Ms. J. Blackwell, nbct
Unit 1 – Modeling with Linear Functions
Day / Date / Topic / Homework
1 / 8/25Mon / Patterns &
Linear Representation / HW 1 & Multiple Intelligence pages = Thurs
2 / 8/26Tues / Graphing Linear Inequalities, Max, & Min / HW 2
3 / 8/27Wed / Lego Activity / HW 3 & Study Island Lab # 1 due 9/8
4 / 8/28Thurs / Reverse Linear Programming Problems / HW 4
5 / 8/29Fri / Jeopardy Review / HW 5 On line due Tues
6 / 9/1Mon / Holiday
7 / 9/2Tues / Quiz & Project Plan Day / HW 6 – Read & Practice On line Tutorials
8 / 9/3Wed / Excel Practice & Project Plan Day / HW 7 due Mon
9 / 9/4Thurs / Project Plan Day / Prj & HW 7
10 / 9/5 Fri / Project Plan Day
Early Release Day
11 / 9/8Mon / Project Presentation Day / Study & Study Island Lab # 1
12 / 9/9Tues / Unit Test 1 / Give 3 Teachers a Compliment!
Unit Reflection: (Specific items to review)
Unit Vocabulary List (Highlight the words as they appear in the Unit)
Patterns / Trend Line / Linear / Equations & InequalitiesX & Y Intercepts / Regression / Simplify / Describe
Maximum / Slope / Standard Form / Slope – Intercept
Evaluate / Applications / Minimum / Correlation
Scatter Plot / Constraints / Corner Points / Feasible Region
Vertices / Objective Function / Profit/Cost / Sensitivity Analysis
- Unit 1 – FoM3 Essential Standards The Learner will be able to:
Unit 1 – Modeling with Linear Functions / Creating Equations A - CED
Create equations that describe numbers or relationships.
A-CED.1 Create equations and inequalities in one variable and use them to solve problems.
A-CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.
Reasoning with Equations & Inequalities A - REI
Represent and solve equations and inequalities graphically.
A-REI.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
Modeling with Geometry G-MG
Apply geometric concepts in modeling situations
G-MG.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).
Class Work – Day 1 – Patterns & Linear Representations
Linear Representations Notes
What would Figure 4 and Figure 5 look like? What would Figure 0 look like?
How many squares were in Figure 0? ______This is called the initial value.
How many squares are added to each figure to find the next? ______This is called the rate of change.
x (figure number) / y (number of squares)0
1
2
3
4
5
10
50
100
x
Circle the initial
value on the
graph.
What’s
another word
for this on
graphs?
Where can you
see the rate of
change on the
graph?
What’s another
word for this on
graphs?
What are the different linear representations?
- Story/Picture
- Table
- Equation
- Graph
What can be found in all linear representations?
- Initial value
- Rate of change
Slope-intercept form of an equation:
slope y-intercept
Solve the following equations and inequalities. Show your work on every step.
13. 14.
15. 16.
Verbal:
Algebraic:
______
Table
______(x) / Function: ______/ ______(y)Graph
HW # 1 # 1 – 12
Linear Representations
Use the picture below to find the following. In each representation clearly label the initial value and rate of change.
1. Fill in the table.2. Draw the graph.
x (figure number) / y (number of squares)0
1
2
3
4
5
10
50
100
x
3. What is the slope-intercept form of the equation?
4. Would you be able to draw Figure 11? Why or why not?
5. Would it make sense to have negative x values on your table? Why or why not?
Find the initial value and the rate of change for each of the following.
6. Sarah has 11 pairs of earrings. Once she gets to high school she decides that earrings greatly improve her appearance and starts to collect them. She buys 3 pairs of earrings each month.
7. 8.
9. Graph for # 9
x / y-3 / 5
-2 / 8
-1 / 11
0 / 14
1 / 17
2 / 20
3 / 23
Write a story (like problem 6) or make a figure pattern for the following.
10.
Solve each of the following equations and inequalities. Show each step.
11. 12.
Class Work – Linear
Make a reasonable guess at a solution for the following problems. Then, do the math to find the actual solution.
Louise has $336 in five-dollar bills and singles. Let x be five-dollar bills and y be singles. She has 56 singles. How many five-dollar bills did she have?
- How do I write a linear inequality from a story problem?
Define your variables
Look for keywords to tell you what symbol to use
Write an inequality
Use common sense to see if your symbol makes sense
Seth is ordering balloons for his friend’s birthday party. He has up to $15 to spend. Decorative balloons cost $3 each and solid color balloons cost $0.50 each. Write an inequality to represent how many balloons Seth can buy.
