CAS with Percentages

When I was first introduced to a Computer Algebra System (CAS) device, I thought it was a great tool for my AP Calculus class. The more I used CAS activities the more I realized it would be a great tool for all math students.

I believe student investigations are key in deeper understanding of mathematics.

CAS devices such as the TI-Nspire™ CX CAS handheld and the TI-Nspire™ CAS App for iPad® give students the opportunity to investigate the why’s and how’s of math.

As I think about important skills for students, percentages stand out to me as an important skill for both elementary and middle school students to learn that is not understood completely. The students memorize the algorithms we set before them but never really reach the mathematical understanding of why and how we use them. Using the TI-Nspire™ CX CAS handheld and some teacher preparation, students can delve into the why’s and how’s of percentages. For example, start the lesson by putting the following slide on the board or send to student handhelds.

Ask students the following questions:

  • What stays the same?
  • What changes?
  • Why do you think the last one is false?

Using a Quick Poll in the TI-Nspire™ CX Navigator™ system or a cooperative learning strategy facilitates student discussions on their answers. The students can use their devices to investigate other percentages to see if their theories hold true. Teachers can use the activity Solving Percent Problems from the Math Nspired website as a follow-up activity or intro activity for the lesson on using percentages to solve problems. As the unit progresses, other investigations and discussion starters could look like this:

Ask questions such as:

  • What do you notice about the numbers?
  • What is the relationship between the numbers?
  • What conclusion can you make based on this pattern?

Also show some other percentages such as the slide below asking similar questions.

Of course as in any good unit of study, opportunities for practice and hands-on applications are needed throughout the unit to master the skill but getting students motivated to understand the math is the first step. Investigations such as these will allow students to delve deeper into the math instead of skimming the surface with algorithms only.

Michelle Bonds



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