Mathematics · Grade 3 · Fractional Thinking · Term 2

Equivalent Fractions with Visual Models

Students explore different fractions that represent the same amount using visual models.

• Ontario Curriculum Expectations
• 3.NF.A.3.A
• 3.NF.A.3.B

About This Topic

Equivalent fractions name the same amount of a whole, even if written with different numerators and denominators. Grade 3 students explore this through visual models like partitioned rectangles, circles, and number lines. They shade 1/2 of a shape, then repartition into fourths and shade 2/4 to see the portions match. This meets Ontario curriculum standards 3.NF.A.3.A and 3.NF.A.3.B, where students explain why fractions are equivalent and generate simple pairs like 1/2 = 2/4 or 1/4 = 2/8 using models.

Visual models connect partitioning to multiplication of unit fractions by whole numbers, building flexible fraction sense. Students justify equivalences verbally and prepare for comparing fractions without models. Key questions guide inquiry: why do 1/2 and 2/4 represent the same amount, and how to find equivalents efficiently.

Active learning shines here with concrete tools like fraction strips or grid paper. Students build, compare, and manipulate models in groups, discovering patterns through trial and error. This approach makes equivalence intuitive, reduces anxiety, and deepens understanding beyond rote memorization.

Key Questions

1. Explain why two different fractions can represent the same amount.
2. Design a visual model to demonstrate that 1/2 is equivalent to 2/4.
3. Justify how we can find equivalent fractions without drawing pictures.

Learning Objectives

• Compare visual models to identify equivalent fractions.
• Explain why two fractions with different numerators and denominators can represent the same value.
• Design a visual model to demonstrate the equivalence of simple fractions, such as 1/2 and 2/4.
• Justify how to find equivalent fractions using multiplication or division of the numerator and denominator by the same number.
• Create pairs of equivalent fractions using visual models and numerical methods.

Before You Start

Understanding Unit Fractions

Why: Students need to understand what a unit fraction (like 1/2, 1/3, 1/4) represents as one part of a whole.

Partitioning Shapes into Equal Parts

Why: The ability to divide shapes into equal parts is fundamental for creating visual models of fractions.

Key Vocabulary

Equivalent Fractions	Fractions that represent the same portion of a whole, even though they have different numerators and denominators.
Numerator	The top number in a fraction, which tells how many parts of the whole are being considered.
Denominator	The bottom number in a fraction, which tells how many equal parts the whole is divided into.
Fraction Bar	The line separating the numerator and the denominator, indicating division.
Partition	To divide a whole into equal parts or pieces.

Watch Out for These Misconceptions

Common Misconception

1/2 is always bigger than 2/4 because the top number 2 is larger than 1.

What to Teach Instead

Visual models reveal equal shaded areas despite different numerals. Students overlay fraction pieces or trace shapes to compare directly. Group discussions of their models correct size misconceptions through shared evidence.

Common Misconception

Fractions are equivalent only if the drawings look identical.

What to Teach Instead

Different partitions show the same whole amount. Hands-on repartitioning of one shape into halves then quarters helps students see varied representations. Peer teaching reinforces flexible visuals.

Common Misconception

Finding equivalent fractions always requires drawing pictures.

What to Teach Instead

Models build understanding of multiplying numerator and denominator by the same number. After visual practice, students explain rules verbally in partners, transitioning to mental strategies.

Active Learning Ideas

Pairs: Fraction Folding

Give each pair square paper. Fold to show 1/2, unfold and refold into fourths to shade 2/4. Partners discuss and label why amounts match. Share one model with class.

25 min·Pairs

Small Groups: Strip Matching Game

Provide precut fraction strips for halves, fourths, thirds, sixths. Groups sort and match equivalents by laying strips side-by-side on a mat. Record pairs on chart paper.

35 min·Small Groups

Whole Class: Number Line Parade

Draw large number lines on floor with tape. Students hold cards for 0, 1/2, 1, 2/4. Walk to mark positions, adjust to show equivalence. Discuss overlaps.

40 min·Whole Class

Individual: Shape Partition Challenge

Students draw rectangles or circles, partition into 2, 4, or 8 parts, shade equivalents like 3/4 = 6/8. Self-check with ruler for equal parts.

20 min·Individual

Real-World Connections

• Bakers use equivalent fractions when scaling recipes. For example, if a recipe calls for 1/2 cup of flour and they need to make double the amount, they need to know that 1/2 cup is equivalent to 2/4 cup, or even 1 cup if they double the entire recipe.
• Construction workers use equivalent fractions when measuring materials. A carpenter might need to cut a piece of wood that is 1/2 inch thick, but the available measurements on their ruler might be in eighths of an inch, requiring them to recognize that 1/2 inch is the same as 4/8 inch.

Assessment Ideas

Quick Check

Provide students with pre-drawn shapes (circles, rectangles) divided into different numbers of equal parts. Ask them to shade 1/2 of one shape, then shade an equivalent amount on another shape divided into fourths or eighths. Have them write the two equivalent fractions and explain why they are the same.

Exit Ticket

Give students a card with the fraction 1/3. Ask them to draw a visual model to show an equivalent fraction and write the new fraction. Then, ask them to explain in one sentence how they know the fractions are equivalent.

Discussion Prompt

Pose the question: 'Imagine you have a pizza cut into 6 equal slices and another identical pizza cut into 12 equal slices. If you eat 3 slices from the first pizza, how many slices from the second pizza would be the same amount of pizza?' Facilitate a discussion where students use drawings or fraction strips to justify their answers and connect it to equivalent fractions.

Frequently Asked Questions

What visual models best teach equivalent fractions in grade 3?

Area models like circles and rectangles, linear models such as number lines, and set models with counters work well. Start with fair-sharing scenarios: divide a pizza into 2 or 4 slices. Students shade and compare, noting same portions. Rotate models across lessons to build versatility and meet standards 3.NF.A.3.A-B.

How do you address key questions on equivalent fractions?

Pose: 'Why do 1/2 and 2/4 show the same amount?' Use models for students to investigate, then justify in journals. For designing 1/2=2/4 visuals, provide grids; for non-drawing methods, reveal patterns from repeated model-building. Scaffold with sentence starters for explanations.

How can active learning help students grasp equivalent fractions?

Manipulatives like fraction tiles let students physically match 1/2 to 2/4 by aligning edges, making abstract equality concrete. Collaborative challenges, such as group strip sorts, encourage debate and pattern spotting. Movement activities like number line walks reinforce through kinesthetic input. These methods boost engagement, correct errors on the spot, and improve retention over worksheets.

What hands-on tools support fractional thinking in Ontario grade 3?

Fraction strips, pattern blocks, and grid paper align with curriculum unit on fractional thinking. Students cut or assemble to show equivalences, fostering unit fraction multiplication intuition. Combine with digital tools like virtual manipulatives for extension. Track progress via model sketches in math notebooks.