# Tech Math 2 – 1

|Foundations of Math 3 |

|Ms. J. Blackwell, nbct |

|[pic] |

| |

|Unit 1 – Modeling with Linear Functions |

|[pic] |

|Day |Date |Topic |Homework |

|1 |8/25 Mon |[pic] Patterns & |HW 1 & Multiple Intelligence pages = |

| | |Linear Representation |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 9/8 |

|4 |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 |Holiday[pic] |

|7 |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 Mon |

|9 |9/4 Thurs |Project Plan Day |Prj & HW 7 |

|10 |9/5 Fri |Project Plan Day |

| | |Early Release Day |

| |

|11 |9/8 Mon |[pic] Project Presentation Day |Study & Study Island Lab # 1 |

|12 |9/9 Tues |Unit Test 1 |Give 3 Teachers a Compliment! |

[pic]Unit Reflection: (Specific items to review)

[pic]Unit Vocabulary List (Highlight the words as they appear in the Unit) [pic]

|Patterns |Trend Line |Linear |Equations & Inequalities |

|X & 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 |Creating Equations A - CED |

|– |Create equations that describe numbers or relationships. |

|Modelin|A-CED.1 Create equations and inequalities in one variable and use them to solve problems. |

|g with |A-CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as |

|Linear |viable or nonviable options in a modeling context. |

|Functio|Reasoning with Equations & Inequalities A - REI |

|ns |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: [pic]

slope y-intercept

Solve the following equations and inequalities. Show your work on every step.

13. [pic] 14. [pic]

15. [pic] 16. [pic]

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. [pic] 8. [pic]

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. [pic]

Solve each of the following equations and inequalities. Show each step.

11. [pic] 12. [pic]

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 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 ( 6 6. x ( 1 7. x + y ( 4

3x – 2y ( – 4 y ( 0 3x – 2y ( 12

5x + y ( 15 2x + y ( 6 x – 4y ( – 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 ( 2

1 ( y ( 3 y + 2x ( 6 2y ( 3x – 6

y ( – 0.5x + 6 2 ( x ( 6 4y ( x + 8

f ( 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 Hours |

|Trim & Turn | | | |

|Finish | | | |

|Profit (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.

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 [pic] a second point: [pic]

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.

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) | | | |

Class work

Mix, Freeze, Pair

1. Point 1 _________________________

Point 2 ___________________________

Slope __________________________

Equation

_________________________________________________

2. Point 1 _________________________

Point 2 ___________________________

Slope __________________________

Equation

_________________________________________________

3. 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:

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 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.

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 |Total |

|Ingredient A |1 unit per lb |1/3 unit per lb |20 units |

|Ingredient 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?

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.

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 |Increase in CD sales |

|ads | |

|0 |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

1. 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|Increase in CD sales|

|ads | |

|1 |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

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.

| |(objective function) | |

|(x, y) | |f (x, y) |

|Vertex Point | |Total Sales |

| | | |

| | | |

| | | |

| | | |

| | | |

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 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 |Section 2 |

|_____ I have always been interested in plants, animals, and the world around |_____ I easily pick up on patterns and rhymes. |

|me |_____ I have sensitive hearing and often hear sounds around me that other |

|_____ Ecological issues are important to me |don’t |

|_____ Classification helps me make sense of new data |_____ I enjoy making music and often have a tune or melody running through |

|_____ I enjoy having plants growing in my living space and know what they |my mind |

|need to flourish |_____ I am aware of “music” in sounds and voices around me; pitch, duration,|

|_____ I believe preserving our National Parks is important |rhythm, etc. |

|_____ I am aware of characteristics of plants and animals that many people |_____ I respond to the cadence (rhythmic sequence) of poetry |

|don’t even see. |_____ I use the rhythm and inflection of words to help me learn and recall |

|_____ Animals are important in my life |vocabulary |

|_____ My home has a recycling system in place |_____ Concentration is difficult for me if there is background noise |

|_____ I enjoy studying biology, botany and/or zoology |_____ Listening to sounds in nature can be very relaxing |

|_____ I take pleasure being out in “nature” |_____ Musicals are more engaging to me than dramatic plays |

