### Examples

Gerald is trying to gain muscle and needs to consume more protein every day. If he has a protein shake that contain 32 grams and the entire shake is 340 grams, what percentage of the entire shake is protein? What is the ratio between grams of protein and grams of non-protein?### Clarifications

*Clarification 1:*Instruction includes the comparison of to in order to determine the percent, the part or the whole.

**Subject Area:**Mathematics (B.E.S.T.)

**Grade:**6

**Strand:**Algebraic Reasoning

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## Benchmark Instructional Guide

### Connecting Benchmarks/Horizontal Alignment

### Terms from the K-12 Glossary

- Rate

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

In elementary grades, students worked with creating equivalent fractions, as well as operations with whole numbers and fractions. In grade 6, students use ratio relationships to solve problems involving percentages. In grade 7, students will solve multi-step problems and proportional relationships involving percentages.- Students should understand that percent (%) represents a part to whole relationship.
- Instruction includes the connection to ratio relationships to determine the part, the whole or the percentage
*(MTR.5.1)*.- For example, when determining the how much 40% is of 24, students should compare the ratio $\frac{\text{x}}{\text{24}}$ to the ratio $\frac{\text{40}}{\text{100}}$.

- Instruction does not include the use of proportions or cross multiplication to solve problems involving percentages.
- Instruction includes the use of models to represent percentages such as bar models, number lines or ratio tables to help visually represent the relationship
*(MTR.2.1)*.- Bar Models70% $o$$f$ 120 = 84
- Number Lines70% $o$$f$ 120 = 84
- Ratio Tables70% $o$$f$ 120 = 84

- Bar Models

### Common Misconceptions or Errors

- Students may not understand the difference between an additive relationship and a multiplicative relationship.
- Students may incorrectly set up ratios because of a misunderstanding of the part and the whole addressed in the situation.
- Students may not recognize simplified forms of ratios in order to find equivalent ratios to determine the percentage, the whole or the part.

### Strategies to Support Tiered Instruction

- Instruction includes finding an equivalent unit rate (either part or whole) then multiplying to find the desired equivalent ratio.
- For example: Steve wants to determine how much a 15% tip is if the bill is $80.00.

Use a visual representation to show 80 represents 100%Divide the ratio by 80Multiply the resulting ratio by 15Using the equivalent ratios, 12 is 15% of 80, so the tip is $12.00.

- For example: Steve wants to determine how much a 15% tip is if the bill is $80.00.

### Instructional Tasks

*Instructional Task 1*

**(MTR.4.1, MTR.6.1, MTR.7.1)**Carlos predicts that his math homework will take him 60 of the total of 75 minutes he has available for homework tonight.

- Part A. At this rate, how many minutes would Carlos spend on math homework out of a total of 100 available minutes?
- Part B. What percentage of the available homework time does Carlos predict he will spend doing math? Explain how the answer to this question is related to the answer in Part A.

### Instructional Items

*Instructional Item 1*

Find the percent equivalent to $\frac{\text{60}}{\text{115}}$. Round to the nearest tenth percent.

*Instructional Item 2*

15% of 80 is what value?

*Instructional Item 3*

Sami is keeping track of the amount of salt she consumes each day. According to the label on her macaroni and cheese box, one serving contains 470 mg of sodium (salt). If 470 mg is 20% of the recommended daily amount, how many milligrams of sodium are recommended for the whole day?

**The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.*

## Related Courses

## Related Access Points

## Related Resources

## Educational Game

## Formative Assessments

## Lesson Plans

## Perspectives Video: Professional/Enthusiasts

## Problem-Solving Tasks

## Teaching Idea

## Tutorials

## Video/Audio/Animation

## STEM Lessons - Model Eliciting Activity

In this Model Eliciting Activity, MEA, students will utilize mathematical computation skills involving percentages and critical thinking skills to select the best tire deals advertised.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

In this Model Eliciting Activity, MEA, students will create a procedure for ranking high school basketball players. Students are given statistics for each player and are asked to recommend the best player to play for an all-star team after determining the free throw, three-point, and field goal percentages. Students write about the procedure used to make their decisions. In a twist, students are given additional data to determine the mean points per game.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

