.
• Using mathematical language, symbols, diagrams and physical materials to communicate thinking.
• Reasoning, explaining and checking solutions collaboratively, as emphasised in the refreshed New Zealand Mathematics and Statistics curriculum.

Lesson structure (60 minutes)

1. 0–7 minutes – Connect to the context and hook Open with the shearing-shed introduction slides. Show a paddock divided into eight equal sections and ask: “Which paddock has more land marked—one-eighth, three-eighths or six-eighths? How can we prove it?” Accept predictions, but do not confirm yet. Explain that teams are fraction detectives racing to solve the evidence.

2. 7–17 minutes – Build the idea with materials Give pairs fraction strips from the fraction wall and strip cards. Ask students to make one whole using eight equal parts, then build one-eighth, three-eighths and six-eighths. Emphasise that the denominator tells how many equal parts the whole is split into, while the numerator tells how many parts are selected. Compare the strips physically before recording symbols.

3. 17–25 minutes – Model comparing and ordering On the comparison and ordering slides, model: 1/8 < 3/8 < 6/8. Place each fraction on a simple 0–1 number line. Ask: “What stays the same? What changes? Why does the fraction with the greater numerator show more?” Include a non-example with unequal-sized pieces and discuss why it is not fair to compare them.

4. 25–42 minutes – Cooperative fraction relay Arrange six mixed-ability teams of three, or teams of four if there are 22 students. Each team receives fraction strips and a set of teacher-prepared shaded paddock cards showing same-denominator fractions. One student selects a card, one builds or checks it with strips, and one places it in the team’s smallest-to-largest line. Rotate roles each round. Before a card is accepted, a student must explain: “The denominator is the same, so I compare the numerators. ___ is greater than ___, so ___ is greater than ___.” Use the relay instruction slides for the routine and discussion prompts.

5. 42–52 minutes – Independent evidence Distribute the fraction detective worksheet. Students complete short tasks: identify equal-sized parts, circle the greater fraction in pairs with the same denominator, order three fractions, and draw or place one set on a number line. Encourage students to use a strip or sketch before writing symbols. Confer with students who reverse the role of the numerator and denominator.

6. 52–60 minutes – Explain, reflect and assess Return to the plenary slides. Ask pairs to explain the opening problem using the sentence frame: “The denominator is ___, so each part is the same size. The numerator ___ means ___ parts, therefore ___ is greater.” Invite one student to show a model and another to show a number line. Collect worksheets and note who can compare independently and who still needs materials.

Resources

• the shearing-shed fraction race slide deck
• the fraction detective worksheet
• the fraction wall and strip cards
• Teacher-prepared shaded paddock cards showing fractions with denominators 2, 4, 6, 8 and 10
• Large 0–1 number lines
• Blu-tack or magnetic strips
• Pencils, highlighters and mini-whiteboards
• Space for teams to lay out ordered fractions

Assessment

• During modelling and the relay, listen for accurate use of numerator, denominator, equal parts, greater than and less than.
• Observe whether students compare the number of parts only after confirming that the denominators are the same.
• Use the worksheet and final explanation to identify students ready to work without models and those needing further practice with equal-sized parts.

Differentiation

• Support: begin with physical strips and shaded models before symbols; use denominators of 2, 4 and 8; provide a 0–1 number line and the frame “___/8 is greater because it has ___ eighths”.
• Provide tactile pieces, enlarged high-contrast cards, reduced writing and oral response options. Read instructions aloud, use clear sans-serif print, generous spacing and avoid requiring students to copy lengthy text.
• Pair students strategically and give relay roles that allow building, pointing, speaking or recording. Recheck understanding individually rather than relying only on written work.
• Extension: students design an ordering puzzle using denominators up to 12. They must include at least four fractions and prove whether there is more than one possible order or only one, using a model or number line.