This post explores some ideas for reviewing concepts for TEKS A.7C.
determine the effects on the graph of the parent function f(x) = x^2 when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d
Staar Performance
On recent STAAR tests, here is how students across the state of Texas have performed.
2023 #38 - 30% full credit, 35% partial credit, 35% no credit
Active, Playful Learning
The activities shared in this post are designed to follow the six principles of Active, Playful Learning:
Active
Engaging
Meaningful
Social
Iterative
Joyful
These six principles, together with a clear learning goal, help students learn.
Students learn through active, engaged, meaningful, socially interactive, iterative and joyful experiences in the classroom and out. When we add a learning goal or engage in guided play we achieve Active Playful Learning.
In other words, math review doesn't have to be boring STAAR prep or mindless worksheets. Instead, students' learning is enhanced when playing with numeracy and algebraic concepts in a guided context. Who says math can't be fun? You can watch a video to learn more about Active, Playful learning here.
Activities
Here's a walkthrough of all the activities on this blog post.
Desmos Tic-Tac-Toe
Learning objective: Students will manipulate the parent function of f(x) = x^2 with various transformations using a graphing tool.
On your interactive white board, open a graph on Desmos.
Click Settings to change the boundaries of the axes.
Change the x-axis to 0 ≤ x ≤ 9 and change the step to 3.
Change the y-axis to -6 ≤ y ≤ 3 and change the step to 3.
This creates a large, 9 x 9 grid with darker lines on the 3 x 3 tic-tac-toe grid. The lines marking the tic-tac-toe grid can be drawn on the interactive white board to make them more visible.
Split the class into two teams to play tic-tac-toe. Each team marks a square with their sign (i.e., X or O) when they supply a quadratic function with the vertex in one of the 9 squares. Vertices on the darker lines are not completely in a square and do not count. Once a square has been claimed, any other functions graphed in that square are ignored.
Play until a team wins or the game ends in a draw.
Variations
Change the boundaries of the x-axis and the y-axis to focus on moving the child function to different quadrants.
Make each of the nine quadrants smaller to create tighter target areas.
Have one team submit functions that open upward and another team submit functions that open downward.
Place a time limit on each teams' submission.
Only allow one submission per team. If the submission does not work, that turn is forfeited.
Play Battleship instead of Tic-Tac-Toe. On graph paper, teams draw a game board with the same axes boundaries and select the location of five ships. Teams then graph functions to try and sink the other ships (integers only).
Transformation Hot Potato
Learning objective: Students will recognize the changes on the parent function of f(x) = x^2 by various transformations.
Use floor tiles, chart paper, or butcher paper to mark a large 4-quadrant grid with the boundaries -5 <= x <= 5 and -5 <= y <= 5.
Print up game cards and place the parabola facing up on the origin.
Shuffle the game cards and split them evenly among four teams, each assigned to one quadrant.
One at a time, teams flip over a game card and move the parabola's vertex based on the transformation noted. Discard each game card after use.
The parabola cannot be moved off the coordinate grid. Cards that would move it outside of the boundaries result in a lost turn.
Play until the cards run out. The purpose of the game is to NOT have the vertex's parabola in your quadrant when the cards run out.
For the cards with an *asterisk, describing the transformation allows the team to move the parabola.
Variations
Instead of pulling cards that are flipped over, let teams look at and select the cards to play.
Instead of ending the game when the cards have been played once, set a timer. When each card is used once, shuffle all cards back together and redistribute. Play continues until the timer goes off.
Give teams the option of playing two cards at once. Teams that choose this option would then miss their next turn.
Have a student represent the function and stand on the point representing the parabola's vertex. Teams direct the student to move based on the card and the other team checks using the answer key.
Place hot spots on the coordinate grid. If the vertex lands on that coordinate, the team that moved the vertex there automatically wins (or gets to move the parabola again up to four spaces in any direction).
Flip the equations and descriptions. Create game cards that describe the movements of the parabola and students can only move it if they write the correct equation (e.g., Card says Move vertex 1 unit to the right so students would have to write on a whiteboard g(x) = f(x - 1) ).
Transformation Two-step
Learning objective: Students will physically represent the parent function of f(x) = x^2 and its various transformations.
