I can statements:
Level 1: I can create a visual representation of a design problem. 100% Strongly Agree or Agree
Level 2: I can decompose geometric shapes into manageable parts. 94% Strongly Agree or Agree
Level 3: I can estimate and calculate measures as needed to solve problems. 100% Strongly Agree or Agree
Level 4: I can use geometry to solve a design problem and make valid conclusions. 100% Strongly Agree or Agree
Modeling with Geometry G-MG
Apply geometric concepts in modeling situations
1. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).
2. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).
3. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).
Which Standard of Mathematical Practice did you use most often in this unit? In which other Standard of Mathematical Practice did you engage often during the unit?
Students answered that they used make sense of problems and persevere in solving them the most and model with mathematics next.
Think back through the lessons. Did you feel that any were repeats of material that you already knew? If so, which parts?
11A Volumes of Compound Objects
11B 2D Representations of 3D Objects
11C A Tank of Water
11D Popcorn Picker
11E Hot Coffee
- I didn’t think any of these were repeated. We really looked at geometry and used it to solve hard real world problems, and I’ve never had to do that before.
- I do not feel like this was a repeat. Many of us knew about basic areas and volumes of course, but in this unit we went into depth with them and learned how to get the dimensions of more complex shapes. I think we covered new material, because we have mainly been going over coordinates, trig, and triangles previously and this seemed like a new and fun topic to cover for us.
- I already knew how to find the volumes of compound objects from unit 10.
Think back through the lessons. Was there a lesson or activity that was particularly helpful for you to meet the learning targets for this unit?
- 11F Popcorn Picker was very helpful in helping me learn the targets for this unit. It helped me realize that although two objects may have the same surface area, their volumes may not be the same.
- Popcorn Picker definitely helped me understand how exactly different dimensions affect the volume of a cylinder even though the dimensions are nearly the same. Using the piece of paper to compose a cylinder using 8.5 and 11 as two different circumferences as well as the height helped me see that the volumes will be different.
- The coffee one helped me because it made me talk with others at my table and look for ways to solve the problem.
- Although I enjoyed the popcorn activity, I feel like the most helpful activity was the one where we cut out the cards and thought through the gradual shapes of the water as it emptied the top figure and filled the bottom figure. Â It allowed me to work with a team to reason out our arguments and working with my peers in a collective effort enlightened me with thoughts and ideas that I had not previously thought of or would have otherwise ventured to discuss.
- I really liked the Hot Coffee unit. I understood it well, and it was a good problem to work and figure out. It was also really good for me to make sure to use the right units and convert correctly, which I don’t do sometimes.
What have you learned during this unit?
- This unit helped me to realize how much I’ve learned this year in geometry and how to do many things like finding volumes and areas of different shapes.
- How to use the least amount of information to find the need item.
- I’ve ;earned how to divide a complex geometric objects into parts and calculate It’s volume. I can find out the necessary information needed to solve this kind of problem and how to use them to solve the problem. I can apply math to every day life and model with mathematics. I can also make visual representation of a design problem.
- I have learned to attend to precision. Throughout not only the homework lessons but also in class, I learned to be careful and slow down. I often hurried over the question and did not take into account the measurements. For example, I hardly ever noticed when the question gave dimensions in feet but asked for the answer in inches. It’s not a hard concept, but it requires patience and effort that I was trying to shortcut on.
- During this unit, i learned a lot about using what i already knew and combining that to solve difficult problems.
- I’ve learned how to break down 3D shapes into simple 3D shapes so I can get their volume, and how to do actual geometry problems with all of the things I’ve learned this year. I’ve learned what the different cross sections of objects can look like, and I learned that the world’s largest coffee cup help 2015 gallons of coffee.
- I learned that I need to model with mathematics more often.
And so the journey continues … figuring out how to provide more opportunities throughout the course for my students to model with mathematics.