Teaching lessons where patterns are involved is fun!
When I began having students make charts as they were learning about negative integer exponents, it made it so much easier for them to understand rules and concepts.
Let’s face it - to students, it's not logical that negative exponents result in fractions. Looking at a chart and examining patterns changes promotes understanding.
I begin by having students complete a chart like the one below.
Next, I have them extend the chart as shown. Then, ask students to study the chart and explain what is happening as they examine the chart which goes from 625 to 125, 125 to 25, and 25 to 5. Hopefully, they'll recognize that each number is divided by 5 as they work their way down the chart.
I always tell my students that math is all about patterns.
They love to look for patterns!
We complete the rest of the chart together by continuing with the pattern of dividing by five. This is a perfect way to review the exponent of zero rule and introduce negative exponents at the same time.
After completing this chart with students, I have them complete a similar one on their own. Then, I follow that up with a brief class discussion to reinforce the observation that negative exponents result in fractional answers.
