# Going The Distance

## Objective

SWBAT apply the area and perimeter formulas for rectangles in real world and mathematical problems.

#### Big Idea

Students often apply the wrong formula when trying to find the perimeter of a two-dimensional figure. In this lesson, students will be able to apply formulas for these figures.

## The Distance Around

20 minutes

In this lesson, I want my students to understand that area and distance have two different  formulas.  I explain to students that perimeter is the distance around a two-dimensional shape. For example, I display a rectangle on the board with the dimensions 3,7,3,7. I explain that all sides can be added to find the perimeter, however, the correct formula for perimeter is P=2l+2w. I work both out so that students can visually see that both will give the correct  perimeter. What is 3 plus 7? 10. plus 3? 13. plus 7? 20. So, the perimeter for this rectangle  is 20. The correct way to find the perimeter of this rectangle is to apply the formula p=2l+2w.  The length of the rectangle is 3 inches and the width is 7 inches. I write the formula on the board while explaining

p=2l+2w
p=2(3)+2(7)
p=6+14
p=20

I display a square with different measurements, a rectangle, a quadrilateral, and a

pentagon. I explain that the same formula can’t be used when both sides are not the same measurement. I explain that in some instances, the sides have to be added all around.

Triangle  P= a + b + c

Square    P = 4 x a

Quadrilateral  P = a + b + c + d

Pentagon  P = a + b + c + d + e

This lesson will focus on the following Mathematical Practice:

MP.2. Reason abstractly and quantitatively.

MP.4. Model with mathematics.

MP.5. Use appropriate tools strategically.

MP.6. Attend to precision.

MP.7.Look for and make use of structure.

## Did You Go!

20 minutes

Material: practice work.ppt

I would like for you all to work in groups of four. I will give each of you two shapes and it will have your measurements written on them. I want you all to apply the formula for perimeter or the formula based on the shape that you have. The formulas are written on the board for you to refer back to if you forget. I will walk around to assist those of you that need assistance. Can a volunteer explain what perimeter is? The distance around a two-dimensional shape.  What did the formula for a triangle? Perimeter equals a plus b plus c.  What are we doing basically with all of these two dimensional figures. Adding all of the sides. Great job.  I walk around and monitor the students as they are working. I ask one student, what is your shape? It is a pentagon. What formula are you going to apply? P=a+b+c+d+e.  Why are you not applying P=2L+2W? Because it has 5 sides and all of the measurements are different.

## How Far Did You Go

15 minutes

Material: note taking paper.pdf

In this part of the lesson, I want my students to draw shapes based on the total perimeter.

I use geo-boards, straws cut into 2, 3, and 4 inch pieces. I ask students to make shapes with a perimeter of 12, 16, 9, and 10. The students did exceptionally well on this portion of the assignment. Some used rubber bands and geo-boards to make rectangles with 4 as the width and 2 as the length; which gave the perimeter of 12. Squares with 3 inches on each side for a total of 12 for the perimeter

## Going The Distance

15 minutes

TSW use worksheets to assess their knowledge on perimeter. I have a triangle, square, trapezoid, rectangle, and pentagon with the measurements already on them. I give the perimeter and give each student a ruler to draw a 2D figure with that total perimeter.

assessment for perimeter and area.ppt

As students are working, I will circle the room to check for understanding. However, I want to see how much of the assessment they can do on their own. So, I am careful not to guide to much.