Week 2: Tables & Graphs

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Vocabulary

Ratio | Proportion | Equivalent | Table | Graph | Unit rate | Scale

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Day 1: Identify Proportional Tables

Objective

I can identify proportional relationships using ratio tables.

Success Criteria

• I can explain what makes a table proportional.
• I can fill in missing values in a proportional table.
• I can tell if a table is proportional by checking if the same rule applies.

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Anticipatory Set (3 minutes)

Show an image of snack bags with prices.
Ask: “If 1 bag costs $2, how much for 2 bags? 3 bags?”
Together, build a simple ratio table on the board.

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Explicit Instruction (7 minutes)

I Do:

• Model a ratio table (e.g., 1 → 2, 2 → 4, 3 → 6)
• Say aloud: "Each output is multiplied by the same number as the input. This means the table is proportional."
• Display key rule poster:
  ✔ A table is proportional if the same multiplication factor applies across every row.

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Kagan Structure: Think-Pair-Share (5 minutes)

• Think: Is this given table proportional?
• Pair: Explain your reasoning to a partner.
• Share: Groups share one consensus answer aloud.

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Checks for Understanding

• Thumbs up/down after examples.
• Prompt: “Which row shows the multiplication factor?”
• Quick whiteboard response: ✔ proportional or ✖ not proportional.

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Exit Ticket (2 minutes)

Students circle: Proportional or Not proportional for a short table.

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Differentiation

• For struggling learners: Provide ratio tables with clear patterns and visual multiplication clues. Use color coding.
• For advanced learners: Ask students to create their own proportional tables and explain their rule.

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Dyslexia-Friendly Tips

• Use large, clear fonts with high contrast colors for tables.
• Read ratio numbers aloud and display visually alongside.
• Provide physical manipulatives (counters or blocks) to represent ratios concretely.

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Day 2: Find the Unit Rate

Objective

I can find the unit rate in a proportional table.

Success Criteria

• I can divide values to identify unit rate in a table.
• I can explain why the unit rate is constant in a proportional relationship.

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Anticipatory Set (3 minutes)

Scenario: “If 10 miles takes 2 hours, how far in 1 hour?”
Use a number strip or drawing to visually divide.

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Explicit Instruction (7 minutes)

I Do:

• Model dividing 10 ÷ 2 = 5 miles per hour.
• Explain: “The unit rate is the amount per 1 unit of the first quantity — always the same in proportional tables.”
• Visual anchor posted: Unit rate = Divide output by input.

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Kagan Structure: Rally Coach (5 minutes)

• Partner A solves a table’s unit rate.
• Partner B coaches, using this sentence frame:
  “First, divide ___ by ___, then ___.”

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Checks for Understanding

• Choral response: “Divide!” when asked how to find unit rate.
• Students point to unit rate value on sample tables.
• Provide color-coded small cards for correct/incorrect unit rates.

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Exit Ticket (2 minutes)

Circle the unit rate from a given ratio table.

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Differentiation

• Struggling learners: Provide step-by-step guided dividing with visual aids or calculators if needed.
• Advanced learners: Challenge with larger or decimal numbers; ask for real-world interpretation.

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Dyslexia-Friendly Tips

• Present division problems vertically and clearly spaced.
• Pair verbal explanation with written steps.
• Use audio support reading the instructions aloud.

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Day 3: Graphing Proportional Relationships

Objective

I can graph proportional relationships and identify straight-line patterns.

Success Criteria

• I can plot points from a ratio table accurately.
• I can recognize that proportional graphs pass through (0,0) and form straight lines.

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Anticipatory Set (3 minutes)

Show two graphs: one straight line through origin, one curved.
Ask: “Which shows a fair, steady proportional relationship?”

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Explicit Instruction (7 minutes)

I Do:

• Graph points from a sample table on graph paper.
• Highlight the line starts at (0,0).
• Emphasize: “Proportional graphs always go through zero because the relationship starts from nothing.”
• Point out the straight-line pattern.

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Kagan Structure: Quiz-Quiz-Trade (5 minutes)

• Each student receives a card with a graph image.
• Ask: “Does this graph show a proportional relationship? Why or why not?”
• Students quiz a partner, then trade cards, repeating with new partner.

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Checks for Understanding

• Fingers: 1 = yes, 2 = no for proportional graph question.
• Students circle the origin point on the graph.
• Quick thumbs up/down if line bends.

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Exit Ticket (2 minutes)

Circle: Proportional or Not Proportional for two graph images.

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Differentiation

• Supporting learners: Use graph paper with highlighted axes and points to plot.
• Advanced learners: Predict missing points or write equations for the lines.

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Dyslexia-Friendly Tips

• Use clear, bold gridlines and large points.
• Provide printed graph sheets with grids and labeled axes.
• Use tactile graphing boards if available.

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Day 4: Real-World Proportional Review

Objective

I can determine if real-world situations show proportional relationships.

Success Criteria

• I can sort word problems as proportional or not.
• I can explain reasoning using vocabulary words clearly.

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Anticipatory Set (3 minutes)

Use play money: “If 3 tickets cost $9, is the price fair every time? Why?”

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Explicit Instruction (7 minutes)

We Do:

• Sort together word problems into “Proportional” or “Not proportional” piles.
• Use sentence frame:
  “This is proportional because ___.”
  “This is not proportional because ___.”

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Kagan Structure: Stand-Up, Hand-Up, Pair-Up (5 minutes)

• Students stand and find a partner quickly.
• Use yes/no cards during discussion.
• Share their reasoning using vocabulary words.

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Checks for Understanding

• Show green/red cards for true/false statements.
• Teacher circulates to listen for correct vocabulary use.
• Provide immediate corrective feedback.

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Final Exit Ticket (2 minutes)

Match: Table → Graph → Word Problem demonstrating the same proportional relationship.

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Differentiation

• Supports: Provide sentence starters and example problem frames.
• Extensions: Create their own real-world examples showing proportional or non-proportional relationships with explanation.

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Dyslexia-Friendly Tips

• Chunk complex word problems into smaller parts.
• Use plain language and avoid unnecessary jargon.
• Provide read-aloud or audio recorded problems.

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Summary

This lesson sequence activates prior knowledge with clear visuals and student-centered discussions. Frequent interaction and Kagan cooperative learning structures build engagement and retention. Utilizing universal design — visual anchors, sentence frames, and tactile tools — supports all learners, including those with dyslexia. Extension tasks keep advanced students challenged and deepen conceptual understanding grounded in rigorous Common Core standards.

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Standards Covered

7.M.RP.A.2
Recognize and represent proportional relationships between quantities.

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Empower your students with confidence and clarity in proportional reasoning!