This post explores some ideas for reviewing concepts for TEKS 8.5I.
write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations
Staar Performance
On recent STAAR tests, here is how students across the state of Texas have performed.
2023 #20 - 36% correct
2023 #30 - 30% full credit, 33% partial credit, 36% 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.
Real-world Scenario Race
Learning objective: Students will write a function in the form y = mx + b from verbal descriptions.
Put students in pairs.
Give each pair a copy of the real-world scenarios from STAAR.
Pairs work together to complete as many as possible in a short time limit (e.g., 90 seconds).
After the time limit, quickly share the correct answers with the class and have students score their papers.
With the same partner, repeat the activity with a new set of problems and the same time limit. Teams are trying to beat their previous score.
Variations
Adjust the time limit for the skill level of your students.
Different groups can use timers on their phones to set varying time limits, based on the level of challenge they want to give themselves.
The problems can be recreated endlessly to repeat this activity in the future. Simply copy the text of a problem and paste it into at AI site (e.g., ChatGPT) and ask it to create another problem like that one.
Make this a weekly task and ask groups to graph their progress over time.
Linear Identification
Learning objective: Students will identify parts of a linear equation, create a table of values, and graph it.
Materials: Sticky notes
Pair students up.
Give each pair a linear equation to work with.
Students work together to identify the slope and y-intercept from the equation.
Using the equation, students generate a table of values and graph the coordinates.
Each pair then covers up the left side of their paper with a sticky note and swaps papers with another pair.
Students work to identify the slope and y-intercept of the new linear equation from the graph, writing them on a sticky note.
Variations
Instead of starting with a linear equation, start pairs with the slope and y-intercept (alternative version) and have students write the equation, table of values, and graph the equation.
If students struggle with identifying the slope and y-intercept from just the graph (after swapping), have the sticky notes only cover the top-left portion of the paper, leaving the graph and table of values visible.
In the blank space in the bottom-left portion of the paper, students can write a real-world scenario to match the equation.
Table Race
Learning objective: Students will write an equation from a table of values.
Put students into groups of three.
Either display or print out ten tables and the ten matching equations in random order. A sample set (with the correct equation written underneath) can be found here.
Have teams race to see which group can match the ten tables with the ten correct equations first.
Ask students to share their strategies for finding the matching equations.
Variations
To begin with, start with just five tables and equations. After the class shares their strategies, highlight different ways to match tables with equations. Then give the next set of five, allowing teams to try out new strategies.
To raise the difficulty, withhold the equations for a set amount of time (e.g., five minutes). This allows students practice deriving equations by finding the slope and using the point-slope formula instead of simply using substitution.
Use the same equations but change all the x-values on the tables to be identical (e.g., 1, 2, 3). You will need to change the y-values so they still match the equation.
Match the Graph
Learning objective: Students will create a graph to match a linear equation using an online graphing tool.
Materials: Chromebooks/netbooks
Put students into pairs.
Have students open an online graphing tool such as Desmos.
Give students a verbal description of a linear equation problem (see examples).
Underneath each problem are three clues to use to create the graph.
Pairs work together to create a graph to match the problem and insert it into their document.
Students can check their work by referencing the visual on the released item (on the page after each problem).
Variations
For an extra challenge, only give students the first clue that names two points the graph passes through.
After creating the graph and inserting, have pairs find another pair that created a graph for a different problem. Pairs swap problems and solve.
If access to the internet is difficult, students can complete the task with graph paper.
After students have completed all three examples, they can create one of their own.
Graphing Time
Learning objective: Students will use an online graphing tool to create linear equation graphs.
Materials: Chromebooks/netbooks
On their Chromebooks/netbooks, have students open Desmos.
Give clues for students to describe the linear equation you'd like them to graph (e.g., it has a slope of -2 and it passes through the origin; it has a slope of 1/2 and has a y-intercept of -3).
Students write an equation to match the clues and graph the function.
Go over the correct answer as a class.
Variations
After students have participated multiple times, allow them to graph a linear equation of their choice and then come to the front of the class and give clues for their classmates to use in creating a graph.
Instead of giving the slope, you can give proportions equivalent to unit rate (e.g., the line rises 5 units as it move 2 units to the right).
Display a graphed linear function and have students match it on their Chromebooks/netbooks by using visual clues.
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