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* *Reflection: Flexibility
Area & Perimeter Cubes - Section 5: Homework

Giving this prompt for homework didn't really do this task justice. **I think I would take another day to explore this prompt** in a similar way to the perimeter activity. I might ask them instead, to use what they figured out with the perimeter to help them make a plan or an estimate for the area and then carry out that plan the following day.

In particular I would focus on the tools they might choose in conjunction with the cubes. **I would want to ask them questions that would highlight the difference between linear and square measurement**. I might ask questions like:

**"why would a pencil not be a useful tool for area, but the notebook still would?"****"what part of the little white boards did you use to measure the perimeter and what part would you use for area?"****"what would the desk look like when you were done?"**

**I think the focus on exploring and the units (linear or square) really helps students conceptualize area and perimeter more so than a focus on dimensions or formulaic procedures.**

*Necessary time*

*Flexibility: Necessary time*

# Area & Perimeter Cubes

Lesson 8 of 16

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

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.

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#### Warm Up

*15 min*

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)

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#### Exploration

*25 min*

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.

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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.

#### Resources

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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.

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- UNIT 1: Order of operations & Number properties
- UNIT 2: Writing expressions
- UNIT 3: Equivalent Expressions
- UNIT 4: Operations with Integers
- UNIT 5: Writing and comparing ratios
- UNIT 6: Proportionality on a graph
- UNIT 7: Percent proportions
- UNIT 8: Exploring Rational Numbers
- UNIT 9: Exploring Surface Area
- UNIT 10: Exploring Area & Perimeter

- LESSON 1: Fancy Flooring
- LESSON 2: The Punk Prank Payback
- LESSON 3: Cover or Surround? Sub Plan
- LESSON 4: Garden Border Sub Plan
- LESSON 5: Border Problem: Day 2
- LESSON 6: Area & Perimeter Assessment
- LESSON 7: Chickens and Goats
- LESSON 8: Area & Perimeter Cubes
- LESSON 9: Sorting Out Perimeter
- LESSON 10: Making Sense of Area Formulas
- LESSON 11: Making Shutters
- LESSON 12: Venn Do We Use Area or Perimeter?
- LESSON 13: What Does it Look Like?
- LESSON 14: Area & Perimeter Retest
- LESSON 15: Floor Plan Areas (Day 1 of 2)
- LESSON 16: Floor Plan Areas (Day 2 of 2)