Carpe Diem! Problem Solving on a Morning Bike Ride
Wednesday, July 21, 2010 at 8:36AM 
This weekend, I took our 6 year old for a bike ride around SELU’s campus. Along the way, something interesting began to happen: a spontaneous, math discussion. Let me explain! As we were running/riding, we each pretended to do “tricks” as if we were part of the latest Mario Wii game. 60 points if mom “jumps” the curb! 50 points if Ellie “pops” her front wheel! You get the idea. Then, the conversation shifted from video gaming fun to a lesson in critical thinking and problem solving. Check out our dialogue.
Mom: How many points would you score if you “popped” your wheel twice?
Ellie: 100 points.
Mom: Great! How did you know that?
Ellie: Well, two 50’s make 100.
Mom: Great! Can you make an addition sentence out of this?
Ellie: 50 + 50 = 100.
Mom: Fantastic! can you tell me the corresponding multiplication sentence?
Ellie: Easy! 50 x 2 = 100.
Mom: Super cool! Way to go! What if you “popped” your wheel 4 times? How many points would you score?
Ellie: Let me think. Well, 50 + 50 = 100 and another 50 + 50 = 100 and two 100”s are 200. So, I would score 200 points. Right?
Mom: Wow! Great thinking! So, 50 + 50 + 50 + 50 = 200. What would be the matching multiplication sentence?
Ellie: Easy! 50 x 4.
Mom: Now, for the bonus round! What if you want to score 400 points? How many times would you have to “pop” your wheel?
Ellie: Let me see... I would just double the number of times because 200 and 200 make 400. So, I would need to “pop” 8 times.
Mom: Wow! I am so proud off you! Great thinking! You’re awesome! What would be the multiplication sentence?
Ellie: 50 x 8 = 400.
We rode on for a few minutes. Along the way, I have to admit, I was beaming with delight! She actually got it! She clearly understands the relationship between addition and multiplication and was able to apply that knowledge to find solutions. Yea! My enthusiastic thoughts were then interrupted by Ellie.
Ellie: Mom, let’s do more math. That was really fun! Now, I am going to do this trick for 25 points. (She was standing up while riding her bike. So, we called this cool move the “stand!”)
Mom: Okay, great! Cool move! How many “stands” would you have to do to reach 100 points?
Ellie: Well, each “stand” is 25 points. That’s like a quarter, right? So, it takes 4 quarters to make a dollar. So, I would need to do 4 “stands.”
Mom: Totally correct! Now, what if you wanted to earn 200 points?
Ellie: Well, 200 is just 100 doubled. So, I would double the 4 and get 8. I would have to do 8 “stands.”
Mom: Super thinking! Are you ready for the bonus round?
Ellie: Yes!
Mom: What if you wanted to score 150 points? How many “stands” would you have to perform?
Ellie: Let me think...this one is harder. I think I would need 7 “stands.” No, that’s not right. I know it has to be less than 8.
Mom: True, but how do you know that?
Ellie: Because 150 is between 100 and 200. So, I have to do between 4 and 8 “stands.”
Mom: Great! Let’s think about it this way. You said it takes 4 “stands” to make 100 and you need to get to 150. So, how many more points do you need to add to 100 to make it to your goal of 15o points?
Ellie: Hmm...I need 50 more points.
Mom: Great! So how many “stands” do you need to do to score 50 points?
Ellie: Oh, I get it. I need to do 2 stands to make 50 points because they are each 25 points. Right?
Mom: Now, you’re getting it! So, how many “stands” do you need to perform to score 150 points?
Ellie: Let’s see. I need 4 to get 100 points and 2 more to get 50 points. So, that gives me 4 + 2, which is 6. I need to do 6 “stands.” Wow! That one was the hardest.
Mom: Yes, but great thinking!
At this point, she asked me what grade she would be in to do problems like that. I told her probably third grade. Of course, this made her smile because we are “officially” homeschooling second grade this fall. I told her it doesn’t really matter, though. The important thing was to focus on what she was understanding in math and that I was super proud! We rode on for a few more minutes in silence. Then, Ellie told me this had been so much fun. She said she loved bike riding with me, but also loved doing math.
As a mom and educator, this really made me smile! She LOVED doing math! Did you catch that? There is a great deal of conversation buzzing around about the need for schools to meet the ever-changing demands of today’s students. One of the most essential, I feel, is to help students develop their critical thinking skills. I love that I was afforded the opportunity to have a spontaneous, meaningful math lesson with our daughter. Unfortunately, these moments don’t come along too often or do they? As parents and teachers, we need to seize every opportunity to promote critical thinking among children. Carpe Diem! Sometimes these “moments” are designed and planned in formal learning situations. Other times, they may simply arise when taking your child for a bike ride, on field trips or waiting with students for their bus to come. Regardless, we should tap into the power of their imagination (and ours), establish meaningful dialogue, and create learning opportunities wherever they may arise.
