Make Math Moments Academy › Forums › Full Workshop Reflections › Module 2: Engaging Students Using Problems That Spark Curiosity › Lesson 24: How to transform textbook problems into captivating tasks › Lesson 24 Question & Sharing › Reply To: Lesson 24 Question & Sharing

Original Problem taken from 8th grade math (prealgebra) unit on solving systems of equations: A taxi ride costs $3 plus $2 for each mile driven. You spend $39 on a taxi. This can be modeled by the equations 2m+3=39, where m represents the number of miles driven. How long was your taxi ride?
Curious problem:
Step 1: My mom is taking a taxi ride.
Step 2: WDYN&W? Maybe they wonder where she’s going. She must not have her own car OR she’s in an unfamiliar place (my Alabamian students will immediately go to NYC!). How long is the ride? How much money is she going to spend?
Step 3: Pick the wonder about how far she traveled and make an estimation. Allow students to google the average cost of a taxi and come up with a reasonable distance for a taxi to be taken. Ask students, what questions do you have that would help you make your estimate better?
Step 4: Slowly introduce information. The equation that models the cost of the ride is 2m+3=39. What does this tell us? WDYN&W now? Can you update your estimate?
ALTERNATIVELY for Step 4: First say that the taxi driver charges $3 up front. Update estimate. Then say the taxi driver also charges $2 per mile. Update estimate. Then say the total cost of the drive. Update estimate.
Would love for someone to weigh in here and critique this! I’m wondering which information is best to give them since the goal of the word problem is to give them an equation in hopes they solve it with inverse operations…but is that really necessary here? I feel like as an extension (if using my alternative step 4) I could ask the students to write a linear equation that shows the relationship between miles and cost, but then I’m not really asking the same thing this question is asking. To be fair, I really don’t think this question is asking something practically applicable to the real world!