warm up evaluate each expression for x = 9. 1. 7 + x 2. 4 x 3. 2 x + 1 4. 36

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2-2 Translate Between Words and Math

16

36

19

4x

Warm UpEvaluate each expression for x = 9.

1. 7 + x

2. 4x

3. 2x + 1

4. 36

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Objective write verbal phrases as simple algebraic expressions.

Common Core State Standards6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers.

6.EE.2a Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y.

6.EE.2c

Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2.

6.EE.6Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

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In word problems, you may need to translate words to math.

Action Operation

Put together or combine

Find how much more or less

Put together groups of equal parts

Separate into equal groups

Add

Subtract

Multiply

Divide

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37 + 28

• 28 added to 37• 37 plus 28• the sum of 37 and 28• 28 more than 37

• 28 added to x• x plus 28• the sum of x and

28• 28 more than x

x + 28

+Operation

Numerical Expression

Words

Algebraic Expression

Words

There are several different ways to write math expressions with words.

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• 12 subtracted from k• 12 minus k• the difference of k and 12• take away 12 from k

k — 12

Operation


Words


Words

90 — 12

• 12 subtracted from 90• 90 minus 12• the difference of 90 and 12• 12 less than 90• take away 12 from 90

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• 8 times w• w multiplied by 8• the product of 8 and w• 8 groups of of w

8 w or (8)(w) or 8w

Operation


Words


Words

8 48 or 8 48

• 8 times 48• 48 multiplied by 8• the product of 8 and 48

or (8)(48) or

8(48) or (8)48

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• n divided by 3• the quotient of n and 3

n 3 or

Operation


Words


Words

327 3 or

• 327 divided by 3• the quotient of 327 and 3

3273

n3

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Lake Superior is the largest lake in North America. Let a stand for the area in square miles of Lake Superior. Lake Erie has an area of 9,910 square miles. Write an expression to show how much larger Lake Superior is than Lake Erie.

Additional Example 1A: Social Studies Application

To find how much larger, subtract the area of Lake Erie from the area of Lake Superior.

a – 9,910

Lake Superior is a – 9,910 square miles larger than Lake Erie.

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Let p represent the number of colored pencils in a box. If there are 26 boxes on the shelf, write an algebraic expression to represent the total number of pencils on the shelf.

To put together 26 equal groups of p, multiply 26 times p.

26p, or 26 • p

There are 26p pencils on the shelf.

Additional Example 1B

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The Nile River is the world’s longest river. Let n stand for the length in miles of the Nile. The Paraná River is 3,030 miles long. Write an expression to show how much longer the Nile is than the Paraná.

Check It Out: Example 1A

To find how much longer, subtract the length of the Paraná from the length of the Nile.

n – 3,030

The Nile is n – 3,030 miles longer than the Paraná.

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Check It Out: Example 1B

Let p represent the number of paper clips in a box. If there are 125 boxes in a case, write an algebraic expression to represent the total number of paper clips in a case.

To put together 125 equal groups of p, multiply 125 times p.

125p or 125 • p

There are 125p paper clips in a case.

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Write each phrase as a numerical or algebraic expression.

Additional Example 2: Translating Words into Math

A. 987 minus 12

987 12

B. x times 45

45 • x or 45x

C. 42 less than 79

D. y divided by 22

y 22 or y22

79 42

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B-4

12fS+8

3+4p

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GAME TIME!

On an index card, write your own word problem. Your word problem must generate

an algebraic expression.

Use Example 2 as your model.

We will play a game to solve the class’s problems. The more difficult and global your

problem is, the more points you will earn!

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1. Let x represent the number of minutes Kristen works out in one week. Write an expression for the number of minutes she works out in 4 weeks.

Exit Ticket

Write each phrase as a numerical or algebraic expression. 2. 7 less than x

3. The product of 12 and w

4x

x 7

12w

Define a variable and write an algebraic expression. 4. Six years less than Tracy’s age. t 6; t is Tracy’s age

warm up evaluate each expression for x = 9. 1. 7 + x 2. 4 x 3. 2 x + 1 4. 36

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