Mathematics · Grade 3

Active learning ideas

Defining the Whole

Active learning works for this topic because fractions are abstract until students physically engage with them. When students manipulate objects or debate ideas, they build mental models of how the 'whole' shapes the 'part,' which is essential for later fraction comparison and operations.

• Ontario Curriculum Expectations
• 3.NF.A.1

• 25–45 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Formal Debate
• 25 min · Whole Class

Formal Debate: Is it a Fair Fraction?

Show images of shapes divided into unequal parts (e.g., a triangle split down the middle vs. a triangle with a small slice off the top). Students must vote on whether the shape shows 'halves' and defend their choice based on the 'equal parts' rule.

Explain why it is essential that the parts of a fraction are equal in size.

Facilitation Tip

During 'Structured Debate: Is it a Fair Fraction?', position students to physically hold or point to the 'whole' object when making claims about fairness.

What to look for

Provide students with two different-sized rectangles, each divided into four equal parts. Ask them to shade 1/4 of each rectangle and write one sentence explaining why the shaded amounts are different, even though the fraction is the same.

• Analyze
• Evaluate
• Create
• Self-Management
• Decision-Making

Activity 02

• Inquiry Circle
• 30 min · Small Groups

Inquiry Circle: The Changing Whole

Give each group a different 'whole' (a 10cm string, a 30cm string, a 1m string). Ask them to find 'half' of their string. They then line up their 'halves' at the front to see how the same fraction can represent different lengths.

Analyze how the same fraction can represent different actual sizes depending on the whole.

Facilitation Tip

For 'Collaborative Investigation: The Changing Whole,' assign small groups different-sized paper cutouts to ensure varied whole examples are explored simultaneously.

What to look for

Present students with images of objects divided into unequal parts (e.g., a pizza cut into very different slice sizes). Ask: 'Can we call one of these slices 1/8 of the pizza? Why or why not? What needs to be true about the slices for us to use fractions?'

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Activity 03

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: Fraction Creators

Students rotate through stations where they create fractions using different 'wholes': a set of 12 counters, a square piece of paper, and a volume of water in a measuring cup.

Differentiate what the denominator tells us about how the whole was divided.

Facilitation Tip

In 'Station Rotation: Fraction Creators,' rotate materials so students repeatedly experience how dividing the same whole differently affects the fraction size.

What to look for

Show students a collection of objects (e.g., 12 marbles). Ask them to identify the 'whole'. Then, ask them to divide the whole into 3 equal groups and state what fraction each group represents (1/3). Repeat with a different number of objects and a different number of groups.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Teach this topic by starting with concrete, familiar objects students can hold and compare. Avoid introducing fraction notation until students demonstrate comfort with partitioning wholes into equal parts. Use frequent questioning to push students to articulate their reasoning, such as 'How do you know these parts are equal?' or 'What would happen if we changed the size of the whole?' Research shows that students who verbalize their understanding during hands-on tasks retain concepts longer.

Successful learning looks like students confidently identifying and justifying the 'whole' in various contexts, dividing wholes into equal parts without prompting, and explaining why equivalent fractions can represent different-sized amounts. They should actively challenge incorrect assumptions during discussions.

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Watch Out for These Misconceptions

• During 'Structured Debate: Is it a Fair Fraction?', watch for students accepting unequal parts as valid fractions.

  Redirect by asking the group to 'fair share' the shape using counters or drawings, emphasizing that fairness requires equal parts before moving to fractions.

• During 'Collaborative Investigation: The Changing Whole,' watch for students believing 1/2 is always the same size.

  Have students physically compare 1/2 of a small paper square to 1/2 of a large sheet of paper, then ask them to explain why the shaded areas differ in size.

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Methods used in this brief

• Formal Debate
• Inquiry Circle
• Stations Rotation