THE GAME MATH!!! NEXT OF NEXT JACK LEAVES FOR SCHOOL AT 7:00 A.M. AND WALKS AT 1 MILE PER HOUR. JAMIE LEAVES FOR SCHOOL AT 7:30 A.M. AND CAN WALK AT.

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Presentation transcript:

THE GAME MATH!!! NEXT OF

NEXT

JACK LEAVES FOR SCHOOL AT 7:00 A.M. AND WALKS AT 1 MILE PER HOUR. JAMIE LEAVES FOR SCHOOL AT 7:30 A.M. AND CAN WALK AT 2 MILES PER HOUR. WHERE WILL THEY MEET FOR LUNCH NEXT WEEK?

TEACHERS CARD: (These are placed strategically throughout the activity to provide both instruction and as a guideline of the activity that students are performing.) In order for students to successfully complete this game, students should possess the following: English as 1 st language speaker, reading at 6 th -8 th grade level. Definitions and examples placed where required and/or dictionaries may be used. Use the following math skills: Addition, Subtraction, Multiplication, Division (whole numbers and fractions) Monetary Calculations Rounding Numbers to “real” units Units of Measurement (English Only) Pre-algebra (reading formulas and substitution) Basic comprehension skills of Written, Audio and Visual Instructions at 7 th -9 th grade reading level. MATERIALS REQUIRED: Computer with Microsoft Office 2010 or higher WITH access to YouTube (embedded videos only) ( NOTE: INDIVIDUAL COMPUTERS ARE PREFERRED, BUT GAME MAY BE PLAYED IN GROUPS OF 2-4 STUDEN TS.) ( NOTE 2: STRONGLY ADVISE REMOVING LINKS TO YouTube & EMBEDDING VIDEO FILES LOCALLY. THIS WAS DONE TO FACILITATE UPLOADING TO WEBSITE.) Pencil Basic Scientific Calculator Worksheet (provided – see link) Headphones (audio and video in presentation) WORKSHEET

CHALLENGES OF THE GAME: READING SKILLS – The grammar has been verified by the Flesch-Kincaid reading level to be at or below the 6 th - 8 th grade level. However, due to the amount of information provided, this may be too much to comprehend. Video and audio have been provided to address, but may require assistance for ESL or students with poor comprehension skills. Audio & Video problems have been provided in written form. Examples provided for each that are SIMILAR to provide instruction. MOTIVATION: Unfo rtunately, math can be boring. I have tried to limit this by making problems valid to real-life so the student knows real-world application. Prizes for completion and/or highest score. Keeping students focused will require some involvement and/or instruction on the teacher’s part. INTERNET ACCESS: The videos used link to YouTube to reduce file size. It is STRONGLY suggested that the links to the movies be deactivated and moved so that no internet access is required. Otherwise, supervision of the students will be EXTREMELY important.

Given a standard tape measure (1/16” divisions), students will be able to identify the indicated measurements with 100% accuracy. Given dimensional measurements, students will compute Area and Volume of rectangular shapes to estimate materials with 100% accuracy. Given unequal units of measurement and conversion factors, students will calculate unit conversions with 100% accuracy. Given this simulation, students will operate this game to apply mathematical skills of addition, subtraction, multiplication, and division to compute answers for the tutorials and quiz with 100% completion. Given the lesson activities, students will compute answers for the tutorials and quiz with a score of 80% or higher. NEXT

USE THE FOLLOWING MATH SKILLS: Addition, Subtraction, Multiplication and Division Area Volume Money (We all use that, right?) NEXT TO SOLVE PROBLEMS WITH: Cars Craft/Construction Projects Home Repairs Bills (Do you want some of mine?)

1.READ THE RULES FIRST!!! 2.READ AND/OR LISTEN TO THE PROBLEM. 3.WRITE DOWN GIVEN INFORMATION ON WORKSHEET. 4.ASK “WHAT AM I TRYING TO FIND” ? 5.SOLVE THE PROBLEM. MAKE SURE TO SHOW ALL WORK!!! 6.MARK ANSWER ON WORKSHEET, THEN CHOOSE ON SCREEN. NO CHEATING!!! 7.COMPLETE THE 10 PROBLEMS, THEN TAKE QUIZ. MARK ANSWERS ON WORKSHEET. 8.TURN IN YOUR WORKSHEET. 9.SIT QUIETLY AND READ UNTIL EVERYONE IS FINISHED. NEXT RULES

Work at your own pace. Do your best. I want you to understand how you did the problem more than the answer. Show all work on worksheet. Pencils have erasers, so don’t be afraid to make a mistake. No CHEATING on any part of the activity!!! Ask for help if you need help. That’s why I’m here…to help you learn. HOW TO PLAY

ACCEPT THE CHALLENGE DECLINE THE CHALLENGE

YOU ARE BRAVE. TAKE A MOMENT TO RELAX. CLICK NEXT WHEN YOU ARE READY TO BEGIN. HAVE FUN GOOD LUCK ! NEXT

QUIZ GO BACK TO LESSON YOU THINK THAT YOU ALREADY KNOW WHAT TO DO? IF SO, TRY TO TAKE THE QUIZ. IF NOT, GO BACK! GOOD LUCK! YOU WILL NEED IT!

