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Level
1= beginning
Question
2= middle
3= end
Calculator
1
What is the most important thing to use in the
calculator? (you will need to train them on this
question)
1
How would you square a negative number?
1
2
How would raise a number to a power of 4? (or any
number greater than 2?)
What is the difference in entering a fraction vs. a
mixed number like 2¾ on the calculator?
1
How do you enter a fraction in the calculator
2
If substituting a number for a variable, how do you
enter it in the calculator?
What is the difference between an x and the “times”
sign?
1
1
How do you change a decimal to a fraction and vice
a versa?
1
What is a mixed number?
1
An improper fraction?
1
How can you changed to a mixed number from an
improper fraction in the calculator?
2
How do you reduce in the calculator? (ex: 6/8)
1
How do you enter a negative?
3
Is there difference between 3 – -2 and 3-2?
Answers
PARENTHESES!!!
Use parentheses. The exponent goes outside the
parentheses and use the x2 button.
Type the base number and then the carrot and the
exponent ex: 2^4 = 24
For a fraction (without a whole number) you will
only use the “fraction key” (abc button) once,
whereas with a mixed number you must use the
“fraction key” (abc button) twice. Ex: 1,2 vs.
2,3,4 (1/2 vs 2 ¾ )
Use the “fraction key” (abc button). Type the
numerator first and then the “fraction key” and
then the denominator.
Use parentheses!!!! Ex: 2x+4 when x = 3
Calc: 2(3)+4
X is a variable from now on in algebra. On the
calculator the x is near the tope left while the
“times” sign is near the bottom right. They are
NOT interchangeable.
Use the fD button. Type 1, 2 (1 fraction 2). Hit
exe (equals). Hit fD; Start with 1.5 then hit
exe. Hit fd
A mixed number has a whole number in front of
a fraction. Ex 3 ½
An improper fraction has a larger number in the
numerator (top). Ex: 4/3
Type in the calculator 1.5 (Continue from
previous question?) hit exe then fd. Calculator
should say 3,2. Hit shift, fraction key (abc)
Type 6 divided by 8. (calc will say 0.75) use
fd to change to fraction.
OR: Type in as a fraction: 6 fraction 8 (6,8) then
hit exe. Will automatically switch to 3,4
Use the (-) key at the bottom next to “exe.” The –
above “exe” will work for negative AND
subtraction, but (-) will only work for negatives
Yes. (check by typing in the calculator) ask
WHY?) 3 – -2 actually means 3 +2 because of
the double sign.
Order of Operations
1
What does PEMDAS mean?
1
1
2
(Please Excuse My Dear Aunt Sally- requires
further explanation): Parentheses, Exponents,
multiplication, division, addition, subtraction.
When multiplying and dividing which comes Go in order from left to right. Ex1: 20/4(3):
first? Adding and subtracting?
divide 20/4 first then 5 (3). Ex2: 10-4 +3,
subtract 10-4 first. Then add 6 +3.
(demonstrate the wrong way and show that the
results are NOT the same!)
1. Parentheses: Add 3+2 =5
When simplifying 4  2(3  2)  2 , list the
2. multiply -2 (5)= -10
operations in order.
3. divide -10/2 = -5
After:
4. Subtract 4-5= -1
Why did we add first?
We added because that’s what was INSIDE the
Parentheses and parentheses come first.
3
What do brackets mean?
3
What is the difference between 3  4 2 and
(3  4) 2 ?
8  (3  2 )
2
What does the line mean (the dividing line)?
Should we type the entire expression in the
calculator at once?
The same thing as parentheses. If we have
brackets and parentheses, we do the innermost
first. Ex 2+[4-6/(3-1)] the parentheses are
innermost because the are INSIDE of the
brackets. Subtract 1st then divide then subtract
and last add 2
On (3  4) 2 we have to “do” the parentheses
first. We do what’s inside: 3+4 first THEN
square = 49. For 3  4 2 we do exponents first
THEN add = 19
Ex:
2
2
List three different ways to write the
solution.
Divide
No- always type the top first, hit exe, write
down answer, then type the bottom (if
necessary), write answer and LAST divide.
