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Today we wrote and evaluated expressions to describe perimeter and area. Here’s an example!
We can write an expression to describe the area of the rectangle: 7m.
Let’s find the area when m = 18
7m = 7 • 18 = 126, so the area is 126 units.
1)
a. Write an algebraic expression that
represents the perimeter of the figure.
b. Evaluate the algebric expression to find
the perimeter when p = 6, and then
when p = 2.
2)
a. Write an algebraic expression that
represents the perimeter of the figure.
b. Evaluate the algebric expression to find
the perimeter when y = 20.
PowerTeaching: i3
© 2012 Success for All Foundation
Level F Unit 7 Cycle 3 Lesson 9
Homework Problems
1
3)
a. Write an algebraic expression that represents the area of the square.
b. Evaluate the algebric expression to find the area when k = 3, and then when k =
4
.
7
4)
a. Write an algebraic expression that
represents the area of the square.
b. Evaluate the algebric expression to find
the area when g = 2, and then when g = 8.
5) Which shape has a greater area? Explain your thinking.
2
PowerTeaching: i3
© 2012 Success for All Foundation
Level F Unit 7 Cycle 3 Lesson 9
Homework Problems
6)
a. Write an algebraic expression that represents the area of the rectangle.
b. Evaluate the algebric expression to find the area when c = 10, and then when c = 6.
7)
a. Write an algebraic expression that
represents the perimeter of the figure.
b. Evaluate the algebraic expression to find the
perimeter when d = 54.
8) Charlie designed two diagrams for his school project. Which diagram has a greater perimeter?
Explain your thinking.
PowerTeaching: i3
© 2012 Success for All Foundation
Level F Unit 7 Cycle 3 Lesson 9
Homework Problems
3
Mixed Practice
9) Write an algebraic expression to represent the sum of 6.5 and the difference of x and 14.
10) What is the coefficient of m? What is the coefficient of 3m?
11) Simplify.
2
2 + (29 – 4 )
12) Jane bought a pack of cards for $3.12. If 52 cards come in the deck, what is the unit price for
each card?
Word Problem
13) Write an expression for the area of a rectangle that has a length of t and height of 4. What will the
area be if the length of the rectangle is 21?
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PowerTeaching: i3
© 2012 Success for All Foundation
Level F Unit 7 Cycle 3 Lesson 9
Homework Problems
For the Guide on the Side
Today your student learned to write and evaluate algebraic expressions that describe area and perimeter.
Given a diagram, your student used what he or she already knows about geometry to write an
expression. Then, he or she evaluated the expression. Sometimes, your student evaluated the
expression for more than one value. For example, each side of a square is x. The area of the square is
2
2
2
x • x or x . If x = 5, the area is 5 = 25 square units, and if x = 7, the area if 7 = 49 square units.
Your student should be able to answer the following questions about evaluating expression:
1)
2)
3)
4)
5)
How does your expression describe area/perimeter?
How did you know all the lengths of the sides of the figure?
How did you evaluate the expression?
Will you get the same result if the variable equals a different number?
What would happen to the value of the expression if the length of this side was shorter/longer?
Here are some ideas to work with evaluating expressions:
1) Write an algebraic expression to find the area or perimeter of an object in your home. Take a
guess at the length or width of the object so you can evaluate the expression. Then measure the
object and find the perimeter or area. How close was your guess?
2) Watch a video from Khan Academy to review evaluating expressions:
http://www.khanacademy.org/math/algebra/solving-linear-equations/v/variables-and-expressions1?exid=evaluating_expressions_1
PowerTeaching: i3
© 2012 Success for All Foundation
Level F Unit 7 Cycle 3 Lesson 9
Homework Problems
5
Homework Answers
1) a. 3p + 3p +3p + 3p + 2.5p + 2.5p
b. The perimeter is 102 units when p = 6 and 34 units when p = 2.
2) a. 0.5y + y + 17
b. The perimeter is 47 units if y = 20.
3) a. 4 • 7k
b. The area is 84 square units when k = 3, and 16 square units for k =
4
.
7
4) a. 4.5g • 4.5g
b. The area is 81 square units for g = 2 and 1,296 square units if g = 8.
5) Shape 2 has a greater area.
Possible explanation: Each shape has a width that is 6 units. However, the length of Shape 2 is
13t + 2, whereas Shape 1 has a length of only 13t. If t = 1, Shape 1 would have an area of 19 square
units, and the area of Shape 2 would be 21 square units.
6) a. 8 • 2 1 c
2
b. The area is 200 square units when c = 10 and 120 square units if c = 6.
7) a. d + d + d
b. The perimeter is 162 units when d = 54.
8) Diagram A has the greater perimeter.
Possible explanation: Diagram A and diagram B have all of the same measurements except diagram
A has 2 sides that are longer than diagram B’s sides. If b = 2, Diagram A’s perimeter is 68 units and
Diagram B’s perimeter is 56 units.
Mixed Practice
9) (x – 14) + 6.5
10) 1 and 3
11) 15
12) The unit price is $0.06 per card.
Word Problem
13) The expression that represents the area of the rectangle is 4t. If the length of the rectangle
is 21 units, then the area is 84 square units.
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PowerTeaching: i3
© 2012 Success for All Foundation
Level F Unit 7 Cycle 3 Lesson 9
Homework Problems