This document contains notes and exercises from a math lesson on replacing letters in formulas with numbers. It introduces concepts like using letters to represent unknown numbers, evaluating expressions by substituting values for letters, and calculating properties of geometric shapes using formulas with substituted letter values. Examples include finding the area of squares using A=s^2 and the volume of rectangular prisms using V=lwh. Corresponding exercises have students complete tables and calculations to demonstrate understanding of evaluating formulas with substituted numbers.

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Problem Set Lesson 6 Answers

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Problem Set Lesson 6 Answers ­ Continued
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Problem Set Lesson 6 Answers ­ Continued
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MODULE 4 Expressions and Equaons
Topic B: Special Notaons of Operaons
Lesson 7: Replacing Leers with Numbers
Student Outcomes
§ Students understand that a leer represents one number in an expression. When that number replaces the leer, the expression
can be evaluated to one number.

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Classwork
Example 1
What is the length of one side of this square?
What is the formula for the area of a square?
What is the square’s area as a mulplicaon expression?
What is the square’s area?

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We can count the units. However, look at this other square. Its side length is 23
cm. That is just too many ny units to draw. What expression can we build to find
this square’s area?
What is the area of the square? Use a calculator if you need to.

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A leer represents one number in an expression. That number was 3 in our first
square and 23 in our second square. When that number replaces the leer, the
expression can be evaluated to one number. In our first example, the expression
was evaluated to be 9, and in the second example, the expression was evaluated
to be 529.

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Exercise 1
Complete the table below for both squares.
Note: These drawings are not to scale.

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Example 2
What does the leer b represent in this blue rectangle?
With a partner, answer the following queson: Given that the second
rectangle is divided into four equal parts, what number does the x
represent?
How did you arrive at this answer?
What is the total length of the second rectangle?
If the two large rectangles have equal lengths and widths, find the
area of each rectangle.

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Exercise 2
Complete the table below for both rectangles.
Note: These drawings are not to scale. Using a calculator is appropriate.

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Example 3
The formula V = l x w x h is a quick way to determine the volume of right rectangular prisms.
What does the l represent in the first diagram?
What does the w represent in the first diagram?
What does the h represent in the first diagram?
Since we know the formula to find the volume is V = l x w x h, what number can we
substute for the l in the formula? Why?
What other number can we substute for the l?
What number can we substute for the w in the formula? Why?
What number can substute for the h in the formula?

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Determine the volume of the second right rectangular prism by substung the leers in
the formula with their appropriate numbers.
V = l x w x h

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Exercise 3
Complete the table for both figures. Using a calculator is appropriate.

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Closing
Please take out your exit ticket for Lesson 7, close your
binder, and complete the exit ticket. This will be collected.

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