Ex: 8-(3+2)= 3 THEN 3/2
3/2 (improper fraction)
1 ½ (mixed number)
1.5 (decimal)
Evaluating Expressions
1
What do you use when substituting a value?
Parentheses Ex: 2x+4 when x = 3
Calc: 2(3)+4
Plug in number and find numerical answer
(solve)
Plug in something
A letter or symbol that represents a number
(emphasize this!!!)
Various answers x, y, r, , <3 ….
A constant is a number by itself with no
variable. The value of this term never changes,
ie: remains CONSTANT (the SAME)
A coefficient is a number in front of a
variable. The coefficient is being multiplied
with the variable
A constant term does not have a variable. The
value of this term never changes. A coefficient
has a variable next to it. The value of this term
can change. 2x: if x = 3 then the value is 6, if x
= 10, the value is 20.
1
What does evaluate mean?
1
1
What does substitute mean?
What is a variable?
1
1
Give some examples of variables.
What is a constant?
1
What is a coefficient?
2
What is the difference between a constant
and a coefficient?
2
If the variable is alone (ex: x), does it have a YES. There is always a coefficient of invisible
coefficient? (If yes, what is it?)
1. If there was not any x’s (zero) then why
would we write it? For ex x+ 3x = 4x b/c
1x+3x: 1+3=4. if there were only 3, why would
we even write the “x” term?
When substituting -3 for x into x², how
With parentheses. The exponent goes outside
would we write it? Where does the
(-3)2
exponent go?
What is a term?
A number or variable or a coefficient with a
variable. Terms do NOT have + or What separates one term from another?
+ or - Ex: 3x – 4 +7yz has 3 terms. (draw lines
where you see the – and +
Describe the difference between an
An equation has an equal sign and an
expression and an equation.
expression does not.
Give an example of an Algebraic Expression Algebraic : various answers; must have
and a numerical expression. Be able to
variables (no equal sign)
explain the difference.
Numerical: various answers; cannot have
variables (no equal sign)
Algebraic expressions have variables,
numbers and operation symbols. Numerical
expressions only have numbers and operation
symbols.
Lead in:
What is different about algebra vs “old/8th
Algebra has variables
grade” math?
So what do we think ALGEBRAIC
Variables
expressions have different than numerical
expressions?
1
1
1
2
3
3
What is an example of something you would
have done in 8th grade? (or earlier) What
does this have?
Now if we want to make it ALGEBRAIC,
what would we change?
What is the proper way to write the sum of a
number and a variable term? (ex. 4
increased by 2x)
A numerical expression: 3+4
Numbers and symbol (plus sign)
Put in variables: 3x+4x
2x+4. The variable term should go FIRST.
Explain that it is not wrong to write 4+2x, but it
is “improper,” Just like it is not “wrong if we
write “juan”(its still the same name) but it is
“improper.” Also 2x+4 is how students will see
it on tests so they need to get used to the
“proper” way of writing algebra.
“Three times the QUANTITY x minus 2”
3x: the number (coefficient) goes in the
front. If they just say “number” ask: What is
this number called when it is in front of a
variable? Coefficient
Four.
3
2
How would you read/say 3( x  2) ?
What is the proper way to write an x times
3?
2
How many terms does the expression
 6 x 2  2 x  3 y  4 have?
How can we determine the number of terms? Separate the terms with the + and – signs.
Constant: -4 (NOT 4!!!!)
In the expression  6 x 2  2 x  3 y  4 what
Coefficients: -6, -2 and 3 (NOT 6 and 2!!!)
are the constants and the coefficients?
2
1
Simplifying
1
What does the unit tile represent? (show unit
tile)
1
What does this tile represent? (show variable
tile)
1
What does this tile represent? (show variable
squared tile)
1
What is the difference between the shaded
and non shaded tiles? (or if using actual
tiles, “the different colors”)
1
Where do you find information about
algebra tiles?
1
Show and explain a “zero pair.”
1
1
1
2
2
2
2
1
1
1
3
1
1
1
One
X or variable
x2 or variable squared
Shaded means negative and un-shaded is
positive.
Or Red is negative and other colors are positive
The KEY
A zero pair is one negative and one positive
tile of the same type/size (2 units or 2 vaiables).
They cancel out because -1(x) and 1(x) make
zero and the tiles go: “POOF- BE GONE!”