This MEA requires students to formulate a comparison-based solution to a problem involving choosing the BEST daycare based upon safety, playground equipment, meals, teacher to student ratio, cost, holiday availability and toilet training availability. Students are provided the context of the problem, a request letter from a client asking them to provide a recommendation, and data relevant to the situation. Students utilize the data to create a defensible model solution to present to the client. Students will receive practice on calculating a discount, finding the sum of the discounts, working with ratios and ranking day cares based on the data given.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

In this activity, students will engage critically with nutritional information and macronutrient content of several fast food meals. This is an MEA that requires students to build on prior knowledge of nutrition and working with percentages.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

This MEA asks the students to decide which company would be the “best and the worst” to use to purchase scuba diving masks for Tino’s Scuba Diving School to provide to their diving certification students. Furthermore, the students are asked to suggest which type of scuba diving masks should be purchased in term of multiple panes – single pane mask, double pane mask, full face mask, skirt color, fit, durability, and price. Students must provide a "top choice" scuba diving mask to the company owner and explain how they arrived at their solution.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Students will read a letter from a painting company from New York who are planning to expand to Florida. They need help deciding on which paint sprayers to purchase. Students will use their understanding of rate and percentages to analyze data and make suggestions.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

## MFAS Formative Assessments

## Student Resources

## Educational Game

In this activity, students are quizzed on their ability to estimate sums, products, and percentages. The student can adjust the difficulty of the problems and how close they have to be to the actual answer. This activity allows students to practice estimating addition, multiplication, or percentages of large numbers. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Educational Game

## Problem-Solving Tasks

This problem asks the student to find a 3% sales tax on a vase valued at $450.

Type: Problem-Solving Task

Students are asked to determine the percent of the area of a store covered by a security camera. Then, students are asked to determine the "best" place to position the camera and support their answer.

Type: Problem-Solving Task

Use the information provided to find out the original price of Selina's shirt. There are several different ways to reason through this problem; two approaches are shown.

Type: Problem-Solving Task

Use the information provided to find out what percentage of Dana's lot won't be covered by the house.

Type: Problem-Solving Task

This problem provides an interesting geometric context to work on the notion of percent. Two different methods for analyzing the geometry are provided: the first places the two squares next to one another and then moves one so that they overlap. The second solution sets up an equation to find the overlap in terms of given information which reflects the mathematical ideas reason about and solve one-variable equations and inequalities.

Type: Problem-Solving Task

## Tutorials

In the video, we find the percent when given the part and the whole.

Type: Tutorial

This video demonstrates how to find percent of a whole number.

Type: Tutorial

You're asked to find the whole when given the part and the percent.

Type: Tutorial

This video demonstrates how to write a decimal as a percent.

Type: Tutorial

This video deals with what percent really means by looking at a 10 by 10 grid.

Type: Tutorial

This video demonstrates a visual model of a percent greater than 100.

Type: Tutorial

## Video/Audio/Animation

Percentages are one method of describing a fraction of a quantity. the percent is the numerator of a fraction whose denominator is understood to be one-hundred.

Type: Video/Audio/Animation

## Parent Resources

## Problem-Solving Tasks

This problem asks the student to find a 3% sales tax on a vase valued at $450.

Type: Problem-Solving Task

Students are asked to determine the percent of the area of a store covered by a security camera. Then, students are asked to determine the "best" place to position the camera and support their answer.

Type: Problem-Solving Task

Use the information provided to find out the original price of Selina's shirt. There are several different ways to reason through this problem; two approaches are shown.

Type: Problem-Solving Task

Use the information provided to find out what percentage of Dana's lot won't be covered by the house.

Type: Problem-Solving Task

This problem provides an interesting geometric context to work on the notion of percent. Two different methods for analyzing the geometry are provided: the first places the two squares next to one another and then moves one so that they overlap. The second solution sets up an equation to find the overlap in terms of given information which reflects the mathematical ideas reason about and solve one-variable equations and inequalities.

Type: Problem-Solving Task