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DISCRETE MATHEMATICS

Summer 2018

BELLMORE-MERRICKCENTRAL HIGH SCHOOL DISTRICT

BOARD OF EDUCATION 2018-2019

Nina Lanci, President

Wendy Gargiulo, Vice President

Marion Blane

Edward Corona

John Ferrara

Janet Goller

Nancy Kaplan, Ed.D.

Gina Piskin

CENTRAL ADMINISTRATION

John DeTommasoSuperintendent of Schools

Mara Bollettieri, Psy.D.Deputy Superintendent

Kate FreemanMichael Harrington

Assistant Superintendents

DISCRETE MATHEMATICS

1

Written by:

Dan Bloomfield (Mepham High School)

Jaclyn Rothschild (Mepham High School)

Project Administrator:

Christopher Riccardi

District Chairpersons - Mathematics

TABLE OF CONTENTSUNIT PAGE NUMBERS

PAYCHECKS 1-4PURCHASES, RENTING & BUDGETING 5-10BANKING & CREDIT/DEBIT CARDS 11-15PROBABILITY & STATISTICS 16-18GEOMETRY 19-21MATRICES 22-27

PLACEMENT TESTS (NCC, SAT, ASVAB) 28FINAL EXAM/REVIEW/PROJECT 29PROJECTS

MALL MADNESS LIVING ON YOUR OWN FANTASY BASEBALL SCALE DRAWINGS BUILDING A PARK TREASURE HUNT CROSS COUNTRY TRIP

30

Unit #1 – Paychecks (34 Days) : Hourly Wages and Deductions (11 Days):

1) Hourly Wagesa. How do I calculate my weekly pay if I work 40 hours and get paid $8.25 per hour?b. Jared worked for 22.5 hours this week. He makes $7.95 an hour. How much did he make this

week? 2) Hourly Wages with Overtime

a. How do I calculate my weekly pay if I work 46 hours and get paid $8.25 per hour?b. Jesse worked for 51 hours this week. He earns $12.50 for every hour he works and time and a half

for overtime. How much did Jesse earn this week?3) Word Problems

a. How do I calculate my weekly pay if I worked for 7 hours a day Monday through Friday and 10 hours on Saturday given I earn $10.00 per hour?

b. Ashley has a job that pays $8.80 an hour. Mike has a job that pays $8.10 an hour. Ashley worked for 50 hours while Mike worked for 55 hours. Both earn time and a half for overtime. Who earned more money and how much more did they make?

4) Review5) QUIZ6) Salary Deductions – Day #1

a. What’s the difference between gross and net pay?b. Anthony’s gross pay is $1000. How much is his net pay, if the federal government takes 12% out

in taxes?7) Salary Deductions – Day #2

a. What deductions will be taken out of my paycheck?b. James makes $1675 each week and pays 5% in State taxes, 13% in Federal taxes and 2% for

Health Insurance. How much is his net pay?8) Finding Percentages

a. If FICA takes out $203.75 of my paycheck, what percentage of my pay are they taking?b. Diana works for Taco Bell and earns $683.77 per week. She pays the deductions listed below.

Determine her net pay and what percent of her pay each deduction consists of:

1

Deductions Percent of Gross Pay (round to nearest tenth)

Federal Income Tax: $80.00

State Income Tax: $19.50

F.I.C.A.: $51.35

Total Deductions

Net Pay

9) Evaluating Paychecksa. What percentage of my paycheck goes toward Medicare? Taxes? Disability? Etc.?

b. Given the paycheck below find the percentage of your paycheck that goes towards Social Security? State Tax? And Federal Income Tax?

c. Reviewd. QUIZ

Pay Cuts & Raises (6 Days):1) Percentage Raises

a. If I get a 5% raise on my pay, how much will I make per hour?b. Why would I get a raise?c. You earn $605.00 per week and receive a 4% raise. Find your new earnings.

2) Percentage Decreasesa. If I get paid 15% less, how much am I getting paid?b. Why would a company decrease my pay?c. Find the new salary of someone who earns $2450 with a 4.2% decrease.

3) Time Cardsa. How do I read a time card to see how many hours I worked this week?b. How do I calculate my pay using a time card?c. Time Card

Employee: Victoria Social Security No: 590-94-508Day IN OUT IN OUT TOTAL HOURS

Monday 7:00 AM 12:00 PM 12:30 PM 5:30 PMTuesday 8:00 AM 11:00 AM 12:00 PM 4:00 PM

Wednesday 8:30 AM 1:30 PM 2:45 PM 6:45 PMThursday 8:00 AM 1:00 PM OFF

Friday OFF 1:00 PM 8:00 PMSaturday 8:30 AM 11:30 AM 1:00 PM 5:00 PMSunday 9:30 AM 11:30 AM 2:00 PM 7:00 PM

HOURS SALARYPER HOUR

TOTALSALARY

Regular Hours $18.00Overtime

TOTAL

4) Practice5) Review6) TEST

Commission (11 Days):

1) Commissions Day #a. What is commission?b. What kinds of jobs get paid on commission?

2) Commissions Day #2a. If I work in a commission based industry, how do I calculate my paycheck?b. Tracey works for a car dealership and makes 4.5% commission on every car she sells. If she sells

a car for $27,500, how much commission will she make?3) Salary, Commissions & Sales Over a Baseline Day #1

a. I get paid an hourly rate and 10% on sales over $4000, what is my paycheck?

b. Warren has a job that pays $10.25 an hour plus 2% commission on his weekly sales. This week he worked 26 hours and sold $2,600.40 worth of products. How much money did he make in total for the week?