Can we make a zero pair with a unit tile and No. We cannot cancel these because they are
a variable tile? Why or why not?
not like terms. 1 and -1x cannot be combined
What does “combine” mean?
To put two or more terms together. IT DOES
NOT ONLY MEAN ADD. Example: 3x – 5x is
SUBTRACTING
What are “like terms?”
Terms that have the same exact variable and
exponent. X and x2 are not like terms because
they have different exp. X and xy are not b/c
not same EXACT variable.
Create an example of an expression with two Various answers
like terms. Simplify this expression.
5x+2x, 4y-2y…..
Can we combine “x” and “xy”? why or why NO. the xy has a y next to it, but the x is all
not?
alone, so they are not exactly the same
Can we combine “x” and “x²”? why or why
No. They have different exponents
not?
Why does 3x + x = 4x?
Because the x is really 1x and 3+1 = 4
What is the result of 3x – 5x?
-2x. type 3-5. You cannot type variables in
How could you type this in the calculator?
the calculator. You type what you see. Do not
type 5-3 just because the 5 is bigger.
Should we type variables in the calculator
No. Never type variables in the calculator
when combining like terms?
when using the “run” screen. (we will type them
in later for graphing, but do not tell them this
now)
Does the answer to an algebra problem
No. the answer could be an expression: 2x-4.
HAVE to be a number?
Expressions (3x+2) is allowed because there is
Example: Is “3x+2” a valid answer? (to
nothing else that we can do. 3x and 2 cannot be
extend this: Are 3x and 2 like terms?
added anymore b/c they are not like terms.
Can we combine anything else? )
What operation are we doing when
Multiplying- parentheses mean multiply!
distributing?
How do we simplify (x-2)3?
Distribute (multiply) the 3 to the x and the -2.
Can we rewrite (X-2)3 another way? Will
Yes, we can change it to 3(x-2) if we want.
the result change?
The result will be the same.
1
Express in words what is being multiplied in
the problem 4(2x-6)?
1
Express in words what is being multiplied in
the problem -4(2x-6)?
3
Is (x-2)3 and (x-2) – 3 the same thing?
3
How could we write it if we want to show
that we are multiplying the quantity x-2 with
-3?
In the expression 6-2(3+x), WHAT is being
distributed?
2
1
2
3
What step comes first when simplifying?
What does perimeter mean?
Does the answer to a perimeter problem
have to be a number?
3
How would you write the perimeter of a
square with a side of 4x?
What happens to the parentheses after you
have simplified inside the parentheses?
1
1
2
2
What is the coefficient of a variable that is
by itself?
What do you do if there is no number
outside the parentheses, just a negative
(minus)?
What happens to each term inside
parentheses when multiplying by a negative
outside of parentheses?
4 is being multiplied with 2x the result is 8x.
And 4 is being multiplied with NEGATIVE
SIX and the result is -24. Therefore the answer
is 8x-24.
-4 is being multiplied with 2x the result is -8x.
And -4 is being multiplied with NEGATIVE
SIX and the result is POSITIVE 24. Therefore
the answer is 8x +24. (if the students write
8x 24, ask “what kind of a 24 is it?” [positive]
“How can we show that it is positive?” Explain
since these are 2 different terms they must be
separated with a + or – sign.)
NO. in the first one, the 3 is being multiplied
with the quantity (x-2), in the second one the 3
is being subtracted from the quantity (x-2).
-3(x-2) or (x-2)(-3)
NEGATIVE TWO. Not 2. we must distribute
first and not subtract 6-2 because multiplying
comes before subtracting.
DISTRIBUTING
Add all sides
No, if the problem has variables in it, there is a
good chance our answer has variables also. See
example below
4x+4x+4x+4x or 4(4x) = 16x
Remove them
One
Treat it as a negative one and change the signs
of everything inside or multiply everything
inside by -1
All signs inside parentheses change
TRANSLATING- equations and expresssions
2
What is the difference between “twice a
term” and “square the number”?
1
What are common words for the four basic
operations?
2
2
What are the “turn around words?”
Describe what a turn around word does to an
expression or equation.
What is special about the phrase “the sum
of” and “the difference of”? How do we
represent these phrases?
