Transcript Equations and Inequalities - Mendenhall-Jr-PLC

PowerPoint created by
Parsheena Berch
Resource: JBHM material
Pictures: Google Images
Equations and Inequalities
How well do you balance with math?
• Explain why the scale is not balanced
• How do I make the scale balance?
• Today’s lesson will focus on equations and
inequalities.
• It is important for you to remember that the
key is balance.
• The two sides must always balance or be
equal just like the water on the balance scale.
Page 128
__ + 2 = 5
What number goes in the blank?
x+2=5
What is different about these two sentences?
The only difference is one uses a blank and one
uses an x to take the place of the number 3.
Variable – a symbol such as a letter, box, star,
question mark, etc. that is used to represent
an unknown or undetermined value in an
expression or equation.
Can you find the variables?
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267 + y = 573
z – 24 = 13
a ÷ 42 = 6
? • 4 = 48
Variables can take different forms, letters,
symbols, etc. but they are still variables and
the process to solve or determine values is the
same.
• Equation – a statement that two
mathematical expressions are equal
• x + 3 = 12
• y – 2.8 = 9
• 2•4=7+z
• 2½+y=6
• Write an equation on your own.
Before going any farther and beginning
to work with equations, you need to
learn some different methods of
writing some of the operations you
have been working with for years.
You are going to learn some new
ways to show multiplication and
division without using the traditional
operational symbols x and ÷.
• Multiplication:
• 2 x 5 = 10
2 • 5 = 10
2x = 10
2(5) = 10
• (You should not use the traditional symbol, x,
for a multiplication sign when working with
equations and variables as it can easily be
mistaken for a variable rather than
multiplication sign.)
• Division:
• 10 ÷ 2 = 5
10/5 = 2
Write the equation that I say on your
white board.
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fourteen divided by a equals two
(14 / a = 2
or use the division symbol)
X divided by twenty equals five
(x ÷ 20 = 5
x/20 = 5)
y times six equals eighteen
(6y = 18
6• y = 18)
Four times y equals twelve
(4y = 12
4 • y = 12)
Solving Equations:
• When working with equations, you will be
working to solve for the variable. This means
you will be working to determine the value of
the variable or what number the variable is
taking the place of. There are different
methods that can be used to solve equations
and you will be learning multiple strategies.
Then you will be able to decide which strategy
or method you are most comfortable working
with.
Inverse Operations
(Page 128 at the bottom)
• Addition and Subtraction
Tamatha was planning her birthday party, and she wanted to use lots of
balloons. Because her cake was going to be purple and blue, she decided
on these two colors for her balloons. If she needed 125 balloons and she
bought 45 purple balloons, how many blue balloons would she need to
buy? (Page 129 in student binder of JBHM)
• Brainstorm and give me your ideas.
• She would need 80 blue balloons because 125 total balloons minus 45
purple balloons leave 80 blue balloons. Go a step further and see if
students can match this equation to the story.
• Example: b + 45 = 125
• This equation says that 45 (purple balloons) plus (b) some unknown
number (blue balloons) = 125 total balloons.
b + 45 = 125
• If you had been given this equation first without the
story, how would you have solved it? Look at your
Binder Notes and the chart that shows the addition
operation with the inverse being subtraction. Inverse
means opposite.
• The equal sign means that the sides are to always
remain the same so the equation balances. An
equation is a statement that two mathematical
expressions are equal.
• I need two students who are the same height.
• Now let us go back to the balloon story.
• b + 45 = 125
• The answer reveals the number of blue balloons
needed.
Example of Balloon Problem Solution:
• b + 45 = 125 (addition operation)
• b + 45 – 45 = 125 – 45 (inverse operation of
subtraction)
• b = 80 (how many blue balloons are needed)
Substitute the answer in the equation
and check for accuracy.
b + 45 = 125
80 + 45 = 125
125 = 125
• This is an inverse operation. Inverse
operations are opposite operations. Addition
is the opposite of subtraction. All equations
are solved using inverse operations. An inverse
operation “undoes” an operation and leaves
the unknown weight (variable) standing alone
or isolated.
Example #1
• x + 3 = 12
Operation – addition
• x + 3 – 3 = 12 – 3
Inverse operation –
subtraction
• x=9
• Check your work!
• x + 3 = 12
• (9) + 3 = 12
Example #2
• x – 3 = 12
Operation – subtraction
• x – 3 + 3 = 12 + 3
Inverse operation –
addition
• x = 15
• Check your work!
• x – 3 = 12
• (15) – 3 = 12
Example #3
• x – 3.5 = 10
Operation – subtraction
• x – 3.5 + 3.5 = 10 + 3.5
Inverse operation addition
• x = 13.5
• Check your work!
• x – 3.5 = 10
• (13.5) – 3.5 = 10
Example #4 (Page 130)
• x + 4.6 = 12
Operation – addition
• x + 4.6 – 4.6 = 12 – 4.6 Inverse operation –
subtraction
• x = 7.4
• Check your work!
• x + 4.6 = 12
• (7.4) + 4.6 = 12
Example #5
• x–½=4
Operation – subtraction
• X–½+½=4+½
Inverse operation –
addition
• X=4½
• Check your work!
• X–½=4
• (4 ½) – ½ = 4
Example #6
• x + 3 ¼ = 5 3/4 operation – addition
• X + 3 ¼ - 3 ¼ = 5 ¾ - 3 ¼ Inverse operation –
subtraction
• X=2½
• Check your work!
• x+3¼=5¾
• (2 1/2) + 3 ¼ = 5 ¾
Work these on page 131
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x + 8 = 19
x – 4 = 42
x – 22 = 12
x + 2.7 = 10
x – 4.9 = 11
x+¾=8
Closure:
• Explain what you have learned about
equations today.
• Does the (Left side = right side) always?
Homework:
1st, 2nd, and 7th
You HAVE to check your work!
• x + 25 = 89
• 34 + y = 89
• a – 14 = 75
• x – 9 = -7
Homework:
3rd, 4th, and 6th
You HAVE to check your work!
• x + 5 = 16
• x – 4 = 12
• 3+x=9
• 18 + x = 20