Linear Fraction Models

Overview

Students will explore fractions by representing them on number lines. They will construct personal number lines and place various fractions accurately, deepening their understanding of the spatial relationship between fractions and whole numbers. This hands-on activity aligns with the British Columbia Mathematics Curriculum for Grade 3.

---

Curriculum Alignment

Content: Number - Fractions and Decimals

• Big Idea: Fractions represent parts of a whole and can be represented in various ways such as through number lines.
• Curricular Competencies:
  • Reasoning and analysing: Develop mental math strategies and visual representations to make sense of numbers and fractions.
  • Communicating and representing: Use mathematical vocabulary and models to explain thinking on fractions.
  • Connecting and reflecting: Represent and compare fractions using visual fraction models and number lines.

Learning Standards:

• Number
  • Use concrete materials, visuals, and symbolic representation to represent fractions (e.g., number lines).
  • Model and explain equivalent fractions and their placement between whole numbers.

---

Learning Objectives

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

• Construct a number line divided into fractional parts between 0 and 1 (e.g., halves, quarters, thirds).
• Accurately locate and place fractions (like 1/2, 3/4, 2/3) on their number lines.
• Verbally explain and reason about the relative size of fractions compared to whole numbers and each other.
• Reflect on how number lines help visualise fractions and their relationships.

---

Materials Needed

• Rulers or strips of paper (for drawing number lines)
• Whiteboards or paper for each student
• Markers or pencils
• Fraction cards (with fractions such as 1/2, 1/3, 2/3, 3/4, 5/4)
• Large classroom whiteboard or chart paper
• Sticky notes or small stickers for fraction placement

---

Lesson Structure

1. Introduction (5 minutes)

• Begin by asking students what they remember about fractions from previous lessons.
• Briefly introduce today’s focus: "We will use number lines to show where fractions fall between whole numbers."
• Display a large number line (from 0 to 1) on the board and show how 1/2 is placed in the middle.

2. Guided Practice (10 minutes)

• As a class, draw a number line from 0 to 1 on the board, partitioned into halves, then quarters.
• Ask volunteers to come up and point to certain fractions (e.g., 1/4, 1/2, 3/4).
• Discuss how some fractions are closer to 0, some closer to 1, and why.
• Demonstrate adding fractions greater than one (e.g., 5/4 will be placed between 1 and 2).

3. Main Activity - Create Your Own Number Line (15 minutes)

• Distribute rulers or paper strips. Guide students to draw a number line from 0 to 2, marking whole numbers clearly.
• Assist them in dividing the segments between 0-1 and 1-2 into fractions appropriate for the lesson (halves, thirds, quarters).
• Hand out fraction cards; students will place each fraction on their number lines using pencil or stickers.
• Encourage paired discussion: "Which fraction is bigger? How do you know from your number line?"

4. Reflection and Discussion (7 minutes)

• Ask students to share one fraction placement and explain their reasoning aloud.
• Discuss how number lines can help us understand fractions better than just looking at numbers alone.
• Highlight equivalent fractions on the board and discuss why they occupy the same position.

5. Assessment and Closing (3 minutes)

• Use a quick exit card: Each student writes down one fraction and draws its approximate position on a mini number line (0 to 1) on their whiteboard or paper.
• Collect for a brief formative check.
• Summarise the lesson: "Number lines help us see where fractions belong and how they relate to whole numbers."

---

Differentiation & Extensions

• Support: Provide printed pre-drawn number lines for students who need more guidance with segmenting the line.
• Extension: Challenge advanced learners to place improper fractions (e.g., 7/4) and explain their positions.
• Use real-world connections: Relate fractions on number lines to measuring length using rulers and tape measures.

---

Teacher Reflection

• Were students able to accurately place fractions on number lines?
• Did they verbalise their understanding of fraction size and equivalencies?
• Were number lines effective tools for visualising fractions across the class?
• How might this activity be adapted for virtual or hybrid learning settings?

---

By connecting fractions with linear spatial models, students gain a foundation for future concepts such as decimal fractions and measurement, sustainably building their number sense in a concrete and engaging way consistent with B.C.’s mathematics framework.