HW # 2 (# 6, 8, 10, 11)
5-10:Graph each system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum and minimum values of the given function for this region.
5.2x + 3y 66.x 17.x + y 4
3x – 2y –4 y 03x – 2y 12
5x + y 152x + y 6x – 4y –16
f(x, y) = x + 3yf(x, y) = 3x + yf(x, y) = x – 2y
8.y 2x + 19.yx + 610.x + y 2
1 y 3y + 2x 62y 3x – 6
y –0.5x + 62 x 64yx + 8
f(x, y) = 3x + yf(x, y) = –x + 3yf(x, y) = x + 3y
11. Superbats, Inc., manufactures two different quality wood baseball bats, the Wallbanger and theDingbat. The Wallbanger takes 8 hours to trim and turn on a lathe and 2 hours to finish it. Ithas a profit of $17. The Dingbat takes 5 hours to trim and turn on a lathe and 5 hours to finish,but its profit is $29. The total time per day available for trimming and lathing is 80 hours andfor finishing is 50 hours.
Wallbangers / Dingbats / Total HoursTrim & Turn
Finish
Profit (w, d)
- Organize the information from the word problem into the chart above.
- Write a system of inequalities to represent the number of Wallbangers and Dingbats thatcan be produced per day.
- Write an equation “P =” for the profit per day.
d.Make a guess as to how many of each type of bat should be produced to have
the maximum profit?
HW # 3 (# 1 – 4)
- Suppose you receive $100 for a graduation present, and you deposit it in a savings account. Then each week thereafter, you add $5 to the account but no interest is earned. The amount in the account is a function of the number of weeks that have passed.
Identify the variables in this situation: x= ______y= ______
What is the given information in this problem (find all that apply)?
y-intercept ______slope ____ one point a second point:
a. Find an equation for the amount y you have after x weeks.
b. Use your equation to find when you will have $310 in the account.
- Create a word problem that will produce the following inequality solution and graph.
3. Graph the system of inequalities, and classify the figure created by the solution region.
x 2
x - 3
y 2x + 2 ______
y 2x – 1
4.The available parking area of a parking lot is 600 square meters. A car requires 6 square metersof space, and a bus requires 30 square meters of space. The attendant can handle no more than60 vehicles.
- Organize the information from the word problem into the chart below.
- Let c represent the number of cars, and b represent the number of buses. Write a systemof inequalities to represent the number of cars and buses that can be parked on the lot.
- If the parking fees are $2.50 for cars and $7.50 for buses, how many of each
type of vehicleshould the attendant accept to maximize income? What is the maximum income?
- The parking fees for special events are $4.00 per car and $8.00 for buses. How
many ofeach vehicle should the attendant accept during a special event to maximize income? Whatis the maximum income?
Cars / Buses / TotalProfit (c, b)
Profit (c, b)
Class work
Mix, Freeze, Pair
- Point 1 ______
Point 2 ______
Slope ______
Equation
______
- Point 1 ______
Point 2 ______
Slope ______
Equation
______
- Point 1 ______
Point 2 ______
Slope ______
Equation
______
HW # 4 (1, 2, 1)
1. A carpenter makes bookcases in 2 sizes, large and small. It takes 4 hours to make a large bookcase and 2 hours to make a small one. The profit on a large bookcase is $35 and on a small bookcase is $20. The carpenter can only spend 32 hours per week making bookcases and must make at least 2 of the large and at least 4 of the small each week. How many small and large bookcases should the carpenter make to maximize his profit? What is the maximum profit you can find?
Define your variables:
X=
Y=
Organize the information to write inequalities:Write the constraints and objective function:
Graph the system:Choose points to maximize profit:
- Fashion Furniture makes two kinds of chairs, rockers, and swivels. Two operations, A andB are used. Operation A is limited to 20 hours a day. Operation B is limited to 15 hours perday. The following chart shows the amount of time each operation takes for one chair. Theprofit for a rocker is $12, while it is $10 for the swivel.
Operation A / Operation B / Total Hours
Rocker / 2 hrs / 3 hrs
Swivel / 4 hrs / 1 hr
Profit (r, s)
How many chairs of each kind should Fashion Furniture make each day to maximize profit?
Word Problem:
HW # 5 = On – line worksheet “Corn & Beans”
HW # 5 – On – line Assignment – Print and complete the pdf file on Corn and Beans due Tuesday
HW # 6 – On – line Excel Scatter Plot tutorial & Linear Programming “Solver” feature
HW # 7 – Linear Programming due Monday. Use the LIGHT Method for both problems. Computer, Excel, and Graphing Calculator usage is “strongly” recommended.
