The Arizona STEM Acceleration Project

Friendly Percentages: Helpful Tools

Friendly Percentages: Helpful Tools

A 6th Grade STEM Lesson

Narey Zaragoza

7/31/23

Notes for Teachers

• Length of lesson: 45 minutes
• Students will work with partners.
• Lesson is written to embed several of the mathematical practices.

List of Materials/Tools

• Paper/pencil
• White boards/dry erase markers
• Double number lines
• Tape diagrams
• Tables
• Access to Technology - Google Slides

Arizona Mathematics Standards

Math:

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6.RP.A.3 Use ratio and rate reasoning to solve mathematical problems and problems in real-world context (e.g., by reasoning about data collected from measurements, tables of equivalent ratios, tape diagrams, double number line diagrams, or equations).

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Mathematical Practices

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1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

Arizona Educational Technology Standards

Creative Communicator

6-8.6.b. Students create original works or responsibly repurpose digital resources into new creative works.

Objective(s):

Today

• I will use tape diagrams, double number lines, and or tables to solve problems involving benchmark percentages.
• I will create a Google Slides presentation to demonstrate what I learned and create a word problem for others to solve.

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Agenda

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1. Warm-up (5 minutes)
2. Challenge 1 (10 minutes)
3. Challenge 2 (10 minutes)
4. Challenge 3 (10 minutes)
5. Cool down (10-20 minutes)

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Vocabulary

Percentage

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• Percent means for every 100.
• It is represented by the percent symbol: %.
• We use percents to represent ratios and fractions.

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Words to emphasize throughout strategies applied:

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Tape Diagrams

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Double Number Lines

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Tables

Warm-up: Friendly Percentages (5 minutes)

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Students will use tape diagram to determine what is the bikers goal.

Instructions:

1. Arrange students in partners.
2. Display image to the left. Reminding students that 100% would be represented as a full bar, tell students they will get 1 minute of QUIET think time to solve how many Km represent 100% (Provide them a hand signal to show you when they are ready to explain their thinking.)
3. After majority of students have shown you the requested hand signal, provide around 2 minutes for students to share their response using Pair Share (Walk around and select students to share their solution and strategies)
4. Have your selected students share their responses. Other students can contribute with additional notices or extensions to others’ ideas.
5. Acknowledge any math terminology used by students, and encourage all to use math terminology when justifying their reasoning.

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Image from Desmos.com

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Solution

• 60 km = 100%

Explanations vary.

• 25% is like 1/4 so the whole goal would be 100% or 15 x 4=60 kilometers.
• There are four 25 percents in 100%, so you need to multiply by `4` to get the goal distance.

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Challenge 1 (10 minutes)

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Students will use double number lines to determine how far the biker rode.

Instructions:

1. Arrange students in partners.
2. Display image to the left. State the following:
• The biker’s goal was to ride 12 kilometers. Her app says she rode 150 % of her goal. How far did she ride.

3. Provide around 5 minutes for students to share their

response using Pair Share (Walk around and select students

to share their solution and strategies)

1. Have your selected students share their responses. Other students can contribute with additional notices or extensions to others’ ideas.
2. Acknowledge any math terminology used by students, and encourage all to use math terminology when justifying their reasoning.

​

Image from Desmos.com

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Solution

• 18 km = 150%

Explanations vary.

• ½ of 100 is 50, therefore half of 12 is 6. Top scale is going up by 6 so 150% is 18 km.

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Challenge 2 (10 minutes)

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Students will use double number lines to determine how far the biker’s goal distance.

Instructions:

1. Arrange students in partners.
2. Display image to the left. State the following:
• The biker’s app says they biked 8 kilometers, which is 20% of their goal. What was their goal distance?

3. Provide around 5 minutes for students to share their

response using Pair Share (Walk around and select students

to share their solution and strategies)

1. Have your selected students share their responses. Other students can contribute with additional notices or extensions to others’ ideas.
2. Acknowledge any math terminology used by students, and encourage all to use math terminology when justifying their reasoning.

​

Image from Desmos.com

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Solution

• 40 km = 100%

Explanations vary.

• Bottom scale is going up by 20 so skip count by 20 to 100 or multiply by 5. So 8 x 5 = 40 km.

Challenge 3 (10 minutes)

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Students will use double number lines to determine how far the biker’s goal distance.

Instructions:

1. Arrange students in partners.
2. Display image to the left. State the following:
• The biker’s app says he biked 30 km, which is 120%. What was his goal distance?

3. Provide around 5 minutes for students to share their

response using Pair Share (Walk around and select students

to share their solution and strategies)

1. Have your selected students share their responses. Other students can contribute with additional notices or extensions to others’ ideas.
2. Acknowledge any math terminology used by students, and encourage all to use math terminology when justifying their reasoning.

​

Image from Desmos.com

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Solution

• 25 km = 100%

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Assessment (10-20 minutes)

1. What is the definition of percent?

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2. Which tool helps you the most when dealing with percents?

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3. How much did Miko pay for his sneakers? Show your work using a tool and/or explain your strategy.

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Image from desmos.com

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Differentiation

Throughout the lesson, the teacher will walk around with a clipboard to check off students that are applying different strategies as they are discussed throughout.

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After looking at clipboard data and the cool down problem work, the teacher will look for common misconceptions, students that are setting up information incorrectly or making careless mistakes. The teacher can form different groups to meet needs in small group instruction.

Remediation

Extension/Enrichment

Students can research real-world examples of percentages used in sports. They can document their research, create a unique problem, and offer it to the class to solve.