Using a resource for a different concept

Demitra's school has a copy of the resource "Puddle Questions:  Assessing Mathematical Thinking."  In it there is a question about how you would measure a puddle.  Demitra decided to modify the question to meet her needs for assessing what the students know about area.  She also wanted them to self-reflect on their work and she wanted to be able to give them some descriptive feedback on what they could do better.  Sounds like a tall order, but when it fit together nicely and the students really got a lot out of the lesson.

Minds-On:  Each group was given a large triangle made out of construction paper.  They were asked how they could find out the area of it.  They then set to work discussing and trying different ways.  What was great was that each group came up with a different way, and they all knew that the units that they used must all be the same.

Action:  After being given the task, Demitra reviewed the success criteria that had been co-created together.  The students gave examples of what the criteria might look like in terms of the task.  For the actual task, the students were asked to draw a puddle and find the area of it.  They could use any way they wanted to.  Some students drew lines, others used cubes, pentominoes, finger spaces, and some even drew shapes that they thought would be "easy" to count.

Consolidation:  Demitra had one-on-one conferences with each of the students to not only assign them a mark (based on the four categories in the achievement chart) but also to give them some feedback on what they had done well on, and what they could improve upon

When this student brought his work up, he came up ready to chat about why he thought he needed to make a smaller puddle.  He said it was because a smaller puddle would have a smaller area and that would be faster to count than the puddle he had drawn.  He also said that he would have used a bigger unit to measure the area with and this would also cut down on the number of units he had to use.  This is why his feedback was to think about how he could have shared his oral knowledge in a written way.

This student used a K-W-C chart to help them make sense of what they had done.  You can see there was a bit of a thinking error in their work as they used pentominoes to answer the question, but when they couldn't successfully draw them onto their puddle, they jumped to just drawing lines on the shape they had traced.  When probed, this student was unable to share why it was important that all tools they used to find the area needed to be the same size.

This lesson left Demitra feeling pretty confident in her student's abilities to find the area of a shape.  The one-on-one conferences also helped her ask some deeper questions to help determine the students knowledge and understanding of area and how well they were able to apply that knowledge and understanding to the problem at hand.