DETAILED LESSON PLAN: SPORT STATS - midschoolmath.com · MidSchoolMath Lesson Plan: Sport Stats 4 Lesson Plan Day 1, cont'd. Materials • Sport Stats Resolution video 4. After determining

MidSchoolMath Lesson Plan: Sport Stats 1

7.RP.A.3Ratios & Proportional RelationshipsUse proportional relationships to solve multi-step ratio and percent problems. Examples: simple interest, tax, markups

and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

The ability to use proportional relationships to solve multi-step ratio and percent problems is a skill that will benefit students in real world situations. In Sport Stats, Dave and Shannon are broadcasting live for Game 1 of the American East Division Unicycle Hockey Playoffs on the TV show, Ultimate Obscure Sports. During the broadcast, they planned to provide the viewers the win percentages for each of the four teams, but they don’t have the percentages! They only have the win-loss records for each team. The data provided is Shannon’s notes with the win-loss records for the four teams.

DETAILED LESSON PLAN: SPORT STATSWhat is the win percentage for each team?

Lesson Plan OverviewLesson Length: 4 Days

English Language Learners: Students will likely need explanations of terms like simple interest, tax, markup, gratuity/tip, and commission.

Standards for Mathematical PracticeMP1: Make sense of problems and persevere in solving them.On Day 2 during the Clicker Quiz and Practice Printable phases, students will utilize the ideas they’ve grasped about proportional relationships to solve multi-step problems.

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Prerequisite Standards6.RP.A.3, 7.RP.A.2•

Cluster Connection

Direct Connection: In Sport Stats, students will use proportional relationships to determine the win percentage for each unicycle hockey team.Cross-Cluster Connection: This activity connects 7.RP.A to 6.RP.A as students will apply their knowledge of ratio reasoning and proportional relationships to solve multi-step problems.

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Cluster Heading: Analyze proportional relationships and use them to solve real-world and mathematical problems.

VocabularyProportional relationship: A relationship between two variables that vary directly with each other; when two variables have a constant ratio between them.Percent: A rate per 100.

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Common MisconceptionsStudents may not use the correct “whole” when working with percents.Students may struggle with determining the numerator and denominator when calculating percent error.

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7.RP.A.3Ratios & Proportional Relationships

KevinSimpson

GladysGraham

MeganLeBleu

Practice Printable

Instruction at a Glance Clicker Quiz

Full-sized Answer Key available in printed Teacher’s Guide

Gladys: Students may better comprehend problems if they are asked to verbalize the situation in their own words, ensuring understanding of key words (commission, markup, fee, percent error).

Kevin: When working with percent problems, direct students to pay careful attention to what the "whole" or 100% amount refers to.

Megan: This standard has numerous connections to financial literacy. Spend ample time allowing students to explore these concepts. A place to begin might be with a low-anxiety matching activity, in which students are provided many questions using the concept of percent (tax, tip, commission, simple interest, etc.) and the corresponding answers.

SPORT STATSWhat is the win percentage for each team?

Dave and Shannon, of the TV show Ultimate Obscure Sports, are once again following the Unicycle Hockey League. They are in the middle of their live broadcast, about to announce the overall team standings, when they realize they do not have the win percentages for the teams. They only have the win-loss records.

Help them determine the win percentage for each team based on Shannon’s notes below.

7.RP.A.3

Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest; tax; markups and markdowns; gratuities and commissions; fees; percent increase and decrease; percent error.

About this standard

Date PeriodName

MidSchoolMath Sport Stats 1 of 2

APPLYING THE STANDARD

MidSchoolMath 2 of 2

Date PeriodName

How might this standard appear on a test?

Sport Stats

Complete the table. Round to the nearest cent.1)

During a science lab, Rocco determined that the boiling point of ethyl alcohol is 75°C. The actual boiling point of ethyl alcohol is 78°C. What is Rocco’s percent error?

2)

A shop owner marks up the price he pays for each item by 30% to determine the selling price. What is the selling price of a pair of sneakers, for which he pays $45.00?

