Using CAS to allow students to investigate unit rates opens up a world of options due to the device recognizing words as variables. Teachers can actually enter one cup of sugar makes 2 cookies in fraction form on a TI-Nspire CX CAS and get the results shown below.
Asking questions that promote deep thinking about the topic gets students into the discussion.
- Why are these true?
- What stays the same?
- What changes?
- What other ratios would work?
- What other ratios would NOT work?
Asking the right questions is key to starting effective discussions, but what then? Multiple representations help students visually see what the math is doing which in turn leads to better understanding and skill mastery. Look at the following situation:
Joe can mow 7 lawns in 4 hours. How many lawns can he mow in 3 days?
Now look how the CAS can investigate this problem using Numerical form, a table, and a graph.
This allows students to see relationships between “doing the math” and “using the math.” See how long it takes the students to realize that the data is in hours but the problem is in days. The number 3 is nowhere in the data which will generate questions from students. This opens up a broad range of “teachable moments” which is what teachers love to see. The students want you to explain instead of you begging them to listen. Now let’s throw in some geometry.
This introduces using the unit rates for unit conversion. Although unit rates are a 6th grade skill, students can see how solving equations will play a part even though they haven’t mastered that particular skill. Ask the students to investigate how the device got that answer. You may never have to teach “cross multiply” again. 🙂