Unit U3

Side Effects of Texting

Ratio, Rate, and Percentage

Find Your Natural Walking Pace

Breathing Rate and Heart Rate Correlations

Free Throw Strategy Study

Writing: Free Throw Strategy Study

Duration: Approximately 30 minutes

Students design an experiment to determine a basketball player's accuracy, and whether she would have a greater success rate shooting more frequently or taking more time to prepare for a shot.

Students use proportional relationships among different types of quantities to provide information about the magnitude of properties and processes.

Students understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

Students understand the concept of a unit rate and use rate language in the context of a ratio relationship.

Teacher Tips

- This activity can be done independently or with a partner.
- Optional: if students test their own procedure, provide paper to crumple and throw and baskets/boxes OR basketball and hoop.

Teacher Tune-ups

Teaching Notes

ACTIVITY OVERVIEW

- Introduce rates of accuracy or effectiveness (10 min)
- Design the experiment (10 min)
- Optional: Try your experiment (10 min)
- Post-writing / post-lab discussion (5 min)

Introduce rates of accuracy or effectiveness (10 min)

This introduction explains how rate is also used to measure accuracy or effectiveness, using a basketball player’s success with free throws as an example.

When measuring accuracy, the rate is expressed as a percentage. In order to arrive at the percentage, students may need a review of the mathematics involved in converting a ratio to a percentage.

The dialogue at the end of this section demonstrates how a coach and player would discuss rates of accuracy.

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Who can explain what a "free throw" in basketball is?

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Competitive basketball players always try to improve the number of free throws that they make. As most of you know, when you are fouled, you can shoot a free throw. That means you stand alone on the free throw line, and no one blocks you. When you make it, the team scores a point. Sound easy? Actually, even professional basketball players miss a lot!

Michelle is a starting point guard for Patterson High. In the last 10 games, she made 27 out of 42 free throws. That’s 27 made per 42 attempts.

To find the unit rate of Michelle’s accuracy with free throws, this is what you do:

That unit rate is totally valid, but it’s kind of strange to think of Michelle making .64 of a basket. One way that can help everyone understand how good (or bad) Michelle is at shooting free throws is to convert the unit rate into a percentage rate.

It’s very easy:

.64 made per attempt = 64% accuracy

Percentage is a lot like unit rate. The difference is that unit rate is per one, and percentage rate is per 100. So in this case, we can think of Michelle making about 64 out of 100 of her free throws. Not bad!

Overheard during halftime at a recent game:

Coach: Michelle, so far in tonight’s game, you’ve made 3 out of the 12 free throws you took. That is a rate of .25 baskets per 1 shot. Or just 25 percent.

Michelle: Geez coach, that’s not too good. My free throw success rate is usually much higher. What should I do?

Coach: Well, you always shoot as soon as you get the ball from the official. Try to slow down to give yourself a few seconds before you shoot.

Michelle: Okay, sure! Lots of times if I slow down, I am more accurate!

Design the experiment (10 min)

This activity asks students to consider the scenario and design an experiment that allows Michelle to determine if she would have a greater success rate shooting more frequently or taking more time to prepare for a shot.

This activity can be done independently or with a partner. Students design a process that lets Michelle determine her accuracy.

Decide if your class will have time to try their experiment designs, or if they will only design the experiments.

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When Michelle and Jordan have the same free time, they enjoy competing in a friendly game of wastebasket-ball. The way they usually play is by crumpling up lots of paper from the recycling bin and shooting as many times as they can in one minute. Whoever gets more “baskets” wins.

But Michelle was thinking about what her coach told her the other day. On her real basketball team, she’s trying to balance the frequency and accuracy of her shooting.

Michelle asked Jordan to design an experiment with her using the same materials they use when they play their game.

Michelle wants to explore whether she would have a greater success rate making baskets if she attempts as many shots as possible or if she prepares more carefully for each shot.

If you were Jordan, how would you recommend Michelle set up her experiment?

Optional: Try your experiment (10 min)

If your class has time to try their experiment designs, use their experimental setups they developed in the last section here.

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Let's do an experiment.

Using the setup you designed in the last step to test Michelle's success rate under different conditions, record data, analyze it, and share your findings with the class.

Post-lab writing / discussion (5 min)

The writing prompt asks students to consider whether success in their life comes from doing things quickly and frequently or taking their time and paying attention to accuracy or precision.

It can also be used as the basis for a discussion by the whole group or in small groups or pairs.

Remind students to use the focus words for the unit, defined on the unit U3 overview page.

There is an old saying: “Quality over quantity.” It’s nice and poetic, but is it always true? Write about aspects of your life when you feel your success is measured by speed or frequency more than how carefully you do things. In addition, write about times when you feel most successful by striving for accuracy or precision. Do you believe one is more important than the other? Do you think one is not emphasized enough in your life right now? Is your pace too fast? Too slow? Just right?

Try to use the focus words in your response: per • speed • rate • ratio • frequency • accuracy • precision • pace • correlate

BETA Version - Please send comments and corrections to designcenter@serpinstitute.org