4) Salary, Commissions & Sales Over a Baseline Day #2a. I get paid an hourly rate and a commission of 5% on sales over $4000and 15% on sales over

$10,000, what is my paycheck?b. Brett has a job that pays $850 per week plus 3% commission on all weekly sales over $625. This

week he sold $2,566.83 worth of products. How much did he make this week?5) Review6) QUIZ7) Commission with Overtime

a. How do I calculate my paycheck if I work 53 hours at $10.25 per hour and receive commission on sales over $150?

b. Joe works 47 and hours per week and he makes $9.25 per hour. He also makes 3.2% commission based on his sales for the week. He sold $1,297 worth of merchandise. What is his gross pay for the week?

8) Commission with Overtime & Salesa. How do I calculate my paycheck if I work 53 hours at $10.25 per hour and receive 4% on sales

over $150?b. Melanie works 10 hours Monday through Friday and 8 hours on Saturday and makes $13.00 per

hour. On Monday she sold $257 worth of merchandise, Tuesday $2,005, Thursday $722, Friday $1,298 and Saturday $872. Her commission rate is 2.5%. What is her gross pay for the week?

9) Sales & Discountsa. How much would a sweatshirt cost if it was 15% off?b. How much does a sweater cost that is on sale 2 for $38?c. You go to American Eagle and buy jeans for $48.99. If you use a coupon for 25% off, how much

will you pay for the jeans (not including sales tax)?10) Review11) TEST Mall Madness Project (6 Days)

Unit #2 – Purchases, Renting & Budgeting (30 Days) : Renting/Leasing vs. Owning (9 Days):

1) Renting an Apartment Day #1a. How do we estimate the amount of money to spend for rent?b. What characteristics would you look for in an apartment that you want to rent? c. If Paula makes $52,000 per year, what is the most amount of money that she should spend on

rent?2) Tenants & Landlords Rights

a. If something breaks, whose responsibility is it to fix the broken object?b. Who is responsible for maintaining the property?c. Is the landlord or the tenant responsible to mow the lawn?

3) Renting an Apartment Day #2a. If you move in with a roomate, what kind of a roomate would you look for?b. How much rent could you afford with a roomate?c. Peter works 45 hours per week at $27 per hour and receives time and a half for overtime hours.

Nancy works 43 hours per week at $13.50 per hour and receives time and a half for overtime hours. What is the most they should spend on rent if they were splitting an apartment?

4) Moving Costsa. How much does it cost to rent a moving truck/van?b. How much gas will it take to travel?c. Do I have to pay insurance on a rented moving truck/van?d. You are moving 120 miles and you need to rent a truck. Option A: You Rent a U-Haul mid-size truck that costs $25.99, and $.99 per mile. How much will this cost you?

Option B: You Rent a Home Depot Truck that costs $19.99 an hour, with the base fee of $29.00 and only 90 miles are included and its $1.79 for each mile over that and it takes you 3 hours. How much will this cost you?

Before you pay for gas, Which option is better and why? e. Your car gets 22 miles per gallon and holds 14 gallons of gas.

How many miles can you travel on a full tank of gas? How much will it cost you to fill your tank if gas prices are $3.58?

5) Transportation and Cars Chapter 5a. How will I get around on a daily basis? Car? Bus? Train? Walk?b. How much does it cost for the bus daily/monthly? Train daily/monthly? Roundtrip?

6) Leasing vs. Buyinga. If I need a car, is it better to buy or lease?b. How much can I afford to pay monthly, given my salary?c. If you wanted to buy a car with a total vehicle price of $17,500. What would the price be after

taxes and licensing fees? How much would you pay in Taxes (8.625%) on this car?How much would you pay in Licensing fees (2%) on this car? What is the total amount you would pay on this car? If you made $61,000 a year, could you afford this car? Find your monthly gross income: Find 7% of your monthly gross income: What should your payment be per month?How many months are in 5 years? Total you can afford to pay: So could you afford this car over 5 years?

7) Budgetsa. Setup a budget using the previous 6 days and see if the students can afford to do what they want to

do. b. This can but used as a template to have students record what they spend:

Day Monday Tuesday Wednesday Thursday Friday

Total

8) Review 9) QUIZ

Sales and Discounts (6 Days):1) Furniture Shopping

a. You are buying furniture for your new apartment, how do I calculate the price aftrer the sales plus tax and shipping?

b. Jessica wanted to buy a new bed for $999. How much with she pay after sales tax (8.675%) if shipping is free?

2) Buying Appliancesa. How much would a $1300 appliance cost if I had a 25% coupon?b. Is there a warranty? Do I have to pay for it?

c. Kristen and Mike bought a new washer and dryer at PC Richards. They paid $399 for the washer and $425 for the dryer. The got a 15% discount for opening a new credit card. How much with they pay before tax?

3) Percentage off vs. Money offa. Is it better to take a 15% off coupon with me of a $20 off any item over $125?b. Kevin went to Brands bike shop and bought a brand new bike with a helmet and a mini computer

for the bike. The bike cost $759 while the helmet costs $30 and the mini computer is $55. He has 2 coupons, one for $45 off and the other for 5% off. Which coupon should he use and why?

4) Going to a Restaurant - Breakfasta. How much does it cost to go to restaurants? Do I have to tip my waiter/waitress? Bus boy?

Chef?b. Jenna goes to La Piazza and has dinner with her family. They order 3 large pizzas at $11 per pie, 2

bottles of soda at $1.50 per bottle, and 3 orders of baked ziti at $9 per order. If they pay tax of 8.625 % and tip 20%, how much will their total be?

5) Going to a Restaurant – Lunch & Dinnera. How much does it cost to go to restaurants? Do I have to tip my waiter/waitress? Bus boy?

Chef?b. Nicole goes out to dinner with 3 of her girlfriends (So there are 4 people in total). They each order

an appetizer, entrée, dessert and a drink. The appetizers cost them $17 each, the entrée costs them $32 each, dessert costs them $8 each and the drinks cost them $2 each. Nicole found a coupon in the paper for $15 off the entire bill. The sales tax is 9% and they will tip 18%. How much is their total?