Use the game cards from Transformation Hot Potato or create a set of similar equations.
Have students stand in a large, open area (e.g., gym, hallway, cafeteria, outdoors) lined up in columns and rows.
Show an equation from a game card and have students move in the indicated direction (e.g., forward for transformations up, backward for transformations down).
For transformations that do not move: Reflection over the x-axis (e.g., y = -(x)^2), students turn around 180°; Stretching (e.g., y = 1/2x^2), students spread out arms and legs, making an X shape; Narrowing (e.g., y = 2x^2), put arms and feet together, standing stiff as a board.
Variations
After showing each equation, count down from 3 and have everyone move simultaneously.
Ask students that are confident to close their eyes and move, removing the visual confirmation of their peers.
Allow students to write their own equations and share them, checking to be sure that their classmates are correct.
Place a spot on the floor/ground under one of the students. Make that a spot to avoid or a spot to try to stand on as a result of the transformations.
If your classroom desks are in an array, play this while seated. Students move desks according to the transformation. Once at the end of a column or row, the student wraps around to the other side.
Go Fish!
Learning objective: Students will match the effect of transformations on a parent function with a graph, an equation, and a verbal description.
Use the game cards from Go Fish! or create a set of similar cards using Desmos. Play in pairs or groups of three. Keep an extra copy of the game cards for an answer key.
Each student starts with five cards in their hand. The remaining cards make up the fishing pile.
The goal is to match a graph (red), an equation (yellow), and a description (blue) to make a book. When players make a book, they place all three matching cards in front of them.
Play begins with player one asking for a graph, equation, or description that matches one of theirs from another player. If that player does not have a card that matches, the original player draws a card from the fishing pile.
When the fishing pile is empty, players that do not get a match do not draw a new card. Play ends when all the books have been made.
The student with the most books wins.
Variations
For added challenge, do not allow students to show their cards when asking for a pair. Instead, have them describe what they see. For example, "The graph is flipped over pointing down. It's moved up 4 units but not to the left or the right. Also, it looks skinnier or narrower."
Using the game cards from Go Fish!, students can instead play memory match.
For a focus on just two representations, remove from the deck all the graphs (red cards), equations (yellow cards), or verbal descriptions (blue cards). Students will then make pairs instead of books of three.
Make a copy of the game cards as a template and allow students to add their own game cards using Desmos. For the purpose of the visuals, set the x-axis to -6.5<= x<=6.5 with a step of 1 and minor gridlines unchecked. Do the same for the y-axis.
Have page 7 of the game cards available as a scaffold for students (as needed).
Print out multiple sets of game cards (note them on the back with different numbers or symbols to separate them later). Have students or pairs of students race to match them up, making 12 complete books.
Desmos Sliders
Learning objective: Students will manipulate transformations on a parent function with a graphing tool.
Have students work individually or in pairs on Desmos while you demonstrate on the interactive whiteboard.
Choose one of the transformations to work on (e.g., vertical shifts) and have students enter that equation into Desmos (e.g., y = x^2 + d). Be sure that students click "Add slider" when it appears.
Give students a transformation and have them match that by manipulating the slider (e.g., Move the vertex 5 units down).
Check students' work or have them share their screen to the interactive whiteboard.
Repeat with other transformations and sliders: y = ax^2; y = (x - c)^2; y = (bx)^2.
Variations
Have students keep a graph of y = x^2 on the graph and manipulate a slider in a second graph (e.g., y = x^2 + d) for a visual reference.
Call out the new equation (e.g., y = x^2 - 4) and have students match that with their graph and then answer aloud with a verbal description (e.g., move the vertex four units down).
Work with two transformational sliders at once (e.g., y = (x - b)^2 + d) to manipulate the vertex in multiple directions.
Allow students to lead the class, taking over the teacher computer and calling out transformations for their class to match. Have the screen off while the new "teacher" sets up the transformation and then turn it on for the class to check their work.
Have students manipulate a and b in y = a(bx)^2. Note what happens to the graph when a < 0 and b < 0 and explain the difference. Ask students why b on its own can never reflect the graph over the x-axis.
For an additional challenge, work with all four sliders at one time (e.g., y = a(bx - c)^2 + d).
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