High School Mathematics Problems from Alaska

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Cutting Cordwood

Brenda Jones
bjones@northstar.k12.ak.us

Standards: Functions and Relationships.

Performance Standards: A4.3.2, A4.3.4, A4.3.5, A4.4.2.

Concepts: Graphing data from a table to a coordinate grid, using variables to write algebraic equations.

Carnegie Chapter: Formula, Tables of Values, and Graphs.

Overview: Two young men are earning money by cutting cords of wood.

Cutting Cordwood

Anthony and Jacob want to earn money to buy a new dog sled by selling cordwood to the residents of Fort Yukon. They have determined that together they can cut 1.8 cords of wood in an 8-hour day.

1. How many cords can they cut in
1. 2 days?

2. 1 week?

3. 1 month?

4. 1 year?

2. Find the algebraic expression for this situation. Define the variables you use.

1. How many days will it take to cut
1. 18 cords?

2. 36 cords?

3. 200 cords?

2. What fraction of an 8-hour day is
1. 4 hours?

2. 5 hours?

3. How many cords of wood can Anthony and Jacob cut in
1. 4 hours?

2. 5 hours?

3. 1 hour?

4. They earn \$250 per cord of wood. How much will they earn by selling
1. 10 cords?

2. 20 cords?

3. 5 cords?

5. Write an algebraic expression for their earnings and explain your reasoning. Define any variables.

1. If they begin next season with 10 cords already cut from the pervious season, how many will they have after
1. 10 days?

2. 20 days?

3. 1 month?

2. Fill in the following chart based on the information in #8.

 Labels Time Cords of Wood Units Expressions 0 10 10 20 30 25 82 118

1. Use the information in the table to complete the given graph. Label axes, include intervals, and create a title for the graph.

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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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