6) Review7) QUIZ

Budgeting (5 Days):

1) Budgeting Sheetsa. How do I setup a budget sheet?

a. Brian and Jessica Smith have a combined monthly net income of $4,200. Use their budget sheet to answer the following questions.

A MONEY MANAGER FOR: The SmithsMonth: April

Monthly Living Expenses

Food/Grocery Bill: $350.00

Household Expenses: Electricity $75 Heating Fuel $36 Telephone $92

Monthly Fixed Expenses

Mortgage Payment $1527.30 Car Payment $230.59Regular Savings $100 Emergency Fund $35

TOTAL MONTHLY FIXED EXPENSES:

Water $15Total Household Expenses:

Transportation: Gasoline/Oil $120 Parking $22 Tolls $50 Repairs $72Total Transportation Expenses:

Personal Spending: Clothing $52 Credit Payments $0 Newspapers, Gifts $30 Pocket Money $75Total Personal Spending: Entertainment Movies/Theatre $40 Dining Out $115Total Entertainment:

TOTAL MONTHLY LIVING EXPENSES:

Annual ExpensesLife Insurance $1052.50Home Insurance $715Car Insurance $850Real Estate Taxes $621.72Car Registration $25Contributions $100Medical/Dental $120Vacation $500

TOTAL ANNUAL EXPENSES:

Monthly Share(¿12 )

Monthly Balance Sheet * Living Expenses: ________ * Net Income: ________ * Fixed Expenses: ________ * Total Monthly Expenses: ________ * Annual Expenses (per month): ________ * Balance: _________ * *Total Monthly Expenses: ___________________ *

2) Using a Budgeta. How much (percentage wise) can I spend on Groceries? Going out with friends? Rent?b. Your monthly net income is $2400. You allocate 10% for clothing, 27% for transportation, 30%

for groceries, 8% for entertainment, 5% for pocket money, and the remainder for savings. Your actual expenses for September are shown. What is the dollar amount allocated for each expense? Find the difference between the actual amount spent and the amount budgeted.

Item Percent of Monthly Budget

Monthly Budget Actual for Sept. Difference

Clothing _______________ _______________ $300.00 _______________

Transportation

Groceries

Entertainment

Pocket Money

Savings

Totals

_______________

_______________

_______________

_______________

_______________

_______________

_______________

_______________

_______________

_______________

_______________

_______________

$625.00

$745.00

$212.00

$100.00

$450.00

___________

_______________

_______________

_______________

_______________

_______________

_________________

Are you over or under your budget? __________________

3) Practicea. Setup budget sheet and see what the students can afford on a certain monthly salaryb. Have Student create a budget sheet using the template above (may have to be modified.)

4) Review5) QUIZ “Living on your Own” Project (10 Days)

Unit #3 – Banking & Credit/Debit Cards (16 Days) : Bank Statements (7 Days):

1) Banking Depositsa. If I deposit my paycheck for $450, a check from mom for $36 and take $40 out of the ATM today,

how much money did I add to my account?b. Joe deposited a check for $326.45 and a check for $183.75. He took $78.00 in cash out of the

ATM. What is his total deposit to his account?c. Matt deposits the following in his checking account: 4 twenty-dollar bills, 18 ten-dollar bills, 14

five-dollar bills, 95 one-dollar bills, 43 quarters, 22 dimes, 16 nickels, 52 pennies and a check for $261.35. What is her total deposit?

2) Checking Ledgersa. What is a debit? A credit?b. What are the parts of a check that I need to fill out?c. How do I write a check?d. Directions: Write out all necessary checks.

Log all transactions on your transaction register Your starting balance on 10/1 is $1,500.00

10/3: You paid your rent to Master Leasing Corp. for $1,250.Acc: GVMESHLTR

10/5: You received $370.00 for your birthday and deposited it in your account.10/7: You paid your electric bill to LIPA for $112.87.

Acc: LTHRBLT10/10: You earned $1.70 in interest10/13: You gave Mrs. Crusius $50.00 for her birthday.

What is your ending balance?

Check Number

Date Transaction Description Payment, Fee, Withdrawal

Deposit, Credit Balance

3) Practice4) Review5) TEST6) Banking Simulation (2 days): http://finlitproject.com/simulator/

a. Reading a monthly statementb. Identifying debits credits and activity on your accountc. Deposit or transfer of fundsd. Paying bills

Credit Cards (9 Days):1) Grocery Shopping

a. How do I stay within my budget when I grocery shop?b. Create a list before you leave to go food shopping. Look in the circulars for coupons. Budget how

much money you have to spend. Can you buy any items that aren’t on your list? 2) Credit Scores Good & Bad

a. What are some advantages nd disadvantages of credt cards?b. How many credit cards should I have?c. Will the following help or hurt your credit?

i. You open up a new savings account from Chase Bank and deposit money biweekly.ii. You have been working at Macys for over a year and plan to continue working there

through college. iii. Three of the checks you have written in the past year have bounced

http://finlitproject.com/simulator/

3) Finance Chargesa. What is a finance charge?b. How do I calculater a finance charge on my existing balance?c. When do I get charged a finance charge?d. Jose wants to buy a stereo for $1500 and pay for it using a credit card that has an annual

percentage rate of 16.75% and a periodic interest rate of 1.40%. How much will interest will he pay if he cannot pay the stereo off for a year? How much will his monthly payments be?

4) Credit Cards Day #1a. How do I pay off my credit card balance over time?b. Marie just used her new credit card to buy a bike for $550. Her budget allows her to pay no more

than $125 per month on her credit card. Marie has decided not to use the credit card again until the bike is paid off. The credit card she used has an annual percentage rate of 27%.

a) What is the periodic rate? (nearest hundredth) b) How long will it take for Marie to pay for the bike?

c) How much interest will she pay? d) What is the total cost of the bike after she completely pays for it (including interest)?

