This post explores some ideas for reviewing concepts for TEKS A.8A.

solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula

### Staar Performance

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

2023 #41 - 30% 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.

##### Countdown

Learning objective: Students will solve quadratic equations by completing the square and by applying the quadratic formula.

Put students in pairs or groups of four.

Display a timer and a quadratic equation for students to solve.

The pairs or groups of four try to find the solutions within the time limit using both methods, each method worth 2 points (i.e., completing the square and quadratic formula) total, 1 point per solution. Students that find both solutions using both methods within the time allotted can earn a total of 4 points per quadratic equation.

Students can work together on each method or divide and conquer the two methods simultaneously.

Variations

Once students have the basic idea of Countdown, and you have a good feel for an appropriate length of time to give them to solve using the two methods, introduce extra point modifiers. Feel free to adjust the points for each modifier and add your own as you see fit.

Keep a running tab of points earned over a week or a month and switch partners to keep things interesting.

Allow students to suggest their own extra point modifiers and add to the menu of options.

Have students provide quadratic expressions to use in Countdown. To be considered, the solutions must be shown using both the quadratic formula and by completing the square.

If you teach multiple periods of Algebra 1, have classes compete against each other. Total the points for each team during the class period, ensuring that there are the same number of teams per class period.

##### Hidden Gallery Walk

Learning objective: Students will work in groups to solve quadratic equations using factoring, square roots, completing the square, and the quadratic formula.

Divide class into four groups, one for each type of strategy (i.e., factoring, square roots, completing the square, and the quadratic formula).

At each starting station, have masking tape, blank paper, any exemplars/scaffolds for that strategy, and a problem to solve (see samples).

Have students spend ____ minutes at their station solving the problem using the correct strategy.

When complete, have the students tape their paper (w/ solution) to the wall at their station. Ensure that the solution is facing the wall and not visible.

If other groups have already completed that station, the students can view other answers and compare before returning them to the wall.

Students move to the next station when time is up.

Variations

If students are stuck, or simply need extra support, make this a visible gallery walk. Have the answers from previous groups facing out for reference as needed.

Instead of working in groups on a timer, make this a station activity. Have students rotate through all four stations at their own pace, in any order, solving using the noted strategy and taping their answer to the wall (hidden). Before moving on, have them check their work with at least 3 other answers for verification.

For variety, add a fifth station that can use any strategy. Divide the wall behind that station into sections and students can tape their answer based on which strategy they used.

This activity can be done digitally through an online whiteboard app (e.g., Jamboard, LucidSpark, FigJam). Students would snap a photo of their solution and post that to the correct page on the whiteboard.

##### Quadratic Relay Race

Learning objective: Students will solve quadratic equations using a variety of methods.

Put students in equal teams.

Have a series of quadratic equations on index cards for students to solve.

At the top of each card have a suggested strategy (e.g., quadratic formula).

The first person in each team grabs a card from the pile and has to solve the quadratic equation on a paper or personal whiteboard using the suggested strategy.

If the student prefers to use another strategy, s/he may do so after walking a circuit around the room once.

If the student needs assistance from a teammate, s/he may choose a teammate to walk two circuits around the room and then help.

When the problem is solved, the next person in line starts working on the next problem.

Variations

Instead of randomly choosing teams, allow team captains to choose the first two students on each team. Randomly assign the unpicked half of the class.

Add more circuits to walk around the room for using an alternate strategy or calling on a friend for help.

Add wild cards into the mix. These quadratic equations can be solved using any strategy.

If the class is struggling to use a specific strategy (e.g., completing the square), make all cards suggest that strategy.

##### Spot the Mistake

Learning objective: Students will analyze worked examples of solving quadratic equations, identify the error, and solve the equation correctly.

Share an example of a solved quadratic equation with a mistake with students. Here are some examples from Hidden Gallery Walk with mistakes highlighted.

Students work in partners or small groups to analyze the problem, step-by-step, to spot the mistake.

When a group spots the mistake, have them come to the front of the class to explain. Give every other group 30 - 45 more seconds to try and spot the mistake before the first group explains.

After hearing the explanation, give groups a minute or two to solve the quadratic equation correctly. Have a group volunteer to come up to the front and explain their work.

Variations

Instead of putting a time limit on it, share the example with the mistake at the beginning of class. Allow students to work on it, alone or with a partner, throughout class. Go over it during the last three minutes before the bell rings.

After a group shares how to solve the equation correctly, ask another group to share how they solved it using a different strategy (e.g., completing the square, quadratic formula).

Every once in a while, share a worked example with no mistakes.

Have students create their own examples, complete with highlights, and submit them for use in the future.

##### Calculate, Draw, Check

Learning objective: Students will draw quadratic equations and check their work with a graphing calculator.

Pass out graph paper to students.

Give students a quadratic equation to solve, ensuring that the solutions are integers (rather than radicals).

Have students also find the vertex by using the formula for axis of symmetry and plugging in that x-value back into the equation to find the y-value.

Knowing the vertex, the solutions, and the y-intercept, have students draw a representation of the quadratic equation.

Either show the correct answer on the interactive whiteboard or allow students to check their work using a graphing calculator or Desmos.

Variations

Pair students up and have one student find the solutions and the other student find the vertex.

Divide the class into groups and give each group a different equation to graph. Graph each equation and print out. When each group has calculated their equation and drawn a graph, have them come to the front and find their graph from among all the graphs.

Add equations whose solutions are radicals, allowing students to estimate their positions on the graph.

This can be turned into a memory match game, in which each equation has four representations to match with: 1) the equation itself; 2) the graph of the equation; 3) the solutions to the equation; 4) the vertex of the equation.