1. by Monica Yuskaitis, M.A. Ed.
6th Grade
Algebra I
Variable, Expression,
Evaluate, Simplify
a · b = ab
by Monica Yuskaitis, M.A. Ed.
Copyright © 2013 by Monica Yuskaitis

2. Copyright © 2013 by Monica Yuskaitis
Objectives
To be able to distinguish between a numerical expression and an algebraic expression.
To be able to simplify algebraic expressions.
To be able to evaluate algebraic expressions.
Copyright © 2013 by Monica Yuskaitis

3. Copyright © 2013 by Monica Yuskaitis
Essential Question
How can I evaluate and simplify
algebraic expressions?
How can I identify if an expression is numerical or algebraic? 3
Copyright © 2013 by Monica Yuskaitis

4. Copyright © 2013 by Monica Yuskaitis
Vocabulary
Sum - what you get when you add = 2
Difference - what you get when you subtract = 1
Product- the answer to a multiplication problem 2 x 1 = 1
Quotient – what you get when you divide ÷ 1 = 2
Factor - a number multiplied to get another number 2 x1 =2
Copyright © 2013 by Monica Yuskaitis

5. Copyright © 2013 by Monica Yuskaitis
Variables
Copyright © 2013 by Monica Yuskaitis

6. Copyright © 2013 by Monica Yuskaitis
Vocabulary
Constant – is a quantity that stays the same. The opposite of a variable.
Inches in a foot.
Copyright © 2013 by Monica Yuskaitis

7. Copyright © 2013 by Monica Yuskaitis
Vocabulary
Variable – A is a quantity that can change.
8 + n =
In this problem n could be 1, 2, 3, 4 or
whatever the author wants it to be.
Note as n changes, so does the answer. 7
Copyright © 2013 by Monica Yuskaitis 7

8. Copyright © 2013 by Monica Yuskaitis
Vocabulary
Variable – A variable is a letter that represents a number (unknown quantity).
8 + n = 12 8
Copyright © 2013 by Monica Yuskaitis 8

9. Copyright © 2013 by Monica Yuskaitis
Vocabulary
A variable can use any letter of the alphabet.
n + 5
x – 7
w - 25
Copyright © 2013 by Monica Yuskaitis

10. Find the Variables ? n % 7 # f v $ b p

11. Variables
Variables are great to use when you are doing a word problem and you don’t know a number.
A full box of crayons with 4 extra crayons.
A box of crayons missing 2 crayons.
3 full boxes of crayons.
A full box of crayons shared equally with 3 people.
n + 4
n - 2 3n
n/3

12. Multiplication in Algebra
Sometimes the x for multiplication gets confused with a variable. So we show multiplication in different ways in algebra.
4 · 5 means 4 times 5 (not this 4.5)
4(5) means 4 times 5
ab means a times b
3b means 3 times b

13. Check Up – What do these mean?3q
s/2 cd
j + 3
6(3)
9 - e
p times 4
3 times q
s divided by 2
c times d
j plus 3
6 times 3
9 minus e

14. Copyright © 2013 by Monica Yuskaitis
Placement Rule
Always write the variable after the number.
b x 6 write 6b
Copyright © 2013 by Monica Yuskaitis

15. Copyright © 2013 by Monica Yuskaitis
Using parentheses
4 x b
4 (b)
(4) b
(4b)
Copyright © 2013 by Monica Yuskaitis

16. Algebraic and Numerical Expressions16
Copyright © 2013 by Monica Yuskaitis

17. Copyright © 2013 by Monica Yuskaitis
Vocabulary
Numerical expression – contains only numbers amd operations
x 3
12 ÷ 3 - 3
Copyright © 2013 by Monica Yuskaitis

18. Copyright © 2013 by Monica Yuskaitis
Vocabulary
Algebraic expression – may contain numbers, operations, and one or more variables.
45 ÷ p - q
r – 3
Copyright © 2013 by Monica Yuskaitis

19. Which ones are algebraic expressions?
y ÷ 5
5 + 9
a + b + c
n + 4
n + 4
area
vertex

20. Which ones are numerical expressions?
29 - 7
7 x 2
9 x 3-7
b + 9
24 ÷ 12
2 + 4
32 x 7a
7x4 + c

21. 3b + 6 - b The Anatomy of An Algebraic Expression Terms – parts
separated by
+ and -.
Coefficient –
# multiplied
by variable.
Like terms -
Terms with
the same
variable. 21
Copyright © 2013 by Monica Yuskaitis

22. Copyright © 2013 by Monica Yuskaitis
Simplifying
Expressions 22
Copyright © 2013 by Monica Yuskaitis

23. Copyright © 2013 by Monica Yuskaitis
Vocabulary
Simplify – Combine like terms and complete all operations. Use parentheses around operations you are going to do first.
m = 2
m m 2 m + 8
(2 x 2) = 12
Copyright © 2013 by Monica Yuskaitis

24. Simplify these expressions
s + s + s
b + b + m
The quantity of c + c + 6 ÷ c when c = 2 3s
2b + m
(4 + 6) ÷ 2
(2c + 6) ÷ c
10 ÷ 2 = 5

25. Copyright © 2013 by Monica Yuskaitis
Evaluating
Expressions 25
Copyright © 2013 by Monica Yuskaitis

26. Copyright © 2013 by Monica Yuskaitis
Vocabulary
Evaluate an expression – To find the value of an expression by substituting numbers for variables.
m + 8 m = = 10
r – 3 r = – 3 = 2
Copyright © 2013 by Monica Yuskaitis