3)

Jody makes a cleaning solution using 3 cups of soap, 2 cups of vinegar, and 6 cups of water.4)

Complete the chart. Use the formula i = prt where i = interest earned, p = principal (starting amount), r = interest rate, and t = time in years.

5)

If she mixes in 3 cups of soap, what is the amount of vinegar and water that she will need?

b)

If she mixes in 6 cups of vinegar, what is the amount of soap and water that she will need?

c)

What part of the solution is soap?a)

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=78 – 7578

≈ 0.038378

Rocco’s percent error is about 3.8%.

The selling price of the sneakers is $58.50.

or 27%311

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Vinegar = 2 cups Water = 6 cups

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Soap = 9 cups Water = 19 cups


7.RP.A.3

MaterialsSport Stats Immersion videoChart paper/Interactive whiteboard

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Procedure1. Play the Immersion video to the whole class.2. Restate the question and keep it visible: What is the win percentage for each team?3. Use the Think-Pair-Share protocol. Ask students: “What do we need to know?”

MaterialsCopies of Sport Stats Data Artifact, one per student •

Procedure1. Distribute the Data Artifact to each student.2. Invite students to work individually or with a partner to arrive at a solution.3. Observe students at work (avoid confirmation of the solution). Look for opportunities to clarify vocabulary, identify student strategies or work samples to be shared, and ask students questions to further their thinking.

Questions may vary depending on the method of simulation chosen by students.

• What is it that we need to help Dave and Shannon do? • What information are we given? • What is the meaning of percent or percentage? • What is the part and what is the whole when looking at the win-loss record? • What ratios can be written from the win-loss record? Which is most helpful to us? • How can we turn that ratio into a percentage representing the wins? • What other ways might you be able to calculate the win-percentage?

Think-Pair-Share Ask students to think individually about what information they need to know and make some notes (≈ 1-2 min). Tell students to pair with a partner and discuss their notes (≈ 2 min). Finally, facilitate whole-class by cold-calling on students to share their strategies on an interactive board (≈ 2 min).

Lesson Plan Day 1

As a warm-up, tell students to log into their account and access Test Trainer Pro. Specify the domain in which you would like students to work (preferably a different one than the prior day) and also the length of time you wish students to work (not a number of items). It is important to remind students to work out the math using paper and pencil when necessary and to look at their feedback.

Test Trainer ProAllow 7 to 10 minutes

The Math SimulatorTM

Allow 12 minutes

Immersion1

Allow 20 minutes

Data & Computation 2


Lesson Plan Day 1, cont'd.

MaterialsSport Stats Resolution video•

4. After determining students are nearing ‘sufficient’ progress, either consider using an additional teaching protocol, or ask students to provide a thumbs up/middle/down to indicate readiness to see the Resolution video. You may grant students additional work time, if necessary.

Here are examples of statements you might make to the class:

Procedure

1. Play Resolution video to the whole class, and have the students mentally compare their solutions as they watch.2. After the video, prompt students with the following questions:

• What did you do that was the same? • What was different? • What strategy do you think was more efficient? Why? It is not always necessary for students to respond. The questions can simply be used to cue thinking prior to instruction.

7.RP.A.3

In Sport Stats, we had to help Dave and Shannon calculate the win percentage for each unicycle hockey team so they could broadcast it on air.They calculated the win percentage by making a ratio of the number of games won to the total number of games played, dividing to create a decimal, and multiplying by 100.

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This is one way of solving this problem, but there are others. I’m wondering how does this relate to proportional relationships we’ve been studying?Let’s look closer at the Samurai Scorpions. Their win-loss record was 6 and 7, which meant they won 6 games and lost 7 games, out of 13 total games that they played. Since we know that percentages represent a part out of a whole, let’s make a part-to-whole ratio using the win-loss record like Dave and Shannon did.

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613

partwhole

Teacher InstructionAllow 6 to 8 minutes

Allow 14 minutes

Resolution3

Answer:Gecko Fireballs 75%Thunder Nerds 100%Awesome Possums 75%Samurai Scorpions 46%


Tyrel earned $22,500 in commission.

Let’s look at one last example:

A homemade glass cleaning solution calls for:

2 cups of water ½ cup of vinegar ¼ cup of rubbing alcohol

If the mixture was made with 5 cups of water, how much rubbing alcohol should be used?