Ex:
The sum of a number and 4
The difference of a number and 4
The difference of 4 and a number
Write the product of 5 and x three different
ways. What is the most common way you
will see this represented?
What does the word “quotient” mean?
What does the word “product” mean?
What is the “proper” way to write “the
product of x and 2?”
Show two ways to write “half of a number”
2
1
1
1
1
1
1*
3
2
3
3
3
What does “is” mean?
What is the difference between “7 less than
x” and “7 minus x?”
When you get a discount, do you pay more
or less than the original amount?
If you buy a shirt and pay a tax rate of 15%,
what equation can you set up?
How do you model complementary angles?
Supplementary?
Vertical?
How can we remember complementary =
90?
Twice means “times 2” ex: twice 6: 2(6)
Square means the number times itself. Ex: 6
square: 62 = 6(6)
Various answers
Add (sum, together, plus, and, increased, more
than, Perimeter,
Subtract (difference, less, minus, decreased,
less than, diminished,
Multiply (product, times, per, of (when follows
a number), twice, Area, Volume
Divide (quotient, divide,
Equal (is, same, equivalent, how much, how far,
find, how, when, what, where)
Than, to, from.
This word reverses the order of the terms.
Switches the first and last term.
These phrases represent “quantities”
(x+4)
(x-4)
(4-x)
5(x)
5 x
5x (is the most common/”proper” way)
Divide
Multiply
2x (Number should be in front)
x
2
equals
THAN flips the order: x-7 and 7 minus x is
written in order how it is written: 7-x
Less. Discount takes money off
1
2
x,
X+ 0.15x where x is the original price.
Take 15% of the original (percents must be
written as decimals) by multiplying .15 with the
price. That is your tax. Then you have to pay
for the tax AND the price of the shirt.
Complementary angles add to equal 90
Supplementary angles add to equal 180
Vertical angles equal each other
Alphabetical order- “C” comes first and it is
the smallest angle (90) OR draw a line on the
“c” to make it look like a “9” and the “o” is a
3
How can we remember supplementary =
180?
3
What is a straight angle?
What is its measure?
3
Draw a pair of complementary angles.
Supplementary.
Vertical.
If the angle 2x and the angle 5x-15 are
complementary, what is the value of x?
What is the value of the larger angle?
Leading ?s:
What does complementary mean?
So what should we do with the 2 angles?
And what do complementary angles equal?
So what does 2x+5x-15 equal?
How can we find the value of x?
How do we solve?
If we know x = 15, how can we find the
value of each angle?
Which is larger?
A triangle has a total of how many degrees
inside?
A quadrilateral has a total of how many
degrees inside?
3
3
3
3
What is an equilateral triangle?
Isosceles?
Right?
Scalene?
“0.”
Alphabetical order- “S” comes second and it is
the larger angle (180) OR draw a line on the “s”
to make it look like a “8” for 1 8 0
A straight line
180 degrees
X=15
Larger angle = 60
Adds to 90
Add (write 2x+5x-15)
90
90 (write 2x+5x-15=90)
Solve.
CLT, add 15, divide
Plug in x
60
180
360
All sides are the same (and angles!)
Only two sides are the same
There is a right angle (90 degree angle)
No sides are equal
* do not teach “is” until we get to “equations”
Solving
2
When an equation contains parentheses,
what must be done before solving the
equation?
1
What happens to the parentheses after you
have simplified inside the parentheses?
1
What is the coefficient of a variable that is
by itself?
1
What do you do if there is no number
outside the parentheses, just a negative
(minus)?
1
What happens to each term inside
parentheses when multiplying by a negative
outside of parentheses?
1
List the steps in solving a (one, two, multistep) equation.
1
1
2
How do you enter a fraction into the
calculator when multiplying it to another
number? Ex: three-fourths times 8
How do you move numbers or variables to
the other side of the equal sign when solving
an equation?
We want to put the variable on the left and
the number on the right of the equal sign, but
is it wrong if the number is on the left and
the variable is on the right? Explain
(2x = 4 vs 4 = 2x )
3
What do we do if do if the variables cancel
in an equation?
3
What is the result of an equation that turns
out to be true or equal on both sides?
How do we represent it?
