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Foundations of Math 3Ms. J. Blackwell, nbct
https://sites.google.com/site/blackwellsbutterflyworld/home Unit 1 – Modeling with Linear Functions
Day Date Topic Homework1 8/25
Mon
Patterns & Linear Representation
HW 1 & Multiple Intelligence pages
= Thurs
2 8/26 Tues
Graphing Linear Inequalities, Max, & Min HW 2
3 8/27 Wed
Lego Activity HW 3 & Study Island Lab # 1 due
9/84 8/28
Thurs
Reverse Linear Programming Problems HW 4
5 8/29 Fri
Jeopardy Review HW 5 On line due Tues
6 9/1 Mon
Holiday7 9/2Tues Quiz & Project Plan Day HW 6 – Read &
Practice On line Tutorials
8 9/3 Wed Excel Practice & Project Plan Day HW 7 due Mon9 9/4
ThursProject Plan Day Prj & HW 7
10 9/5 Fri Project Plan DayEarly Release Day
11 9/8 Mon
Project Presentation Day
Study & Study Island Lab # 1
12 9/9 Tues Unit Test 1 Give 3 Teachers a Compliment!
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Unit Reflection: (Specific items to review)
Unit Vocabulary List (Highlight the words as they appear in the Unit)
Patterns Trend Line Linear Equations & Inequalities
X & Y Intercepts Regression Simplify DescribeMaximum Slope Standard Form Slope –
Intercept Evaluate Applications Minimum Correlation
Scatter Plot Constraints Corner Points Feasible RegionVertices Objective
FunctionProfit/Cost Sensitivity
Analysis
Unit 1 – FoM3 Essential Standards The Learner will be able to:
Uni
t 1 –
Mod
elin
g w
ith L
inea
r Fun
ctio
ns
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).
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Class Work – Day 1 – Patterns & Linear RepresentationsLinear 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)
0123451050100x
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Figure 1 Figure 2 Figure 3
Circle the initial value on the table.Where can you see the rate of change on the table?
How did the initial value and rate of change help you find the number of squares in Figure 10, Figure 50, and Figure 100?
Where is the initial value and the rate of change found in the bottom row of the table?
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.
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Verbal:
Algebraic:___________________________________________________________________
_____Table______________(x) Function: ____________ ______________ (y)
Graph
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You went to the zoo and found out they had a job opening that paid pretty well. You can clean out the gorilla cage and make $12 per hour. But it also just snowed, and they will pay you a flat fee if you shovel the sidewalk outside the gorilla cages as well. If you worked for 8 hours in the gorilla cages, then shoveled the snow, and made a total of $140, how much money did you make shoveling the snow?
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)
0123451050100x
3. What is the slope-intercept form of the equation?
4. Would you be able to draw Figure 11? Why or why not?
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Figure 1 Figure 2 Figure 3
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 # 9x y -3 5-2 8-1 110 141 172 203 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.7
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?
1. How do I write a linear inequality from a story problem? Define your variablesLook for keywords to tell you what symbol to useWrite an inequalityUse 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.
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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 ³ 6 6. x ³ 1 7. x + y ³ 43x – 2y ³ – 4 y ³ 0 3x – 2y £ 125x + y £ 15 2x + y £ 6 x – 4y ³ – 16 f ( x , y ) = x + 3y f ( x , y ) = 3x + y f ( x , y ) = x – 2y
8. y £ 2x + 1 9. y £ x + 6 10. x + y ³ 21 £ y £ 3 y + 2x ³ 6 2y ³
3x – 6y £ – 0.5x + 6 2 £ x £ 6 4y £ x + 8f ( x , y ) = 3x + y f ( x , y ) = – x + 3y f ( x , y ) = x + 3y
11. Superbats, Inc., manufactures two different quality wood baseball bats, the Wallbanger and the Dingbat. The Wallbanger takes 8 hours to trim and turn on a lathe and 2 hours to finish it. It has 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 and for finishing is 50 hours.
Wallbangers Dingbats Total HoursTrim & TurnFinishProfit (w, d)
a. Organize the information from the word problem into the chart above.
b. Write a system of inequalities to represent the number of Wallbangers and Dingbats that can be produced per day.
c. Write an equation “P =” for the profit per day.
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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)
1. 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.
