Dog Pen Problem Solving

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SWBAT solve multi-step area and perimeter problems.

Big Idea

Students will focus on providing a precise model, precise work, a precise equation, and an accurate answer as they solve area and perimeter word problems.

Opening Activity

20 minutes

Unit Explanation

During the first section of this unit, students will construct a house plan, find the area of the house plan, and calculate flooring costs. While finding the area is the focus of this unit, the first few lessons (where students explore the meaning of a polygon, construct house plans, and decompose rectangles into smaller rectangles to find the area) lay the foundation for finding the area of their home plans later on. This also provides students with a meaningful and purposeful context to find the area. 

During the second section of this unit, students will investigate dog pen designs and will primarily focus on finding the perimeter, or amount of fencing needed for different dog pens. Students will also explore odd-shaped polygons by finding the area and perimeter of odd-shaped dog pens. 

Getting Problem Solving Posters Ready

As an opening activity, I ask students to assemble problem solving posters that they will need later on in today's lesson. I show students an example: Front and Back. Then, I explain as I model each direction: 

1. Make a burrito with your paper. This helps students fold an 11x17 paper into thirds. As a result, there will be three sections in the front and three sections in the back.

2. Cut out the Word Problems. (I pass out one copy to each student.)

3. Paste problems 1-3 on the front, one in each section, and problems 4-6 on the back, again, one in each section.

As students finish, I ask them to help each other. When it's time, I want students to be ready to jump into problem solving, instead of focusing on creating their posters.

Precision Model

To begin, I ask: Has anyone ever shot a bow and arrow? I am surprised at the number of hands that shot up and then I remember, "We do live in Montana!" I ask a couple students to share bow and arrow stories aloud and then ask everyone to turn and talk about their experiences! 

When a person is shooting a bow and arrow, he/she really tries to carefully place their fingers in the same spot every time when shooting. When he/she pulls the string back, he/she is careful to pull back to the same spot each and every time. This is because you want to continually improve your accuracy (which means hitting the target in the center circle each and every time).  

We discuss the bulleted points on the Precision Poster and relate shooting a bow and arrow to math. 

Accurate means, "getting the answer correct" and hitting the targeted goal. We look at each target picture and label: "Accurate" or "Not Accurate." 

Precise means that your technique is the same every time, which means you hit almost the exact same spot each time. Again, we look at each picture and label each: "Precise" or "Not Precise."

The main goal of this poster is to encourage students to engage in Math Practice 6: Attend to precision. This will be an especially important practice to have at the forefront of our minds when reading and solving word problems today!

Teacher Demonstration

20 minutes

Goal & Lesson Introduction

First, I present students with the goal: I can solve multi-step problems. I write it on the board, Goal, and we discuss the meaning of "multi-step" ....more than one step.

In order for students to understand problem solving expectations during student practice time, I want to very clearly explain exactly how I want to see student work organized. I present the problem: Jedi has a dog pen that is 4 ft x 2 ft. Josie has a dog pen that is 3ft x 5ft. Which dog has more space? Building off of prior lessons, I insert my own dog's names into the word problem to increase relativity. Immediately students want to know "Which dog is bigger... Jedi or Josie?" 

Prior to solving the problem, I explain how many points this assignment is worth: Points. The purpose of points is to make sure I'm providing students with clear and high expectations. This helps create a rigorous learning environment. These aren't points that I'll keep track of - rather a checklist for students! 

I ask students to begin solving the problem on their white boards. 

When most students are finished, I demonstrate how to create a precise model, precise work, precise equation, and an accurate answer: Modeled Problem.

Student Practice

50 minutes

Further Practice

I explain: Today, I'd like for you to really focus on precision as you solve each of the problems on your Problem Solving Posters. Remember, each problem is worth four points, so be sure that you are checking your work!  

Choosing Partners

Today, I let students choose if they want to work on their own or with a partner. All students but a couple chose to work with others. I think this is because students work collaboratively on math almost every day! 

Monitoring Student Understanding

Once students begin working, I conference with as many students as possible. My goal is to support students by asking guiding questions (listed below). I also want to encourage students to construct viable arguments by using evidence to support their thinking (Math Practice 3). 

  1. What did you do first? 
  2. Can you explain why you _____? 
  3. What did you just learn?
  4. How can you make your work/model more precise?
  5. Is the question asking for the area or perimeter?
  6. What are you going to do differently?

Also, as I check student work, I place a star for each earned point... students love to know that they are on the right track! 

Student Conference

This was one my favorite student conferences during this lesson. Four boys are working together on their problem solving posters. They come to a problem that is a bit more complex. I model decomposing on the board using different numbers: Decomposing Example. Then, I walk one student step-by-step through decomposing: Decomposing 1. After we finish, I watch as another boy in the group, who was listening and watching, solves the same problem. I support him as he uses the decomposing method as well: Decomposing 2. I am so very proud of him for paying such close attention to a peer explanation that he is able to do it on his own! 

Student Work

Here are some student examples of posters: Example 1: Student WorkExample 2: Student WorkExample 3: Student Work, and Example 4: Student Work. You can see that setting clear expectations and having a point system inspired students to earn each point today!