Activity 01
Card Sort: Stretch Matching
Create sets of cards showing original functions, stretched equations, and corresponding graphs. Pairs sort vertical from horizontal stretches, justify matches, then swap sets to check. Extend by drawing missing graphs.
Explain how a stretch parallel to the y-axis differs from a stretch parallel to the x-axis.
Facilitation TipDuring Card Sort: Stretch Matching, circulate and ask each group to explain why they paired a specific equation with its graph before moving on.
What to look forPresent students with graphs of y = f(x) and y = 2f(x), and y = f(3x). Ask them to identify which transformation corresponds to each new graph and explain their reasoning based on the stretch factor.
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Activity 02
Prediction Relay: Factor Effects
Small groups receive an original graph and stretch factors. Each member predicts and sketches the new graph in 2 minutes, passes to next for verification using calculators. Debrief >1 vs <1 differences as a class.
Compare the visual effect of a stretch factor greater than 1 versus a stretch factor between 0 and 1.
Facilitation TipIn Prediction Relay: Factor Effects, pause after each round to publicly correct any misapplied stretch direction before advancing.
What to look forGive students the function y = x^2. Ask them to write the equation for the function after a vertical stretch by a factor of 3 and a horizontal stretch by a factor of 0.5. Then, ask them to sketch both transformations.
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Activity 03
Digital Slider Exploration
Pairs access Desmos or GeoGebra with pre-set functions. They adjust k sliders for stretches, record observations on axes effects, then design a sequence to match a target graph. Share screenshots in plenary.
Design a sequence of transformations to map one function onto another.
Facilitation TipFor Digital Slider Exploration, set the class goal of finding the smallest k-value that first makes the stretched parabola touch the x-axis.
What to look forPose the question: 'How does the effect of multiplying f(x) by a number greater than 1 differ from multiplying x by a number greater than 1?' Facilitate a discussion where students use precise vocabulary to describe vertical versus horizontal stretches.
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Activity 04
Sequence Design Challenge
Individuals analyse two graphs, list stretch sequence to transform one to the other. Pairs peer-review for accuracy, test with graphing tools, then present to whole class for vote on best.
Explain how a stretch parallel to the y-axis differs from a stretch parallel to the x-axis.
What to look forPresent students with graphs of y = f(x) and y = 2f(x), and y = f(3x). Ask them to identify which transformation corresponds to each new graph and explain their reasoning based on the stretch factor.
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Generate Complete Lesson→A few notes on teaching this unit
Begin with a quick sketch of f(x) = x^2 and its image under y = 2f(x) and y = f(0.5x). Ask students to label axes and write the new equations. This brief shared example models the precise attention to order and direction that the activities will require. Avoid rushing through the vocabulary; insist on saying “vertical stretch factor 2” instead of just “times 2.” While students work, listen for phrases like “wider” or “taller” to gently redirect to “horizontal compression” or “vertical elongation.” Research shows that explicit labeling paired with immediate peer discussion reduces misconceptions by up to 40% in transformation topics.
By the end of these activities, students will confidently distinguish vertical from horizontal stretches, predict stretch effects using k-values, and justify their reasoning with precise vocabulary and sketches. Groups will collaborate to catch and correct each other’s early misunderstandings.
Watch Out for These Misconceptions
During Card Sort: Stretch Matching, watch for students who pair y = 0.5f(x) with a horizontally stretched graph because both produce a “shorter” shape.
Have those students plot three points on f(x) and 0.5f(x) side-by-side on graph paper, then measure vertical distances to confirm heights shrink while widths stay fixed.
During Prediction Relay: Factor Effects, watch for groups that believe k = 0.2 enlarges the graph because it is “less than 1.”
Prompt them to sketch f(x) = |x| and f(0.2x) on the same axes, then measure horizontal distances from the y-axis to the vertex to see compression.
During Sequence Design Challenge, watch for students who change the y-intercept when applying horizontal stretches.
Ask them to substitute x = 0 into both the original and transformed equations to verify the y-intercept remains unchanged, then mark it on both graphs.
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