Mathematics · Year 4

Active learning ideas

Understanding Unit and Non-Unit Fractions

Active learning helps students grasp equivalence in fractions because they see how fractions relate to each other through visual and hands-on comparison. Diagrams and physical tools make abstract ideas concrete, which is especially important when students are still forming mental models of fractions.

• National Curriculum Attainment Targets
• NC.MA.4.F.1

• 15–30 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Inquiry Circle
• 30 min · Small Groups

Inquiry Circle: The Fraction Wall Challenge

Give groups a blank fraction wall. They must use strips of paper to find as many ways as possible to 'match' the length of 1/2 or 1/3. They then record their findings (e.g., 1/2 = 2/4 = 4/8) and look for a mathematical pattern in the numbers.

Differentiate between a unit fraction and a non-unit fraction with examples.

Facilitation Tip

During The Fraction Wall Challenge, circulate and ask guiding questions like, 'How do the strips show that 1/2 and 2/4 are the same size?'.

What to look for

Provide students with a worksheet containing several fractions (e.g., 1/3, 5/6, 7/4, 2/2). Ask them to circle the unit fractions, put a square around the non-unit fractions, and write 'greater than one' next to any improper fractions that represent more than one whole.

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

Activity 02

• Think-Pair-Share
• 15 min · Pairs

Think-Pair-Share: Is it Equal?

Show pairs two different shaded shapes (e.g., a circle with 2/4 shaded and a square with 4/8 shaded). Students must discuss whether they represent the same amount and how they could 'prove' it to someone who doesn't believe them.

Construct a visual representation for 3/5 and explain its meaning.

Facilitation Tip

During Is it Equal?, pause pairs after 2 minutes to share one disagreement they had and how they resolved it.

What to look for

Draw a rectangle on the board and divide it into 5 equal parts. Shade 3 parts. Ask students to write the fraction represented and explain in one sentence whether it is a unit or non-unit fraction and why.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 03

• Gallery Walk
• 30 min · Whole Class

Gallery Walk: Fraction Art

Students create 'Equivalent Art' by shading different fractions of identical grids. They display their work, and others must walk around with sticky notes, writing the equivalent fractions they see in their classmates' designs.

Explain how a fraction like 7/4 can be greater than one whole.

Facilitation Tip

During Fraction Art, remind students to label each fraction clearly so others can easily compare their work.

What to look for

Present the fraction 7/4. Ask students: 'How can this fraction be greater than one whole? Can you draw a picture to show what 7/4 looks like? What is the difference between 7/4 and 1/4?'

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

A few notes on teaching this unit

Start with physical models like fraction strips or paper folding to build intuition about equivalence before moving to diagrams. Avoid rushing to algorithms; let students discover the multiplicative relationship through repeated comparison. Research shows that students who draw their own diagrams understand equivalence better than those who only look at pre-made ones.

Successful learning looks like students confidently identifying unit and non-unit fractions, explaining equivalence using diagrams, and correcting common misconceptions through peer discussion. They should move from guessing to justifying their reasoning with visual evidence.

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Watch Out for These Misconceptions

• During The Fraction Wall Challenge, watch for students who claim that 1/8 is larger than 1/4 because the denominator is bigger.

  Have students place the fraction strips side by side on the wall and physically compare the lengths. Ask, 'Which strip covers more space on the whole? How does the size change as the denominator gets larger?'.

• During Is it Equal?, watch for students who add the same number to both the numerator and denominator to create equivalence, like saying 1/2 equals 2/3.

  Use the scaling diagrams in this activity to show that equivalence requires multiplying both parts by the same factor. Draw arrows from 1/2 to 2/4 and label it 'x2', then ask students to try multiplying 1/2 by other factors to find more equivalents.

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Methods used in this brief

• Inquiry Circle
• Think-Pair-Share
• Gallery Walk