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2. 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 meters of space, and a bus requires 30 square meters of space. The attendant can handle no more than 60 vehicles.
a. Organize the information from the word problem into the chart below.
b. Let c represent the number of cars, and b represent the number of buses. Write a system of inequalities to represent the number of cars and buses that can be parked on the lot.
c. If the parking fees are $2.50 for cars and $7.50 for buses, how many of each type of vehicle should the attendant accept to maximize income? What is the maximum income?
d. The parking fees for special events are $4.00 per car and $8.00 for buses. How many of each vehicle should the attendant accept during a special event to maximize income? What is the maximum income?
Cars Buses Total
Profit (c, b)Profit (c, b)
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Class workMix, Freeze, Pair
1. Point 1 _________________________
Point 2 ___________________________
Slope __________________________
Equation
_________________________________________________
2. Point 1 _________________________
Point 2 ___________________________
Slope __________________________
Equation
_________________________________________________
3. Point 1 _________________________
Point 2 ___________________________
Slope __________________________
Equation
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_________________________________________________
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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:
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2. Fashion Furniture makes two kinds of chairs, rockers, and swivels. Two operations, A and B are used. Operation A is limited to 20 hours a day. Operation B is limited to 15 hours per day. The following chart shows the amount of time each operation takes for one chair. The profit for a rocker is $12, while it is $10 for the swivel.
Operation A
Operation B
Total Hours
Rocker 2 hrs 3 hrsSwivel 4 hrs 1 hrProfit (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”
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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.
1. 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 TOTALIngredient 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.
a. Food X costs $0.80 per pound and food Y costs $0.40 per pound. What is the least possible cost per day for feeding the dogs?
b. 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?
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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.
1. If we let x = TV ads and y = magazine ads, write an inequality for our advertising budget.
2. 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.
3. The television station called to say that we are only allowed to purchase up to 7 TV ads. Write an inequality for this constraint.
4. It is impossible to buy a negative number of TV ads. Write an inequality for this constraint.
5. 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.
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Television AdsThe 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 sales
0 05 7252 2506 9004 4503 4005 7503 6002 3504 5753 4505 7001 1502 3256 950
Number of TV Ads
1. What does the slope tell you about how each TV ad affects sales?
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0 1 2 3 4 5 6 7 8 9 10
0
100
200
300
400
50
0 6
00
700
800
900
100
0
Incr
ease
in C
D s
ales
0
100
200
300
400
50
0 6
00
700
800
900
100
0
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 sales
1 1008 7256 590
20
Incr
ease
in C
D s
ales
7 7254 3758 8005 4409 9002 1506 6303 3007 6404 4102 2755 560
Number of Magazine Ads
1. 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.
1. Write an objective function for CD sales. (Hint: Think about how each TV and magazine ad affects sales.)
2. Substitute the coordinates of the vertices into the objective function.
(x, y)Vertex Point
(objective function)f (x, y)
Total Sales
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0 1 2 3 4 5 6 7 8 9 10
3. What is the maximum and where did it occur?4. 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 SurveyAdapted 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
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
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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
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 2Section 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
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
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_____ 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
_____ 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 6Section 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 8Part IINow carry forward your total from each section and multiply by 10 below:
Section Total Forward Multiply Score1 X10 2 X10 3 X10 4 X10 5 X10 6 X10 7 X10 8 X10
Part III Now plot your scores on the bar graph provided. Fill in your NAME, too!
100
90
80
70 24
60
50
40
30
20
10
0 Naturalist(1)
Musical, Rhythmic
(2)
Logical, Mathemati-
cal (3)
Visual, Spatial
(4)
Interpers-onal(5)
Bodily, Kinesthet-ic
(6)
Verbal, Linguistic
(7)
Intrapers-onal(8)
NAME: _______________________________ Multiple Intelligences Survey Top 3#s ___/___/___ Part IVPart V
1. Using the bar graph you created and the section key from part IV that is on Ms. Blackwell’s website to answerr the following questions:
a. In what Multiple Intelligence area did you have the highest score?
i. Describe this type of intelligence using the section key.
b. In what Multiple Intelligence area did you have the lowest score?
c. In what ways do these two categories describe YOU?
d. What do you notice about your bar graph?
Remember:Everyone has all the intelligences!You can strengthen an intelligence!
This inventory is only a snapshot, it can change over time!This is meant to empower you, not label you!
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