High School Mathematics Problems from Alaska

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Standards: Estimation and Computation, Functions and Relationships and Geometry.

Performance Standards: A3.3.4, A.4.3.2, A.4.3.4, A5.4.6

Concepts: Linear graphing, Finding slope, Relationship of x and y on a graph, and Comparing 2 lines on the same graph.

Carnegie Chapter: Formulas, Tables of Values, Graphs.

Overview: Frank has 17 dogs for his dog sled team. He has to determine cost of feeding the dogs during the winter and summer months when using commercially produced dog food.

Extensions: Determine the cost for the entire year with and without harvesting "dog salmon."

Dog Lot Math - Adapted from Alan Dick’s Village Math submissions.

Part I

Frank has 17 dogs that he has to feed during the year. Sacks of dog food cost Frank $12 each. During the summer months (May - September), each bag of dog food lasts 5 days.

1. How much will Frank spend after
   1. 5 days?
      
      
      
   2. 20 days?
      
      
      
   3. 27 days?
      
      
      
   4. 35 days?

       

2. Write an expression to represent how much money Frank will spend to feed his dogs during the summer. Define any variables you use.

    

    

    

3. Complete the table.

4. Construct a graph showing how much Frank will spend to feed his dogs during the summer. Label all axes and intervals and give your graph a title

5. If each month is counted as 30 days, how much will Frank spend to feed his dogs the entire month?  

6. If Frank spent $288 on dog food, how many sacks of dog food did he buy and how long would it last?

Part II

During the winter months (October - April), Frank continues to buy sacks of dog food to feed his dogs. Bags only last 4 days in the winter.

1. How much will Frank spend after
   1. 12 days?
      
      
      
   2. 36 days?
      
      
      
   3. 52 days?
      
      
      
   4. 108 days?

       

    

2. Write an expression to represent the amount of money that Frank will spend during the winter months to feed his dogs. Define any variables.

    

    

    

    

3. Complete the table.

4. Graph the table from Part II in the same graph as Part I.

5. What do you notice about the graphs of the two lines?

6. Which line is steeper?

7. Find the slope of each line.

8. What does the slope represent in each graph?

9. What does Frank spend per day
   1. During the winter?
      
      
      
      
   2. During the summer months?

    

10. How do your answers to question 9 relate to the slope?

For the Teacher's Guides, please email Alaska Native Knowledge Network

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."