# Math In Motion

## Visual Approach to Parabolas

Lydia Baker, Sherry Franklin | Published: August 21st, 2023 by K20 Center

• Grade Level 9th, 10th, 11th, 12th
• Subject Mathematics
• Course Algebra 2
• Time Frame 100
• Duration 2-3

### Summary

Students will use their knowledge of real world scenarios to graph a situation. After graphing, the students will use prior knowledge to connect vocabulary terms to the graphs that were created before practicing their own scenario to be graphed. This lesson is intended to introduce the basics of quadratics, including name, visual representation, and common vocabulary.

### Essential Question(s)

What do real life events look like when graphed?

### Snapshot

Engage

Students work in groups to bounce a ball in specific ways. As pairs bounce the ball, the other group members analyze and sketch the movement.

Explore

Students are shown a set of images and must describe what is happening in the images before graphing the movement of the ball as the distance from the ground over time. Students will share their work with the class.

Explain

Students will work in pairs to analyze a given graph and describe predetermined characteristics of the graph before the teacher shares the correct answers.

Extend

Students will brainstorm their own scenario of what would create a parabola and graph the motion as a function over time.

Evaluate

Groups will exchange scenarios with one another and determine the characteristics of the students’ work.

### Materials

• Lesson Slides (attached)

• Bouncing Balls (example: Tennis ball) (1 per pair of students)

• Interpreting Math in Motion (attached, 1 per student)

• Movement Test Handout (attached, 1 per group)

• Math in Motion (attached, 1 per student)

• Math in Motion Teacher Edition (attached, optional)

• Writing utensils

• Blank paper or index card (1 per student)

• Graph paper (digital)

• Device with recording capabilities

• Blank or lined paper (optional)

### Engage

15 Minute(s)

Use the attached Lesson Slides to guide the lesson.

Display slide 2-4 to introduce the lesson, essential question, and lesson objectives.

Put students into groups of four, display slide 5, and pass out Movement Tests handout. Inform students that they will be working in groups to bounce balls and observe the path the ball takes when it bounces. They will take turns completing the series of tests twice. One time they will be the student to bounce the ball. The other time, they will draw the path of the ball on their handout. Once students are in groups, have them spread out around the room and go through the series of tests. Remind students to take turns: one pair watches as the other creates the motion. Have students sketch the path of the ball each time.

### Explore

25 Minute(s)

Transition to slide 6, and pass out the Interpreting Math In Motion handout. Direct students’ attention to the interpreting portion of the handout, asking students to look at the sequence of images on the slide and use complete sentences to describe what they believe is happening.

After students have had the opportunity to complete the description, move to slide 7, direct students’ attention to the graphing portion of the Interpreting Math In Motion handout, and ask students to independently graph the distance of the ball from the ground as a function of time on the graph provided.

Once students complete their graph, move to slide 8, and introduce the Think-Pair-Share strategy. Ask students to turn to the person sitting next to them and compare graphs, analyzing what is similar and different. Ask students to consider if their partner’s graph matches the description that they wrote.

Using the hidden slides 10-13, facilitate a whole class conversation about the graphs that the students created. Emphasize the connections between the written description and the graph by asking the class to analyze if they displayed the same information.

### Explain

25 Minute(s)

Transition to slide 14, and introduce this graph as one interpretation of the pictures. Explain to the students that this graph will be used for the next part of the lesson so that everyone is learning from the same graph.

Transition to slide 15, and point out the area between the red lines, informing the students that they will be focusing on a small portion of the graph. Then display slide 16; this will show the class the smaller portion of the graph they will focus on for the activity.

Display slide 17 to introduce the class to the basic facts and identification of the graph. Play the Khan Academy video to introduce the origins of this type of graph, stop the video at 1 minute 38 seconds.

Transition to slide 18, and pass out the Math in Motion Student Edition handout. Introduce the Elbow Partners strategy to the class as you assign partners. Instruct the students to use the graph at the top of the handout to answer the questions in the table with their partner. Tell the students they have at least 10 minutes to complete the table and then you will be going over the answers as a class.

Start the timer on the slide. Using the Math in Motion Teacher Edition, display slide 19 and 21 and write directly on the slides to fill in the missing parts of the table. Instruct the students to correct answers on their handout as necessary.

### Extend

20 Minute(s)

Move to slide 23, and combine sets of elbow partners to create groups of 4. Have the groups brainstorm a scenario that illustrates a parabola, asking students to choose one of three ways listed on the slide to create their set up. They can illustrate the scenario, write a narrative, or digitally record it. Provide students with the materials and time needed to work on their scenarios. Once all groups have created the description of their situation, provide each group with graph paper and have them graph the action.

Inform the students that when they are finished, they will be presenting their work to another group.

### Evaluate

15 Minute(s)

Once all groups have had enough time to complete their graph, move to slide 24, and ask each group to exchange their work with another group. Groups will present their scenario to each other and then trade their graphs to compare. On a piece of scratch paper, ask each group to review the other groups’ work and answer/identify the 6 prompts on the slide based on the other groups’ information. These responses can be turned in as an Exit Ticket for assessment purposes.

### Resources

Dyke, F. V. (1998). A visual approach to algebra. Dale Seymour Publications.

K20 Center. (n.d.). Elbow Partners. Strategies. https://learn.k20center.ou.edu/strategy/116

K20 Center. (n.d.). Exit Ticket. Strategies. https://learn.k20center.ou.edu/strategy/125

K20 Center. (n.d.). Flip. Strategies. https://learn.k20center.ou.edu/tech-tool/1075

K20 Center. (n.d.). Google jamboard. Tech Tool. https://learn.k20center.ou.edu/tech-tool/2336

K20 Center. (n.d.). QR codes. Tech tools. https://learn.k20center.ou.edu/tech-tool/2449

K20 Center. (n.d.). Think-Pair-Share. Strategies. https://learn.k20center.ou.edu/strategy/139