Embedded Files
AKS: 4MA.E.8 identify and draw geometric objects, classify polygons based on properties, and solve problems involving area and perimeter of rectangular figures.
Learning Targets: I can explain the area formula.
I can explain the perimeter formula.
I can solve real-world problems involving area and perimeter.
Activating Strategy
Activating Strategy
Mini-Lesson
Mini-Lesson
In 3rd grade, we learned how to find the area and perimeter of polygons. We counted square units to solve the area problem and added the sides of the polygon to determine the perimeter.
Today, we will apply perimeter and area formulas to solve real-world mathematical problems using color tiles.
Let’s take a look at this scenario.
Mr. Jones bought 16 feet of chicken wire fencing to build a chicken coop in his backyard. What different rectangular figures could he construct to use all 16 feet of chicken wire fencing? Determine the area and perimeter of these rectangular figures and explain which figure you think he should use.
Listen as I think aloud …
First, it is important to make sense of the problem. As I reread the problem, I saw that Mr. Jones would build a chicken coop. He has already purchased 16 feet of chicken wire to enclose the coop. The problem asks us to determine the different rectangular figures that could be made with 16 feet of chicken wire fencing. To solve the different rectangular shapes, I will have to build rectangular shapes with a perimeter (or the distance around a figure) equal to 16 feet.
Let’s start by building a rectangular shape with some color tiles. The side length of each tile will represent 1 foot. Let’s begin with a rectangle with a width of 1 foot on each end. Since this means 2 feet of the fencing has been used, there will be 14 more feet. I know that 16 – 2 = 14.
The other parallel side lengths of the rectangle will each need to be 7 feet long.
I know that 2 x 7 = 14, or 7 + 7 = 14
Now, let’s build a rectangular shape with a width of 2 feet on each end. That means 4 feet of fencing will be used, leaving me with 12 more feet. I know that 16 – 4 = 12.
The other parallel side lengths of the rectangle will need to each be 6 feet because I know that 6 x 2 = 12 or 6 + 6 =12.
Next, let’s build a rectangular shape with a width of 3 feet on each end. That means 6 feet of the fencing will be used for the widths. 3 + 3 = 6.
10 more feet of fencing will remain. I know that 16 – 6 = 10.
The other parallel side lengths must be 5 feet because 5 x 2 = 10 or 5 + 5 =10.
I will continue building rectangles until I discover the side length options. This time, I will make a rectangular shape with a width of 4 feet on each end.
That means I will have used 8 feet of the fencing. 4 + 4 = 8.
8 more feet of fencing will remain. 16 – 8 = 8.
The other parallel side lengths will need to be 4 feet long. I know that 4 x 2 = 8 or 4 + 4 = 8.
Wow! Check that out! I built a figure that is a perfect square.
I know that I have built all the possible rectangular shapes at this time because if I build one that has 5 feet on each end, I will have used up 10 feet, leaving me with 6 feet. That rectangular shape would look just like this one, rotated in a different orientation.
Consider this scenario:
Mr. Jones bought 16 feet of chicken wire fencing to build a chicken coop in his backyard. What different rectangular figures could he construct to use all 16 feet of chicken wire fencing?
Determine the area and perimeter of these rectangular figures and explain which figure you think he should use.
Not only did I need to find the area and perimeter of the figures, but I also needed to explain which rectangular figure he should use.
Chickens need a lot of area to move and run around. I am going to choose the figure with the largest area.
I know fences go around things, and the perimeter measures the distance around a 2D figure. Since I am using all 16 feet of fencing, the perimeter will be the same for all the rectangles. The area will change depending on the length and width of the rectangle. I would suggest that Mr. Jones use the dimensions that give him the greatest area, so he should create a chicken coop that is square or 4 feet by 4 feet since it has an area of 16 square feet.
Guided Practice
Guided Practice
Mathematicians, it is your turn to try!
As you work with your math partner to solve the next problem, challenge yourself to find all the possible rectangles. Record and keep each of your figures to justify or prove your mathematical thinking.
Mrs. James bought 20 feet of garden edging around a garden she wants to plant in the spring. She is trying to decide what dimensions to build a garden. What are some different rectangular figures that she could choose from using all 20 feet of garden edging?
Determine the area and perimeter of these rectangular figures.
Explain which figure you think she should use.
Independent Task
Independent Task
1. FRECKLE - Complete THREE Freckle Assignments each week. DUE FRIDAY. Your HIGHEST score in Targeted Practice is your weekly math grade - Click HERE for Freckle website
GRADED Targeted Practice - Current skill (5 questions; Score Goal=80% or higher)
Fact Practice - Multiplication Fact Practice
Adaptive Practice - At YOUR level
2. iREADY Math - Complete 30 minutes at your level each week
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