 # Replacing Letters with Numbers

Videos to help Grade 6 students learn what is an expression and how to build expressions.

New York State Common Core Math Module 4, Grade 6, Lesson 7

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Lesson 7 Student Outcomes

Students understand that a letter represents one number in an expression. When that number replaces the letter, the expression can be evaluated to one number.

Example 1

What is the length of one side of this square?
What is the square’s area as a multiplication expression?
What is the formula for the area of a square?
What is the square’s area?

We can count the units. However, look at this other square. Its side length is 23 cm. That is just too many tiny 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.

A letter 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 letter, 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.

Example 2

The formula A = l × w is an efficient way to find the area of a rectangle without being required to count the area units in a rectangle.

Remember, a letter represents one number in an expression. When that number replaces the letter, the expression can be evaluated to one number.

Example 3

The formula V = l × w × h is a quick way to determine the volume of right rectangular prisms.

Lesson Summary

Expression: An expression is a numerical expression, or it is the result of replacing some (or all) of the numbers in a numerical expression with variables.

There are two ways to build expressions:

1. We can start out with a numerical expression and replace some of the numbers with letters.

2. We can build such expressions from scratch, as in x + x(y - z), and note that if numbers were placed in the expression for the variables x, y, and z, the result would be a numerical expression.

Lesson 7 Examples and Exercises

Exercise 1
Complete the table below for both squares. Note: These drawings are not to scale.
Exercise 2
Complete the table below for both rectangles. Note: These drawings are not to scale. Using a calculator is appropriate.
Exercise 3
Complete the table for both figures. Using a calculator is appropriate. Problem Set
1. Replace the side length of this square with 4 in., and find the area.

2 Complete the table for each of the given figures.
Length of Rectangle, Width of Rectangle, Rectangle’s Area Written as an Expression, Rectangle’s Area Written as a Number

3. Find the perimeter of each quadrilateral in Problems 1 and 2.

4. Using the formula V = l × w × h, find the volume of a right rectangular prism when the length of the prism is 45 cm, the width is 12 cm, and the height is 10 cm.

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