Lesson 1: Unknown Numbers

LEARNING ACTIVITIES

QUESTIONS FOR STUDENTS

TEACHER SUPPORT

“Today, we’re going to be exploring ways to represent expressions. Please take 30 seconds to think about how you would define ‘expression’ to someone else. At the end of that 30 seconds, I’ll ask you to share your thoughts with a partner.”

Allow time for students to think about the definition and then ask them to share with a partner.

“Now, who can explain to the class what an expression is?” (An expression is a variable or combination of variables, numbers, and symbols that represents a mathematical relationship.)

“One way to represent a mathematical situation is to write an expression. I’m going to write some examples of expressions.”
(Write the following on the overhead)

p + 5

12 – 3

28 ¸ a

6c

6 / 2

x + y

LEARNING ACTIVITIES

QUESTIONS FOR STUDENTS

TEACHER SUPPORT

“How are the expressions alike?” (They all have numbers in them.)

“How are they different?” (Some have operation symbols and letters or numbers; some just have letters and numbers.)

“Bob has 28 extra pieces of candy that he wants to share equally among his friends.

We don’t know the number of friends Bob has. In mathematics, we can use letters to represent unknown quantities in expressions. Since we don’t know the number of friends Bob has, we can use the letter “a” to represent that number. We refer to letters that we use to represent unknown amounts as variables. Variables hold the place of an unknown value, allowing us to represent a mathematical situation without knowing all the numbers.”

“Are there any unknown values in this statement? (number of friends)

“Which expression from the list on the overhead would represent this problem?” (28 ¸ a)

“Do we know the value of letter ‘a’?” (No.)

“Is there more than one value that ‘a’ could represent? (Yes.)

“What numbers could the letter ‘a’ represent? (2, 4, 7, 14)

“We like to write expressions as efficiently as possible. Not only do we use variables in writing mathematical expressions, we also use different representations for multiplication and division. For example, 25 ¸ 5 can also be written as 25 / 5, and
6 ´ c can also be written as 6c.”

LEARNING ACTIVITIES

QUESTIONS FOR STUDENTS

TEACHER SUPPORT

The teacher should then hold up a brown paper bag with the letter “n” written on the outside and containing some tiles.

“This bag has some tiles in it. I have written the number of tiles on the outside of the bag.”

“Who can tell me how many tiles are in the bag?” (n)

Some students may respond that they don’t know the number of tiles in the bag. Remind them that the label on the bag tells them how many tiles are in the bag.

Have students work with a partner to write in words a situation that uses the number of tiles in the bag.

After students have completed their examples, have them share with the whole class and discuss some of the examples.

There are a variety of examples students could provide, such as

•  the number of tiles in the bag minus 1

•  8 plus the number of tiles in the bag

“Since we know there is “n” number of tiles in the bag, let’s use that information to help us write some expressions to represent the number of tiles in the bag.”

LEARNING ACTIVITIES

QUESTIONS FOR STUDENTS

TEACHER SUPPORT

“Suppose we add 7 tiles to the bag, what expression could we write to represent the number of tiles in the bag?” (n + 7 or 7 + n)

“What expression could be used to represent each situation below? I want everyone to write an answer on their paper.”

(Write the following on the overhead):

•  n decreased by 12

•  the product of n and 15

•  the quotient of n and 9

As students are recording their answers, tour the classroom to check for understanding, and assist students who might be having difficulties. When everyone is done, call upon students with correct answers to respond.

Project the “Paper Bag” transparency, and have students pair up and write an expression to represent each of the four mathematical situations described on the overhead.

Call upon students to report the expressions they

wrote, and discuss whether they are correct or

incorrect.

Answers to “Paper Bag” transparency problems:

•  n – 8

•  n / 4

•  3n

•  12 – n

Distribute “A Bagful of Problems” formative assessment to each student to complete.  Answer key provided.