The home screen encompasses the four major activities of this activity. A brief explanation of each are covered below. Cars, Cars, Cars: (Algebra/Pre-Algebra, Thought) Computing fuel economy using MPG = DISTANCE (MILES) / FUEL USED (GAL) Interpret costs over a 1 year period of time Can they afford to drive? Around the House: (Surface Area, Volume, Money, Percentages) Area for Paint from A = L * W. Compute Quantity required Volume for Mulch from V = L*W*H. Compute Quantity required/cost Calculate Sales Tax from % given. Round accordingly for total cost. Build it Right: (Reading a tape measure, Area, Fractions, Money) Reading Length from a Tape Measure Area of Material from A = L*W Bills – (Money, Percentages, Critical Thought) Exposure to open ended problem with money, percentages) Examples provided are similar, but not the same and yes, I do trick them, so be warned!

QUIZ (5) CARS, CARS (1) AROUND THE HOUSE (2) BUILD IT RIGHT (4) BILLS (3)

NEXT 1975 Plymouth Gran Fury Station Wagon I MUST BE THE GREATEST TEACHER OF ALL TIME BECAUSE I’M GIVING YOU MY OLD CAR, BUT CAN YOU AFFORD IT???

In this exercise, students will compute miles per gallon, cost to operate the car per week, then operating costs per year. They will be given the opportunity to consider efficiency and determine in a real world situation, their ability to drive. FORMULA’S PROVIDED MPG = DISTANCE DRIVEN / GALLONS OF FUEL CONSUMED OPERATING COST (WK.) = SUM OF WEEKLY EXPENSES OPERATING COST (YR.) = WEEKLY EXPENSES * 52 + FIXED EXPENSES CONCEPTS: UNITS OF MEASUREMENT, BASIC MATH, SIGNIFICANT FIGURES

PLEASE WATCH THE FOLLOWING BEFORE CONTINUING: NEXT

I HAVE JUST GIVEN YOU TOO MUCH INFORMATION, SO LET’S MAKE A LIST OF WHAT WE HAVE SO WE CAN START, OKAY? CAR: 1975 PLYMOUTH STATION WAGON ENGINE: 440 V8 – 4 BARREL CARBURETOR, AUTOMATIC TRANSMISSION WEIGHT = 5,000 POUNDS (ESTIMATED) FUEL TANK HOLDS 26.5 GALLONS (HERE’S WHERE VOLUME OF A CUBE CAN BE USED) RATED FUEL ECONOMY (1975) : 10 CITY / 16 HIGHWAY GAS = $3.50 per gallon HERE’S MORE THAT YOU DID NOT GET: DRIVE 210 MILES PER WEEK IN BOTH CITY AND HIGHWAY EQUALLY. MAKE $8.00 PER HOUR AFTER TAXES AND WORK 20 HOURS PER WEEK YOU HAVE NO EXPENSES IF YOUR GRADES ARE ABOVE A “B”. OTHERWISE, $40.00 PER WEEK FOR INSURANCE.

NEXT FIND: 1.HOW MANY MILES PER GALLON DO YOU GET PER WEEK? 2.HOW MUCH DOES IT COST TO DRIVE PER WEEK? 3.CAN YOU AFFORD TO DRIVE THIS CAR FOR A YEAR?

