Non-Unit Fractions of a WholeActivities & Teaching Strategies
Active learning helps Year 2 pupils grasp non-unit fractions because they see how multiple equal parts combine to form a whole. By handling shapes, folding paper, and sharing food, children move from abstract symbols to concrete understanding.
Learning Objectives
- 1Identify the numerator and denominator in given non-unit fractions.
- 2Represent non-unit fractions, such as 2/3 and 3/4, using pictorial models.
- 3Compare unit fractions to non-unit fractions, explaining the difference in terms of the number of parts.
- 4Construct a whole object divided into equal parts, then shade a specified non-unit fraction of it.
- 5Analyze how many unit fractions are combined to form a given non-unit fraction.
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Manipulative Modelling: Fraction Shapes
Provide interlocking cubes or fraction tiles divided into thirds and quarters. Pupils build rectangles showing 2/3 or 3/4 shaded or assembled. Partners compare models and explain compositions using unit fractions. Record findings on mini-whiteboards.
Prepare & details
Explain how a non-unit fraction is different from a unit fraction.
Facilitation Tip: During Fraction Shapes, circulate to ensure children use the same-size whole for accurate comparisons when stacking transparencies.
Setup: Flexible workspace with access to materials and technology
Materials: Project brief with driving question, Planning template and timeline, Rubric with milestones, Presentation materials
Paper Folding: Fraction Rectangles
Give A4 paper rectangles. Instruct pupils to fold into three or four equal parts, shade 2/3 or 3/4, then unfold to count units. Groups swap and critique each other's folds for equal parts. Discuss differences from unit fractions.
Prepare & details
Construct a model to show 2/3 of a rectangle.
Facilitation Tip: For Fraction Rectangles, model the first fold step-by-step to prevent uneven partitions that distort fraction sizes.
Setup: Flexible workspace with access to materials and technology
Materials: Project brief with driving question, Planning template and timeline, Rubric with milestones, Presentation materials
Sharing Circle: Food Fractions
Use paper plates as circles divided into 3 or 4. Pupils colour or cut 2/3 or 3/4 to represent fruit sharing. Whole class shares models, answering how many 1/4 make 3/4. Photograph for display.
Prepare & details
Analyze how many unit fractions are needed to make a given non-unit fraction.
Facilitation Tip: In Food Fractions, use real food items to reinforce the idea that fractions represent parts of a whole that can be shared fairly.
Setup: Flexible workspace with access to materials and technology
Materials: Project brief with driving question, Planning template and timeline, Rubric with milestones, Presentation materials
Stations Rotation: Fraction Builds
Set stations with geoboards, playdough, drawings, and counters. At each, create 2/3 or 3/4 of a shape. Rotate every 7 minutes, noting methods in journals. Debrief comparisons.
Prepare & details
Explain how a non-unit fraction is different from a unit fraction.
Setup: Tables/desks arranged in 4-6 distinct stations around room
Materials: Station instruction cards, Different materials per station, Rotation timer
Teaching This Topic
Start with concrete manipulatives to build visual understanding before moving to pictorial representations. Avoid rushing to abstract symbols without solid grounding in equal partitioning. Research shows that hands-on partitioning followed by verbal explanations deepens comprehension more than isolated shading tasks.
What to Expect
Children will correctly identify, represent, and explain non-unit fractions using models and drawings. They will articulate how multiple unit fractions combine to form a non-unit fraction and justify their reasoning to peers.
These activities are a starting point. A full mission is the experience.
- Complete facilitation script with teacher dialogue
- Printable student materials, ready for class
- Differentiation strategies for every learner
Watch Out for These Misconceptions
Common MisconceptionDuring Fraction Shapes, watch for pupils who assume a fraction with a larger numerator is always bigger, such as thinking 3/4 is smaller than 2/3 because 3 is greater than 2.
What to Teach Instead
Have children overlay same-size transparencies of both fractions and compare the shaded areas directly. Ask them to explain which fraction covers more of the whole and why the denominator matters.
Common MisconceptionDuring Paper Folding: Fraction Rectangles, watch for pupils who treat non-unit fractions as single pieces rather than combinations of unit fractions.
What to Teach Instead
Guide students to unfold their rectangles and count the unit fractions, such as two 1/3 pieces making 2/3. Ask them to rebuild the fraction while explaining how the parts combine.
Common MisconceptionDuring Sharing Circle: Food Fractions, watch for pupils who shade disconnected or uneven parts instead of continuous regions.
What to Teach Instead
Provide rulers for drawing equal divisions and prompt students to explain why the shaded area must be connected. Peer checks ensure continuous shading reflects the fraction’s value.
Assessment Ideas
After Fraction Shapes, present pre-drawn shapes divided into equal parts. Ask students to shade a specific non-unit fraction, for example, 'Shade 3/4 of the rectangle.' Observe if they correctly identify and shade the required number of parts.
During Station Rotation: Fraction Builds, show a picture of a shape divided into 6 equal parts with 4 shaded. Ask: 'How many equal parts is the whole shape divided into? How many parts are shaded? What non-unit fraction does this picture show?' Listen for correct use of numerator and denominator.
After Paper Folding: Fraction Rectangles, give each student a card with a non-unit fraction, such as 3/5. Ask them to fold a rectangle to represent this fraction and label the parts. Collect these to check their ability to model non-unit fractions accurately.
Extensions & Scaffolding
- Challenge: Ask students to create equivalent fractions using their folded rectangles, such as showing how 2/4 is the same as 1/2.
- Scaffolding: Provide pre-divided shapes for students to shade, reducing the cognitive load of partitioning.
- Deeper exploration: Introduce simple fraction addition by combining two non-unit fractions on the same whole, such as 1/3 + 2/3, to explore totals.
Key Vocabulary
| fraction | A number that represents a part of a whole or part of a set. It has a numerator and a denominator. |
| numerator | The top number in a fraction, showing how many equal parts are being considered. |
| denominator | The bottom number in a fraction, showing the total number of equal parts the whole is divided into. |
| non-unit fraction | A fraction where the numerator is greater than one, meaning more than one equal part of the whole is represented. |
| unit fraction | A fraction where the numerator is one, representing a single equal part of the whole. |
Suggested Methodologies
Planning templates for Mathematics
5E Model
The 5E Model structures lessons through five phases (Engage, Explore, Explain, Elaborate, and Evaluate), guiding students from curiosity to deep understanding through inquiry-based learning.
Unit PlannerMath Unit
Plan a multi-week math unit with conceptual coherence: from building number sense and procedural fluency to applying skills in context and developing mathematical reasoning across a connected sequence of lessons.
RubricMath Rubric
Build a math rubric that assesses problem-solving, mathematical reasoning, and communication alongside procedural accuracy, giving students feedback on how they think, not just whether they got the right answer.
More in Parts of the Whole
Equivalence and Fairness
Understanding that fractions must consist of equal parts of a whole.
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Halves and Quarters of Shapes
Identifying and shading halves and quarters of 2D shapes.
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Halves and Quarters of Quantities
Finding halves and quarters of small numbers and quantities of objects.
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Fraction Families: Thirds and Equivalence
Recognising, finding, naming and writing 1/3, 1/4, 2/4 and 3/4 of a length, shape, set of objects or quantity. Recognising the equivalence of 2/4 and 1/2.
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Unit Fractions of a Whole
Identifying and representing unit fractions (1/2, 1/3, 1/4) of a whole object.
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