Date PreviousBalance

InterestCharge

Balance plus Interest Marie’s Payment

Remaining Balance

5) Credit Cards Day #2a. How do I pay down my credit card debt (periodic vs annual rates)?b. Name some strategies you can you to get out of credit card debt.

6) Reading a Credit Card Statementa. How do I read a credit card statements and all of the parts of that statement?

7) Practice8) Review 9) TEST

Unit #4 – Probability & Statistics (28 Days) : Venn Diagrams (4 Days):

1) Venn Diagrams(2 Circle)a. How do I solve a venn diagram problem with 2 circles?b. What do the spaces mean/represent?c. How do I fond out the”both” section?d. Out of 800 homes, 78 only have a washing machine, 88 only have a dryer and 204 have both. How

many don’t have a washer or a dryer?2) Venn Diagrams(2 Circle)

a. How do I fond out the”neither” section?b. How do I fond out the”x not y” section?c. How many people were surveyed?d. A survey found that 215 people eat only meat, 107 people eat only fish and 154 people eat both. If

29 people do not eat meat or fish, how many people participated in the survey?3) Review4) TEST

Probability (7 Days):1) Simple Probability (using and & or)

a. What is probability?b. How do I calculate a single probability?c. How do I calculate multiple probabilities?d. A single standard die is rolled once. What is the probability of rolling an even number or a three

(3)? 2) Tree Diagrams & Sample Spaces

a. How do I show all of the possible outcomes of an event?b. A hat contains 1 red marble and 3 yellow marbles. Suppose one marble is drawn at random, its

color noted and then the marble is put back in the hat. A second marble is then drawn. Draw a tree diagram or list a sample space to show all possible outcomes for this situation.

3) Counting Principlea. How do I calculate the amount of total possible outcomes?b. The McDonalds menu includes 5 kinds of burgers, 3 sizes of fries and 3 types of milkshakes.

How many ways can you make a meal of a burger, a fry and a milkshake? 4) Permutations

a. How do I calculate total possible outcomes when order does not matter?b. How many ways can 6 people finish a race if the top 2 finishers get trophies?c. How many different “words” can be created using the letters of the word “BLOOMFIELD”?

5) Combinationsa. How do I calculate total possible outcomes when order does matter?b. There are 20 players trying out for a basketball team that can have only 15 players on the teams.

How many different teams of 15 can be made from the 20 trying out? If there are 5 returning players that automatically make the teams, how many different teams can now be formed?

6) Review7) TEST

Statistics (8 Days):1) Measures of central tendency & outliers

a. How do I find the mean, median, mode and range?b. The grades in Mr. White’s English class are as follows: 62, 67, 76, 76, 85, 86, 89, 90, 91, 95, 96

Find the mean, median, mode and range.2) Box and whisker plots (quartiles & extremes)

a. How do I read and graph a box plot?b. How do I find the quartiles and interquartile range?c. The ages of the 15 employees of the Red Hook Curry House are given below: 16, 17, 17, 18, 19,

22, 25, 26, 29, 33, 33, 37, 40, 42, 44. i. Determine the median and quartile values for this data set.

ii. Create a box-and-whiskers diagram below.3) Dot plots

a. How do I create and read a dot plot?b. Charlie’s Food Factory currently employs 28 workers, whose ages are shown below on a dot plot.

Answer the following questions based on this plot

How many of the workers are 18 years old? 4) Frequency tables

a. How do I read and graph a frequency table?b. The following is a list of grades for the 2nd quarter of Mrs. Smith’s math class. Complete a

frequency table for the grades: 68, 79, 81, 84, 60, 77, 53, 82, 89, 83, 77, 85, 91, 86, 97, 855) Histograms

a. How do I read and graph a histogram?b. When do I use a break in the graph?c. The following is a list of grades for the 2nd quarter of Mrs. Smith’s math class. Complete a

histogram for the grades: 68, 79, 81, 84, 60, 77, 53, 82, 89, 83, 77, 85, 91, 86, 97, 856) Circle graphs

a. How do I read and break up a circle into percentages?b. You monthly net income is $3200. You spent $300 for clothing, $725 for transportation, $650 for

groceries, and the remainder for savings. What is the percent of your budget allocated for each expense? Create a pie graph in order to see where your money went this month.

7) Review8) TEST Fantasy Baseball Project (9 Days)

Unit #5 – Geometry (27 Days) : Scale Drawings (3 Days):

1) Scale Factorsa. What is a scale factor?b. How does a scale factor relate to the real world?

2) Dilationa. What are dilations?b. How do I make something bigger or smaller on a graph?c. How does the area and perimeter change when a dilation occurs?

3) Scaling in the real worlda. Where is scaling used in the real world?b. Create a scale model of your bedroom after taking measurements.

Scale Drawing Project (3 Days)

Geometry (11 Days):1) Area and Perimeter of Rectangles and Squares

a. How do I find the perimeter and area of rectangles & squares?

b. Chris bought a desk that is in the shape of a triangle. The desk is 4.5 feet long and 2.7 feet wide. What is the area of the desk?

2) Solving Problems with Area and Perimetera. How do I find the perimeter and area of rectangles & squares in word problems?b. If I have a bed, dresser and nightstand that take up 50 square feet and my bedroom is 250 square

feet, how much room is left on the floor?c. The wall of a room is 9 feet by 14 feet. I bought 2 posters; each poster is 1.25 foot wide by 3.2

feet long. How much of the wall is not covered by the posters?3) Pricing with Perimeter and Area

a. How do I calculate the price of wall to wall carpeting?b. How do I calculate the amount of fencing needed to enclose my yard?c. One of the walls in Mike’s bedroom has 2 windows. Each window is 2.25 feet wide by 3.6 feet

tall. The wall is 15 feet long by 8 feet wide. i. How much wall space does Mike have?

ii. Mike wants to paint the wall blue and each can covers 19 square feet. How any cans of paint does Mike need to buy?

iii. If the price of the paint per can is $21.55 and the sales tax is 9.25%. What is the total cost of the paint?