- The table below shows the amounts of nutrient A and nutrient B in two types of dog food, X and Y.
Food Type /
X
/Y
/Total
Ingredient A / 1 unit per lb / 1/3 unit per lb / 20 unitsIngredient B / 1/2 unit per lb / 1 unit per lb / 30 units
Profit
The dogs in Kay’s K-9 Kennel must get at least 40 pounds of food per day. The food may be a mixture of foods X and Y. The daily diet must include at least 20 units of nutrient A and at least 30 units of nutrient B. The dogs must not get more than 100 pounds of food per day.
- Food X costs $0.80 per pound and food Y costs $0.40 per pound.
What is the least possiblecost per day for feeding the dogs?
- If the price of food X is raised to $1.00 per pound, and the price of food Y stays
the same,should Kay change the combination of foods she is using?
List the inequalities and function needed to answer the problem. Graph the inequalities and list the found vertices. Answer the problem.
2. The North Carolina Farmer’s Market Seafood Restaurant owner orders at least 50 fish. He cannot use more than 30 flounder or more than 35 tilapia. Flounder costs $4 each and tilapia costs $5 each. How many of each fish should he use to minimize his cost?
LINEAR PROGRAMMING Magazine Ad Activity
You are the new owner of a music shop at Triangle Towne Center Mall. The previous owner fled the city to join the circus as a magician . Your first duty as new owner and store manager is to create an advertising plan based on the budget available. You must figure out how many magazine and TV ads to purchase.
- TV ads cost $600 per airing.
- Magazine ads cost $1200 per issue.
- You total advertising budget is $9,000.
- If we let x = TV ads and y = magazine ads, write an inequality for our advertising budget.
- Due to space limitations, the magazine publishers tell us that we are only allowed to purchase up to 6 magazine ads. Write an inequality for this constraint.
- The television station called to say that we are only allowed to purchase up to 7 TV ads. Write an inequality for this constraint.
- It is impossible to buy a negative number of TV ads. Write an inequality for this constraint.
- It is impossible to buy a negative number of magazine ads. Write an inequality for this constraint.
Graph this system of inequalities on the graph to determine our region of feasibility.
Television Ads
The following data was collected in past years to try to determine how TV ads affect CD sales. Plot the points and find the Trend Line using Excel.
Number of TV ads / Increase in CD sales0 / 0
5 / 725
2 / 250
6 / 900
4 / 450
3 / 400
5 / 750
3 / 600
2 / 350
4 / 575
3 / 450
5 / 700
1 / 150
2 / 325
6 / 950
Number of TV Ads
- What does the slope tell you about how each TV ad affects sales?
For every TV ad, CD sales increased by about ______.
Your Turn – Repeat the process with the following data.
Magazine Ads
The following data was collected in past years to try to determine how magazine ads affect CD sales. Plot the points and find the Trend Line using Excel.
Number of magazine ads / Increase in CD sales1 / 100
8 / 725
6 / 590
7 / 725
4 / 375
8 / 800
5 / 440
9 / 900
2 / 150
6 / 630
3 / 300
7 / 640
4 / 410
2 / 275
5 / 560
Number of Magazine Ads
- What does the slope tell you about how each magazine ad affects sales?
For every magazine ad, CD sales increased by about ______.
We now have all of the information we need to solve the linear program.
- Write an objective function for CD sales. (Hint: Think about how each TV and magazine ad affects sales.)
- Substitute the coordinates of the vertices into the objective function.
(x, y)
Vertex Point / (objective function) / f(x, y)
Total Sales
- What is the maximum and where did it occur?
- Knowing this information, how many TV and magazine ads should you buy?
Part 2 – Excel Solver Feature
Fill – out an Excel Solver Outline page before typing the information into Excel.
Now that you have found your optimal solution, think about how a change in our allowable advertising values might affect the solution. This is called sensitivity analysis. Your job now is to find out how much a change in one of your constraint values will affect your final profit.
- For example, what if instead of being allowed to buy 7 television commercials, you were only allowed to buy 5. What would be the new optimal solution? (show your work by printing your Excel spreadsheet using the Solver Feature.)
- If you were allowed to increase one constraint value in order to increase your profit, which one should you change? In other words, would you rather be allowed to buy one more TV ad or one more magazine ad? Why?
Multiple Intelligences Survey
Adapted from W. McKenzie (1999), Performance Learning Systems (2003), and D. Lazear (2003)
Part I: Beside each statement place a zero or a one to indicate how much you identify with the description. For example, if you strongly identify with the statement, place a one (1) next to it; if you do not identify with it, place a zero (0) next to it.
