This post explores some ideas for reviewing concepts for TEKS 8.8C.
model and solve one-variable equations with variables on both sides of the equal sign that represent mathematical and real-world problems using rational number coefficients and constants
Staar Performance
On recent STAAR tests, here is how students across the state of Texas have performed.
2023 #10 - 39% correct
2023 #36 - 25% 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.
Roundtable
Learning objective: Students will draw algebra tiles, create a linear equation, find a solution, and use substitution to verify the solution.
Put students into groups of four.
Give each member in the group (4 total) a different 2 x 2 table with a verbal description of a system of linear equations (see example).
Each member draws a representation of the problem using algebra tiles in the top-left cell.
Each student should then rotate their paper one student (clockwise). On their new paper, students use the algebra tiles (top-left cell) and the problem (middle) to write a linear equation (top-right cell).
Each student should then rotate their paper one student (clockwise). On their new paper, students use the algebra tiles (top-left cell), the linear equation (top-right cell), and the problem (middle) to solve for the variable (bottom-left cell).
Each student should then rotate their paper one student (clockwise). On their new paper, students should use the solution (bottom-left cell) and the linear equation (top-right cell) to double-check the solution using substitution (bottom-right cell).
Each student should then rotate their paper one student (clockwise). Students should have their original paper in front of them, now complete. Give them a few moments to check the work of their group and make corrections as needed.
Variations
For smaller groups, put students into trios. The third group member can write both the solution and use substitution to check their work before rotating the paper back to its original owner.
For additional scaffolding, start with half of either the algebra tiles or linear equation cells already completed.
After groups complete their Roundtable, have students with the same problem from multiple groups gather together to check their work.
Equation Balance
Learning objective: Students will use gram stackers or weights to represent a one-variable linear equation.
Materials: Balance, gram stackers or weights
Group students with no more than 6 students in a group.
Borrow a set of balances and gram stackers or weights for each group.
Have each group split into two halves.
The first half of the group physically represents an equation with weights or gram stackers (see example).
The other half of the group creates an equation for the representation and solves for the unknown.
Switch and have the other half of the group physically represent a new equation for the first half.
Variations
Ask groups to create their own balanced equations and cover up a value. Have them switch and solve with another group.
Have students verbally describe how to solve the equation for the variable to their group, naming the zero pairs as they remove them from the balance.
For students looking for an extra challenge, create an equation with two types of weights or gram stackers covered up. This simulates solving an equation with two variables.
Digital Algebra Tiles
Learning objective: Students will use an online algebra tile tool to create models of linear equations.
Materials: Chromebook/netbook for each student
Have students navigate to an online algebra tile tool (e.g., Oryx, Mathsbot, Didax).
Display a one-variable linear equation and have students represent it using their algebra tiles.
Ask students to talk with their neighbors and compare representations.
Have a student either display their answer to the class or recreate it on the interactive whiteboard.
Variations
Have students copy the equation and a representation of the algebra tiles into their math journals for future reference.
After displaying the equation, have students create zero pairs and solve for x.
Give students verbal descriptions of linear equation problems to create models for.
The virtual algebra tiles on NCTM also have a self-check mode that students can use to not only model linear equations but solve them as well.
Write the Equations
Learning objective: Students will write a one-variable linear equation with a variable on both sides of the equal sign from a verbal description.
Materials: Index cards
Put students into groups of two or three.
Print and paste (or write out) a word problem involving writing a one-variable linear equation on each card (see STAAR examples).
Give each group an index card with the word problem.
Students work together to write a one-variable linear equation that represents the word problem scenario on the back of the index card.
Groups complete as many index cards as possible within the allotted time.
Review the answers as a class.
Variations
Repeat the exercise later with additional examples.
After a designated amount of time, have groups pair up and review their equations for any common problems they created an equation for.
Save the index cards for self-review.
Have groups find the solution and draw an algebra tile representation for each problem. Put those and the equation itself on separate index cards and save for quadruple memory match (i.e., verbal description, equation, algebra tiles, solution).
Solution Relay Race
Learning objective: Students will solve one-variable linear equations with the variable on both sides of the equal sign.
Place students into three teams.
For each team, have each linear equation problem randomly written on index cards or on the board covered up.
Team members run to the board, one at a time, to solve the problem.
When complete, students run back to their team and tag the next person to solve the next problem.
Variations
To add a layer of complexity to the game, have two people from each team run up to the board simultaneously. Have the first student solve the problem and the second student check the validity of the solution using substitution.
Provide calculators if necessary.
Instead of solving the problem, students could be asked to draw an algebra tile representation.
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