A common core standard for Grade 8 states “Know and apply the properties of integer exponents to generate equivalent numerical expressions.”
No matter how you approach this standard, students seem to struggle with how abstract the concept is and why they need to learn it in the first place.
Last year, I decided to show them the importance of learning exponents by introducing them to the concept of exponential growth through inquiry, and then go back to showing them the need to simplify exponential expressions.
We watched “Pay it Forward”. The movie talks about a middle school boy who was challenged by his teacher to find a way to change the world. So, Trevor, the boy, decides to help three people in a way that will change their lives, and then ask each one of them to pay it forward to three others.
After watching the movie, students were asked to create:
- A tree diagram modeling the situation for 4 rounds using Google Drawing
- A table of values, showing the number of people reached after 6 rounds
- An equation that can generalize the pattern (students were only familiar with linear equations by then)
- A graph using a tool of their choice to model the situation
- Some used Geogebra (as an app on Google Drive)
- Some used Google Spreadsheets:
Students then were asked to predict using the graph, the number of people reached if people paid it forward for 10 rounds, and compare to a population of a country or city. Another prediction was using the equation, for round 20.
Students reflected on the whole process and compared to linear growth, and they were astonished! We had a good class discussion after the mathematical component was done.
Part two of the task was the writing part. They had to research and write about someone in history whose life was dedicated to helping others. Students wrote about Mahatma Gandhi, Mother Teresa, Martin Luther King, John Lennon, and others. They also cited their research.
Part three was optional. Students were regularly encouraged throughout the year to reach out to people. They were encouraged to write journal entries about it. Some examples are shown below:
Students shared all components via Google Drive.
Through this task, students understood the impact of exponential growth and the purpose of the standard in their curriculum. They learned about people who dedicated their lives serving others, and more importantly, students learned to get out of their comfort zones, see the need around them, and reach out to those in need.
Hilda Hanania
Math Educator at American Community School
Beirut, Lebanon
Twitter Handle: @hilda_hanania
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