© K12 Inc. Assignment: Shopping List Using Multi-Step Equations Write a multi-step equation for each of the three scenarios below to find the answer to the question. Show all the steps needed. Then write two more shopping scenarios (in the Solve Your Own Problem section) where multi-step equations can be written and solved. Explain all your work. Write a shopping list to show what you will purchase, including the amounts and costs for each item and the total cost. Scenario 1: The technical crew of the play needs shirts. Each shirt color matches the job the crew will be working on. Different color shirts have different designs and therefore cost different amounts. You will need: 6 red shirts, at $10.90 each for the lighting crew 4 yellow shirts at $ $10.50 each for the props crew 5 purple shirts at $12.50 each for the make-up crew You have $200.00 to spend on all the shirts. How many green shirts can you purchase for the ushers if those shirts cost $11.50 each? If you spend less than your budget, how much money do you have left over? © K12 Inc. Scenario 2: Refreshments will be sold during the play’s intermission. The servers estimate that they need: 74 bottles of water at $0.75 each 150 bags of chips at $0.40 each. You have $150.00 total to spend on refreshments. Find out how much you will spend for the water and chips. In addition, how many boxes of gummy bears, costing $0.50 each, can you buy with the remaining budget? If you spend less than your budget, how much money do you have left over? © K12 Inc. Scenario 3: The actors need make-up for the play. You estimate that they will need: 10 bottles of foundation at $5.25 each 7 containers of eye shadow at $3.25 each 5 tubes of lipstick at $4.75 each. The total budget for make-up is $124.00. Find out how much you will spend for the foundation, eye shadow, and lipstick. In addition, how many containers of face powder can you buy at $2.50 each? If you spend less than your budget, how much money do you have left over? © K12 Inc. Solve Your Own Problem: Write two more shopping scenarios where multi-step equations can be written and solved. Explain all your work. Write a shopping list to show what you will purchase, including the amounts and costs for each item and the total cost. Text1: Text2: Text3: Text4: ! "#$ %&'( Assignment: Real-World Multi-Step Equations Translate each real-world situations into a multi-step equation. Solve the equation, showing all steps to solve the equation. Then write an explanation of the answer to the problem. 1.

1. © K12 Inc.
Assignment: Shopping List Using Multi-Step Equations
Write a multi-step equation for each of the three scenarios
below to find the answer to the question. Show
all the steps needed.
Then write two more shopping scenarios (in the Solve Your
Own Problem section) where multi-step
equations can be written and solved. Explain all your work.
Write a shopping list to show what you will
purchase, including the amounts and costs for each item and the
total cost.
Scenario 1: The technical crew of the play needs shirts. Each
shirt color matches the job the crew will be
working on. Different color shirts have different designs and
therefore cost different amounts.
You will need:
6 red shirts, at $10.90 each for the lighting crew
4 yellow shirts at $ $10.50 each for the props crew
5 purple shirts at $12.50 each for the make-up crew
You have $200.00 to spend on all the shirts. How many green
shirts can you purchase for the ushers if

2. those shirts cost $11.50 each? If you spend less than your
budget, how much money do you have left
over?

3. © K12 Inc.
Scenario 2: Refreshments will be sold during the play’s
intermission.
The servers estimate that they need:
74 bottles of water at $0.75 each
150 bags of chips at $0.40 each.
You have $150.00 total to spend on refreshments. Find out how
much you will spend for the water and
chips. In addition, how many boxes of gummy bears, costing
$0.50 each, can you buy with the remaining
budget? If you spend less than your budget, how much money
do you have left over?

4. © K12 Inc.

5. Scenario 3: The actors need make-up for the play. You estimate
that they will need:
10 bottles of foundation at $5.25 each
7 containers of eye shadow at $3.25 each
5 tubes of lipstick at $4.75 each.
The total budget for make-up is $124.00. Find out how much
you will spend for the foundation, eye
shadow, and lipstick. In addition, how many containers of face
powder can you buy at $2.50 each? If you
spend less than your budget, how much money do you have left
over?

6. © K12 Inc.
Solve Your Own Problem:
Write two more shopping scenarios where multi-step equations
can be written and solved. Explain all
your work. Write a shopping list to show what you will

7. purchase, including the amounts and costs for each
item and the total cost.
Text1: Text2: Text3: Text4:
! "#$ %&'(
Assignment: Real-World Multi-Step Equations
Translate each real-world situations into a multi-step equation.
Solve the equation, showing all
steps to solve the equation. Then write an explanation of the
answer to the problem.
1. You and your friend are shopping for painting supplies. Your
friend wants five bottles of paint
and one set of paint brushes. You want seven bottles of paint
and two sets of paint brushes. Each
bottle of paint costs $3.69. If you and your friend’s total cost is
$51.69, what is the cost of one set
of paint brushes?

