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Day 16 – What Does “Changes Faster” Mean?

I Can...

• I can compare two functions and explain which one changes faster.

Success Criteria

• I can describe rate of change in my own words.
• I can identify which function changes faster using simple data.
• I can explain my thinking using a complete sentence.

Standards Addressed

• 8.M.F.A.3: Analyze and compare properties of two functions each represented in different ways.
• 8.EE.B.5–6: Understand the concept of rate of change; interpret it from data.

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Anticipatory Set (2 minutes)

• Show on board:
  • Person A walks 1 mile in 10 minutes.
  • Person B walks 1 mile in 20 minutes.
• Ask: Who is faster? How do you know?

I DO (5 minutes)

• Define rate of change as "how much y changes when x increases by 1."
• Show two simple function tables side-by-side.
• Think aloud as you compare the changes step-by-step.
• Highlight the rate of change in each.

WE DO (6 minutes)

• Kagan Rally Coach:
  • Partner A explains steps to compare functions.
  • Partner B coaches and gives feedback.
• Post step-by-step instructions visually on the board:
  1. Look at increase in y-values.
  2. Check how much x increases.
  3. Calculate and compare the changes.

YOU DO (4 minutes)

• Students circle the function that changes faster in given tables.
• Use sentence frame:
  “Function ___ changes faster because ___.”

Check for Understanding (CFU)

• Thumbs up/down for confidence.
• Cold call supported by sentence frames.
• Choice-based questions: Which function changed faster? Why?

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Differentiation Strategies

• Supports: Use color coding for rate of change increments.
• Dyslexia-Friendly: Use sans-serif font, increased spacing, and color highlights for key terms (rate, function).
• Advanced: Challenge students to write their own functions describing a real-life scenario with different rates.

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Day 17 – Comparing Functions in Tables

I Can...

• I can analyze tables to compare how two functions change.

Success Criteria

• I can identify changes in y related to x.
• I can confidently say which function is faster, slower, or same rate.

Standards Addressed

• 8.M.F.A.3
• 8.EE.B.5

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Anticipatory Set (2 minutes)

• Ask: What happens to y when x goes up by 1?

I DO (5 minutes)

• Display two function tables.
• Use a highlighter to mark constant increases in y-values.
• Talk students through recognizing the rate of change from tables.

WE DO (6 minutes)

• Kagan Timed Pair Share:
  • Each student explains to partner how to find rate of change.
  • Switch roles after 1 minute.

YOU DO (5 minutes)

• Students compare two new tables.
• Decide if function is faster, slower, or same rate.
• Write answer using sentence frames.

CFU

• Randomly select pairs to share their decisions.
• Prompt rest of class to agree, disagree, or elaborate.

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Differentiation Strategies

• Use visual number lines to show increments of x and y.
• Provide simplified tables with fewer rows for those who need it.
• Encourage advanced learners to create their own tables for peers.

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Day 18 – Comparing Functions on Graphs

I Can...

• I can compare the steepness of graphs and explain which function changes faster.

Success Criteria

• I can identify and describe slope visually.
• I can use the word "steeper" correctly.

Standards Addressed

• 8.M.F.A.3
• 8.EE.B.6

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Anticipatory Set (2 minutes)

• Show two graphs of lines.
• Ask: Which line is steeper? How do you know?

I DO (5 minutes)

• Define slope as “how steep a line is.”
• Trace the slope with finger or ruler to demonstrate.
• Explain why steeper lines mean faster change.

WE DO (6 minutes)

• Kagan Stand Up–Hand Up–Pair Up:
  • Students find a partner and discuss which line is steeper and why.
  • Share out in 2–3 pairs.

YOU DO (5 minutes)

• Circle the steeper line on a new set of graphs.
• Write a one-sentence explanation using sentence frames like:
  “Line ___ changes faster because it is steeper.”

CFU

• Hand signals: thumbs up if confident, sideways if unsure.
• Cold call for explanation.

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Differentiation Strategies

• Visual Learners: Use colored overlays to highlight slopes.
• Kinesthetic: Allow students to use physical rulers or cardboard cutouts to measure slopes.
• Dyslexia-Friendly: Diagrams with color coding, simplified text descriptions.

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Day 19 – Comparing Tables, Graphs, & Equations

I Can...

• I can match tables, graphs, and equations and explain which function changes faster.

Success Criteria

• I can find rate of change (slope) from an equation.
• I can identify which representations show the faster function.

Standards Addressed

• 8.M.F.A.3
• 8.EE.B.6

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Anticipatory Set (2 minutes)

• Show a table and an equation.
• Ask: Do these represent the same function? Do they grow the same?

I DO (5 minutes)

• Model how to find rate of change (m) from equation y = mx + b.
• Compare with the rate of change from the table.

WE DO (6 minutes)

• Kagan Mix–Pair–Share:
  • Students mix and find a partner.
  • Share which representation changes faster and explain why.
  • Rotate to new partners twice.

YOU DO (5 minutes)

• Match given tables to graphs and equations in a sorting activity.
• Identify which function changes faster using sentence frames.

CFU

• Quick oral explanations.
• Peer check with prompting questions.

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Differentiation Strategies

• Provide formulas with color-coded parts for dyslexic learners.
• Visual matching cards to aid comprehension.
• Advanced learners create their own examples relating all three representations.

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Day 20 – Review & Check

I Can...

• I can review how to compare functions and explain which changes faster.

Success Criteria

• I can use all three representations (table, graph, equation) to compare functions.
• I can confidently explain my reasoning orally and in writing.

Standards Addressed

• 8.M.F.A.3
• 8.EE.B.5–6

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Anticipatory Set (2 minutes)

• Show quick real-world examples on slides:
  • Car A speeds up faster than Car B.
  • Tree grows slower than cactus.
• Ask: Fast or Slow?

WE DO (10 minutes)

• Kagan Quiz–Quiz–Trade:
  • Each student gets a card with a function table, graph, or equation.
  • Quiz a partner on which is faster or slower.
  • Trade cards and move to next partner.

YOU DO (6 minutes)

• Complete a quick 2-question skill check worksheet:
  1. Circle the faster function.
  2. Explain your answer orally using sentence frames like:
     “Function ___ changes faster because ___.”

CFU

• Celebrate thumbs up.
• Teacher records responses for assessment.

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Differentiation Strategies

• Provide sentence stems for all explanations.
• Allow oral response for learners who struggle with writing.
• Offer extension: Write a short paragraph summarizing differences in rates across representations with real-life examples.

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Additional Tips for Teachers

• Use consistent color codes throughout these lessons to indicate rate of change.
• Keep all resources dyslexia-friendly by using clear fonts (e.g., OpenDyslexic or Arial), spaced layouts, and minimal text per slide.
• Engage students with physical movement (Kagan structures) to boost retention and collaboration.
• Encourage use of mathematical vocabulary every day; display a “rate of change” word wall.
• Rotate pairings often to build confidence and peer support.

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This five-day progression follows exactly Common Core 8th grade Mathematics standards for comparing functions (8.M.F.A.3) and understanding rate of change (8.EE.B.5–6). It scaffolds learning from conceptual understanding to representation fluency, using active classroom structures and accessible language to maximize student confidence and success.