Fractions in Sets

Overview

In this lesson, students will develop an understanding of fractions as parts of a set. They will use physical counters to create and identify fractions, then represent these fractions both symbolically and pictorially. This hands-on approach aligns with the British Columbia Mathematics Curriculum’s focus on developing number sense and understanding parts of a whole in varied contexts.

Curriculum Alignment

Grade: 3
Subject: Mathematics
Big Idea: Numbers are represented in many ways and can be compared and ordered.
Curricular Competencies:

Reasoning and analysing: Use reasoning to explore and make connections.
Communicating and representing: Express mathematical ideas in concrete, pictorial, and symbolic forms.
Applying and innovating: Apply newly acquired understandings to solve problems.

Content:

Represent and describe fractions in various contexts, particularly as parts of a whole and parts of a set.
Use models, pictures, and symbols to represent fractions.

Learning Standards:

Demonstrate an understanding of fractions using objects and pictorial representations as parts of a set.
Identify and show fractions by partitioning a set of objects into equal groups and describing the fraction represented.

Learning Objectives

By the end of this 40-minute lesson, students will be able to:

Explain what a fraction is in the context of a set of objects.
Create fractions using counters to form parts of a total set.
Represent fractions orally, symbolically (e.g., 3/8), and pictorially (e.g., drawing parts of the set coloured).
Describe the numerator and denominator in relation to the parts of the set.

Materials Needed

Counters (e.g., coloured discs, cubes) – minimum 20 per student or group
Whiteboards and dry-erase markers
Fraction recording sheets with set outlines (for pictorial recording)
Visual fraction charts showing different fractions as parts of sets
Large poster with vocabulary: numerator, denominator, fraction bar
Sticky notes or small cards with fraction symbols for matching activity

Lesson Breakdown

1. Introduction (5 minutes)

Engage: Begin with a question: "If I have 10 counters and 4 are red, what fraction shows the red counters?"
Review vocabulary: numerator (number of parts chosen), denominator (total number of parts in the set), fraction bar.
Show physical set of counters and write the fraction on the board (e.g., 4/10).

2. Hands-on Activity: Creating Fractions (15 minutes)

Organise students into pairs or small groups (max 2-3 per group).
Each group receives 20 counters.
Teacher calls out a fraction (e.g., 3/10, 5/8, 7/20). Students must physically separate the counters to represent this fraction as a part of the total set.
Students explain orally what they created – "I have 5 counters in one colour and 15 in another. So 5/20 are red."
Circulate to support correct grouping and to prompt deeper understanding.
Encourage students to write the fraction next to their counters and draw it pictorially on their recording sheets.

3. Symbolic and Pictorial Representation (10 minutes)

Using whiteboards, students draw a set of objects (circles or squares).
Colour the part representing the fraction they just formed. For example, if they have 7 red counters out of 20, they colour 7 circles and leave 13 uncoloured.
Label their drawings with fraction symbols (e.g., 7/20).
Encourage students to pair-share their drawings, explaining the numerator and denominator.

4. Fraction Matching Game (5 minutes)

Hand out cards with fraction symbols and pictures representing fractions as parts of a set.
Students work in pairs to match fraction symbols to pictorial representations (on cards or the whiteboard).
This reinforces fraction recognition and symbolic understanding.

5. Wrap-Up and Reflection (5 minutes)

Conduct a whole-class discussion with questions like:
- “Can someone explain what the numerator tells us?”
- “Why is it important that all parts in the set are counted?”
- “How does drawing the fractions help us understand them better?”
Ask students to share one thing they learned about fractions today.
Collect fraction recording sheets for assessment.

Assessment Strategies

Formative: Teacher observation during hands-on activities to identify misconceptions (e.g., unequal parts, incorrect fractions).
Student Explanation: Listening to students’ oral explanations during pair-share and class discussion to assess understanding.
Work Samples: Review pictorial and symbolic fractions on recording sheets for accuracy and proper representation of fractions as parts of sets.
Exit Ticket (optional): One question for students to complete on whiteboards: “Draw a set of 12 objects and colour 1/4 of them. Write the fraction.”

Differentiation Strategies

Support: For students requiring additional help, use smaller sets of counters (e.g., 8 instead of 20) for simpler fractions. Provide one-on-one modelling and visual fraction charts.
Extension: Challenge advanced students to create and compare fractions with different denominators or combine parts of sets to form new fractions.

Teacher Reflection Prompts

How well did students grasp the concept of fractions as parts of sets?
Were students able to connect physical counters with symbolic and pictorial fractions?
Did group work encourage mathematical communication and reasoning?
What adaptations might improve engagement or clarity in future lessons?

This lesson offers a multisensory, engaging experience grounded in British Columbia’s curriculum to support solid foundations in understanding fractions in meaningful, collaborative ways.

Teaching Instructions