Lesson Plan Day 1, cont'd. 7.RP.A.3

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We can start with a ratio of the two ingredients we’re comparing, and then set up a proportion with an equivalent ratio.

We can then use cross-products to create an equation to solve. 2n = 5(0.25) 2n = 1.25 n = 0.625 or If 5 cups of water are used, then 5/8 of a cup of rubbing alcohol should be used.

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To convert that to a percentage, we need to remember (from back in 6th grade) that percentages always represent a part out of 100. So, we want to know what part out of 100 is equivalent to 6 parts out of 13?

Proportions help us by setting up equivalent ratios in the form of equations that we can solve to find missing information. Just be careful to double check that the ratios in your proportion are both set up the same way.

To determine Tyrel's commission earnings, we can set up a proportion with the equivalent ratios of 6 out 100 and the unknown amount of Tyrel's commission out of 375,000.

Let’s see how this reasoning might help us in another situation.Tyrel is a real estate agent, and he makes 6% commission on each house he sells. This means he earns 6% of the selling price of the house. He recently sold a house for $325,000. How much commission did Tyrel earn?We can solve this in multiple ways, but let’s focus on our proportional reasoning and make a ratio with what we know. We know that 6% represents 6 parts out of 100.

Did you know that equivalent fractions are proportions? 2/5 and 8/20 are equivalent fractions, both representing the same proportion. And proportions have a special quality where the cross products are equal to each other.

Can you see that right now we could divide 6 by 13, and then multiply by 100 to get the value of n? That is what Dave and Shannon did.

We could use cross-products like we did before, or you may notice that we could multiply 100 by 3750 to get 375000. To maintain equivalency, we then multiply 6 by 3750.

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n = • 100 n ≈ 0.46 • 100

13n = 6(100) 13n = 600 n ≈ 4.6

n ≈ 4.6

613

5n

613

613

partwhole

partwhole

wateralcohol

n100

6100

20.25

n100

58

25

820

= 2(20) = 5(8) 40 = 40

Because we have a proportion set up for the win percentage, and because we know the cross products should be equal, we can use those cross products to create an equation we can solve.

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partwhole

6100

c375000

=part

whole6

10022500

375000x 3750

x 3750


MaterialsCopies of Sport Stats Practice Printable, 1 per student•

Practice Printable/Exit TicketAllow 16 minutes

7.RP.A.3Lesson Plan Day 2

Procedure1. Distribute copies of the Practice Printable. Have students work through the front page. 2. Exit Ticket: Ask students to rate their personal understanding of the problem on a scale of 1 to 3. • 1 = I need more help; 2 = I need more time, yet mostly understand; 3 = I’ve got this! • Have students put the number on their Practice Printable and turn them in. 3. Sort Practice Printable based on student self-assessment and professional teacher judgment

of accuracy of the response. This sorting can be used for grouping students for differentiation of instruction the following day.



Procedure1. Assign the Simulation Trainer to all students.2. Tell students to navigate to the Simulation Trainer assignment.3. Have students work individually to start.4. Consider using varied protocols that include peer teaching.5. Use Progress Monitoring on the Teacher Dashboard to determine which students are having difficulty. Provide individual help when necessary.

Materials• Sport Stats Simulation Trainer• Student Devices• Paper and Pencil• Student Headphones

Allow 25 to 35 minutes

The Math SimulatorTM

Simulation Trainer


Differentiation PlanRemediation

Meet with students who were unsuccessful on the Exit Ticket in a small group. Consider using whiteboards to

work through problems on the Practice Printable together.

Practice

Students who completed the Exit Ticket but need more practice should spend the class period completing the

Practice Printable. Encourage them to confirm strategies and solutions with each other. Any additional time

remaining should be spent getting started on the Student Reflection.

Enrichment

Students who demonstrated confident mastery on the Exit Ticket can finish the Practice Printable and spend

the remaining time getting started on the Student Reflection or completing the following:

• Continue exploring multi-step proportional problems:

http://pbs-ingest.s3.amazonaws.com/eastern_tennessee/7.RP.A.3/01.html

• Create a problem using markup, sales tax, and selling price.

