Download PPT Evaluating/Writing Expressions

6th Grade
Variable, Expression,
Evaluate, Simplify
a · b = ab
by Monica Yuskaitis, M.A. Ed.
Copyright © 2013 by Monica Yuskaitis
1
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
2
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
Vocabulary
Sum - what you get when you add
1 +1 = 2
Difference - what you get when you subtract 2 -1 = 1
Product- the answer to a multiplication problem 2 x 1 = 1
Quotient – what you get when you divide
2÷1=2
Factor - a number multiplied to get another number 2 x1 =2
Copyright © 2013 by Monica Yuskaitis
Variables
Copyright © 2013 by Monica Yuskaitis
5
Vocabulary
• Constant – is a quantity that
stays the same. The opposite of
a variable.
• Inches in a foot.
Copyright © 2013 by Monica Yuskaitis
6
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.
Copyright © 2013 by Monica Yuskaitis
7
Vocabulary
• Variable – A variable is a letter
that represents a number
(unknown quantity).
• 8 + n = 12
Copyright © 2013 by Monica Yuskaitis
8
Vocabulary
• A variable can use any letter of
the alphabet.
•n+5
•x–7
• w - 25
Copyright © 2013 by Monica Yuskaitis
9
Find the Variables
?
n
#
f
p
%
7
v
$
b
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.
n+4
• A box of crayons missing 2 crayons.
n-2
• 3 full boxes of crayons.
3n
• A full box of crayons shared equally with
3 people.
n/3
Multiplication in Algebra
• Sometimes the x for multiplication
gets confused with a variable. So we
show multiplication in different ways
in algebra.
•
•
•
•
4·5
4(5)
ab
3b
means 4 times 5 (not this 4.5)
means 4 times 5
means a times b
means 3 times b
Check Up – What do these mean?
•
•
•
•
•
•
•
p·4
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
Placement Rule
• Always write the variable after
the number.
b x 6 write 6b
Copyright © 2013 by Monica Yuskaitis
Using parentheses
4xb
• 4 (b)
• (4) b
• (4b)
Copyright © 2013 by Monica Yuskaitis
Algebraic and Numerical
Expressions
Copyright © 2013 by Monica Yuskaitis
16
Vocabulary
• Numerical expression – contains only
numbers amd operations
• 15 + 9 x 3
• 12 ÷ 3 - 3
Copyright © 2013 by Monica Yuskaitis
17
Vocabulary
• Algebraic expression – may contain
numbers, operations, and one or more
variables.
• 45 ÷ p - q
• r–3
Copyright © 2013 by Monica Yuskaitis
18
Which ones are algebraic expressions?
h-7
a+b+c
p–6+1
y÷5
5+9
n+4
area
vertex
Which ones are numerical expressions?
7x2
24 ÷ 12
29 - 7
9 x 3-7
b+9
2+4
32 x 7a
7x4 + c
The Anatomy of
An Algebraic Expression
3b + 6 - b
Coefficient –
Like terms # multiplied
Terms with
by variable. Terms – parts
the same
separated by
variable.
+ and -.
Copyright © 2013 by Monica Yuskaitis
21
Simplifying
Expressions
Copyright © 2013 by Monica Yuskaitis
22
Vocabulary
• Simplify – Combine like terms and
complete all operations. Use
parentheses around operations you
are going to do first.
m=2
m+8+m
(2 x 2) + 8
2m+8
4 + 8 = 12
Copyright © 2013 by Monica Yuskaitis
23
Simplify these expressions
3s
•s+s+s
2b + m
•b+b+m
• The quantity of c + c + 6 ÷ c
when c = 2 (4 + 6) ÷ 2
(2c + 6) ÷ c
10 ÷ 2 = 5
Evaluating
Expressions
Copyright © 2013 by Monica Yuskaitis
25
Vocabulary
• Evaluate an expression – To find
the value of an expression by
substituting numbers for variables.
