This post explores some ideas for reviewing concepts for TEKS A.5C.

solve systems of two linear equations with two variables for mathematical and real-world problems

### Staar Performance

On recent STAAR tests, here is how students across the state of Texas have performed.

2023 #23 - 68% correct

2023 #40 - 31% correct

### 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.

##### Scavenger Hunt

Learning objective: Students will solve systems of linear equations with two variables.

Divide class into 9 teams.

Select 9 locations around the school to place the systems of linear equations (example).

Tell students that at each location they'll find a system of linear equations and the name of the location to go to next. They'll need to solve the system of linear equations, place the name of the next location in the answer grid, and then travel to the next location to find the next clue. For example, if a system of equations has the solution of (3, 1), students would place that under x = 3 and y = 1 on the answer grid.

Send each of the nine teams to a different starting location. Students return when they have solve all nine systems of linear equations.

Variations

Adjust the number of locations and systems of linear equations to meet the needs of your students (e.g., 6 locations and systems rather than 9).

Instead of a grid that shares common x and y values, list nine different locations separately and have the students rotate through them in order. Students would write the solution for each location's system of linear equations next to the location name.

For extra support, you can post a QR code at each location that shares the solution. Ask students to use this QR code as a last resort.

Allow students to create the systems of linear equations, giving each team a target solution [e.g., (3, 4)]. Change up the locations and repeat the activity.

##### Desmos Tic-Tac-Toe

Learning objective: Students will create systems of linear equations with two variables that have specific dependent and independent variable values.

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 system of linear equations with the solution in one of the 9 squares. Solutions on the darker lines are not completely in a square and do not count. Once a square has been claimed, any other solutions 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 solution to different quadrants.

Make each of the nine quadrants smaller to create tighter target areas.

Place a time limit on each teams' submission.

Only allow one submission per team. If the submission does not work, that turn is forfeited.

##### DIY Systems of Linear Equations

Learning objective: Students will create a verbal description of a system of linear equations.

Pair students up and give them a copy of DIY System of Linear Equations.

Ask students to read over the STAAR examples on the first page and note the similarities and differences.

Have students read the example contexts on the third page of DIY System of Linear Equations and select one for their verbal description.

Students should identify the units for the dependent and independent variables and name them on the second page.

Students create a verbal description with the chosen context and variable units, writing it on the second page.

Students also put the solution and the values for each variable below the problem.

Variations

Have pairs swap problems with each other (hiding the solution) and solve.

Create a problem as a class so students can see you model your thinking.

For extra support, identify the variable units for students. Their job then would be to create the constant values and put everything together.

For extra points, allow students to add a table of values and a graph for their verbal description.

Save some of the better examples for a extra credit quiz.

##### Make a Table

Learning objective: Students work convert a verbal description system of linear equations problem into a tabular system of linear equations problem.

Note: This activity is designed to help students see systems of linear equations in tabular form. Identifying these types of problems can cause students to struggle, as seen on the 2023 STAAR test.

Start with an example verbal description STAAR problem.

Find the constant labels and create columns for them.

Find the categories of data (e.g., days, descriptors) and create rows for them.

If a total amount exists, create a column and label for it.

Add a few sentences to the text of the problem describing the table (e.g., Each website charges a different amount based on the number of clicks on the advertisement. The table shows the number of clicks on each website and the total cost for each of two days.).

Rewrite the verbal description STAAR problem into a tabular system of linear equations problem.

Variations

Convert one as a class to model the thought process behind converting a verbal description problem into a tabular problem.

For extra scaffolding, provide the constant labels for students to use.

Have students exchange converted problems with a partner to solve.

Save a few of the better conversions for an extra credit quiz.

##### Graphing Challenge

Learning objective: Students will graph systems of linear equations to verify the solution.

Materials: Graph paper

Split class into teams of two or three.

Give teams systems linear equations (see example from Scavenger Hunt).

For each system of linear equations, teams should find the slopes and y-intercepts of each equation and graph them.

For each system of linear equations, teams should also note the intersection of the two lines and label the coordinates as the solution.

After teams are finished, have them check their work on a graphing calculator or an online graphing tool like Desmos.

Variations

Give teams a time limit (e.g., 10 minutes) and see how many they can do in that time frame before checking their work with a calculator.

Give teams problems one at a time. As they show you one solution, hand them the next system of linear equations until time to check on the calculator.

Mix in some problems in tabular form so students have to calculate the slope and y-intercept differently.

Mix in some problems from verbal descriptions so students have to read and decipher a word problem to note the equation.

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