| |_____ I remember things by putting them in a rhyme |

|_____ TOTAL for Section 1 | |

| |_____ TOTAL for Section 2 |

|Section 3 |Section 4 |

|_____ I am known for being neat and orderly |_____ Rearranging a room and redecorating are fun for me |

|_____ Step-by-step directions are a big help |_____ I enjoy creating my own works of art |

|_____ Problem solving comes easily to me |_____ I remember better using graphic organizers |

|_____ I get easily frustrated with disorganized people |_____ I have a heightened sense of color, pattern, and texture |

|_____ I can complete calculations quickly in my head |_____ Charts, graphs and tables help me interpret data |

|_____ Logic puzzles are fun |_____ I am naturally orientated in the space around me and good at knowing |

|_____ I can't begin an assignment until I have all my "ducks in a row" |where I am |

|_____ I enjoy using the computer, especially to organize data I can analyze |_____ I can recall things as mental pictures |

|and interpret |_____ I am good at reading maps and blueprints |

|_____ I enjoy troubleshooting something that isn't working properly |_____ I can visualize three-dimensional (3D) objects and rotate them in my |

|_____ I prefer precise distances (tenth’s of miles) and uncluttered |mind |

|navigational directions |_____ I can visualize ideas in my mind |

| | |

|_____ TOTAL for Section 3 |_____ TOTAL for Section 4 |

|Section 5 |Section 6 |

|_____ I learn best talking and interacting with others |_____ I learn best by doing, as in hand-on activities, role-playing, etc. |

|_____ I enjoy informal chat and serious discussion |_____ I enjoy making things with my hands |

|_____ The more people the better |_____ I am good at sports; I am well coordinated and always have been |

|_____ I often serve as a leader among peers and colleagues |_____ When I talk, I often use gestures and non-verbal cues to emphasize |

|_____ I sense other’s feeling easily and often do so intentionally to |what I am communicating |

|communicate better |_____ Demonstrating is better than explaining |

|_____ Study groups are very productive for me |_____ when I read, I enjoy and remember action-packed content best |

|_____ I am a “team player” |_____ I like working with tools |

|_____ I have been told that I am “people person” |_____ Inactivity can make me more tired than being very busy |

|_____ I belong to more than three clubs or organizations |_____ Hands-on activities are fun |

|_____ I dislike working alone |_____ I live an active lifestyle |

| | |

|_____ TOTAL for Section 5 |_____ TOTAL for Section 6 |

|Section 7 |Section 8 |

|_____ I spell well |_____ I am aware of my internal thought processes, feelings, strengths, and |

|_____ I enjoy reading books, magazines and web sites in my free time |weaknesses |

|_____ I keep a journal |_____ I spend quite a bit of time in thought, I have a private, inner world.|

|_____ I have a good vocabulary and enjoy all things associated with words |_____ I am keenly aware of my moral beliefs |

|_____ Taking notes helps me remember and understand |_____ I learn best when I have an emotional attachment to the subject |

|_____ I am able to write clearly and enjoy doing so |_____ Fairness is important to me |

|_____ It is easy for me to explain my ideas to others |_____ Social justice issues interest me |

|_____ I write for pleasure |_____ I finder personal reflection not only meaningful, but important to my |

|_____ I enjoy word-based humor and joke, like puns, tongue twisters, etc. |well-being |

|_____ I enjoy public speaking and participating in debates |_____ 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 |

|_____ TOTAL for Section 7 |_____ If I am able to choose, I prefer to work on projects alone. I am |

| |self-motivated |

| | |

| |_____ TOTAL for Section 8 |

Part II

Now carry forward your total from each section and multiply by 10 below:

|Section |Total Forward |Multiply |Score |

|1 | |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

| | | | | | | | | |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 IV

Part 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![pic]

-----------------------

0 1 2 3 4 5 6 7 8 9 10

Increase in CD sales

0 1 2 3 4 5 6 7 8 9 10

0 100 200 300 400 500 600 700 800 900 1000

| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |

0 100 200 300 400 500 600 700 800 900 1000

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?

Increase in CD sales

[pic]

[pic]

| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Figure 1 Figure 2 Figure 3

[pic]

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?

| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Figure 1 Figure 2 Figure 3

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