•m + 8
•r – 3
m = 2 2 + 8 = 10
r=5
5–3=2
Copyright © 2013 by Monica Yuskaitis
26
Evaluate each expression
when x = 10
18
•x+8
59
• x + 49
20
•x+x
0
•x-x
3
•x-7
• 42 - x
32
Copyright © 2013 by Monica Yuskaitis
27
Complete This Table
independent dependent
n
5
10
21
32
n-3
2
7
18
29
Copyright © 2013 by Monica Yuskaitis
28
Complete This Table
independent dependent
x
5
10
21
32
x+6
11
16
27
38
Copyright © 2013 by Monica Yuskaitis
29
Stop
Lesson 1.1 PPT
Copyright © 2013 by Monica Yuskaitis
30
Writing Addition
and Subtraction
Expressions 1.2
Copyright © 2013 by Monica Yuskaitis
31
Words That Lead to Addition
•
•
•
•
•
•
•
•
Sum
More than
Increased by
Total of
Plus
Altogether
Added to
And
Copyright © 2013 by Monica Yuskaitis
32
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
33
Now You Try!
Copyright © 2013 by Monica Yuskaitis
34
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
Copyright © 2013 by Monica Yuskaitis
n + 10
w-5
x-6
n+8
n+9
y+4
35
Write the Expressions
• 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
Copyright © 2013 by Monica Yuskaitis
s+2
k-1
x - 31
b+7
n+6
z+9
36
Writing
Multiplication and
Division
Expressions
Copyright © 2013 by Monica Yuskaitis
37
Words That Lead to Multiplication
• Times
• Multiplied by
• Product of
• Groups of
• Twice
• Of
Copyright © 2013 by Monica Yuskaitis
38
Words That Lead to Division
• Divided by
• Divided into
• Quotient of
Copyright © 2013 by Monica Yuskaitis
39
Now You Try!
Copyright © 2013 by Monica Yuskaitis
40
Write the Algebraic Expression
• The product of 5 and a number c
5 x c or 5 • c or 5c
• Seven times a number t
7 x t or 7 • t or 7t
• 6 multiplied by a number d
6 x d or 6 • d or 6d
Copyright © 2013 by Monica Yuskaitis
Write an algebraic expression
• 24 multiplied by a number
24n
• Product of 32 and a number
32n
• 300 times a number
300n
Copyright © 2013 by Monica Yuskaitis
Now Write
Expressions with
All 4 Operations
Copyright © 2013 by Monica Yuskaitis
43
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
Copyright © 2013 by Monica Yuskaitis
6n + 2
3w
b/4
8/n
n/4
3x
44
Write an algebraic expression
• 3 times the sum of 4 and 2
3 (4 + 2)
• Product of 4 and the sum of 3 & 2
4 (3 + 2)
• Multiply 3 times the sum of r & 5
3 (r + 5)
Copyright © 2013 by Monica Yuskaitis
Write an algebraic expression
• Twice the sum of z and 3
2 ( z + 3)
• Multiply z by the sum of 7 and s
z (7 + s)
• 4 times the difference of w and 5
4 (w – 5)
Copyright © 2013 by Monica Yuskaitis
Write an Algebraic Expression
• Twice the sum of q and 5
2 ( q + 5)
• Multiply t by the sum of 8 and p
t (8 + p)
• 6 times the difference of h and 3
6 (h – 3)
Copyright © 2013 by Monica Yuskaitis
Evaluate these Expressions
• m ÷ 3 when m = 12 12 ÷ 3 = 4
• 3p when p = 8
3 · 8 = 24
• k - 5 when k = 18
18 - 5 = 13
• 9 + b when b = 7
9 + 7 = 16
• 18/v when v = 6
18 ÷ 6 = 3
Problem
Solving
Copyright © 2013 by Monica Yuskaitis
49
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?
What strategies will you use?
What operations will you use?
How many steps are there and in what order
must you do them?
Analysis
Representation
How will you solve the problem?
Did you check your answer?
Does your answer make sense?
Resolution
Write an Algebraic Expression
• Scott’s brother is 2 years younger than
Scott.
s-2
• The sum of two numbers is 12.
v + c = 12
• The difference between two numbers is 5.
m–n=5
Copyright © 2013 by Monica Yuskaitis
51
1.2 PPT
Copyright © 2013 by Monica Yuskaitis
52