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Use Variables to Represent Numbers and Write Expressions

For each problem, identify what the variable represents before writing the expression.

Grade 6·21 problems·~25 min·Common Core Math - Grade 6·standard·6-ee-b-6
Work through problems with immediate feedback
A

Recall / Warm-Up

1.

Which word signals multiplication in a verbal math phrase?

2.

Which sentence correctly describes the role of nn in the expression 5n5n?

3.

If x=6x = 6, what is the value of 2x+12x + 1?

B

Fluency Practice

1.

A bookshelf has ss shelves and each shelf holds 8 books. Which expression gives the total number of books?

2.

Which expression means '7 less than a number nn'?

3.

Write the expression for 'the cost of tt tickets at $9 each.' Which is conventional form?

4.

A taxi charges a flat fee of $3 plus $2 per mile. Which expression gives the total cost for mm miles?

5.

Write an algebraic expression for 'five more than twice a number xx':   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .

When x=4x = 4, the value is   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .

expression:
value when x=4:
C

Varied Practice

1.

Write the algebraic expression for each phrase. Use the variable given.

'The quotient of dd and 5' →   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲  

'Three times a number nn, decreased by 4' →   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲  

quotient expression:
three times minus four:
2.

Which expression matches '10 decreased by a number kk'?

3.

Maria earns $12 per hour. Which scenario uses hh as a ranging variable (not a specific unknown)?

4.

Which best describes when a variable represents a specific unknown versus when it ranges over a set?

5.

What does the expression 4n+24n + 2 represent in a real-world context?

D

Word Problems / Application

1.

A recipe uses 2 cups of flour per serving.

The expression for the flour needed for ss servings is   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .

For 6 servings, the recipe needs   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   cups of flour.

flour expression:
cups for 6 servings:
2.

A runner's total distance is described by the expression d+3d + 3, where dd is the distance already run in miles.

1.

If the runner has already run 5 miles, how many miles total does the expression give?

2.

What does the 3 in the expression d+3d + 3 represent in this context?

3.

A plank of wood is cut into two pieces. One piece is 4 feet long. Which expression represents the length of the other piece, if the total length is LL feet?

E

Error Analysis

1.

Lena wrote the expression for '3 less than a number nn' as 3−n3 - n.

What error did Lena make, and what is the correct expression?

2.

A problem says: "A board is cut into two pieces. Write expressions for both pieces." Tomas introduced two variables: xx for the first piece and yy for the second, writing both expressions as xx and yy separately.

What is wrong with Tomas's approach?

F

Challenge

1.

Write a word problem that could be modeled by the expression 5n−35n - 3. Then evaluate the expression for two different values of nn and explain what each result means in context.

2.

A variable tt represents time in hours. In the expression 60t60t, is tt a specific unknown or a ranging variable? Explain the difference, and give one example of each role for tt in a real-world context.

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