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Math Coach Amy
Amy Ferguson Moncure

Algebra 1 · Unit 6

Translate Expressions

Translate real-world situations into algebraic expressions and read expressions back in words.

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Key Ideas Easy Medium Hard Super Challenge
What to Remember

Name the variable

Say what the letter stands for, with units, before you write the expression.

Expression, not equation

An expression has no equals sign. “5 more than n” is n + 5, not n + 5 = …

Times, of, per

“Twice a number” is 2n. “Product of a and b” is ab. “Quotient of x and 4” is x4.

Read an expression back

3x − 7 is “7 less than 3 times a number.” Check that your words match the order.

Level 1

Easy

One quantity. Write the expression, or read one in words.

Example
A kayak rental costs 18 dollars plus 6 dollars per hour. Write an expression for the cost after h hours.

Let h = the number of hours.

18 + 6h

Answer: 18 + 6h

1
Write an expression. 8 less than a number n.
Show Answer

“8 less than n” is n − 8.

n − 8

Answer: n − 8

2
Write an expression. Twice a number k, plus 5.
Show Answer

2k + 5

Answer: 2k + 5

3
Read 4x − 9 in words.
Show Answer

9 less than 4 times a number x.

Answer: 9 less than 4 times x

4
A tank starts with 40 gallons and drains 5 gallons each minute. Write an expression for the gallons left after t minutes.
Show Answer

40 − 5t

Answer: 40 − 5t

5
Write an expression for the area of a rectangle with width w and length 3 more than the width.
Show Answer

Length is w + 3.

Area = w(w + 3)

Answer: w(w + 3)

Level 2

Medium

Two operations, or translate an expression back into a story.

Example
Tickets cost 12 dollars each plus a 5 dollar fee. Write an expression for n tickets, then read it in words.

12n + 5

5 more than 12 times the number of tickets.

Answer: 12n + 5

1
The temperature is 72 degrees and falls 3 degrees each hour. Write an expression after h hours.
Show Answer

72 − 3h

Answer: 72 − 3h

2
Write an expression. The quotient of 2 more than x and 5.
Show Answer

x + 25

Answer: x + 25

3
A store sells notebooks at 3 dollars and pens at 2 dollars. Write an expression for n notebooks and p pens.
Show Answer

3n + 2p

Answer: 3n + 2p

4
Read d4 + 1 in a distance story if d is miles.
Show Answer

1 more than one-fourth of the miles.

Answer: 1 more than d divided by 4

5
A number n is tripled, then 4 is subtracted. Write the expression.
Show Answer

3n − 4

Answer: 3n − 4

Level 3

Hard

Nested wording and two-variable stories.

Example
Write an expression. 5 less than twice the sum of a number x and 3.

The sum of x and 3 is x + 3.

Twice that is 2(x + 3).

5 less than that is 2(x + 3) − 5.

Answer: 2(x + 3) − 5

1
A plumber charges 45 dollars to arrive plus 30 dollars per hour, and uses p parts at 8 dollars each. Write an expression for h hours.
Show Answer

45 + 30h + 8p

Answer: 45 + 30h + 8p

2
Read 2(n − 4) in words.
Show Answer

Twice the quantity 4 less than n.

Answer: twice (n − 4)

3
The length of a garden is 4 more than twice the width w. Write expressions for the length and the perimeter.
Show Answer

Length = 2w + 4

Perimeter = 2(2w + 4) + 2w = 6w + 8

Answer: length 2w + 4; perimeter 6w + 8

4
Write an expression. The product of 3 and the square of a number m, minus 1.
Show Answer

3m² − 1

Answer: 3m² − 1

5
A phone plan is 20 dollars plus 5 dollars per gigabyte after the first 2 GB. Write an expression for g gigabytes when g ≥ 2.
Show Answer

Extra gigabytes: g − 2

20 + 5(g − 2)

Answer: 20 + 5(g − 2)

Super Challenge

Super Challenge

1
Two students translate “6 less than 3 times a number.” A writes 6 − 3n. B writes 3n − 6. Who is right, and what phrase would match A?
Show Answer

“6 less than 3 times n” is 3n − 6. B is right.

A wrote 6 minus 3n, which is “3 times n less than 6.”

Answer: B; A is “3n less than 6”

2
Write two different expressions for “a number n increased by 20%, then decreased by 5.” Show they are not the same as increasing by 15%.
Show Answer

Increase 20%: 1.2n

Then decrease 5: 1.2n − 5

A 15% increase would be 1.15n, which is not 1.2n − 5.

Answer: 1.2n − 5

3
A rectangle has width w and length 12w + 3. Write the area, then read the area expression in words.
Show Answer

A = w(12w + 3)

A = 12w² + 3w

Half the square of the width, plus 3 times the width.

Answer: 12w² + 3w

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