4) Word Problems - Practice5) Review6) Quiz7) Area and Perimeter of Triangles

a. How do I find the perimeter and area of triangles?b. Find the area of a jungle gym in the shape of a triangle. Base = 10 ft. & Height = 7 ft.

8) Area and Circumference of Circlesa. How do I find the circumference and area of circles?b. Find the area and circumference of a fountain in the shape of a circle with a diameter = 6 ft.

9) Area and Perimeter of Triangles and Circles Word Problems a. How do I calculate the amount of space and price it will cost me to put a pool in my backyard?

10) Review11) Test

Volume (7 Days):1) Volume of Prisms

a. What is volume?b. How do I find the volume of a prism?c. How do I know what the shape of the base of a prism is?d. The diagram shows a mini water pool with a length of 27 inches, width of 18 inches and height of

18 inches. The pool is filled with water to a depth of 5 inches. To the nearest percent, what percent of the pool is filled with water?

2) Volume of Cylindersa. How do I find the volume of a cylinder?

b. A soup can is shown as a cylinder in the diagram to the right, with a radius of 4 cm and height of 7 cm.

i. What is the shape of the base of the soup can?ii. What is the area, in term of pi, of the base of the soup can? Use appropriate units.

iii. What is the volume, to the nearest cubic cm, of the can?[Your answer from part b can help] Use appropriate units.

3) Volume of Cones and Pyramidsa. How do I find the volume of a pyramid?b. The Great Pyramid of Giza in Egypt has a square base that measures 756 feet on a side and a

height of 481 feet tall. To the nearest million cubic feet, what is the volume of the Great Pyramid?c. How do I find the volume of a cone?d. Find the volume of a cone with a height of 4cm and a base with a diameter of 10 cm. Round your

answer to the nearest cubic centimeter.4) Volume of Spheres

a. How do I find the volume of a sphere?b. A sphere has a great circle whose circumference is 95 centimeters. Which of the following is

closest to the volume of the sphere, in cubic centimeters? [Hint find the radius first!]5) Volume Word Problems6) Review7) Test

Building a Park Project (3 Days)

Unit #6 – Matrices (10 Days) : Matrices (7 Days):

1) Adding & Subtracting Matricesa. How do I add and subtract Matrices?b. What properties musty exist between two matrices in order for the to be added or subtracted?

c.

A=¿ [2 6 −3 ¿ ] ¿¿

¿¿ +

B=¿ [−3 7 4 ¿ ]¿¿

¿¿

2) Multiplying Matricesa. How do I multiply two matrices together?b. What property must exist in order for the matrices to be multiplied?c. Find the product of C(2x2) and D (2x1)

D=¿ [−1 ¿ ] ¿¿

¿¿C=¿ [−2 6 ¿ ]¿¿

¿¿

3) Determinanta. How do I find the determinant of a matrix?b. What does the determinant represent?

c. Find the determinant of the following matrix:

|3 −2 ¿|¿¿

¿¿

4) Inversesa. How do I calculate the inverse of a matrix?b. What is the inverse used for?

c.5) Solving Matrix Equations

a. How do I solve matrix equations?b. How do I solve a system of linear equations with matrices?c. Use matrices to solve the following systems of equations. Show your matrix

set up and check your solutions: 6) Review7) QUIZ Project: Treasure Hunt (3 Days)

Unit #7 – Placement Tests – NCC, ASVAB & SAT/ACT (14 Days) Summation (4 Days):

1) Basic Summationa. What is sigma notation?b. What is a summation?c. What is a lower/upper limit?d. How do I calculate a bacic summation?

2) Summation in Calculatora. How do I calculate a summation in the calculator?

3) Review4) QUIZ

Placement Tests (10 Days): NCC (Accuplacer) – collegeboard.com ASVAB GED (if necessary) SAT/ACT – khanacademy.com

Unit #8 – Final Review/Exam/Project (19 Days)Final Exam & Review (19 Days):

Moving Cross Country Project

Total Days = 182 days

Extras:Projects (to replace low grades – given over breaks):

Going On Vacation Furnishing Your Home

Name:__________________________________ Store #’s:_________________________

Name:__________________________________ Store #’s:_________________________

Mall Madness in the 21st Century

Name:__________________________________ Store #’s:_________________________

Name:__________________________________ Store #’s:_________________________

Stores at Roosevelt Field Stores at Mall of America (Minneapolis)Stores at Tanger Outlets (Deer Park)

Gameboard: On this gameboard, you and your group will choose 20 different stores that will appear in your mall. Write the name of each individual store in the numbered boxes below.

1 2 3 4 5 6

7 8

9 10

11 12

13 14

15 16 17 18 19 20

Name:____________________________________________________Project: For each store that your group chooses from above, you will look for sales that each store is currently holding. Once you find the sales, copy and paste the sale into the following boxes below.Store 1 Name:

Item:

Price:

Item:

Price:

Percentage: Percentage:

Store 2 Name:

Item:

Price:

Percentage:

Item:

Price:

Percentage:

Store 3 Name:

Item:

Price:

Percentage:

Item:

Price:

Percentage:

Store 4 Name:

Item:

Price:

Percentage:

Item:

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Store 5 Name:

Item:

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Item:

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Percentage: Percentage:

Store 7 Name:

Item:

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Item:

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Store 9 Name:

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Store 10 Name:

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Item:

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Item:

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Store 15 Name:Item:

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Item:

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Store 17 Name:

Item:

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Item:

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Store 20 Name:

Item:

Price:

Item:

Price:

Percentage:

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Let’s Go Shopping: What did I buy?

