Area of the Base...Area of the Base!

Antonia did some creative re-arranging with her teaching partner to allow for our PLC to see her Grade 7s in action for a lesson study.  She used an assessment from ONAP as a way to create a minds on and action for her students to participate in.  Here is a picture of what she gave them for the Minds on activity:

If you notice at the bottom there are two different formula written down for Volume.  The reasoning for this is because we know that in the past students struggle with finding the volume for objects because they forget that they need to find the area of the base first, and then move on from there.  As we took up the minds on, we found that the students also had another misconception:  That you can just divide by two to find out how many candies you need.  While it works in this case, Antonia wanted to make sure that her students understood why it worked - And why it may not work everytime they had to figure out how many of something went into something else.  We also talked about how the formula for finding out the volume of the candies was different than the formula for the box - Because the base was different.  (Once again...area of the base....area of the base...)  Here is what was recorded from the discussion:

For the action, the students were asked to find out what size box they would need to hold 64 candies.  They had to make two boxes (one a rectangular prism and one a triangular prism) and decide which one they thought the candy company should go with and why.  Due to time constraints we did not get to have a consolidation with this group.  However, the teachers that were at the lesson study had some really rich conversations on what we noticed the students were doing well with, and what they were struggling with.  We looked at the student work and talked about what we noticed and what we would do differently in our classrooms with our own classes.

Here are some samples of student work:

This group was very thorough in their answer.

A close up of the math.

You can see they broke their thinking into parts to help them attack the problem.

A close up of some of the writing.

This group started with the notion that they needed to find what half of 64 was.

Trial and Error helped this group decide what the volume of the box needed to be.