Snowshoe Math
Students will determine the surface area of snowshoes and calculate their PSI (pounds per square inch) on a pair of snowshoes.
Materials Needed
Resources
Art Materials
- Graph paper
- Large paper
- Markers
Documents
Activity Process
Motivation:
The class will talk about and apply understandings of the concept of weight distribution over a specific area to the construction of snowshoes. Then students will identify different types of snowshoes and describe the importance of the various shapes in forested or open areas.
Demonstration:
Students will compare psi of different footprints to help understand the concept.They will conduct a "snow test" stepping through deep snow with their regular school shoes and then with a pair of snowshoes. The class will talk about the differences in weight distribution between the two shoes and what makes travel harder/easier.
Activity:
- Have students trace their boot on centimeter graph paper.
- Since the boot does not have straight edges, some estimating will be necessary. Ask the students to count the number of square centimeters covered by the boot surface. Also have the students count the squares that are more than one-half included inside the outline of the boot, but caution students NOT to count squares that are less than one-half included.
- Ask the students what they think it is that makes you sink into the snow. What relationship can students think of between weight and sinking in snow?
- Measure weight in kilograms of all students individually. Use the same scale for everyone.
- Can students think of a numerical relationship (ratio) between the area of their boot and their weight? Call it Psi or "sink in the snow factor." Ask all students to find their own sinking factor (division required!)
- Students then do similar exercise finding the area in square centimeters of a pair of snowshoes.
- What characteristic about snowshoes and large feet might cause users to stay on top of the snow better?
Closure:
Can you think of any other modes of transportation that use this same idea of psi? Or any other areas of daily life? (skis? snow machines? dog sleds?)
Checks:
Have students describe in pictures the relationship between weight and surface area and force, and how psi changes as you increase or decrease the surface area.They will also draw the various examples of snowshoe shapes and sizes, for uses in different terrain.
Vocabulary Words
- Aagim (Snowshoe)
- Biboon (Winter)
- Goon (Snow)
Comments
The Smartboard was an essential piece to help students proceed through the math processes in an engaged way. Without the pictures and connections to winter sport and lifeways, this lesson on graphing and square footage would not have been nearly as interesting for anyone! Constructing snowshoes would be a terrific extension of this lesson.