NEXT GIVEN: You drive 250 miles per week. You use 14 gallons of gas per week It usually costs $35.00 each time per fill-up Gas Costs $4 per gallon. Car is rated to get 22 mpg city and 36 mpg highway. You work 15 hours per week and make, after taxes, $ per week. FIND: a.) Miles Per Gallon per week b.) Cost of Driving Per Week c.) Can you afford to drive this car? SOLUTION: A.) MILES PER GALLON (MPG) = (TOTAL MILES DRIVEN) / (TOTAL FUEL USED) MPG = 250 MILES / 14 GALLONS MPG = (ROUND TO 1 DECIMAL PLACE) MPG = 17.9 MPG

NEXT b.) COST PER WEEK (CPW) = COST OF GAS + COST OF EXPENSES COST PER WEEK = $35.00 per week + 0 (no expenses given) COST PER WEEK = $35.00 PER WEEK c.) COST PER YEAR = COST PER WEEK * 52 INCOME = WEEKLY INCOME * 52 INCOME = $ * 52 INCOME = $9,100 COST PER YEAR = $35.00 PER WEEK * 52 COST PER YEAR = $ (WITHOUT EXTRA EXPENSES) IS THE COST TO DRIVE LESS THAN OR EQUAL TO INCOME? (YES = YES, NO = NO) YES, YOU CAN DRIVE FOR A YEAR

NEXT

1.THE 1975 PLYMOUTH GRAN FURY STATION WAGON, THE CAR GETS APPROXIMATELY _______________ MILES PER GALLON. A. 10 MILES PER GALLON B. 16 MILES PER GALLON C. 13 MILES PER GALLON D. 15 MILES PER GALLON

NEXT YOU HAVE CORRECTLY ANSWERED THE PROBLEM. YOU HAVE EARNED YOUR 1 st POINT, SO PLEASE RECORD IT ON YOUR ASSIGNMENT SHEET. KEEP UP THE GREAT WORK AND CONTINUE PLAYING!

I AM SORRY, BUT YOU HAVE ANSWERED THE QUESTION INCORRECTLY. HERE ARE THINGS TO CHECK: MATH MISTAKES RE-READ THE PROBLEM. DID YOU OVERLOOK SOMETHING? AVERAGE = (SUM OF ALL NUMBERS) / NUMBER OF POINTS DON’T GIVE UP….YOU WILL BE DRIVING BEFORE YOU KNOW IT ! QUIZ REVIEW

NEXT GIVEN: You drive 250 miles per week. You use 14 gallons of gas per week It usually costs $35.00 each time per fill-up Gas Costs $4 per gallon. Car is rated to get 22 mpg city and 36 mpg highway. You work 15 hours per week and make, after taxes, $ per week. FIND: a.) Miles Per Gallon per week b.) Cost of Driving Per Week c.) Can you afford to drive this car? SOLUTION: A.) MILES PER GALLON (MPG) = (TOTAL MILES DRIVEN) / (TOTAL FUEL USED) MPG = 250 MILES / 14 GALLONS MPG = (ROUND TO 1 DECIMAL PLACE) MPG = 17.9 MPG

QUIZ b.) COST PER WEEK (CPW) = COST OF GAS + COST OF EXPENSES COST PER WEEK = $35.00 per week + 0 (no expenses given) COST PER WEEK = $35.00 PER WEEK c.) COST PER YEAR = COST PER WEEK * 52 INCOME = WEEKLY INCOME * 52 INCOME = $ * 52 INCOME = $9,100 COST PER YEAR = $35.00 PER WEEK * 52 COST PER YEAR = $ (WITHOUT EXTRA EXPENSES) IS THE COST TO DRIVE LESS THAN OR EQUAL TO INCOME? (YES = YES, NO = NO) YES, YOU CAN DRIVE FOR A YEAR

2.YOU HAVE THE ESTIMATED FUEL MILEAGE IN PROBLEM 1 AND PAY $40.00 PER WEEK FOR INSURANCE AFTER YOUR GRADES FELL. HOW MUCH DOES IT COST YOU TO DRIVE PER WEEK? A.$ PER WEEK$ PER WEEK B.$ PER WEEK$ PER WEEK C.$ PER WEEK$ PER WEEK D.$92.75 PER WEEK$92.75 PER WEEK

NEXT YOU HAVE CORRECTLY ANSWERED THE PROBLEM. YOU HAVE EARNED YOUR 2 nd POINT, SO PLEASE RECORD IT ON YOUR ASSIGNMENT SHEET. KEEP UP THE GREAT WORK AND CONTINUE PLAYING!

QUIZ REVIEW I AM SORRY, BUT YOU HAVE ANSWERED THE QUESTION INCORRECTLY. HERE ARE THINGS TO CHECK: MATH MISTAKES RE-READ THE PROBLEM. DID YOU OVERLOOK SOMETHING? DID YOU FORGET TO ADD EXPENSES? DON’T GIVE UP….YOU WILL BE DRIVING BEFORE YOU KNOW IT !

