Fraction Farmer Investigators

Overview

Lesson 2 of 10 in Fraction Detectives in Action. Students investigate fractions in familiar rural contexts, using paddock maps and fraction strips to connect equal parts with numerator and denominator. Plan for 18 students working in pairs; add one extra pair if the class has 22.

Learning intentions

• WALT identify the denominator as the total number of equal parts.
• WALT identify the numerator as the parts being considered.
• WALT read and write halves, thirds and quarters in words and symbols.
• WALT explain how a fraction describes part of a whole.

Success criteria

• I can find and name the equal parts in a whole.
• I can identify the denominator and numerator in a fraction.
• I can read and write 1/2, 1/3, 1/4 and other simple halves, thirds and quarters.
• I can explain my fraction using the words “denominator”, “numerator” and “equal parts”.

Curriculum links

• Number: recognise, represent, read and write simple fractions as equal parts of a whole.
• Number: use mathematical language and symbols to describe and communicate fraction thinking.
• Mathematical processes: represent ideas, notice patterns, explain reasoning and check whether an answer makes sense.
• Communication and collaboration: discuss strategies, listen to others and use representations to justify thinking.

Lesson structure (60 minutes)

1. 0–7 minutes – Rural fraction hook and revisit Open with the fraction-farmer introduction slides. Show a paddock divided into equal sections and ask: “A farmer checks 1 out of 4 equal paddocks. What fraction is being checked?” Invite students to explain what the 4 and 1 might mean. Briefly revisit the previous lesson’s idea that a fraction shows part of a whole.

2. 7–17 minutes – Explicit teaching: numerator and denominator Use a large rectangle or paddock model divided into 2, 3 and 4 equal parts. Model writing the fraction underneath each image. Emphasise that the denominator is the total number of equal parts and the numerator tells how many parts we are considering. Use colour coding: denominator in blue, numerator in red. Students practise saying: “The denominator is __ because there are __ equal parts. The numerator is __ because __ parts are considered.” Refer to the numerator and denominator teaching slides.

3. 17–22 minutes – Guided class check Display three examples: one-half, two-thirds and three-quarters. Students show the numerator with one finger and denominator with two fingers, then read each fraction together. Include a non-example where the parts are unequal and ask, “Can this be described as a fraction of equal parts? Why or why not?” Address misconceptions before stations.

4. 22–44 minutes – Rotating fraction stations Arrange three stations with pairs. Rotate every seven minutes, allowing one minute to move. Provide the fraction wall and strip cards at the strip station and distribute the fraction investigator worksheet for students to record one example at each station.

• Strip station: Build halves, thirds and quarters. Match each model to its word and symbol, then identify numerator and denominator.
• Paddock map station: Shade or circle the requested number of equal paddocks. Partners take turns being the “farmer” and “fraction detective”, explaining the fraction using the sentence frame.
• Mystery fraction station: Select a card, identify the whole, numerator and denominator, and draw or describe the model. Prepare mystery cards with halves, thirds and quarters.

Display the station instructions and discussion prompts throughout. Support students with colour-coded numbers, vocabulary cards, matching word-and-symbol cards and audio directions.

5. 44–53 minutes – Pair explanation and reasoning circle Each pair chooses one completed mystery fraction. One student explains it to their group while the partner points to the model and records the fraction. Prompt: “How do you know the denominator?” and “What does the numerator tell us?” Invite two pairs to share contrasting examples, such as 1/4 and 3/4.

6. 53–60 minutes – Plenary and exit check Use the plenary and exit-check slides. Students independently complete the final section of the fraction investigator worksheet: draw a model for 2/3, label numerator and denominator, and write one sentence explaining the fraction. Collect responses as the exit check and celebrate precise mathematical language.

Resources

• the fraction-farmer introduction slides
• the fraction investigator worksheet
• the fraction wall and strip cards
• Paddock maps showing 2, 3 and 4 equal sections
• Mystery fraction cards
• Counters, pencils and colouring tools
• Blue and red highlighters or marker pens
• Vocabulary cards: whole, equal parts, numerator, denominator, halves, thirds, quarters
• Sentence frames and optional recorded/audio directions

Assessment

• Listen during guided practice and stations for correct identification of numerator, denominator and equal parts.
• Check the worksheet for accurate models, symbols, words and explanations.
• Use the final 2/3 response to identify students needing further modelling or ready for greater challenge.

Differentiation

• Support: use only halves first, then thirds and quarters; provide pre-coloured models, colour-coded numerator and denominator labels, word-symbol matching cards and the sentence frame: “The denominator is __ because __. The numerator is __ because __.”
• Dyslexia-friendly options: use a clear sans-serif font, large print, uncluttered worksheet sections, strong colour contrast and oral/audio directions. Allow students to answer verbally, point to models or use a scribe.
• EAL learners: rehearse vocabulary with gestures and pictures, pair each word with a symbol and model complete explanations before independent work.
• Extension: students create a mystery card using halves, thirds or quarters, draw a matching model and explain how changing either the numerator or denominator changes the fraction. Ask them to compare 1/4 and 3/4 using evidence.