Fractions as Equal Parts

Overview

In lesson 26 of 30 in Building Mathematical Thinking, students build on prior work with shapes and sharing by partitioning circles and rectangles into equal parts. They describe halves, thirds, and fourths using models, objects, drawings, and oral language.

Learning intentions

• Students will be able to partition circles and rectangles into two, three, or four equal parts.
• Students will be able to name equal parts as halves, thirds, or fourths.
• Students will be able to describe one part as a half of, a third of, or a fourth of a whole.
• Students will be able to explain why parts must be equal to make a fair share.

Success criteria

• I can divide a shape or object into equal parts.
• I can name the parts as halves, thirds, or fourths.
• I can describe one part of a whole using fraction words.
• I can explain how I know the parts are equal.

Curriculum links

• Grade 1 Geometry — partition circles and rectangles into halves and fourths and describe the shares.
• Grade 2 Geometry — partition circles and rectangles into two, three, or four equal shares and use the words halves, thirds, and fourths.
• Grade 3 Geometry — partition shapes into parts with equal areas and describe each part as a unit fraction of the whole.
• Mathematical practice — reason about equality, use visual models, and explain thinking.

Lesson structure (30 minutes)

1. 0–4 min · Hook: Fair or unfair? Teacher opens with the fair-sharing introduction and displays one rectangle split into equal parts and one split into unequal parts. Students use thumbs up/down to decide which sharing is fair and explain why using the sentence frame, “The parts are/are not equal because…”.

2. 4–9 min · Model equal parts. Teacher uses a large paper circle and rectangle, first folding each in half and then showing fourths; teacher introduces whole, half, third, and fourth, emphasizing that equal parts have the same area even when their shapes may look different. Students echo the vocabulary, trace fold lines, and identify the number of equal shares shown on the vocabulary and folding slides.

3. 9–17 min · Hands-on partitioning. Teacher pairs students and provides paper shapes, fraction circles, and tactile fraction pieces. Students fold or arrange shapes to make halves first, then fourths and thirds, checking whether each share is equal. Teacher asks, “How many equal shares make the whole?” and “What is one share called?” Students say, point to, and name each model; students who are ready draw their partitions.

4. 17–24 min · Guided practice. Teacher distributes the equal-parts practice sheet and completes the first item with the class, modeling how to partition and label a shape. Students partition circles and rectangles into halves, thirds, and fourths, circle the equal models, and complete sentence frames such as “One part is ___ of the whole.” Teacher checks work with individual students and uses concrete pieces beside the worksheet when needed.

5. 24–28 min · Partner explain and challenge. Teacher displays the discussion prompts on the partner discussion and challenge slides. Students explain one answer to a partner using “I made ___ equal parts, so each part is a ___.” Advanced learners compare a third and a fourth with fraction circles and explain which unit fraction is larger and why; other students compare halves and fourths with teacher support.

6. 28–30 min · Exit check. Teacher shows a rectangle and asks students to draw two equal parts, label one part, and answer orally or in writing: “How do you know the parts are equal?” Students complete the task independently or point to and name a matching model before sharing their answer.

Resources

• the equal-parts slide deck
• the equal-parts practice sheet
• Paper circles and rectangles for folding
• Fraction circles
• Tactile fraction pieces
• Crayons or colored pencils
• Scissors and glue, if needed
• Large demonstration shapes
• Vocabulary cards with pictures
• Pencils and chart paper

Assessment

• During modeling and hands-on work, ask students to show two, three, or four equal shares and explain how they checked equality.
• Review worksheet models for correct partitioning and fraction vocabulary; reteach any student who creates unequal shares.
• Use the exit check to identify whether each student can partition a shape, name a share, and explain “equal.”

Differentiation

• Support: Begin with halves before fourths and thirds. Use pre-folded shapes, fraction circles, large diagrams, color coding, and repeated oral practice. Offer sentence starters: “The whole has ___ equal parts” and “One part is a ___.”
• Special education and fine-motor support: Provide tactile fraction pieces, larger paper shapes, thick pencils, reduced worksheet items, hand-over-hand folding only when appropriate, and options to point, build, draw, or answer orally.
• Dyslexia-friendly options: Use a clear sans-serif font, large uncluttered diagrams, short directions, vocabulary cards with pictures, high-contrast colors, tactile materials, and oral directions with opportunities to rehearse answers.
• Advanced learners: Compare thirds and fourths using models, explain why one third is larger than one fourth, and create two different-looking shapes divided into equal shares.

Extension

• Challenge students to partition the same rectangle in two different ways while keeping four equal areas.
• Ask students to use fraction circles to order a half, a third, and a fourth from largest to smallest and justify their thinking.