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

solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides

### Staar Performance

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

**2023** #4 - 22% correct

**2023** #29 - 63% 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.

**Human Equations**

*Learning objective: Students will model the use of the distributive property to solve one-variable equations.*

Display a one-variable equation that requires the distributive property [e.g., 5(2w + 4) = 4(2w + 9)].

Using whiteboards, have students represent terms on each side of the equation to solve for the variable.

Ask additional students to represent additional terms as the distributive property is applied.

For

__example__, two students are needed for the sample equation [5(2w + 4) = 4(2w + 9)]. One student would have 5(2w + 4) on their whiteboard and the other student would have 4(2w + 9) on their whiteboard.As the class applies the distributive property, they can ask 7 additional students to join the original two (for a total of 9). Five of the students would have (2w + 4) on their boards and four of the students would have (2w + 9) on theirs.

As the class continues to solve for the variable by combining like terms, applying properties of equality, etc., increase or decrease the number of students holding whiteboards as needed.

*Variations*

Instead of the entire class directing the students with the whiteboards in how to solve the equation, elect one or two spokespersons that direct the volunteers and listen to suggestions from the class.

Split the class in half and allow both sides to solve the equation using whiteboards. Notice if they use the same steps or if they represent them differently.

If whiteboards are not available or are impractical, have algebra tiles available for students to hold as they represent the equation.

Once students have found the value of the variable, have another group of students use the whiteboards and volunteers to model substitution to verify the variable's value.

**Will It Balance?**

*Learning objective: Students will examine partially solved problems that use the distributive property and identify any errors that exist.*

Ask students to work in pairs or groups of three.

Display a one-variable equation that requires the use of the distributive property (see

__example__).Show a partially distributed/solved equation.

Ask students if the partially distributed equation balances correctly. If so, how do they know? If not, where is the error?

Equation: 10 - 3(m - 5) = 2(5 - m)

Will it balance?: 10 - 3m - 15 = 10 - 2m

Answer: No (-15 should be 15)

*Variations*

Allow students to algebra tiles (physical or online) to represent the equation.

After validating or correcting the partially solved equation, have students solve completely and then use substitution to check their work.

Have students write a paragraph listing the steps need to solve for the variable. Let them peer edit their papers for grammar, syntax, and use of transition words.

Have pairs create their own Will It Balance? problem and swap with another pair to solve.

**Peer Vocabulary Teaching**

*Learning objective: Students will practice teaching each other how to solve one-variable equations that require the use of the distributive property.*

Materials: A list of relevant vocabulary terms with definitions and examples

Pair students together.

Display two different one-variable equations that, on both sides of the equation, have the variable and require the use of the distributive property. For example, [-5x - (-7 - 4x) = -2(3x - 4)] and [0.3(12x - 16) = 0.4(12 - 3x)].

Have Partner A describe to Partner B how to solve the problem. Partner B listens for all the vocabulary terms Partner A uses (e.g., distributive property, property of equality, zero pair).

After the explanation, the partners work together to find any extra opportunities to insert vocabulary terms into the explanation.

Repeat the process with Partner B explaining how to solve the problem and Partner A recording vocabulary terms.

*Variations*

You can make this a competition by adding the cumulative vocabulary terms from each set of partners and seeing which pair got the most.

If students might struggle with this activity, model an explanation first and have students record how many vocabulary terms they hear.

Type out a script for an explanation and highlight the vocabulary terms for an extra scaffold.

After students have completed this activity a few times, they can take over the teacher's role and explain how to solve any future problems the class sees that test standard A.5A.

**Distributive Relay Race**

*Learning objective: Students will solve linear equations with one variable that require the use of the distributive property.*

Divide the class into teams of 3 to 5.

Split the teaching whiteboard into sections, one for each team.

In each section of the whiteboard, display a linear equation that requires the use of the distributive property [e.g., -5x - (-7 - 4x) = -2(3x - 4)].

Have teams line up on the opposite side of the room in straight lines.

Each team sends the first person up to the board to start solving the equation.

Have a timer going (e.g., 15 seconds) and, when the timer goes off, have each team member return to their line and tag the next person to come up and pick up where the previous team member left off.

Continue until all teams have solved for the variable.

*Variations*

Instead of using a timer, allow each team member to perform one operation or step in solving the equation before switching out with the next team member.

If your students might be distracted by the equations on either side of them, give each team a unique equation to solve.

To extend the game, make teams use substitution to double-check their solution before declaring a winner.

If teams need additional support, allow two members to go to the board at a time (though only give each team one marker).

**No Pencil Challenge**

*Learning objective: Students will solve linear equations with one variable that require the use of the distributive property.*

Show students a linear equation that uses the distributive property and has a variable on one side of the equation [e.g., 3(x + 5) = 42/2]

Without using pencils or other writing implements, students mentally solve for the variable on their own for about 60 seconds.

Allow students to share their answer and reasoning with their table groups.

Solve the problem as a class, allowing students to give you the steps to solve one at a time.

*Variations*

Pair students up from the outset, letting them work together to solve the problem.

As proficiency progresses, give students problems that have the variable and/or use of the distributive property on both sides of the equation.

Instead of solving for the unknown, give students a problem [e.g., 3(x + 5) = 42/2] and a value for x [e.g., x = 2] and have them mentally use substitution to validate or invalidate the solution.

Instead of a predetermined amount of silent work, allow students to stand up once they've worked it out. Those that stand can pair up immediately and move to another side of the room to confer. After about half of the students have stood up, have the rest stand up and find a partner to work it out.

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