3.WHAT DO YOU THINK? CAN YOU AFFORD TO DRIVE THE CAR YOU HAVE BEEN GIVEN? A.YESYES B.MAYBEMAYBE C. NONO

NEXT YOU HAVE CORRECTLY ANSWERED THE PROBLEM. YOU HAVE EARNED YOUR 3 RD POINT, SO PLEASE RECORD IT ON YOUR ASSIGNMENT SHEET. PLEASE CONTINUE WHEN READY.

NEXT LET’S REVIEW WHAT WE HAVE DONE AND WHAT WE LEARNED:  AVERAGE = SUM OF ALL NUMBERS / NUMBER OF SAMPLES  MPG = DISTANCE (MILES) / FUEL USED (GALLONS)  COST PER WEEK = GAS COST + FIXED EXPENSES WHY WERE THERE NO WRONG ANSWERS FOR THE 3 RD QUESTION?:  Fuel mileage varies based on:  Weight (heavy cars use more)  Engine Size (Large engines use more)  How you drive  Government standards don’t tell everything. They do not know how you drive.  Fuel Economy is an AVERAGE and not always repeatable.

In this exercise, students will deal with computing materials, costs, and determining if they have enough money to complete the project. They will use the following concepts through this problem: APPLIED CONCEPTS:  Surface Area (A = L * W)  Volume (V = L * W * H)  Unit Conversion (in = ft)  Critical Thinking regarding money and expenses POSSIBLE ADAPTATION: If the student demographic includes mostly apartment dwelling students, hide slides with landscaping materials and/or change them to a painting project, which would utilize surface area, and use flower pots to compute volume.

PROBLEM: YOU AND YOUR FRIENDS ARE FIXING UP A NEIGHBORS HOUSE AFTER A FAMILY MEMBER DIED. A HARDWARE STORE IS PROVIDING DISCOUNTED MATERIALS AND THE SCHOOL IS DONATING MONEY. YOU AND YOUR FRIENDS ARE PROVIDING LABOR. THIS IS WHAT YOU WANT TO DO:  PAINT THE FRONT DOOR AND SHUTTERS  MULCHING FLOWER BEDS  INSTALL NEW MAILBOX, NUMBERS, AND FLAG  CLEAN AND WASH WINDOWS ASSUMPTIONS:  YOU DO NOT NEED TO BUY TOOLS.  YOU DO NOT NEED TO HIRE HELP. GIVEN: THE TABLE ON THE NEXT PAGE THAT YOUR CLASS HAS MADE NEXT

MATERIALCOST (INCLUDES DISCOUNT) Paint (1 gallon covers 300 square feet with no primer required) $42.00 PER GALLON Mulch (1 bag covers 0.5 cubic feet)$3.00 PER BAG Mailbox (includes all hardware)$45.00 Mailbox Post (cedar)$35.00 Mailbox Numbers$2.00/each Bag of Fast Drying Concrete$5.00/each Cleaning Supplies (Window Cleaner, Paper Towel, etc.) $30.00 State Sales Tax7% NEXT

FIND: a)HOW MANY CANS OF PAINT ARE REQUIRED TO PAINT THE FRONT DOOR AND SHUTTERS? (SEE TABLE ON NEXT SLIDE) b)HOW MANY BAGS OF MULCH ARE NEEDED FOR THE FLOWERBEDS TO HAVE A 2-INCH THICK LAYER? c)WILL THE $600 DONATION GIVEN BE ENOUGH FOR ALL THE PROJECTS?

NEXT PART & QUANTITY LENGTH (IN)WIDTH (IN)COLORPAINT CONDITION Front Door8036REDPOOR Large Shutters (6) 4818BLACKGOOD Small Shutters (4) 3612BLACKGOOD Storm Door8136REDFAIR LENGTH WIDTH

NEXT PART A: ESTIMATING PAINT FOR FRONT DOOR, SHUTTERS, AND STORM DOOR GIVEN: A door, in poor condition, measures 32 inches wide by 79 inches tall. A container of paint contains enough material to cover 150 square feet and assumes one coat coverage, which means one coat of paint will fully cover a door in good condition. FIND: How much paint is required? SOLUTION: Area = Length * Width Area = 32 inches * 79 inches Area = 2,528 square inches UNITS FOR DOOR & PAINT NOT THE SAME, SO CONVERT: 1 SQUARE FOOT = 144 SQUARE INCHES Area = 2, 528 square inches * 1 square foot(cross-multiply cancels units) square inches Area = square feet = 18 square feet (round to nearest whole number) 79” 32”