8. 2. In physics the mass energy equivalence is that the mass of a
body is measured by its energy
content. This may be written algebraically as !="#2, where ! is
energy, " is mass, and # is the
speed of light in a vacuum. Transform the equation so that it
will be read as a solution for mass,
". Show all the steps.

9. ! "#$ %&'(
3. The formula to find the surface area of a sphere is to take the
radius of the sphere and square
it and multiply that amount by pi and then multiply that by 4.
This is written algebraically as
!=4 "2, where ! is the surface area, " is the radius, and the value
of #is 3.14. Rewrite the
equation to solve for the radius of the sphere if you know the
sphere’s surface area. Then
estimate the radius of a sphere given a surface area of 500
meters2.
Write two real-world problems that can be solved using multi-

10. step equations that use fractions or
decimals. Solve each equation, showing and explaining all your
steps. Then write an explanation
of the answer to the problem.
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"
Assignment: Converting Between Forms
Convert each equation of a line to the requested form.
Part I: Practice Converting Equations to Different Forms
1. Write the equation
$
*
%
! " in standard form.
2. Write the equation + % ," ! in slope-intercept form.
3. Write the equation * -. $/! " in standard form.

11. 4. Write the equation 0 %. */! " in slope-intercept form.
5. The equation 1 *. %/! " is written in point-slope form. Write
this equation in the
following ways:
a. slope-intercept form
b. standard form
Part II: Create Your Own Conversion Problem
equations of lines to different forms. First, write three (3)
equations of lines in the following
forms: a) point-slope form, b) slope-intercept form, and c)
standard form. Next, choose
another form to write each equation in, and then show all the
steps required to convert each
equation to the other form.
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Assignment: Multiply and Divide Functions
For each given pair of functions, multiply or divide as
instructed. Be sure to show all the steps

12. required to write your answer in simplest form. Review the
rubric to see how your work will be
graded.
1.
)
* + $
* + )
! " "
# " "
* +
,
* +
! "
# "
2.
* + -
* + .
! " "
# " "

13. * + * + ,! " # "
3.
* + $ #
* + ) $
! " "
# " "
*)+
,
*$+
!
#
4.
$* + .
* + ) #
! " "
# " "

14. *-+ * #+ ,! #
5.
* + -
* + ) /
! " "
# " "
*.+ *#+
,
*/+ * $+
! #
! #
! "#$ %&'(
6. Write and solve your own multiplication and division of
functions problems similar to
those above. First, create two unique functions, ) *! " and .
Then multiply and divide

15. the functions to find
) *# "
) * ) *! " # " and
) *
) *
! "
# "
. Next, multiply and divide the functions again,
this time for specific values of x. (Choose integer values for x.)
Be sure to show all the
work necessary to write your answers in simplest form.
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Assignment: Find the Slope of a Line
Use the slope formula to calculate the slope of the line in each
situation described below. Show
all the steps necessary to write your answer in simplest form.
1. Alex and his friends practice skateboarding at a local
community skate park. The line shown
in the graph below represents one of the skateboard ramps.

16. a. Identify two points on the line and write the coordinates of
the points as ordered
pairs (x, y).
b. Use the slope formula to find the slope of the line that
represents the road.
2. A child rolls his toy cars down a dirt hill in his backyard.
Suppose the line shown in the graph
below represents the dirt hill.
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a. Identify two points on the line and write the coordinates of
the points as ordered
pairs (x, y).
b. Use the slope formula to find the slope of the line that
represents the hill.

17. 3. The federal government has set strict specifications for any
new construction where a
wheelchair ramp is to be built.
constructing a wheelchair ramp to the correct specifications.
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a. Identify two points on the line and write the coordinates of
the points as ordered
pairs (x, y).
b. Use the slope formula to find the slope of the line that
represents the ramp.
4. Describe another situation that involves a real-world hill,
road, or ramp. Draw the graph of a
line to represent the situation. Identify two points on the line
and use these points to calculate
the slope of the line with the slope formula. Be sure to show all
the steps necessary to

18. calculate the slope and write your answer in simplest form.
! "#$ %&'(
Assignment: Story Using Algebraic Equations
Create a story that is about one page in length using at least five
different algebraic expressions
and/or equations.
These are some example story starters that you can adapt from
or expand upon. Be creative and
come up with your own characters and scenarios and create
expressions and equations as well.
Story Starter 1: A character is offered five different jobs. They
all include an hourly wage,
as well as a set weekly base pay. One example is a job that pays
$8.50 an hour, plus an
additional $25 bonus for the week. (Weekly base pay is what
you automatically get paid
for working the entire week. A bonus is money you earn in
addition to the weekly base
pay.)
Story Starter 2: A character is searching for the best cell phone
plan to buy. One plan
costs $25 a month, plus $0.89 per minute used.
Story Starter 3: A character is trying to decide which cab to
choose from the five available.