Store Name:_________________________________________ Store #:______________________

Item Name:_________________________________________ Item Sale Price:_______________

Store Name:_________________________________________ Store #:______________________


Store Name:_________________________________________ Store #:______________________


Store Name:_________________________________________ Store #:______________________


Store Name:_________________________________________ Store #:______________________


Store Name:_________________________________________ Store #:______________________


Store Name:_________________________________________ Store #:______________________


Store Name:_________________________________________ Store #:______________________


Store Name:_________________________________________ Store #:______________________


Store Name:_________________________________________ Store #:______________________


Name:_________________________________________

Commission and Salary: You will be paid $350 per week and you make 2% commission on the sales made. Look at all your group members shopping lists. If they bought an item from your store add it to the list below with the cost. Then find the total commission you made and add it to your salary. How much is your total salary plus commission for this week? The salesperson who makes the most money wins.

What percent commission am I earning on the items that were bought from my stores?

Item Price(Not

Including Tax):

Commission

Percent

$0-$49.99

40%

$50-$99.99

20%

$100-$499.99

5%

$500- 2%

$999.99$1000-

$9,999.99

0.3%

$10,000-$24,999.

99

0.05%

$25,000-$100,00

0

0.01%


Item Price(Not

Including Tax):

Commission

Percent

$0-$49.99

40%

$50-$99.99

20%

$100-$499.99

5%

$500-$999.99

2%

$1000-$9,999.9

9

0.3%

$10,000-$24,999.

99

0.05%

$25,000-$100,00

0

0.01%


Item Price(Not

Including Tax):

Commission

Percent

$0-$49.99

40%

$50-$99.99

20%

$100-$499.99

5%

$500-$999.99

2%

$1000-$9,999.9

9

0.3%

$10,000- 0.05%

$24,999.99

$25,000-$100,00

0

0.01%


Item Price(Not

Including Tax):

Commission

Percent

$0-$49.99

40%

$50-$99.99

20%

$100-$499.99

5%

$500-$999.99

2%

$1000-$9,999.9

9

0.3%

$10,000-$24,999.

99

0.05%

$25,000-$100,00

0

0.01%

NAME:__________________________________________________ DATE:____________________

Discrete Math

DISCRETE MATH PROJECT!BUDGETING and Living on Your OWN!!

Congratulations! You have just landed a new job! You have also

just decided that you are going to move out of your parents’ house.

You are going to find your STARTING salary, and you are going to

need to figure out how to budget it for the following things:

Rent

Car

Furniture

Food

Miscellaneous expenses

Each Day of the project you are going to be required to answer questions and add another component to Living on your OWN!! You will be able to explore career options, choose where you want to live, choose what kind of car you want to drive, and you even get to go shopping for furniture and food.

You will be required to hand in all worksheets (with the appropriate work shown), complete a budget sheet and a PowerPoint that you will present to the class.

In REAL LIFE you can’t go over on your budget so you can’t in this project. Please be conservative with your money when creating your “Life”.

DUE DATE:

Living on your Own – RubricName(s):

For every day the project is late you will lose 10 points. If you can not present on the day you are supposed to you will lose 10 points.

Homework Total (120 points):(6 hws @ 20 pts each)

Day 1:____ Day 4:____

Day 2:____ Day 5:____

Day 3:____ Day 6:____

Total:_____

Powerpoint and Presentation must include (50 points): Jobs (5) Rent/Apt Info(5) Car Info(5) Gas Prices/ Distance from work(5) Food(5) Furniture (had and bought) (5) Summary (10) Presentation (creative, energetic, etc.) (10)

Jobs _______ Rent/Apt Info _______ Car Info ________ Gas Prices/ Distance from Work _______ Food _______ Furniture (had and bought) ________ Summary _______ Presentation _______

Total:_______Budget Sheet (30 points):

Complete Accurate Answered questions along with budget sheet

Total:_________

TOTAL SCORE: _______________________

Name: ________________________ Date: ___________

Budgeting Sheet:

Description Balance ($) Cost ($)

NET Pay (PER MONTH) :

Rent (your portion per month):

Car (your payment per month):

Gas:

Insurance: 120

Food (your share for the month):

Entertainment:

Dining Out:

Other expenses (optional):

New Balance:

Additional Expenses: Security Deposit

Pocket Money:

Furniture Budget Cost ($)

Amount given to buy furniture:

Amount Spent on furniture:

TAX:

Total Amount for furniture:

Amount Left (add to pocket money):

Name:_______________________________

Day 1: Which career do I want to pursue?

Log on to: www.careerzone.ny.gov

Find the area/job that appeals to you and click on it.

JOB :

Job Description

Why does this job interest you?

Skills Needed (list 3 or 4)

1.

2.

3.

4.

Education Required(2 year college, 4 year college, trade school, etc.)Training Required(Student teaching, computer training, etc.)GROSS PAY(ENTRY LEVEL)

1. Why are you choosing this job? ________________________________________________________________________________________________________________________________________________________________________________________________________________________

____________________________________________________________________________________________________________________________________________

2. Research where this job will be located. Use www.monster.com for current job openings. List the name of the job and the town it is in.

Name ___________________________________

Town___________________________________

3. What would be your GROSS PAY?

4. If you have taxes taken out for 33% of your gross income, what would your NET PAY be?

5. What would your MONTHLY NET PAY be?

6. Add your MONTHLY PAY to your budget sheet.

Name:________________________________

Day 2: What kind of Apartment do I want?

1. What is your gross pay? (Refer to day 1) ____________________________

2. Find one week’s gross pay. This is how much you CAN spend on Rent. You can spend less but not more than this amount.

3. Are you living with someone or alone? If someone, who?

4. How much can you afford in Rent COMBINED?

5. List 3 towns you might want to live in. (They should be close to where you work.)1.2.

Apartment 1: Apartment 2: Location (town)

Cost (per month)

# of bedrooms

Are utilities included?

Name 5 features of the INSIDE of the apartment

1.

2.

3.

4.

5.

1.

2.

3.

4.

5.

Name 2 features of the OUTSIDE of the apartment

1.

2.

1.

