Math Focus 9
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# Burning Calories

## INTRODUCTION

The number of calories burned during an activity depends on several factors such as the activity, the mass of the person, and the effort used for the activity.

As a personal trainer at a fitness centre, your task will be to present suggestions for activities and to respond to requests for suggestions. You will interpret tables on the Internet that relate the number of calories burned and lengths of time for various exercises. Then you will use equations, tables of values, graphs, and inequalities to make and support suggestions.

## THE PROCESS

1. Go to How Many Calories Am I Burning?. Describe how to read the second table which begins with aerobics (traditional at high intensity), the third table which begins with basketball, and the last table which begins with aerobics (traditional) about the number calories burned for various body masses.
Mass is called weight in the table on the website.
• Explain how the expression 4x and the equation C = 4x represent the number of calories burned in 40 min for an activity in the second table. Choose an activity and a mass. (You can use Conversions to convert the mass from pounds to kilograms.) Use the equation to determine the number of calories burned in 40 min. Then create a table of values and a graph on grid paper to represent the equation. How does the graph show your answer?
• Explain how the equation N = 3x + x + 100 represents the number of calories burned in a 30 min session as well as a 10 min session for an activity in the third table, after burning 100 calories on the way to the fitness centre. Use the equation, a table of values, and a graph to represent the relation for your choice of activity and a mass in the third table on the web site. Solve the equation and explain the graph to make a suggestion for a client.
1. A male client has a mass of about 77 kg. (You can use Conversions to convert the mass from kilograms to pounds.) Suggest an activity from the third table on How Many Calories Am I Burning?. Use an equation, table of values, and graph to represent your suggestion. What would you tell the client about how the representations support your suggestion?
2. Repeat step 2 for a female client with a mass of about 56 kg.
3. A client has already burned 250 calories at the fitness centre and asks you for a suggestion about an activity outside the centre to burn more calories. Use the third table on How Many Calories Am I Burning?. Write an equation to represent a suggestion. Describe what the graph representing the equation would look like. How could explain your suggestion to the client? What mass did you use for the client?
4. Is the relation between the number of calories burned for racquet ball and a person’s mass linear? Explain.
5. Go to Calories Burned During Exercise. Describe how to read the table.
Mass is called body weight in the table on the web site.
• Explain how the equation C = 1000 – c2 represents the number of calories still to be burned for a goal of 1000 calories after 30 min for one of the activities. Use the equation and a table of values to represent the relation for an activity in the table. Describe what the graph representing the equation would look like, or draw the graph. Solve the equation and make a suggestion for a client.
1. Choose a mass, an activity, and a length of time from Calories Burned During Exercise. Use an equation to determine the number of calories burned.
2. A client has a mass of about 59 kg. Her goal is to burn 1500 calories during a few sessions of the same activity at the fitness centre. Make two different suggestions for her. Use an equation or a graph to show her how she can reach her goal. Explain what you would tell her about these representations.
3. A client at the fitness centre asked you for two suggestions for burning more than 600 calories in one session at the fitness centre. Make two suggestions and write an inequality for each. Solve each inequality and verify the solutions. Then graph the solutions. How would you use the representations to explain your suggestions?
4. Choose the relation for one of the questions. What is the rate of change? Explain how you know. What other way could you determine the rate of change?
5. Ask someone to explain your answer for one of the questions. Do you agree with the explanation? Why or why not?

## RESOURCES

Websites:

Conversions

Calories Burned During Exercise

File:

Grid paper

Materials:

a pencil
paper

## ASSESSMENT

 Mathematical Processes Work meets standard of excellence Work meets standard of proficiency Work meets acceptable standard Work does not yet meet acceptable standard Communication Explanations for clients are clear and well organized, with insightful use of visual and written representations. Explanations for clients are complete and clear, with good use of visual and written representations. Explanations for clients are complete, with appropriate use of visual and written representations. Explanations for clients are incomplete, with little use of appropriate visual and written representations. Connections Makes insightful connections between the context and linear relations, and among the representations. Makes meaningful connections between the context and linear relations, and among the representations. Makes simple connections between the context and linear relations, and among the representations. Makes minimal or weak connections between the context and linear relations, and among the representations. Reasoning Comprehensively analyzes the tables and the requirements for clients to make insightful generalizations. Completely analyzes the tables and the requirements for clients to make logical generalizations. Superficially analyzes the tables and the requirements for clients to make simple generalizations. Is unable to analyze the tables and the requirements for clients to make generalizations. Visualization Uses insightful visual representations that lead to effective solutions. Uses insightful visual representations that lead to effective solutions. Uses meaningful visual representations that lead to workable solutions. Uses unclear visual representations that lead to inaccurate solutions.