Grade 8 Mathematics – 60-Minute Session

Class Size: 20 students
Standards:

• CCSS.MATH.CONTENT.8.EE.C.7: Solve linear equations in one variable.
• CCSS.MATH.CONTENT.8.F.A.1: Understand that a function is a rule that assigns to each input exactly one output.
• CCSS.MATH.CONTENT.8.F.A.2: Compare properties of two functions represented in different ways.
• CCSS.MATH.PRACTICE.MP1: Make sense of problems and persevere in solving them.
• CCSS.MATH.PRACTICE.MP3: Construct viable arguments and critique the reasoning of others.
• CCSS.MATH.PRACTICE.MP7: Look for and make use of structure.

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Learning Objectives

By the end of this lesson, 8th-grade students will be able to:

• Conceptually understand linear relationships through contextual problem-solving using tables, manipulatives, and graphs.
• Represent linear relationships concretely, pictorially, and abstractly with equations.
• Use multiple strategies to interpret and justify linear patterns and equations.
• Engage in mathematical discourse by explaining, questioning, and justifying their reasoning.

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Lesson Overview

This lesson uses the Concrete–Representational–Abstract (CRA) model with a focus on student discourse and productive struggle. The starting point is a contextual problem where students explore data and manipulatives to understand linear patterns without direct teacher instruction. Students will collaboratively build from concrete experiences to symbols and equations, making connections visible at every step.

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Materials Needed

• Counters or linking cubes (manipulatives)
• Graph paper or whiteboards with graph grids
• Chart paper or large poster paper
• Markers or colored pencils
• Printed tables showing data from the problem context (partially filled)
• Student notebooks/journals for recording thinking

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Lesson Procedure

1. Engage & Explore (15 minutes) – Concrete Phase

Contextual Problem:
"A local farmer sells baskets of strawberries. On the first day, she sells 3 baskets. Each day afterward, she sells 2 more baskets than the day before. How many baskets does she sell after several days?"

• Activity:

  • Provide students with counters (or linking cubes) and ask them to model the number of baskets sold each day physically.
  • Distribute a partially filled table showing “Day 1 = 3 baskets”, and ask students to fill in the baskets for Days 2, 3, 4, and 5 by adding counters.
  • Guiding questions:
    • What is happening to the number of baskets each day?
    • Can you predict how many baskets will be sold on Day 6? How?
    • How does your model help you see this pattern?

• Teacher Role:

  • Circulate actively, asking open-ended questions.
  • Encourage students to explain their reasoning to peers.
  • Avoid giving direct instructions; instead, support them in making sense of the pattern through exploration.

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2. Represent & Reason (20 minutes) – Representational Phase

• Visual Model: Using graph paper or whiteboards, students plot the points for days vs. baskets sold based on their completed table.

• Discussion Prompts:

  • How does the graph relate to your physical model?
  • What do the points tell you about how the baskets sold change each day?
  • Can you connect the pattern in your table to this graph?
  • Does the graph show a linear pattern? Why or why not?

• Collaborative Task:

  • In pairs, students sketch the graph and describe it to their partner using mathematical language (e.g., constant rate of change, increase, linear trend).
  • Students share different strategies they used to make predictions (adding, skip counting, looking at differences).

• Teacher Role:

  • Facilitate small group conversations.
  • Highlight multiple methods students use to understand the linear relationship.
  • Encourage productive struggle by probing deeper if students reach quick solutions.

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3. Abstract & Apply (20 minutes) – Abstract Phase

• Transition to Equation:

  • Guide students, through questioning, towards writing an equation that represents the situation without direct instruction. For example:
    • What mathematical rule can describe the number of baskets sold on Day d?
    • How can you write this rule as an equation?
  • Encourage students to justify why their equation fits the table and graph they constructed.

• Example exploration:

  • Some students may come up with: Baskets = 3 + 2 × (Day – 1)
  • Others may suggest: Baskets = 2d + 1 (and discuss why this might or might not fit).

• Class Discussion:

  • Compare and analyze different equations students propose.
  • The teacher leads a discourse on which equations correctly represent the pattern and why, using student-generated data and graphs.

• Extension Challenge (optional):

  • Ask students how the equation and graph would change if the farmer started with 5 baskets and increased the daily sales by 4. What parts of the equation would change?

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4. Closure & Formative Assessment (5 minutes)

• Exit Ticket Prompt:

  • Write a brief explanation for how the equation models the number of baskets sold each day. Include a description connecting the table, graph, and equation.
  • Optional: Suggest one other way to check if your equation matches your data.

• Teacher collects exit tickets to assess conceptual understanding and ability to connect representations.

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Differentiation & Supports

• For struggling learners:
  • Use more concrete manipulatives with additional guided questions.
  • Pair with stronger peer(s) for discourse support.
• For advanced learners:
  • Encourage exploration of non-linear functions or discuss slope and y-intercept terminology.
  • Challenge them with writing a general function notation for the problem.

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Reflection & Next Steps

After this lesson, students will have constructed a deep conceptual understanding of linear relationships and how multiple representations—concrete, graphical, and symbolic—interconnect. This lays a crucial foundation for solving more complex equations and understanding functions in Grade 8 and beyond.

Future lessons can build upon this by exploring linear inequalities, systems of equations, or real-world modeling of functions.

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Teacher Tips

• Encourage rich classroom talk and listen carefully to student thinking; record some explanations on chart paper for reference.
• Emphasize that multiple solution paths are valuable; highlight diverse reasoning.
• Celebrate productive struggle as key to deep understanding.
• Use wait time after questions to foster reflection and discussion.

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This lesson plan exemplifies best practices with a balance of conceptual understanding, active student engagement, and rigorous alignment to the CCSSMath standards, all delivered through Open Up Resources' pedagogical approach infused with the CRA model.