2.

Is there a security deposit? If so how much?

3.

6. What are 3 things you are looking for in an apartment? 1.

2.

3.

7. Use the following websites to search apartments. If you have another website you would like to use, please list it below.www.mlsli.comwww.apartmentguide.com Other Websites used

1. 2.8. You need to compare 2 apartments! You must PRINT out the ad for each apartment!

9. Which apartment are you going to choose?

10. Why did you choose that apartment?

11. If you are sharing this apartment what will be the amount YOU contribute to the rent? Add this amount to your budget sheet where it says RENT under fixed monthly expenses.

12. If utilities are included indicate that on your budget sheet. If they are not included put $100 down for utilities on your budget sheet.

Name:_______________________

Day 3: Furnishing my Apartment

1. You are given a budget of $1500 and you need to furnish your apartment. This is your individual amount so if you are renting your apartment with someone, you will be given $2000 combined.

What amount can you spend on furniture? _________________________________

2. You can only bring 5 items from your parents’ house to bring to your new apartment. Those 5 items are:

1.

2.

3.

4.

5.

3. Use the following websites to search furniture and things for apartment. If you have another website you would like to use, please list it below.www.target.com www.bedbathandbeyond.com http://www2.mybobs.com/ www.walmart.com www.ikea.com

Other Websites used1.2.

4. You need to buy 20 things for your apartment! That could include furniture, light fixtures, plates, cups, electronics, etc. Fill in the chart and don’t forget you will need pictures for your powerpoint!

Name: ___________________________ Date: _____________

Group Members: ________________________________________________________________

Website to use for statistics:www.baseball-reference.com

Statistics Project Due Date: _________

Have you ever thought about being a baseball manager?

Have you ever wondered why certain managers last for many years and others are fired after only a few years?

You are now going to become a baseball manager. With your front office, you will evaluate multiple players and see who the best players of the group will be for your baseball team.

How are we going to do this?You and your group (known as your front office) will compare statistics and graphs between different baseball players and decide who the best players for your team will be for this year.

Here is the list of players you will be comparing:Oufielders First Basemen/Designated HittersNelson Cruz ($14 million) Edwin Encarnacion ($10 million)Jose Bautista ($14 million) Prince Fielder ($24 million)Ryan Braun ($19 million) Albert Pujols ($24 million)Matt Kemp ($18 million) Joey Votto ($22 million)Hanley Ramirez ($22 million) Adrian Gonzalez ($22 million)Justin Upton ($22 million) David Ortiz ($16 million)Adam Jones ($14 million) Miguel Cabrera ($31 million)

Each person will be assigned 2 of the 14 players listed above that they will research.

You will find all of the measures of central tendency (mean, median, mode, range, interquartile range, standard deviation), figure out which categories are skewed and which are symmetric, and you will create you statistical graphs for a visual representation (box-and-whisker, dot plot, frequency table, histogram). Through your statistical analysis, you will analyze the 14 players and choose the best for your team, you will identify any outliners that may concern you with choosing any of the players. Round all answers to the nearest tenth of a unit.

What categories will we analyze?Runs (R) Hits (H)Homeruns (HR) Runs Batted In (RBI)Strikeouts (SO) Stolen Bases (SB)

These categories will be analyzed for each player’s career to see how you may project the player to perform for this upcoming year. You will project what you believe the players statistical output will be for this year and describe how you arrived at your conclusion (mean, median, mode, range, etc.). Why is this

measure of central tendency the best choice for the projection of date for this year? (See #7 below)

You and your front office will choose 5 players from the assigned players (3 or 4 Outfielders & 1 or 2 First Basemen/Designated Hitters) to start you baseball team by using your projections.

OUTLINE OF PROJECT DETAILS:1) Research your players and copy down his career statistics in the categories

above (10pts)______

2) Calculate the mean, median, mode, range, interquartile range and standard deviation for each of the recorded statistics (12pts)

______

3) Create a frequency table for each statistical category (12pts)______

4) Create a dot plot for each statistical category (12pts) ______

5) Create a histogram for each statistical category (12pts)______

6) Create a box plot (box-and-whisker) for each statistical category (12pts)______

7) Project what your players will do for this upcoming season (write a sentence describing how you came up with your projections and why you believe that is the best way to project, what statistical information did you use) (10pts)

______

8) You will have a salary of $100,000,000 to start your team. Meet with your front office and negotiate over which 5 players will be the five (5) to start up your team, using your $100,000,000 salary cap, make sure to come to a consensus. (10pts)

______

9) As a class we will argue to see who has the best team, through your projections (10pts)

______

Player’s Name: ___________________________________________________

Year: R H HR RBI SO SB2003200420052006200720082009201020112012201320142015201620172018*

2018* - this should be your projected totals, since the season hasn’t happened yet

Player’s Name: ___________________________________________________

Year: R H HR RBI SO SB2003200420052006200720082009201020112012201320142015201620172018*

2018* - this should be your projected totals, since the season hasn’t happened yet

INTERVAL TALLY FREQUENCY

0-910-1920-2930-3940-4950-5960-6970-7980-8990-99

100-109110-119120-129130-139140-149150-159

ITEM Room it’s being used STORE you purchased it in Price1. Bedroom

2. Bedroom

3. Bedroom

4. Bedroom

5. Bath Room

6. Bath Room

7. Bath Room

8. Bath Room

9. Living Room

10. Living Room

11. Living Room

12. Living Room

13. Kitchen

14. Kitchen

15. Kitchen

16. Kitchen

17. Miscellaneous

18. Miscellaneous

19. Miscellaneous

5. Total up everything you purchased.

6. Tax is 8.25%. How much will the tax be on your total purchase?

7. What is the total purchase price?

8. Did you stay within your budget?

Name:________________________

Day 4: Car1. Your car payment should not be more than 7% of your Gross Monthly pay.

a. What is your monthly gross pay? ___________________________

b. Find 7% of your monthly gross pay.

