# Women in Mathematics: Sophie Germain and Elasticity

## Curriculum Goal

Math

#### Junior: Number Sense

• Represent and solve problems involving the addition and subtraction of whole numbers that add up to no more than 10,000 and of decimal tenths, using appropriate tools and strategies, including algorithms.

Science

#### Junior: Understanding Matter and Energy

• Investigate energy transformation and conservation.

Social Studies

• Introduce students to accomplished female Mathematicians, specifically Sophie Germain and her work on elasticity.

## Context

• Whole-class discussion followed by individual or pair-based work at desks.

## Materials

• Background on elasticity and Sophie Germain (Appendix A)
• Data collection form (Appendix B)
• Elastic/spring powered toy (e.g., plane, wind-up toy)
• Four gummy worms per student
• Elastic bands (thicker is better)
• Rulers
• Scissors
• Paper towels (to keep gummy worms clean for eating)

## Lesson

• Read a short biography about the life and times of Sophie Germain (Appendix A).
• Demonstrate the use of the elastic/spring powered toy and ask students how they think it works. Where does the energy come from? How is it stored?
• Teach the class about elasticity (Appendix A) and tell students that they will determine the elasticity of a gummy worm in comparison to an elastic band.
• Have students measure the length of a gummy worm to the nearest millimetre. Record this as the starting length in the data collection table (Appendix B).
• From the rubber band, cut a section that is the same length as a gummy worm.
• Stretch the gummy worm as far as possible without breaking it and record the stretched length.
• Release the gummy worm, wait for it to stop contracting, and again measure its length. Record as the final length.
• Determine if there is any change in length by finding the absolute difference between the starting and final lengths.
• Repeat with the remaining gummy worms and the section of rubber band.
• Discuss what was observed and why this is important. Share with students how elastics are used in society (Appendix A).

## Look Fors

• Are students able to add and subtract decimals accurately? What strategies are they using?
• Do students recognize any similarities in the difference between the starting length of all gummy worms compared to their final length?
• Do students recognize the immense contribution Sophie Germain made to mathematics?

## Extension

• Experiment with the effect of temperature by conducting the experiment when materials are heated or cooled.

## Related Lessons

Students explore cross-cultural mathematics by examining how economic and political factors might lead to these differences.