Area Investigation

 Students have been exploring area and experimenting with fractional side lengths. 

Warm Up:

What dimensions could you have for the area of 24 units?

Students used sticky notes to represent possible dimensions. Here are some student examples that students shared:

Follow up questions:

Do you have all of the possible dimensions? 

How do you know?

Next: Students were provided with the following question from Illustrative Mathematics!

Using the hallway tiles, which are 1 square foot each, students worked to mark out the dimensions for Chavone's bathroom floor. This helped students make sense of the fractional sides. This problem proved challenging as the fractional parts had different denominators. Students worked together and were able to solve the problem! Can our class fit in Chavone's bathroom? Yes!

Students finished the session by playing Name that Number! 

Rabbits in a Pen: Area and Perimeter

 Recently, I finished my master's degree in elementary math education with a certification as a Math Specialist. I learned a lot and hope to put in the next steps necessary to put the information to use in my classroom and grade level. 

One of the problems introduced in my Geometry class was called Rabbit and Pen.  (Credit unknown but will name Dr. Webel for sharing it.) This problem opens the door for so many concepts to emerge!

• Perimeter
• Area
• Counting for Area
• Multiplying for Area
• Perimeter and Area are not necessarily equal

I encourage teachers to share the problem with some tools for students to explore. If you have large Geoboards, a Geoboard app (found here), or graph paper for students to model their thinking on.

Here is the student version that I made here.  While I thought I retained the images from the whiteboard app that the students created, I apparently did not save them! However, I want to provide a visual of the work that shows the types of models that the kids created that sparked our discussion.

This activity reveals to students that while the perimeter is “fixed” (you have the same amount of fence to use, like 16 ft)  the dimensions produce a different area. The students might also realize that there is a method to making sure they have all of the different combinations possible. If they are not methodical, you could ask how they know they have thought of all of the possible ways to make the most space for the animals? I hope students would ask or wonder if they used a square (and squared numbers) would that always give you the most space? This lesson certainly lays the groundwork for students to wonder if this is a possibility.

16	20	10
1, 7	1, 9	1, 4
2, 6	2, 8	2, 3
3, 5	3,7
4, 4	4, 6
	5, 5