2. Let’s figure out if you bought the car over 5 years, how much can you afford?

So, you should be looking at cars that are this price or BELOW!!!

3. Use the following websites to search new and used cars. If you have another website you would like to use, please list it below.www.honda.com www.toyota.com www.autotrader.com Other Websites used1.2.

Compare two cars:

CAR 1: CAR 2:Make and Model

Price

Miles per gallon

Name 2 things you like about the car:

1. 1.

2. 2.

Name 2 things you don’t like about the car:

1.

2.

1.

2.

Taxes (8.625%)

Fees (2%)

Total Amount of Car:

4. Which car did you choose and Why?

5. Did you spend your entire monthly budget for your car payment? Let’s find out.a. Take the final car amount with taxes and fees and divide that by 60.

b. Compare that to question 1b. on the front and make sure you can afford this car.

6. Add your payment amount to your budget sheet.

Name:______________________________

Day 5: Travel/Gas

1. Where is your job located? ____________________________________________

2. Where is your apartment located? ____________________________________

3. Using www.mapquest.com Map out the route you will take to and from work.

a. Print out the map.b. How many miles is it one way? __________________________c. How many miles will it be for you to go to and from work? _______________

4. Research gas prices in the area your apartment will be in (www.gasbuddy.com )

a. What is the price of gas? ________________

5. Using the information from day 5, answer the following questions:

a. How many miles per gallon does your car get? __________________________

b. How much do you pay for gas when you travel to and from work? Per week? Per month?

c. If you use 25 gallons of gas when you are not working, how much does gas cost you?

d. Add the two gas price amounts from b (per month) and c. Add this to your budget sheet.

Name:____________________________________

Day 6: Food Shopping1. Each member MUST fill in the chart below for what they eat every day for the week.

Day of the Week Breakfast Lunch Dinner Snacks

Sunday

Food:

Drink:

Food:

Drink:

Food:

Drink:

Food:

Drink:

Monday

Food:

Drink:

Food:

Drink:

Food:

Drink:

Food:

Drink:

Tuesday

Food:

Drink:

Food:

Drink:

Food:

Drink:

Food:

Drink:

Wednesday

Food:

Drink:

Food:

Drink:

Food:

Drink:

Food:

Drink:

Thursday

Food:

Drink:

Food:

Drink:

Food:

Drink:

Food:

Drink:

Friday

Food:

Drink:

Food:

Drink:

Food:

Drink:

Food:

Drink:

Saturday

Food:

Drink:

Food:

Drink:

Food:

Drink:

Food:

Drink:

2. Log on to www.peapod.com and enter in the zip code of the town you are living in.

3. You and your partner must go food shopping together so make sure you are creating your shopping cart together.

4. ADD ALL items you want to purchase into the shopping cart.

5. When you are done shopping PRINT out your shopping cart. THIS WILL BE GRADED!!

6. Please fill in the chart below:

Number of Items Purchased

Subtotal

Tax

Fees (if necessary)

Total amount Spent

7. Add the total amount spent to your budget sheet. Don’t forget if you live with someone SPILT the cost!!

Name: _______________________________________________ Date:

Students will choose a picture from those given. They will then create a scale drawing on a large piece of graph paper

Nassau County and Mepham High School are planning on creating a mew park for the citizens of Bellmore. It is your job to help them

The Bedford Ave. Park

design the park. The park should measure 25 ft by 30 ft.

Using a sheet of graph paper, you will create the layout for the park.Hint: (1 box = 1 inch = 1 foot)

Here are the 8 pieces that must be included in the park somewhere:

Sketch a playground in the shape of a rectangle.

o Length = 11 ft. & Height = 812 ft.

Sketch a jungle gym in the shape of a parallelogram.o Base = 10 ft. & Height = 7 ft.

Sketch a tennis court in the shape of a rectangle.o Length = 10 ft. & Width = 8 ft.

Sketch a pool in the shape of a circle.o Diameter = 6 ft.

Sketch a sand box in the shape of a trapezoid.o Base #1 = 7 ft. & Base #2 = 5 ft. & Height = 4 ft.

Sketch a snack hut in the shape of a triangle.o Base = 8 ft. & Height = 7 ft.

Sketch a bathroom in the shape of a square.o Side = 6 ft.

Since you should have space left over, add two more things you would like the playground to have. List the items and dimensions below.

Item #1: _________________________________________ Item #2: _________________________________________

After finishing your blueprints (graph paper), Nassau County needs us to submit the area for each part of the playground in order to help us

calculate the remaining space and cost to build everything.

1. Find the area of the bathroom. 2. Find the area of the Jungle Gym.

3. Find the area of the tennis court. 4. Find the area of the pool.

5. Find the area of the sand box. 6. Find the area of the snack hut.

7. Find the area of Item #1. 8. Find the area of Item #2.

Now we must calculate how much it will cost to fill certain areas of the park. The prices below are the cost of certain material at

Home Depot.

9. It costs $12.00 per square foot for rubber matting to protect the floor of the jungle gym. How much will the town have to spend in order to buy the mat?

10. It costs $21.50 per square foot for the sand to fill the sand box. How much will it cost the town to fill the sand box?

11. It costs $37.99 per square foot in order to pave the tennis courts. How much will it cost the town to pave the tennis courts?

12. It costs $15.25 per square foot to tile the bathroom. How much will it cost the town to tile the bathroom?

13. It costs $9.85 to line the pool. How much will it cost the town to line the pool?

14. It costs $34.00 a foot for fencing. How much will it cost the town to fence in the park? Hint: Find the perimeter of the entire park.

15. The town would also like to seed the areas of the park that have not been used. Find the area of the park that hasn’t been used (Hint: Subtract the 8 areas from the area of the entire park).

16. It costs $12.00 per square foot to seed the lawn (from #15). How much will the town spend to seed the lawn?

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