Unit 1
Using the integers −9 to 9 at most one time each, place an integer in each box to create an arithmetic sequence and a function that represents it.
-9,0,9...
=9x+0
Two of Nalia’s friends are going with her to the fair. Each game, x, costs $2 and each ride, y, costs $3. Jon wants to spend at most $30. Michelle also brought $30 with her, but she does not want to spend all her money.
Which combination can Jon purchase that Michelle cannot? Why is this combination not possible for Michelle?
__ games and __ rides because she doesn't wanna be broke
Two of Nalia’s friends are going with her to the fair. Each game, x, costs $2 and each ride, y, costs $3. Jon wants to spend at most $30. Michelle also brought $30 with her, but she does not want to spend all her money.
Which combination can Jon purchase that Michelle cannot? Why is this combination not possible for Michelle?
_9_ games and _4_ rides because she doesn't wanna be broke
121 Units^2
44
Raj wrote the equation f(n) = n 2 + 2n + 1 to represent the area of the garden. Claire wrote the function f(n) = (n + 1) 2 . Are either Raj or Claire correct?
Both are!!
Using the Claims, Evidence, and Reasoning from Part II, create your own CER Model for the following
question:
How do the mathematical models in Parts I and III of the task com
2^x and 1/2^x they both have x power
2^x is increasing
1/2^2 is decreasing
A baby girl was born and her name is Denise. At her 3-month doctor visit, she was
measured at 23 inches long and weighed 13.5 pounds. At her 8-month doctor visit, she
was measured at 27.5 inches long and weighed 19 pounds. Use this information to
explore the following questions.
Let the function f(x) represent Denise’s length at x number of months. Use function
notation to represent the length of Denise at 3 months and at 8 months. How would
you represent these function values as ordered pairs?
a. 3-months:
Ordered Pair:
b. 8-months:
Ordered Pair:
A baby girl was born and her name is Denise. At her 3-month doctor visit, she was
measured at 23 inches long and weighed 13.5 pounds. At her 8-month doctor visit, she
was measured at 27.5 inches long and weighed 19 pounds. Use this information to
explore the following questions.
Let the function f(x) represent Denise’s length at x number of months. Use function
notation to represent the length of Denise at 3 months and at 8 months. How would
you represent these function values as ordered pairs?
a. 3-months:f(3) =23
Ordered Pair: 3,23
b. 8-months: f(8)=27.5
Ordered Pair: 8,27.5
A homeowner is making plans to landscape her yard. She plans to hire professionals to install
grass sod in some parts of the yard and flower beds in other parts.
Grass sod installation costs $2 per square foot and flower bed installation costs $12 per square
foot. Her budget for the project is $3,000.
1. Write an equation the represents the square feet of grass sod, x, and the square feet of
flower beds, y, that she could afford if she used her entire budget.
2x+12y=3,000
6.70*4=3|5
What is the difference between the rate of change for a linear function and the rate of change for a quadratic function?
The rate of change for a linear function is constant, while for a quadratic function, it changes. Linear function has a constant slope, while quadratic function's slope changes
A half-life is the amount of time it takes for half of a substance to decay or disappear. If
the half-life of Carbon is 5,730 years, how many half-lives of Carbon have occurred in a
fossil that is 51,570 years old?
9
Use the function you created to make predictions for Denise’s height at different
stages of her growth. Remember that the function uses months as the input.
a. Length at 12 months = ________ inches
b. Length at 18 months = ________ inches
c. Length at 3 years (convert to months first) = ______ inches
d. Length at 5 years (convert to months first) = ______ inches
Use the function you created to make predictions for Denise’s height at different
stages of her growth. Remember that the function uses months as the input.
a. Length at 12 months = 31.1 inches
b. Length at 18 months = 36.5 inches
c. Length at 3 years (convert to months first) = 52.27 inches
d. Length at 5 years (convert to months first) = 74.3 inches
A vendor at a Saturday Market makes $9 profit on each necklace she sells and $5 profit on
each bracelet.
1. Find a combination of necklaces and bracelets that she could sell and make:
a. Exactly $100 profit
9x+5y=100
10,2
Is it rational?
5
yes it is because it is a whole number or fraction
f(x) = x 2 + 6x – 7
f(x) = (x + 3) 2–16
f(x) = (x – 1)(x + 7) (0,-7)is the y int
(-3,-16) is the vertex (1,0)(-7,0) are the x int
1.80mg
y=1/2x
A customer opens a checking account and a savings account at a bank. They will deposit a
maximum amount of $600, some in the checking account and some in the savings account.
(They might not deposit all of it and keep some of the money as cash.)
a. Write an inequality to describe the constraints. Specify what each variable represents.
x+y<=600
is it rational?
5/7
yes because it is a fraction
Remember with the Area Model task we created rectangles with our Algebra Tiles. Now we
want to create squares. If we have a square, what do we know about the factors of the square
that we created?
Ax^2 +Bx +c(b/2
Linda’s lifelong dream is to open her own business. After working, sacrificing, and saving, she
finally has enough money to open an ice cream business. The grand opening of her business is
scheduled for the Friday of Memorial Day weekend. She would like to have a soft opening for her
business on the Tuesday before. The soft opening should give her a good idea of any supply or
personnel issues and give her time to correct them before the big official opening.
A soft opening means that the opening of the business is not officially announced; news of its
opening is just spread by word of mouth (see, not all rumors are bad!). Linda needs a good idea
of when she should begin the rumor for it to spread reasonably well before her soft opening. She
has been told that about 10% of the people who know about an event will attend it. Based on this
assumption, if she wants to have about 50 people visit her store on the Tuesday of the soft
opening, she will need 500 people to know about it.
1. Linda plans to tell one person each day and will ask that person to tell one other person each
day through the day of the opening, and so on. Assume that each new person who hears about
the soft opening is also asked to tell one other person each day through the day of the opening
and that each one starts the process of telling their friends on the day after he or she first hears.
When do you think Linda should begin telling others about the soft opening in order to
have at least 500 people know about it by the day it occurs?
the Sunday 2 weeks before
Graph 4: y=1/2x -5
Intercepts (ordered pairs)
y-intercept:(,)
x-intercept: (,)
Slope
Positive (> )
Negative ( < )
Graph 4: y=1/2x -5
Intercepts (ordered pairs)
y-intercept:(0,-5)
x-intercept: (10,0)
Slope
-1=11
Positive (y>0 )
Negative ( y<0 )
Two kinds of tickets to an outdoor concert were sold: lawn tickets and seat tickets. Fewer
than 400 tickets in total were sold.
a. Write an inequality to describe the constraints. Specify what each variable represents.
x+y<400 x=lawn y= seat
it is rational?
0.575
yes because it can be written as a fraction
What number can you fill in the following blank so that x 2+ 10x + ____ will have two equal
factors? What are the factors? Draw the area and label the sides. What shape do you have
10/2= 5 5^2 (x+5)(x+5)
Graph the hypothetical situation described. How did the graph change as compared to part 1
of the task?
(0,1)----(0.1)
(1,2------(1,3)
(2.4)----(2,9)
(3,8)----(3,21)