3
What happens if an equation turns out to be
false, not true, or not equal? How do we
represent it?
Solve inside the parentheses first if possible, or
distribute
Remove them
One
Treat it as a negative one and change the signs
of everything inside or multiply everything
inside by -1
All signs inside parentheses change
1. Distribute
2. Label c and v, border
3. CLT
4. Add or subtract until you have v = c
5. Multiply or divide to get 1x = #
6. Check
Use parentheses
(3,4)*8
By doing the opposite or inverse operation
No, it is still the same thing. We like to say
“variables on the left, constants on the right”
just to be consistent because things can be easier
if we do them the same every time. If you have
4 = 2x, you can simply flip the whole equation
using the symmetric property to make it 2x = 4
if you want.
We ask ourselves if the numbers on the right and
the left are equal. In other words, is the left over
equation True or false? If it is TRUE (4 = 4)
then our answer is “all real numbers” which
means that any number will “work”(is a
solution/ will make the equation true) when we
plug it back in. If the result is FALSE (4 = 3)
then our answer is “no solution” which means
that NO number in the whole world will “work.”
If it is TRUE (4 = 4) then our answer is “all real
numbers” which means that any number will
“work”(is a solution/ will make the equation
true) when we plug it back in.

If the result is FALSE (4 = 3) then our answer is
“no solution” which means that NO number in
the whole world will “work.” Ø
2
What is the difference between solving and
simplifying?
2
When solving for a variable, how do you get
rid of the coefficient in an equation?
Simplifying is ONLY distributing and
combining like terms. The result is an
expression. Simplify when there is no equal
sign.
Solving has multiple steps (distribute, label,
CLT, add/subtract, mult/divide, check). Your
answer is x= a number. Solve when you see an
equal sign
Use the inverse operation- divide by that
SAME number
If its negative, divide by negative, positive
divide by positive
Literals and Reference Chart
1
What do we mean by ‘Literal equations’?
1
Explain the process of solving a literal
equation.
2
Can we relate the process to evaluating a
literal equation to anything else we have
been doing?
1
1
What is another name for a Reference chart?
What does a reference chart give you?
1
What is the difference between B and b on
the reference chart?
2
Why are there no formulas for squares on
the reference chart?
2
2
3
What is the difference between area and
volume?
Describe what the area of a rectangle
represents.
Why do we label area with units squared: in2
cm2 m2
2
Describe what the volume represents.
3
Why do we label area with units cubed: in3
cm3 m3
Literal equations have more than one variable.
We don’t find a numerical answer. We are
basically re-arranging the equation
1. Identify the variable we want to solve for
(isolate)
2. Circle the given variable
3. Identify what needs to be moved to the
other side to get the circled variable alone
4. Identify HOW those things are “attached”
(multiplying, dividing, adding, subtracting?)
5. Use inverse operations to remove those
things from step 3. Start with the adding and
subtracting just like in a “normal” equation
Solving equations
Cheat sheet
The rules or directions to solve for a specific
thing (volume, area, surface area….)
B represents the AREA of the BASE and b is
just the base. B is used for 3-d shapes. b is used
for 2-d(flat) shapes
Squares are types of rectangles, so we use the
same formulas we would use for rectangles.
Explain that shapes have different categories,
like clothes or shoes or phones [pick your
analogy]. Within “shoes” we have different
types: sneakers, sandals, dress shoes… [let
them get involved in the different types]. Then
from there, we still have more types; with
sneakers, we have: basketball shoes/hi-tops,
running shoes…; dress shoes: heels, flats, open
toed, closed toed…. ; Then use this to explain
we have rectangles (just like sneakers) and
squares are a type of rectangle (just like running
shoes are a type of sneaker)
Area is used for 2-d /flat shapes and volume is
for 3-d shapes
Area is the amount of space inside the
rectangle.
Area is the number of squares that fit inside
that shape. Ex: on the floor, the area would be
the number of square (foot) tiles on the floor.
Volume is the amount of space inside of a 3-d
shape.
Volume is the number of cubes that fit inside
that shape.
1
1
2
3
3
What is the formula, or how do we find, the
perimeter of any shape?
Why isn’t there a formula for perimeter on
the reference chart?
