High School Mathematics Problems from Alaska

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Firewood Problem

Mary Lou Smart
Southeast Island School District
msmart@sisd.k12.ak.us

Standards: Functions and Relationships

Performance Standards: A4.3.2, A4.3.4, A4.3.5

Concepts: Creating a table of ordered pairs, variables (dependent and independent), writing equations

Carnegie Chapter: Formulas, Tables of Values, and Graphs

Overview: The student will write and solve equations for the cost of firewood by the cord, then use this information to develop tables of values and graph their equations.

Firewood

A neighbor charges \$110.00 for each cord of firewood plus a \$50.00 delivery fee.

1. What will the neighbor charge for delivering:
1. 3 cords?

2. 5 and one half cords?

3. Write a complete sentence describing how you found these answers.

1. Write an algebraic equation for this problem. Define any variables.
1. Total cost of firewood =

1. Write an equation you can use to find out how many cords of firewood you would receive if the neighbor charged you \$875.00. Solve this equation, showing your work, and write your answer in a complete sentence. Write a sentence describing how you solved the equation.

1. Write an equation you can use to find out how many cords of firewood you would receive if the neighbor charged you \$270.00. Solve this equation, showing your work, and write your answer in a complete sentence. Write a sentence describing how you solved the equation.

1. Write an equation you can use to find out how many cords of firewood you would receive if the neighbor charged you \$1,370.00. Solve this equation, showing your work, and write your answer in a complete sentence. Write a sentence describing how you solved the equation.

1. Use the information from questions 1-5 to complete this table.
 Labels Units Expressions 380 655 7.5 2 12

1. Graph the equation for this problem situation. Label and choose an appropriate scale for each axis.

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Firewood

Your neighbor's son has volunteered to stack the firewood for \$10.00 per hour. He can stack 1 and one half cords an hour.

1. What will you be charged for stacking: (Round to the nearest cent.)
1. 3 cords?

2. 5 and one-half cords?

3. Write a complete sentence describing how you found these answers.

4. Write an algebraic equation for this problem situation. Define any variables.

Cost of stacking wood =

1. Using the information from Task 1 write an algebraic equation for the total cost of the firewood delivered and stacked.

Total cost of delivered and stacked firewood =

1. The total cost for delivered and stacked firewood from your neighbor was \$1,100. How much firewood did you receive?

1. Use the information from questions 1-3 to complete this table to show the total cost of delivered and stacked firewood.

 Labels Units Expressions 3 5.5 1100 575 750

1. Graph the equation for this problem situation. Choose appropriate scales for the axes and label them.

1. Looking at the graph, what would be the approximate cost of 9.5 cords of firewood delivered and stacked?

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Handbook for Culturally Responsive Science Curriculum by Sidney Stephens
Excerpt: "The information and insights contained in this document will be of interest to anyone involved in bringing local knowledge to bear in school curriculum. Drawing upon the efforts of many people over a period of several years, Sidney Stephens has managed to distill and synthesize the critical ingredients for making the teaching of science relevant and meaningful in culturally adaptable ways."

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