Connections with Proportionality Part 2

I have been spending a lot of time with my students on what it means for two quantities to be in a direct proportion.  Instead of working out of the textbook for the unit, I have done the following tasks:

  • Growing Rectangles
  • Vegetable Garden
  • Skittles
  • Track Meet (I didn’t blog about this one because it was a hot mess and I totally anticipated student responses incorrectly.  Although it’s a great task it won’t be in this sequence next time)
  • MARS Proportion or Not a Proportion

There are already many things I would change about how I implemented these  tasks, especially the Skittles Task (which probably could be an entire unit within itself). After the Skittles task, I gave a quiz.  Most of the kids totally bombed it.  I was so confused.  I felt like the Skittles task was so rich that they should have done better. They lacked the ability to make connections when the context changed. Then when I started grading their Skittles packets (they held on to each piece daily and turned it all in at the end), I realized that even though they were participating in the discussions, they were not writing down other student strategies presented in class.  They didn’t record how the ideas and strategies from class related to their own.  And sadly, the implementation of my new homework (HW) reflections has been mildly successful because they are just not doing their HW.  The kids that do however, have a greater depth of knowledge than those that didn’t take it seriously.  There are many reasons the kids bombed the quiz, and it’s not totally their fault either.  Because of this, I decided to do the MARS activity Proportion or Not a Proportion.

I gave them a pre-test to see how they were thinking about proportional relationships.  I graded them but didn’t assign a score as this was strictly formative. I only wrote questions for each problem they got wrong (yes this took FOREVER).  Then we did the MARS activity, which really helped them work through what it means for quantities to be in direct proportion.  After the activity, I gave them a similar quiz and saw a lot of improvement.

Even with the improvement, the bad quiz scores from before still weighed heavily in my mind because I keep thinking, “Man, I must have done something wrong.”  So on a Friday I gave a short response quiz.  I didn’t want the students to wonder, “Why are we doing these isolated activities?”  I knew they weren’t isolated tasks but did they? So I asked them these questions and requested no less than a 5 sentence paragraph for each one:

  1. How are the activities Growing Rectangles, Vegetable Garden and Skittles all similar?
  2. Does Growing Rectangles represent a proportional relationship? Explain how you know.
  3. Does Vegetable Garden represent a proportional relationship? Explain how you know.

This was also a open note quiz because I wanted them to take out all of their tasks, make generalizations and look for similar structure within the problems.  I was thoroughly please with the majority of the responses.




However, not all of the responses were as good as the ones above.  I’d be lying if I said they were.  I realized that my class that struggles with discourse during class has more trouble connecting the activities.  Their responses went something like these:

“The similarity between the Growing Rectangles, Vegetable Garden and Skittles activities are pretty much they same.  The reason why they’re pretty much the same is because the math that’s involved in it.  You have to find out what goes where and for all of them we made a graph that was also the same as the rest of the activities.”

“The Growing Rectangles, Vegetable Garden and Skittles activity all include multiplication, addition and not proportional relationships. The Vegetable Garden and Growing Rectangles only included (multiplying, addition and areas of ft. or inches).  The Skittles activity included multiplying, addition, doubling, division, number lines.”

“All include graphs, numbers, and answers. Also involve lots of thinking. These activities work without a graph but if you didn’t use a graph, you probably got something wrong.  The activities we did use addition, subtraction, multiplication and division.  Growing Rectangles, Skittle activity and Vegetable Garden all have missing numbers and you have to figure out those numbers by divide, multiply, add, subtract, graph even a number line.”

These are somewhat comical.  They are a great example of writing a whole lot about nothing.  However, they show what they don’t know.  So clearly there is more work to be done on my part.

Next Steps:

I’m really struggling with discourse in one of my classes.  I ask them to partner talk and either they don’t at all, or they talk about something else, even when I’m standing right there!  And even when I ask them a low level question that everyone should have an answer to.  Looks like I need to go back into Principles to Actions for some answers. Do you have advise?

Homework will always be an ongoing battle that I am not willing to fight.  I just know personally that the kids that do spend time on their reflections and do them thoroughly have more depth than the other students and will be more successful later.  I guess I will have to be happy with that.

So what now?  I’m thinking of creating a HW assignment where students actually graph on a coordinate plane some Growing Rectangles.  Then they will see that the rectangles that are proportional to each other fall on the same line, which may clear up some misunderstandings. Then they can make more connections with this new graph to the graphs they did in the Skittles activity.

Until next time…S

3 thoughts on “Connections with Proportionality Part 2

  1. Thanks for sharing, Shannon! Do you think your kids had enough time with the math from the skittles task before being assessed?
    Last year, and sometimes this year, I think I get so focused on the tasks that I don’t spend enough time pulling the math out afterward and then balancing it with procedural fluency. I think I sometimes undervalue procedural fluency… which is funny when you consider where I came from.
    Have you tried “Would you rather math” with that struggling group? The focus of those tasks look pretty engaging… Maybe something like that could get things going. Hmm…


  2. I appreciate how reflective you are in your teaching. I am impressed by your ability to indentify an obstacle and develop a strategy to address it; specifically, kids not making connections. Brilliant solution. I’m certain that as both you and your students gain more experience connecting tasks, everyone will improve. Maybe they will even start to make connections before you ask for them! This is good stuff. Totally plan to use it myself, so thank you for sharing!
    It’s strange how much class dynamics can impact the culture and attitudes in the room. I struggle with this as well, so the only thing I have to offer is empathy. I wonder if kids struggle to converse mathematically because they basically don’t know how, or if there are too many kids in the room with fixed mindsets. I am curious to know if employing Elizabeth S’s Talking Points would help.


    1. Pat,
      Thanks for the suggestion on talking points. I have heard of them, and done them at conferences, but never in my class. Maybe it’s worth a try now. I probably need to dip into Jo Boaler and Carol Dweck with how to transition kids from a fixed mindset to a growth mindset. If you try any of the lessons, let me know how they go and if you changed something that ended up working better. I feel like I always have room to improve! 🙂


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