Why are there 2 different circumference
formulas? What is the difference?
What is the diameter?
What is the radius?
Why does the one with the “r” have a 2 in it?
Ex: get some cube manipulatives for this and
put them in a container. Explain the volume
would be the number of centimeter/inch cubes
inside that shape.
ADD
Because we do not need a formula. Perimeter is
the same for any shape: just ADD!!!
One can be used for when you know the radius
and one is for when you know the diameter.
All the way across the circle
Half-way across the circle
Because 2 radii equal the diameter, so you
have to multiply it by 2 to make it the same
Are there any formulas will we NOT use this Regular polygon
year on the reference chart?
What is a prism?
A 3-d rectangle (or 3-d triangle- not very
common)
Inequalities
1
What does the word “inequality” mean?
1
How do inequalities differ from equations?
3
When do you think the word inequality
would be used in real life? Give an example.
1
What do the symbols <,>,≥,≤, mean?
2
What would “x = 4” look like on the number
line? What would “x >= 4” look like?
Explain the differences.
2
What is the difference between “x > 3” and
“3 > x”?
2
What values can be used for y if “y ≤ 3”?
If y ≥ 3”?
Do they have any values in common?
3
What algebraic statement would explain to
someone that you have at least $4 in your
pocket?
Leading ?:
Would you have less than $4?
More than $4?
Exactly/ equal to $4?
What is the difference between “at most”
and “at least”?
2
Not equal
Inequalities have more than one value that
satisfies it. They have greater than or less
than symbols.
When comparing different values. When more
than one number will work
Various answers
John has more apples than Sue or 5<6
You must be at least 16 to drive
You can be no more than 12 to eat off the kids
menu
Less than, greater than, greater than or equal to,
less than or equal to
A shaded dot at 4.
A shaded dot at 4 AND the numbers to the
right would be shaded.
x>3 means x must be bigger than 3 (ex 4, 5, 10)
3>x means 3 is bigger than x, therefore x is
smaller (ex 2, 0, -1)
3, 2, 2.5, -4….
3, 4, 7 ½ , 15….
3
x>=4
no
yes (>)
yes ( = )  so your symbol is >=
At most means that value is the MOST or
largest amount you could have, so you could not
have more; only LESS  less than;
At least means that value is the LEAST or
lowest you could have, so you could not have
smaller than that; only bigger  greater than
open circle and shaded arrow
1
How do you represent greater than or less
than on a number line?
1
How do you represent less than or equal to
or greater than or equal to on the number
line?
A closed circle and shaded arrow
3
How do you indicate on the graph that the
solutions are infinite?
Shade the entire number line
2
Why is there more than one solution to an
inequality?
1
What does the phrase “solution set” mean?
2
Why is zero not included in the solution set
of positive numbers but it is included in the
set of nonnegative numbers?
1
What is the difference between less than and
less than or equal to?
1
Describe the difference between included
and excluded.
How would we represent excluded on the
number line? Included?
1
2
2
2
1
2
If x ≠ 4, what does x equal?
How would you represent x ≠ 4 on the
number line?
How can 5 > x be written another way?
What is this called?
When dealing with negative numbers, how
can you tell which one is bigger or greater in
value?
How do you solve a multi step inequality?
2
When solving for a variable, how do you get
rid of the coefficient in an equation or
inequality?
2
If a negative coefficient is in an inequality,
what happens to the symbol when the
inverse operation is performed?
1
When graphing an inequality, does it matter
if it is written as 7 < x? How would this be
graphed?
And inequality is NOT EQUAL, which means it
doesn’t just equal one thing. If x>4, there are
many numbers that make this true
All of the numbers which are solutions or
“work” or make the inequality true
Zero is not positive or negative. It is not with
the positives because it is not positive, but it IS
with nonnegatives, because it is not negative
either
Less than or equal to includes the number
that is given; x<3 does not include 3 whereas
x<= DOES include 3
Included means that number IS a solution and
excluded means that number is NOT a solution
Excluded would have an open circle because
that value is not a solution, so we do NOT shade
it. Included would have a closed/shaded
circle because that value IS a solution.
Anything else! 4.1, 3.999999, -4, 7…..
Circle 4, and leave it unshaded. Shade
everything else.