• List three other real-world situations where percentages are used and explain.

Practice PrintableAllow 26 minutes

MaterialsSport Stats Practice Printable•


Procedure1. Group students according to the prior day's Exit Ticket evaluation.2. Redistribute previous copies of the Practice Printable and implement the Differentiation Plan as they finish the Practice Printable. Encourage them to show their work.3. Collect completed Practice Printable.






7.RP.A.3

Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest; tax; markups and markdowns; gratuities and commissions; fees; percent increase and decrease; percent error.

About this standard

Date PeriodName



Lesson Plan Day 3, cont'd.

Date PeriodName

Instructions:1. Draw a visual representation of the story and math concept. Include a “relevant title”. Be creative and use color!2. Write a clear explanation of the math concept in the story.3. Show the math problem from the story and its solution.4. Create your own multiple choice test question using the same math concept from the story. Circle the correct answer.5. Use the rubric below to grade yourself by circling how you did in each category. Turn this in with your Student Reflection Artifact.

My drawing and title are creative, colorful, and relevant to the story. I put sincere effort into my work.

My math explanation is clear and concise. I showed complete understanding of the math concept.

My solution to the math problem is correct and shows my work.

My test question is original and directly relates to the math concept. I have the correct answer.

My test question is original and directly relates to the math concept. I have an incorrect answer.

My test question is not original, but it relates to the math concept. I have the correct answer.

My drawing and title are somewhat creative, colorful, and relevant to the story. I put good effort into my work.

My math explanation is somewhat clear and concise. I showed partial understanding of the math concept.

My solution to the math problem is incorrect, but shows my work.

I didn’t include a title, but my visual is creative, colorful, and relevant to the story. I put some effort into my work.

My math explanation is not very clear nor concise. I showed limited understanding of the math concept.

My solution to the math problem is correct, but does not show my work.

I didn’t include a visual representation. I included a relevant title, but my effort was minimal.

My math explanation is not clear. I didn’t understand the math concept.

My solution to the math problem is incorrect and does not show my work.

My test question doesn’t relate to the math concept.

I didn’t include a visual representation or title.

I didn’t explain the math.

I didn’t include a math problem or solution.

I didn’t include a test question.

Visual Representation

4 3 2 1 0

Math Explanation

Math Problem

Test Question

MidSchoolMath

STUDENT REFLECTION ARTIFACTThis will help you with in-depth understanding.

Example:

Student Reflection 1

7.RP.A.3Student Reflection

Allow 20 minutes

Materials• Copies of Student Reflection rubric, 1 per student• White Paper• Colored Pencils

Procedure1. Available in the Student Reflection lesson on Teacher Dashboard, print and distribute the rubric. Discuss requirements with students.2. Distribute white paper and colored pencils to students.3. Have students begin the Student Reflection by sketching a draft. They will have additional time the following day to complete it.





Clicker QuizAllow 30 minutes

MaterialsSport Stats Clicker Quiz Student DevicesPaper and Pencil

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1. Ask students to log into their account and access Virtual Clicker. 2. Open the Clicker Quiz, whole class. 3. Prompt students to enter the quiz code on their device. 4. Launch quiz. 5. For each question: a. Show question and give students time to work. Consider using various protocols (i.e., students work individually, work with a partner, or maybe they have to agree with an entire table). b. Click “Vote,” and students will have 10 seconds to enter a response. c. Analyze class distribution. Decide whether more teaching is necessary, either a mini-lesson from you or by having students share strategies. d. Click “>” to advance to the next question. e. You may either then “Skip” the question or repeat steps a through e.

Procedure


Procedure1. Students continue working and complete their Student Reflections.2. Consider having a Gallery Walk when they are complete, using the I Wonder…, I Notice… protocol and sticky notes.

Gallery Walk (16-20 min)Display student work (such as Student Reflections) on classroom walls. Assign groups with tasks focused on

specific details (such as identifying different ways to solve a problem) and/or larger patterns (such as general

misconceptions). Tell groups to walk around, complete their task (≈ 8-10 min), then prepare and report brief

remarks to the class with their broader “a-ha” and “why” understandings (≈ 8-10 min).

