Alge
bra
1 St a
nda
rds:
Algebra
1 CCSSPrep
for
A.APR.7
Students will learn how to simplify rational expressions using
the factoring of polynomials.
Essential Question: How do we use the factoring of polynomials to
simplify
Esse
nt iarational
l Que stexpressions?
ion: _________________________________________________
Se c t ion:
HW
___________________________________________________________
___________________________________________________________
Que st ions, V oc a bula ry,
Side not e s:
Note: a rational
expression is in simplest
form when the numerator
and denominator have no
common factors other
than 1 or -1
Steps to simplify rational
expressions:
1) Factor the numerator
2) Factor the denominator
3) Cross out the equivalent forms
of 1
DOK 1
A rational expression is a quotient of two polynomials
Se c t ion:
Que st ions, V oc a bula ry,
Side N ot e s:
DOK 1
DOK 1
DOK 1
Algebra
1 CCSSAlge
bra
1 StA.APR.7
a nda rds:
Students will learn how to multiply and divide rational
expressions using the factoring of polynomials.
Essential Question: How do you use the factoring of polynomials to
multiply
divide
rational
expressions?
Esse
nt iaand
l Que
st ion:
_________________________________________________
Se c t ion:
HW
___________________________________________________________
___________________________________________________________
Que st ions, V oc a bula ry,
Multiplying Rational expressions
Side not e s:
Note: We multiply and divide
rational expressions the same
way we multiply and divide
fractions. Except now we have
fractions that have polynomials as
numerators and denominators.
DOK 1
DOK 1
We will follow the
same process of
multiplying fractions
of multiply rational
expressions
Examples: Multiply. Leave
answers in factored form.
Se c t ion:
Que st ions, V oc a bula ry,
Side N ot e s:
Dividing Rational Expressions.
DOK 1
Examples:
Note: dividing rational
expressions is very similar to
multiplying them. Just
remember to take the reciprocal
of the fraction after each
symbol.
DOK 1
Alge
bra
1 StA.APR.7
a nda rds:
Algebra
1 CCSSStudents will learn how to add and subtract rational
expressions with like denominators using the factoring of
polynomials.
Essential Question: How do you add and subtracted rational
expressions
with
like _________________________________________________
denominators?
Esse
nt ia l Que
st ion:
Se c t ion:
HW
___________________________________________________________
___________________________________________________________
Que st ions, V oc a bula ry,
Side not e s:
DOK 1
DOK 1
We add or subtract rational
expressions with like denominators
in the same way we add fractions.
Se c t ion:
Que st ions, V oc a bula ry,
Side N ot e s:
DOK 1
DOK 1
DOK 1
Se c t ion:
Que st ions, V oc a bula ry,
Side N ot e s:
DOK 1
DOK 1
Alge
bra
1 StA.APR.7
a nda rds:
Algebra
1 CCSSStudents will learn how to add and subtract rational
expressions with unlike denominators using the factoring of
polynomials.
Essential Question: How do you add and subtracted rational
expressions
with
unlike
denominators?
Esse
nt ia l Que
st ion:
_________________________________________________
Se c t ion:
HW
___________________________________________________________
___________________________________________________________
Que st ions, V oc a bula ry,
Recall: To add and subtract fractions we need to have common denominators.
To add and subtract rational expressions we also need common denominators!
Side not e s:
Note: We will use this same
method to add or subtract
rational expressions with
unlike denominators as we do
to add fractions with unlike
denominators
DOK 1
DOK 1
Se c t ions:
Que st ions, V oc a bula ry,
Side N ot e s:
DOK 1
DOK 1
Se c t ion:
Que st ions, V oc a bula ry,
Side N ot e s:
DOK 1
DOK 1
DOK 1
Alge bra
1 StA.CED.1,
a nda rds:
Algebra
1 CCSSA.REI.2
Students will learn how to solve rational equations using the
factoring of polynomials.
Essential Question: How do you solve rational equations and what are
extraneous
solutions?
Esse
nt ia l Que
st ion: _________________________________________________
Se c t ion:
HW
___________________________________________________________
___________________________________________________________
Que st ions, V oc a bula ry,
Steps to solving rational equations:
Side not e s:
1) Find the LCD.
2) Multiply both sides of the equations by LCD to clear all fractions.
3) Solve the equation by isolating the variable.
4) Make sure to check for extraneous solutions
Note: The process of cross multiplying or multiplying both sides of a rational
equation by the LCD may create an ______________________________.
These are solutions that solve the new equations but not the original equation.
Examples: Solve. Make sure to check for extraneous solutions.
DOK 1
Se c t ions:
Que st ions, V oc a bula ry,
Side N ot e s:
DOK 1
DOK 1
DOK 1
Se c t ion:
Que st ions, V oc a bula ry,
Side N ot e s:
DOK 1
DOK 1
Algebra
1 CCSSA.REI.2
Alge
bra
1 StA.CED.1,
a nda rds:
Students will learn how to apply rational equations to solve
work rate word problems.
Essential Question: how do we solve work rate problems using rational
equations?
Esse
nt ia l Que st ion: _________________________________________________
Se c t ion:
HW
___________________________________________________________
Examples:
___________________________________________________________
Que st ions, V oc a bula ry,
Side not e s:
1) A contractor finds it takes crew A 6 hours to construct a wall of a certain
size. It takes crew B 8 hours to construct a wall of the same size. How long
will it take if both crews are working together?
Steps to solving word
problems:
1) Read the problem
2) Define the variable(s)
3) Set-up the equation(s)
4) Solve the equations
5) Answer the problem
DOK 1
2) Paco can eat a box of popcorn in two minutes. Pancho can eat the
same size box of popcorn in 3 minutes. If Paco and Pancho share a box
of popcorn, how long will it take them to eat a box of popcorn?
Se c t ion:
Que st ions, V oc a bula ry,
Side N ot e s:
DOK 1
DOK 1
3) A cyclist travels 20 mph faster than a person who is walking. The
cyclist traveled 25 miles in the same time it took the person to walk five
miles. Find their speeds.
4) The reciprocal of two more than a number is 3 times the
reciprocal of the number. Find the number.
Algebra
1 CCSSAlge bra
1 StF-BF.4
a nda rds:
Students will learn how to find the inverse of a function and
compare the graphs of functions and their inverse.
Se c t ion:
HW
Essential Question: What is the inverse of a function and how do the
graphs
a function
their inverse compare?
Esse
nt iaofl Que
st ion:and
_________________________________________________
___________________________________________________________
Def- An ___________________________ is a function that switches
___________________________________________________________
the input (X) and output (Y) values of the original function. The
Que st ions, V oc a bula ry,
functions are ______________________ of each other.
Side not e s:
Note: We use ____
to represent the
inverse of a function
Example: Graph the original function Find the inverse of
the function and graph the inverse function.
DOK 1
Se c t ion:
Que st ions, V oc a bula ry,
Side N ot e s:
DOK 1
DOK 1
Example: Graph the original function Find the inverse of
the function and graph the inverse function.