X<5
Symmetric property
Graph, and the farther to the left, the smaller
the number, the farther to the right, the larger
the number
Same as a multi-step equation, but don’t
forget about flipping the symbol!
1. Distribute
2. Label c and v, border
3. CLT
4. Add or subtract until you have v = c
5. Multiply or divide to get 1x = # (don’t
forget flip if negative!)
6. Graph
7. Check
Use the inverse operation- divide by that
SAME number
If its negative, divide by negative, positive
divide by positive
The inequality symbol ‘flips’
YES! Never graph unless the variable is on the
left!!!
7<x would be flipped to x>7 and then open
circle on 7 and shade to the right.
(Explain the common mistake if they try to
graph straight from 7<x: Most would put open
1
What do the words “reasonable solution” or
“reasonable value” mean? Explain
1
How do you test to see if a solution is
reasonable?
Explain what the “arrow” tells us and/or the
meaning of the number line under the arrow.
Describe, in a real life situation, the
following:
At least
At most
No less than No more than
Greater than Less than
Greater than or =
less than or =
1
3
3
3
1
If you need “at least 90” on a test, do you
need any grade up to a 90 or a grade above a
90?
If you have no more than 12 dollars, do you
have more or less than $12?
What do the open and closed circle
represent?
circle on 7 and then see “less than” and shade to
the left. But then if we use one of the shaded
values (5) and plug it back in to 7<x you would
have 7<5, which is not true!!! So this is wrong!
These are the values or solutions or numbers
that are possible answers to the inequality.
They are reasonable because they make sense.
Plug it in for the variable (x) and see if it comes
out true
The arrow shows that the numbers and the
shaded part go on forever.
Various answers
At least 16 to drive
At most 4 feet to ride the kiddie ride
You should get no less than a 70%
You can get no more than 100% on report cards
I have to have greater than or equal to $50 to go
buy shoes
I want to have less than or equal to 3 tardies in
class
You want above, or equal to a 90%.
(who wants below a specific grade…?)
Less than. ‘No more’ means NOT more, which
means you could only have less.
Open- that number is NOT a solution;
Closed- that number IS a solution
Functions
1
Describe a coordinate plane.
1
1
1
1
1
1
3
What other words can be used to describe xaxis?
The Y-axis?
What is the intersection of the x and y axis
called?
What does this point tell us?
What is the ordered pair for this point?
What direction do we go when naming the
quadrants?
Where do we start when counting the
quadrants?
In what order do we write an ordered pair?
How do we plot a point on the graph?
Many answers. See what the kids know then
move on to specific questions
Domain, horizontal & independent
Range, vertical & dependent
The origin
Where you begin
(0,0)
Counterclockwise. Like a letter “c”
Top right. (Quadrant 1)
(x,y) – alphabetical order
When plotting an ordered pair, begin at the
origin, and go to the right or left on the x axis
first then up or down on the y axis
x-intercept
2
What is the point where a graph intersects
(crosses) the x-axis?
The y-axis?
The x-axis and the y-axis divide the
coordinate plane into 4 _______?
In quadrant 1, what are the signs of the x &
y coordinates?
In quadrant 2?
In quadrant 3?
In quadrant 4?
What does an ordered pair show between x
and y values?
What are 5 ways we can represent a
function?
How do we say f(x)?
2
F(x) is called?
Function notation
2
2
What is another way of writing f(x)?
What is the difference between a function
and a relation?
Y
A relation can only be called a function if:
every x-value pairs with exactly one y-value)
(no hoes)
(each ‘person’ can go to only 1 place)
2
In a table, how do we check if it represents a
function?
x’s do not repeat
2
In a set, how do we check if it represents a
function?
In a graph, how do we check if it represents
a function?
x’s do not repeat
1
1
2
2
2
y-intercept
Quadrants
Quad 1- x&y – both Positive
Quad 2- x – negative; y – Positive
Quad 3- x &y – both Negative
Quad 4- x – Positive; y – Negative
A relation
Table, Set, Graph, Mapping, and Equation
“function of x”
Vertical line test (student should be able to
describe what this means)- each line can only
2
In a mapping, how do we check if it
represents a function?
touch the graph once
X’s cannot go to 2 different y’s