3rd Graders Apply Their Knowledge about Area

The third grade classes at our school recently finished their unit about measurement.  During this unit, one of the topics they studied was area.  As a way to help them apply their knowledge, we brought in floor tiles and carpet samples.  (If you tell the store these samples are for a school project, they will often donate them to you!)  Students are working to determine how they would like to remodel the classroom - choosing the tiles and carpet they like best.  The tiles are of different sizes - 6"x6", 12"x 12", and 16"x16".  We were purposeful in having only samples.  Students do not have enough tiles to lay them across the floor and count them to find the area.  They will have to find another method to calculate the area.

Students have a variety of tools to help them find the area of the classroom: rulers, yardsticks, grid paper, posterboard (to cut out squares congruent to the tiles they have selected), and chart paper.  The students are to create a diagram of the classroom detailing what sections of the room will be tile and what sections will be carpet.  Once they have this plan, they will calculate the costs of the materials and write persuasive letters to our principal in an attempt to convince her to remodel their classroom.

One "a-ha" moment for students was the difference between square feet and square yards.  We had a discussion today about the importance of using correct units.  If, for example, we order 100 square yards of carpet when we really need 100 square feet of carpet, we will spend a lot of money and have a lot of carpet left.

Students have been very motivated by this project!  They are working to be precise in their measurements and detailed in their design.  This is a great example of students engaging in the mathematical practices!

Lunch conversations

I have the pleasure of spending my lunch duty with our fifth grade students.  They are a great group of kids but have a tendency to get a little noisy and sometimes lack appropriate conversation topics.  To help them have a topic for conversation at their tables, I found some "conversation starters" (i.e., math problems) from the Investigations series for them to discuss.  I love these problems because there are multiple correct answers and they were easy for students to try without paper and pencil to record their thinking.

At first, the students wanted to share their answers with me.  As I asked whether others at their table agreed with their possible solution, students began to ask one another about the answers.  This was fantastic!  Rather than viewing me as the keeper of the answers, the students began to reason about the problem with one another and build their understanding together.

Another benefit was that students in other grades talked about the problems as well.  Students were practicing counting skills, math reasoning, and many of the mathematical practices all while eating lunch!  I hope you will consider trying to find a way to involve more conversations about math at your school!

Here are some examples of the problems we used: