Thirds and Quarters

Overview

This is lesson 2 of 5 in the unit Fractions: Equal Parts. Students build from their understanding of halves to partitioning wholes into equal thirds and quarters, connecting practical models with fraction names and notation.

Learning intentions

• WALT divide wholes into equal thirds and quarters.
• WALT connect fraction diagrams with fraction names and symbols.
• WALT explain what the denominator tells us about a fraction.
• WALT describe our mathematical thinking clearly to others.

Success criteria

• I can divide a whole into three or four equal parts.
• I can name one part as one-third or one-quarter.
• I can write (1/3) and (1/4).
• I can explain that the denominator tells how many equal parts make the whole.

Curriculum links

• Mathematics and Statistics — fractions and equal parts within the refreshed curriculum.
• Mathematical practices — represent, reason, communicate and justify mathematical ideas using materials, diagrams, words and symbols.
• Mathsteasers — deepen understanding through challenging questions and explanation.
• Mathsteasers / Alignment — connect challenge activities with relevant classroom mathematics learning.

Lesson structure (60 minutes)

1. 0–8 min · Revisit halves. Teacher displays a rectangle and asks, “How can we split this whole into two equal parts?” and “What would make the parts unequal?” Students use hand gestures, drawings or oral explanations to review whole, equal parts and half. Open with the introduction and halves review slides.

2. 8–18 min · Model thirds and quarters. Teacher folds or draws a paper strip into three equal parts, carefully checking that the parts are the same size. Introduce third, (1/3), and explain that the 3 is the denominator: it tells how many equal parts make the whole. Repeat with four equal parts, introducing quarter and (1/4). Students predict where folds or guide marks should go, then rehearse: “One of three equal parts is one-third.” Use the modelling and denominator slides to show clear diagrams and prompts.

3. 18–30 min · Make and label. Teacher pairs the eight students and gives each pair scrap paper strips and pencils. Model the task: make one strip showing thirds and another showing quarters; shade or circle one part and label it with the fraction name and symbol. Students fold or draw, compare the sizes of their parts, and record their examples on the thirds and quarters recording sheet. Confer with every pair, asking, “How many equal parts?” and “How many parts are selected?” Support students to check equality rather than accepting pieces that merely look similar.

4. 30–45 min · Match and sort. Teacher forms two groups of four and provides teacher-made matching cards showing diagrams, words and symbols for (1/3) and (1/4). Students first sort the cards collaboratively, explaining why each belongs together. They then check their thinking with the fraction wall and strip cards from the Fraction Wall and Strip Cards. Each group prepares one match to explain to the class. Remind students that the whole must be considered before judging the size of a part.

5. 45–53 min · Share and reason. Each group presents one matched set. Teacher asks, “How do you know this is one-third?” and “What does the denominator tell us?” Students respond using a diagram, words or symbols and respectfully agree, question or add to the explanation. Show the discussion prompts in the matching and sharing slides. Address the misconception that a quarter is simply any small-looking piece: it must be one of four equal parts of the same whole.

6. 53–60 min · Individual check and exit. Teacher gives each student three quick prompts on a mini-whiteboard or paper: identify a diagram as (1/3) or (1/4), write the matching symbol for a named fraction, and explain what the denominator tells us. Students complete the prompts independently, then hold up responses one at a time for checking. Finish with the plenary and exit-question slide and collect the completed recording sheet.

Resources

• the thirds and quarters teaching deck
• the thirds and quarters recording sheet
• the Fraction Wall and Strip Cards
• Scrap paper strips
• Pencils and colouring tools
• Teacher-made matching cards for diagrams, words and symbols
• Mini-whiteboards or small pieces of paper
• Board and markers

Assessment

• During pair work, observe whether students create equal parts, count the parts accurately and distinguish one selected part from the whole.
• During conferencing and group explanations, listen for correct use of whole, equal parts, third, quarter and denominator.
• Use the individual mini-whiteboard or paper prompts to identify who can connect a diagram, name and symbol, and who interprets the denominator correctly. Record students needing further support in lesson 3.

Differentiation

• For support, use larger strips, clearly marked guide points, colour coding and repeated oral rehearsal: “The whole is split into ___ equal parts, so one part is one-___.” Let students demonstrate with folding or pointing before recording symbols.
• Provide a completed example and limit the first choice to two cards. Do not rely only on symbolic notation; accept concrete models, drawings and oral explanations as evidence of understanding.
• For EAL learners and students requiring additional support, pair spoken vocabulary with gesture, diagrams and sentence frames. Recast mathematical language naturally and allow extra processing time.
• For advanced learners, ask students to show thirds and quarters in more than one shape and explain why a quarter is not simply any small-looking piece. Challenge them to create a deliberately incorrect model and explain how to fix it.

Extension

• Students draw thirds and quarters in different shapes, such as rectangles, circles or irregular wholes, and label one selected part.
• Students compare two pieces and justify whether both represent the same unit fraction, referring to the number of equal parts in the whole.