The document discusses writing variable expressions to represent word phrases and vice versa. It provides examples of commonly used variables like x and y and explains that variables are placeholders that represent unknown quantities. The document shows how to translate phrases like "four more than a number" to the expression x+4. It also gives the reverse translation from expressions like 3(x+10) to word phrases. Examples are provided to demonstrate translating real world word problems into variable expressions and vice versa. Homework problems from the textbook are assigned.

1. SECTION 2-3
Write Variable Expressions

2. ESSENTIAL
QUESTIONS
How do you write variable expressions to represent word
phrases?
How do you write word phrases to represent variable
expressions?
Where you’ll see this:
Part-time jobs, space science, photography, population

3. SOME VERY
IMPORTANT IDEAS

4. SOME VERY
IMPORTANT IDEAS
Most commonly used variables: x and y

5. SOME VERY
IMPORTANT IDEAS
Most commonly used variables: x and y
Only place holders

6. SOME VERY
IMPORTANT IDEAS
Most commonly used variables: x and y
Only place holders
Represents something we don’t know

7. SOME VERY
IMPORTANT IDEAS
Most commonly used variables: x and y
Only place holders
Represents something we don’t know
Remember: Variables represent a number

8. SOME VERY
IMPORTANT IDEAS
Most commonly used variables: x and y
Only place holders
Represents something we don’t know
Remember: Variables represent a number
Translate!

9. TRANSLATIONS
Rewrite the word phrase as a variable expression
Four more than a number

10. TRANSLATIONS
Rewrite the word phrase as a variable expression
Four more than a number
x+4

11. TRANSLATIONS
Rewrite the word phrase as a variable expression
The difference of a number and 15

12. TRANSLATIONS
Rewrite the word phrase as a variable expression
The difference of a number and 15
q - 15

13. TRANSLATIONS
Rewrite the word phrase as a variable expression
Three times a number

14. TRANSLATIONS
Rewrite the word phrase as a variable expression
Three times a number
3r

15. TRANSLATIONS
Rewrite the word phrase as a variable expression
The quotient of a number and 5

16. TRANSLATIONS
Rewrite the word phrase as a variable expression
The quotient of a number and 5
t
5

17. TRANSLATIONS
Rewrite the word phrase as a variable expression
Eight less than a number

18. TRANSLATIONS
Rewrite the word phrase as a variable expression
Eight less than a number
y-8

19. TRANSLATIONS
Rewrite the word phrase as a variable expression
The sum of a number and -10

20. TRANSLATIONS
Rewrite the word phrase as a variable expression
The sum of a number and -10
b + -10

21. TRANSLATIONS
Rewrite the word phrase as a variable expression
The sum of a number and -10
b + -10 = b - 10

22. TRANSLATIONS
Rewrite the word phrase as a variable expression
The product of a number and 15

23. TRANSLATIONS
Rewrite the word phrase as a variable expression
The product of a number and 15
15u

24. TRANSLATIONS
Rewrite the word phrase as a variable expression
Six divided by a number

25. TRANSLATIONS
Rewrite the word phrase as a variable expression
Six divided by a number
6
w

26. TRANSLATIONS
Rewrite the word phrase as a variable expression
A number increased by twelve

27. TRANSLATIONS
Rewrite the word phrase as a variable expression
A number increased by twelve
h + 12

28. TRANSLATIONS
Rewrite the word phrase as a variable expression
A number multiplied by four

29. TRANSLATIONS
Rewrite the word phrase as a variable expression
A number multiplied by four
4j

30. TRANSLATIONS
Rewrite the word phrase as a variable expression
Negative five decreased by a number

31. TRANSLATIONS
Rewrite the word phrase as a variable expression
Negative five decreased by a number
-5 - f

32. TRANSLATIONS
Rewrite the word phrase as a variable expression
Twelve less than the quotient of a number and seven

33. TRANSLATIONS
Rewrite the word phrase as a variable expression
Twelve less than the quotient of a number and seven
m
− 12
7

34. EXAMPLE 1
Write each phrase as a variable expression.
a. Twice the sum of a number and three
b. Six less than the product of a number and ten

35. EXAMPLE 1
Write each phrase as a variable expression.
a. Twice the sum of a number and three
2(v + 3)
b. Six less than the product of a number and ten

36. EXAMPLE 1
Write each phrase as a variable expression.
a. Twice the sum of a number and three
2(v + 3)
b. Six less than the product of a number and ten
10p -6

