We’ve been focused on proportional reasoning all week. Hopefully you have noticed that rarely were any of the activities the ‘process’ of solving proportions – i.e. ‘cross-multiply then divide’. While that may have come up at some point to help answer a question, the activities really were about using ratios and proportional comparisons in real situations to make decisions or model a situation. Today’s lesson is more of the same, and I would say fits in the category of an application. It’s not straight forward – instead, students have to use their understanding of proportion and scaling to come up with their own scale for a situation.
The image in this activity is a fun one – a chef juggling peppers. For those of you who think this is unrealistic, I will tell you that my husband (an amateur chef for sure) juggles whatever produce he can find, be it eggs, vegetables or utensils (thankfully not knives). The activity starts with an image on a coordinate grid and the first thing students are asked to do is come up with reference points that would help them make an estimate of realistic distance from chef’s shoulders to his head. This involves so much more than just looking – i.e. where on the head? Do you include the hat? Where on the shoulders? What is an average distance? Would I need to measure people around me to get a more realistic measurement? Once they determine this realistic distance, then they look at the y-axis and determine what an appropriate scale would be (i.e. how many inches does each mark on the y-axis represent?). The cool thing about this is different students will have different interpretations, so you are not going to get the same answer, which leads to amazing discussions about reasonableness and approximations and proportion.
After students determine there scale, then they actually look at the peppers and determine the height each pepper is above the chef’s hands. This again is more involved than it looks. Where do they place the points on each pepper so that they are consistent? What distance are we measuring? Where on his hands are we measuring from? How does the scale enter in to our calculations?
It’s a fun problem and there is no one ‘right’ answer, which to me is the beauty of this because students are forced to justify their choices and work based on their own understandings and interpretations of the situation.
Here is the link to the activity and also the video overview of the activity.
- Proportional Reasoning – Juggling Peppers
- Video Overview – Proportional Reasoning: Juggling Peppers (Scale, Reference Values, Application)
The tool being used in these mini-math lessons is the FREE web-based math software, ClassPad.net.
Remember – if you want to save and/or modify any of these activities, create a free account. Some useful links below:
- How to create a free ClassPad.net account (for anyone – students, parents, teachers)
- How to organize activities & share activities
- Some Ready-to-use activities that are already out there
- ClassPad.net YouTube Channel