27. Evaluate each expression when x = 10
x + x
x - x
x - 7
42 - x 18 59 20 3 32
Copyright © 2013 by Monica Yuskaitis

28. Copyright © 2013 by Monica Yuskaitis
Complete This Table
independent
dependent n
n - 3 5 10 21 32 2 7 18 29
Copyright © 2013 by Monica Yuskaitis

29. Copyright © 2013 by Monica Yuskaitis
Complete This Table
independent
dependent x
x + 6 5 10 21 32 11 16 27 38
Copyright © 2013 by Monica Yuskaitis

30. Copyright © 2013 by Monica Yuskaitis
Stop
Lesson 1.1 PPT
Copyright © 2013 by Monica Yuskaitis

31. Copyright © 2013 by Monica Yuskaitis
Writing Addition
and Subtraction
Expressions 1.2 31
Copyright © 2013 by Monica Yuskaitis

32. Words That Lead to Addition
Sum
More than
Increased by
Total of
Plus
Altogether
Added to
And
Copyright © 2013 by Monica Yuskaitis

33. Words That Lead to Subtraction
Decreased by
Less than
Difference of
Minus
How many more
Subtract from
Fewer than
Take away
Copyright © 2013 by Monica Yuskaitis

34. Copyright © 2013 by Monica Yuskaitis
Now You Try!
Copyright © 2013 by Monica Yuskaitis

35. Copyright © 2013 by Monica Yuskaitis
Write the Expressions
Ten more than a number
A number decrease by 5
6 less than a number
A number increased by 8
The sum of a number & 9
4 more than a number
n + 10
w - 5
x - 6
n + 8
n + 9
y + 4
Copyright © 2013 by Monica Yuskaitis

36. Copyright © 2013 by Monica Yuskaitis
Write the Expressions
s + 2
A number s plus 2
A number decrease by 1
31 less than a number
A number b increased by 7
The sum of a number & 6
9 more than a number
k - 1
x - 31
b + 7
n + 6
z + 9
Copyright © 2013 by Monica Yuskaitis

37. Copyright © 2013 by Monica Yuskaitis
Writing
Multiplication and
Division
Expressions 37
Copyright © 2013 by Monica Yuskaitis

38. Words That Lead to Multiplication
Times
Multiplied by
Product of
Groups of
Twice Of
Copyright © 2013 by Monica Yuskaitis

39. Words That Lead to Division
Divided by
Divided into
Quotient of
Copyright © 2013 by Monica Yuskaitis

40. Copyright © 2013 by Monica Yuskaitis
Now You Try!
Copyright © 2013 by Monica Yuskaitis

41. Write the Algebraic Expression
The product of 5 and a number c
Seven times a number t
6 multiplied by a number d
5 x c or 5 • c or 5c
7 x t or 7 • t or 7t
6 x d or 6 • d or 6d
Copyright © 2013 by Monica Yuskaitis

42. Write an algebraic expression
24 multiplied by a number
Product of 32 and a number
300 times a number
24n
32n
300n
Copyright © 2013 by Monica Yuskaitis

43. Copyright © 2013 by Monica Yuskaitis
Now Write
Expressions with
All 4 Operations 43
Copyright © 2013 by Monica Yuskaitis

44. Write the Algebraic Expressions
6 times a number plus 2
Product of a number and 3
Number divided by 4
Quotient of 8 divided by n
4 divided into a number
3 groups of x
6n + 2 3w
b/4
8/n
n/4 3x
Copyright © 2013 by Monica Yuskaitis

45. Write an algebraic expression
3 times the sum of 4 and 2
Product of 4 and the sum of 3 & 2
Multiply 3 times the sum of r & 5
3 (4 + 2)
4 (3 + 2)
3 (r + 5)
Copyright © 2013 by Monica Yuskaitis

46. Write an algebraic expression
Twice the sum of z and 3
Multiply z by the sum of 7 and s
4 times the difference of w and 5
2 ( z + 3)
z (7 + s)
4 (w – 5)
Copyright © 2013 by Monica Yuskaitis

47. Write an Algebraic Expression
Twice the sum of q and 5
Multiply t by the sum of 8 and p
6 times the difference of h and 3
2 ( q + 5)
t (8 + p)
6 (h – 3)
Copyright © 2013 by Monica Yuskaitis

48. Evaluate these Expressions
m ÷ 3 when m = 12
12 ÷ 3 = 4
3p when p = 8
3 · 8 = 24
k - 5 when k = 18
= 13
9 + b when b = 7
9 + 7 = 16
18/v when v = 6
18 ÷ 6 = 3

49. Copyright © 2013 by Monica Yuskaitis
Problem
Solving
Copyright © 2013 by Monica Yuskaitis

50. Analysis Representation Resolution Problem Solving Steps
What information do you need?
What is the problem asking you to find out?
Is the answer going to be larger or smaller?
Analysis
Representation
What strategies will you use?
What operations will you use?
How many steps are there and in what order must you do them?
Resolution
How will you solve the problem?
Did you check your answer?
Does your answer make sense?

51. Write an Algebraic Expression
Scott’s brother is 2 years younger than Scott.
The sum of two numbers is 12.
The difference between two numbers is 5.
s - 2
v + c = 12
m – n = 5
Copyright © 2013 by Monica Yuskaitis

52. Copyright © 2013 by Monica Yuskaitis
1.2 PPT
Copyright © 2013 by Monica Yuskaitis