Section 1_____ I have always been interested in plants, animals, and the world around me
_____ Ecological issues are important to me
_____ Classification helps me make sense of new data
_____ I enjoy having plants growing in my living space and know what they need to flourish
_____ I believe preserving our National Parks is important
_____I am aware of characteristics of plants and animals that many people don’t even see.
_____ Animals are important in my life
_____ My home has a recycling system in place
_____ I enjoy studying biology, botany and/or zoology
_____ I take pleasure being out in “nature”
_____ TOTAL for Section 1 / Section 2
_____I easily pick up on patterns and rhymes.
_____ I have sensitive hearing and often hear sounds around me that other don’t
_____ I enjoy making music and often have a tune or melody running through my mind
_____ I am aware of “music” in sounds and voices around me; pitch, duration, rhythm, etc.
_____ I respond to the cadence (rhythmic sequence) of poetry
_____ I use the rhythm and inflection of words to help me learn and recall vocabulary
_____ Concentration is difficult for me if there is background noise
_____ Listening to sounds in nature can be very relaxing
_____ Musicals are more engaging to me than dramatic plays
_____ I remember things by putting them in a rhyme
_____ TOTAL for Section 2
Section 3
_____ I am known for being neat and orderly
_____ Step-by-step directions are a big help
_____ Problem solving comes easily to me
_____ I get easily frustrated with disorganized people
_____ I can complete calculations quickly in my head
_____ Logic puzzles are fun
_____ I can't begin an assignment until I have all my "ducks in a row"
_____ I enjoy using the computer, especially to organize data I can analyze and interpret
_____ I enjoy troubleshooting something that isn't working properly
_____ I prefer precise distances (tenth’s of miles) and uncluttered navigational directions
_____ TOTAL for Section 3 / Section 4
_____ Rearranging a room and redecorating are fun for me
_____ I enjoy creating my own works of art
_____ I remember better using graphic organizers
_____ I have a heightened sense of color, pattern, and texture
_____ Charts, graphs and tables help me interpret data
_____ I am naturally orientated in the space around me and good at knowing where I am
_____ I can recall things as mental pictures
_____ I am good at reading maps and blueprints
_____ I can visualize three-dimensional (3D) objects and rotate them in my mind
_____ I can visualize ideas in my mind
_____ TOTAL for Section 4
Section 5
_____ I learn best talking and interacting with others
_____ I enjoy informal chat and serious discussion
_____ The more people the better
_____ I often serve as a leader among peers and colleagues
_____ I sense other’s feeling easily and often do so intentionally to communicate better
_____ Study groups are very productive for me
_____ I am a “team player”
_____ I have been told that I am “people person”
_____ I belong to more than three clubs or organizations
_____ I dislike working alone
_____ TOTAL for Section 5 / Section 6
_____ I learn best by doing, as in hand-on activities, role-playing, etc.
_____ I enjoy making things with my hands
_____ I am good at sports; I am well coordinated and always have been
_____ When I talk, I often use gestures and non-verbal cues to emphasize what I am communicating
_____ Demonstrating is better than explaining
_____ when I read, I enjoy and remember action-packed content best
_____ I like working with tools
_____ Inactivity can make me more tired than being very busy
_____ Hands-on activities are fun
_____ I live an active lifestyle
_____ TOTAL for Section 6
Section 7
_____ I spell well
_____ I enjoy reading books, magazines and web sites in my free time
_____ I keep a journal
_____ I have a good vocabulary and enjoy all things associated with words
_____ Taking notes helps me remember and understand
_____ I am able to write clearly and enjoy doing so
_____ It is easy for me to explain my ideas to others
_____ I write for pleasure
_____I enjoy word-based humor and joke, like puns, tongue twisters, etc.
_____ I enjoy public speaking and participating in debates
_____ TOTAL for Section 7 / Section 8
_____ I am aware of my internal thought processes, feelings, strengths, and weaknesses
_____ I spend quite a bit of time in thought, I have a private, inner world.
_____ I am keenly aware of my moral beliefs
_____ I learn best when I have an emotional attachment to the subject
_____ Fairness is important to me
_____ Social justice issues interest me
_____ I finder personal reflection not only meaningful, but important to my well-being
_____ I need to know why I should do something before I agree to do it
_____ When I believe in something I give more effort towards it
_____If I am able to choose, I prefer to work on projects alone. I am self-motivated
_____ TOTAL for Section 8
Part II