37. EXAMPLE 2
Translate the following variable expressions back into word phrases
a. 3(x + 10)
b. 8n - 5

38. EXAMPLE 2
Translate the following variable expressions back into word phrases
a. 3(x + 10)
Three times the sum of a number and ten
b. 8n - 5

39. EXAMPLE 2
Translate the following variable expressions back into word phrases
a. 3(x + 10)
Three times the sum of a number and ten
b. 8n - 5
Five less than the product of eight and a number

40. WHAT’S THE BIG
DEAL?

41. WHAT’S THE BIG
DEAL?
Helps solving real world situations

42. WHAT’S THE BIG
DEAL?
Helps solving real world situations
Helps break into steps

43. WHAT’S THE BIG
DEAL?
Helps solving real world situations
Helps break into steps
Solve in steps, not as a whole

44. EXAMPLE 3
Matt Mitarnowski makes and sells candles. For his medium-sized
pillar candles, he charges $5.50 each for the unscented ones and
$7.00 each for the scented ones. Write a variable expression to
show how much Matt earns when he sells his medium-sized pillar
candles. Then figure out how much he has made when he sells 6
unscented and 10 scented candles.

45. EXAMPLE 3
Matt Mitarnowski makes and sells candles. For his medium-sized
pillar candles, he charges $5.50 each for the unscented ones and
$7.00 each for the scented ones. Write a variable expression to
show how much Matt earns when he sells his medium-sized pillar
candles. Then figure out how much he has made when he sells 6
unscented and 10 scented candles.
Let u = unscented candles and s = scented candles

46. EXAMPLE 3
Matt Mitarnowski makes and sells candles. For his medium-sized
pillar candles, he charges $5.50 each for the unscented ones and
$7.00 each for the scented ones. Write a variable expression to
show how much Matt earns when he sells his medium-sized pillar
candles. Then figure out how much he has made when he sells 6
unscented and 10 scented candles.
Let u = unscented candles and s = scented candles
5.50u + 7.00s

47. EXAMPLE 3
Matt Mitarnowski makes and sells candles. For his medium-sized
pillar candles, he charges $5.50 each for the unscented ones and
$7.00 each for the scented ones. Write a variable expression to
show how much Matt earns when he sells his medium-sized pillar
candles. Then figure out how much he has made when he sells 6
unscented and 10 scented candles.
Let u = unscented candles and s = scented candles
5.50u + 7.00s 5.50(6)+ 7.00(10)

48. EXAMPLE 3
Matt Mitarnowski makes and sells candles. For his medium-sized
pillar candles, he charges $5.50 each for the unscented ones and
$7.00 each for the scented ones. Write a variable expression to
show how much Matt earns when he sells his medium-sized pillar
candles. Then figure out how much he has made when he sells 6
unscented and 10 scented candles.
Let u = unscented candles and s = scented candles
5.50u + 7.00s 5.50(6)+ 7.00(10) = 33.00 + 70.00

49. EXAMPLE 3
Matt Mitarnowski makes and sells candles. For his medium-sized
pillar candles, he charges $5.50 each for the unscented ones and
$7.00 each for the scented ones. Write a variable expression to
show how much Matt earns when he sells his medium-sized pillar
candles. Then figure out how much he has made when he sells 6
unscented and 10 scented candles.
Let u = unscented candles and s = scented candles
5.50u + 7.00s 5.50(6)+ 7.00(10) = 33.00 + 70.00 = $103.00

50. EXAMPLE 3
Matt Mitarnowski makes and sells candles. For his medium-sized
pillar candles, he charges $5.50 each for the unscented ones and
$7.00 each for the scented ones. Write a variable expression to
show how much Matt earns when he sells his medium-sized pillar
candles. Then figure out how much he has made when he sells 6
unscented and 10 scented candles.

51. EXAMPLE 3
Matt Mitarnowski makes and sells candles. For his medium-sized
pillar candles, he charges $5.50 each for the unscented ones and
$7.00 each for the scented ones. Write a variable expression to
show how much Matt earns when he sells his medium-sized pillar
candles. Then figure out how much he has made when he sells 6
unscented and 10 scented candles.
Matt makes $103.00 by selling 6 unscented and 10 scented candles

52. HOMEWORK

53. HOMEWORK
p. 64 #1-13 all, 14-40 even
“Our greatest glory is not in never failing but in rising every time
we fall.” - Confucius