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.

• Year 4
• Mathematics
• 3 activities
• 15 min–30 min

Learning Objectives

1. Identify and represent unit fractions and non-unit fractions using pictorial representations.
2. Compare and contrast unit fractions and non-unit fractions, providing examples of each.
3. Construct visual models for fractions greater than one and explain their meaning.
4. Classify fractions as proper, improper, or mixed numbers based on their value relative to one whole.

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.

Prepare & details

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?'.

Setup: Groups at tables with access to source materials

Materials: Source material collection, Inquiry cycle worksheet, Question generation protocol, Findings presentation template

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

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.

Prepare & details

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.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

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

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.

Prepare & details

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.

Setup: Wall space or tables arranged around room perimeter

Materials: Large paper/poster boards, Markers, Sticky notes for feedback

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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?'.

Common Misconception

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.

What to Teach Instead

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.

Assessment Ideas

Exit Ticket

After The Fraction Wall Challenge, provide students with a worksheet containing fractions such as 1/5, 3/4, 6/3, and 7/8. 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.

Quick Check

During Fraction Art, ask students to hold up their drawings and explain one equivalence they discovered. Listen for language like 'same size' or 'multiplied by 2'.

Discussion Prompt

After Is it Equal?, present the fraction 8/4 and ask, 'How can this fraction be greater than one whole? Can you draw a picture to show what 8/4 looks like? What is the difference between 8/4 and 1/4?'

Extensions & Scaffolding

• Challenge: Provide a set of three fractions (e.g., 3/6, 4/8, 5/10) and ask students to find two more equivalent fractions using scaling diagrams.
• Scaffolding: Give students fraction strips with labeled unit fractions (1/2, 1/3, 1/4) and ask them to build equivalent fractions step by step.
• Deeper: Ask students to create a 'fraction family tree' showing how fractions like 1/2 connect to 2/4, 3/6, and 4/8 through multiplication.

Key Vocabulary

Unit Fraction	A fraction where the numerator is 1, representing one equal part of a whole. Examples include 1/2, 1/4, 1/8.
Non-Unit Fraction	A fraction where the numerator is greater than 1, representing multiple equal parts of a whole. Examples include 2/3, 3/5, 5/4.
Numerator	The top number in a fraction, which indicates how many parts of the whole are being considered.
Denominator	The bottom number in a fraction, which indicates the total number of equal parts the whole is divided into.
Improper Fraction	A fraction where the numerator is greater than or equal to the denominator, meaning the value is one whole or more than one whole.