19. All the cabs have different rates per mile. They also charge
different flat rates in addition
to the rates per mile. One cab is offering a rate of $0.75 per
mile, plus a flat fee of $25.
Example Story Using Five Equations
Luke is shopping for a movie to watch with his family. He goes
to a video store and reads the sign
in the store that describes their rental policy.
He thinks to himself as he reads. “To rent a DVD, I must pay
the flat rate of $4.99 for three days,
plus $1.99 for every day it's late.” To make a mathematical
equation, the cost to rent one DVD, y,
is $4.99, plus $1.99 for every day it is late, x. He comes up with
this equation: y= $4.99 + $1.99x.
As Luke drives home from the store, he wonders if he will have
enough gas to get there. He
thinks, “I know my car gets 30 miles per gallon.” He then thinks
about an equation that he can use
to model the situation where d is the total number of miles he
can drive, and g is the number of
gallons of gas that he has. He comes up with d = 30g.
Luke decides to get a drink at the neighborhood store. The store
is advertising a special on all
their giant smoothies, which are Luke’s favorite. The sign for
the giant smoothies reads: “Buy a
giant cup for $0.99 and fill it up for $0.50 an ounce. Luke is
really thirsty and wants to figure out if
he has enough money to buy a big drink. If he lets the variable s
be the cost of the smoothie and
n be the number of ounces he buys, then the total cost of the
drink will be s = 0.99n.

20. Before he leaves the store, Luke remembers that he went to a
basketball game a few nights ago.
It was a great game, down to the last second! He logs on to his
computer to read an article about
the game. The article begins: “The Spartans won the game by
scoring 30 points every hour.”
What equation would represent this situation? Luke thinks of p
as the total points earned in a
game and h as the number of hours played. He decides on the
equation p = 30h. As he thinks of
the problem, he realizes that this equation fits the information
in the story but might not be the
way to figure out the number of points scored in every
basketball game.
While he's browsing the site, Luke then considers reading some
items in the business section. He
has been reading lately about how the stock market works, and
he is interested in stock trends
over the past year. He reads that the stock for a medical
company has earned money this year
with an average rate of return of about 10 percent. He thinks of
an equation for this. The change
of the cost of one share of stock over the past year is 0.10. If he
uses the variable c for new cost
! "#$ %&'(
of the stock, and b for the cost of one share of the stock, he
would arrive at the equation c =
0.10b to find the new cost of the stock.

21. !"#$%"&'()"
Assignment: Subtract Polynomials
"
Part I: Practice Subtracting Polynomials
Subtract the polynomials, showing all the steps necessary to
write the answer in simplest form.
1. *+ ,- *. %-! !
2. % %*. /- *% $-! !
3. % %*0 . ,- * 1 -! ! ! !
4. % %*$2 0- *$% , .-! ! !

22. 5. . % .*3 , %- *% 0 3-! ! ! !
6. . % %* . % - * +-! ! ! !
7. 0 , . % 0 , .* . - *+ , . 0 -! ! ! ! ! ! ! !
8. 0 . % 0 .*$0 , . $$- *% . + /-! ! ! ! ! !
!"#$%"&'()"
Part II: Create Your Own Subtraction Problems
There are special names for polynomials depending on the
highest power and the number of
terms. For example, % % *! ! is considered a second degree
trinomial because the largest
power is 2, and there are three terms in the polynomial. Another
example is *+! , which is a third
degree monomial because the largest power is 3, and there is
one term in the polynomial. Review
some common types of polynomials in the table below.

23. Polynomial Type Definition Examples
Monomial A polynomial with one term %
,
*
-
!
!
!
Binomial A polynomial with two terms
%
*
, .
,
* +
!
!
! !
Trinomial A polynomial with three terms %

24. * %
. * %
% + $
, *
+ .
! !
! ! !
! ! !
Now create your own problems that involve subtracting
different types of polynomials. Write each
problem according to the directions. Then subtract the
polynomials, showing all work necessary
to write the answer in simplest form.
9. Subtract a first degree binomial from a second degree
trinomial.
10. Subtract a second degree trinomial from a second degree
trinomial.

25. 11. Subtract a second degree binomial from a third degree
trinomial.