I Wonder . . . , I Notice . . . (8-10 min)Following a completed whole-class assignment, set ground rules for peer critique, including being thoughtful,

specific, helpful and joining in (≈ 1 min)! Choose a student to be “the originator” who is tasked to explain his or

her approach and solution to a problem (≈ 2 min), while other students listen only. Then ask other students to

ask “the originator” clarifying questions or comments that start with ‘I wonder’ and ‘I notice’ (≈ 5-6 min).

Date PeriodName

Instructions:1. Draw a visual representation of the story and math concept. Include a “relevant title”. Be creative and use color!2. Write a clear explanation of the math concept in the story.3. Show the math problem from the story and its solution.4. Create your own multiple choice test question using the same math concept from the story. Circle the correct answer.5. Use the rubric below to grade yourself by circling how you did in each category. Turn this in with your Student Reflection Artifact.

My drawing and title are creative, colorful, and relevant to the story. I put sincere effort into my work.

My math explanation is clear and concise. I showed complete understanding of the math concept.

My solution to the math problem is correct and shows my work.

My test question is original and directly relates to the math concept. I have the correct answer.

My test question is original and directly relates to the math concept. I have an incorrect answer.

My test question is not original, but it relates to the math concept. I have the correct answer.

My drawing and title are somewhat creative, colorful, and relevant to the story. I put good effort into my work.

My math explanation is somewhat clear and concise. I showed partial understanding of the math concept.

My solution to the math problem is incorrect, but shows my work.

I didn’t include a title, but my visual is creative, colorful, and relevant to the story. I put some effort into my work.

My math explanation is not very clear nor concise. I showed limited understanding of the math concept.

My solution to the math problem is correct, but does not show my work.

I didn’t include a visual representation. I included a relevant title, but my effort was minimal.

My math explanation is not clear. I didn’t understand the math concept.

My solution to the math problem is incorrect and does not show my work.

My test question doesn’t relate to the math concept.

I didn’t include a visual representation or title.

I didn’t explain the math.

I didn’t include a math problem or solution.

I didn’t include a test question.

Visual Representation

4 3 2 1 0

Math Explanation

Math Problem

Test Question

MidSchoolMath

STUDENT REFLECTION ARTIFACTThis will help you with in-depth understanding.

Example:

Student Reflection 1

Student ReflectionAllow 20 minutes

• Student Reflections from Day 3• White Paper• Colored Pencils• Student Calculation Devices• Sticky Notes

Materials

Lesson Plan Day 4, cont'd. 7.RP.A.3

SPORT STATSArtifact 1




7.RP.A.3

Use proportional relationships to solve multi-step ratio and percent problems. Examples: simple interest; tax; markups and markdowns; gratuities and commissions; fees; percent increase and decrease; percent error.

About this standard

Date PeriodName


APPLYING THE STANDARD

MidSchoolMath 2 of 2

Date PeriodName

How might this standard appear on a test?

Sport Stats

Complete the table. Round to the nearest cent.1)

During a science lab, Rocco determined that the boiling point of ethyl alcohol is 75°C. The actual boiling point of ethyl alcohol is 78°C. What is Rocco’s percent error?

2)

A shop owner marks up the price he pays for each item by 30% to determine the selling price. What is the selling price of a pair of sneakers, for which he pays $45.00?

3)

Jody makes a cleaning solution using 3 cups of soap, 2 cups of vinegar, and 6 cups of water.4)

Complete the chart. Use the formula i = prt where i = interest earned, p = principal (starting amount), r = interest rate, and t = time in years.

5)

If she mixes in 3 cups of soap, what is the amount of vinegar and water that she will need?

b)

If she mixes in 6 cups of vinegar, what is the amount of soap and water that she will need?

c)

What part of the solution is soap?a)

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Documents

DETAILED LESSON PLAN: SPORT STATS - midschoolmath.com · MidSchoolMath Lesson Plan: Sport Stats 4 Lesson Plan Day 1, cont'd. Materials • Sport Stats Resolution video 4. After determining