Area & Perimeter Cubes

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Objective

Students will be able to figure out the perimeter and area of their desks using unconventional units.

Big Idea

The relationship between linear and square units underscores the meanings of area and perimeter.

Intro & Rationale

My students often get the procedures for calculating area and perimeter mixed up and don't have a solid understanding of the meaning of either. This lesson is designed to give my students hands on experiences that should help cement the concepts of perimeter and area. It also gives them opportunities to visualize and plan a  strategy. By limiting the number of manipulative tools they have access to, I force the students to think of alternate tools they can use. It is my belief that this creates more opportunities to think about, visualize, build, and talk about the meaning of perimeter as they consider the usefulness of a variety of unconventional  tools that could be used to measure.

Warm Up

15 minutes

My students are told that they will be given a bunch of tiny blocks to help them figure out how many blocks it will take to show the perimeter of their desktops. Before the blocks are handed out I ask them to figure out a plan with their partner for how they will go about the task. This gets them to think about and clarify the meanings of perimeter and area and helps them visualize what it would look like with the blocks. Visualizing and making a plan helps engage my students in the MP1 (making sense & persevering). 

When I do hand out the blocks my students object that there aren't enough to make the whole perimeter or area, because I only give them a small bag. This again is a good way to engage them in MP1 when they have to switch gears and revise their plan by using an alternative method. I expect them to use other objects like pencils, notebooks, etc. to help them.

Students work in pairs or individually to figure out first how many blocks it will take to make the perimeter. (You could just as easily use paper clips instead of blocks)

Exploration

25 minutes

As I pass out the bags of blocks I tell my students that they will be asked to write an explanation of how they figured out the number it would take to make the whole perimeter. I tell them to keep track of steps they take and the reasons why they decide to do what they do. As they are working I circulate and ask them to show me or describe their Problem solving strategy. When I see my students using something other than the manipulatives I gave them I ask why they chose the new tool and how it is helpful. This is a great way of engaging students in MP5 (using tools)  If I find a group that is off task I tell them to see if they can get an idea from looking at what other groups are doing.

Using manipulatives is especially helpful for giving access to ELL students. Using academic language and explaining mathematical ideas is really hard for students who don't even have conversational English mastered. This provides them the opportunity to use the manipulatives to share their ideas, participate in the planning process, and demonstrate their understanding visually.

Whole Class Discusion/Exit Ticket

7 minutes

At the end of class I give students time to individually write up a description of what they did. As I circulate I am looking for students to share with the whole group the way they solved it. I will call on other volunteers as well, but I want to ensure that a variety of strategies are presented. I will also look for good examples of diagrams or unique strategies or strategies that make connections to related knowledge or other content standards. 

 

Homework

I don't collect their exit ticket, because I want them to use it as a reference for their homework problem:

Using what you know about the number of cubes it would take to fit along the perimeter of your desk, how would you go about figuring out the number of cubes it would take to completely cover the top of your desk?

My hope is that they continue to visualize what the area would look like using the blocks and also begin to recognize the relationship between perimeter, area, and the dimensions of the figure.