NEXT PART A: ESTIMATING PAINT FOR FRONT DOOR, SHUTTERS, AND STORM DOOR Area = 17.6 square feet = 18 square feet (round to nearest whole number) # COATS PER CAN = AMOUNT PER CAN / AREA OF OBJECT PAINTED # COATS PER CAN = 150 SQUARE FEET PER CAN / 18 SQUARE FEET # COATS PER CAN = 8 COATS IN THIS CASE, ONE CAN OF PAINT WILL COVER 8 COATS, WHICH SHOULD BE ENOUGH. ASSUME THE FOLLOWING FOR THIS PROBLEM: Good Condition: 1 Coat Fair Condition: 2 Coats Poor Condition: 4 Coats

4.HOW MANY GALLONS OF RED AND BLACK ARE REQUIRED TO PAINT BOTH DOORS AND THE SHUTTERS? A.1 gallon red / 1 gallon black1 gallon red / 1 gallon black B.½ gallon red / ½ gallon black½ gallon red / ½ gallon black C.¼ gallon red / ¼ gallon black¼ gallon red / ¼ gallon black D.2 gallons red / 1 gallon black2 gallons red / 1 gallon black LENGTH WIDTH

NEXT YOU HAVE AGAIN CORRECTLY ANSWERED THE PROBLEM. YOU WILL SOON BE COVERED IN PAINT FROM HEAD TO TOE BEFORE YOU KNOW IT. YOU HAVE EARNED YOUR 4 TH POINT, SO PLEASE RECORD IT ON YOUR WORKSHEET. KEEP UP THE GREAT WORK AND CONTINUE PLAYING!

QUIZ YOU HAVE CORRECTLY ESTIMATED THE PROBLEM, BUT UNFORTUNATELY, PAINT IS NOT SOLD IN HALF GALLON CONTAINERS. IT TYPICALLY IS SOLD IN QUARTS, WHICH IS ¼ OF A GALLON, 1 GALLON AND 5 GALLON CONTAINERS. ROUND YOUR ANSWER ACCORDINGLY AND TRY AGAIN.

QUIZ REVIEW I AM SORRY, BUT YOU HAVE ANSWERED THE QUESTION INCORRECTLY. HERE ARE THINGS TO CHECK: MATH MISTAKES DID YOU FORGET THE UNIT CONVERSION? DID YOU ROUND WRONG? EITHER REVIEW OR TRY AGAIN.

NEXT YOU ARE TIRED NOW AND COVERED WITH PAINT, BUT IT FEELS GOOD TO HELP OTHERS, DOES IT NOT? TIME TO MEASURE FOR MULCH! PLEASE WATCH THIS SHORT VIDEO ON READING A TAPE MEASURE BEFORE CONTINUING. BE SURE YOU KNOW HOW BECAUSE YOU MIGHT NEED IT AGAIN!!!

NEXT HERE ARE YOUR MEASUREMENTS: FLOWER BEDLENGTH (INCHES)WIDTH (INCHES) Bed 191 5/822 ¼ Bed /822 ¼ Bed /1616 3/16 WE ALSO KNOW:  Mulch is 2” deep  1 Bag covers 0.5 cubic feet and costs $3.00 per bag  1 FOOT = 12 INCHES, 3 FEET = 1 YARD, 1 CUBIC FOOT = 1,728 CUBIC INCHES WIDTH LENGTH

In this portion of the exercise, student’s are exposed to the following: APPLIED CONCEPTS:  Volume = L * W * H  Unit Conversion  1 cubic foot = 1,278 cubic inches APPLICATION: Students will use the relationship of V = LWH, be required to convert to standard units (cubic feet), and estimate costs of the material. They will work with fractions and round their answer accordingly.

NEXT GIVEN: YOU HAVE MEASURED A RECTANGULAR FLOWER BED AND DETERMINED THAT IT IS 88 3/8 INCHES LONG AND 21 INCHES WIDE. YOU WANT TO MULCH THE BED AT 1 INCH THICK. THE MULCH YOU PLAN TO USE COSTS $4.75 PER BAG AND COVERS 0.25 CUBIC FEET PER BAG. FIND: HOW MANY BAGS YOU NEED AND HOW MUCH THEY WILL COST SOLUTION: LENGTH = 88 3/8” WIDTH = 21 INCHES HEIGHT = 1 INCH VOLUME = L * W * H VOLUME = (88 3/8 IN) * (21 IN) * (1 IN) VOLUME = /8 CUBIC INCHES (NEED UNIT CONVERSION) VOLUME = CUBIC INCHES * 1 CUBIC FOOT 11, 728 CUBIC INCHES (CROSS MULTIPLY) VOLUME = 1.1 CUBIC FEET “NEXT SLIDE” 1” 88 3/8” 21”

NEXT Volume = 1.1 cubic feet Number of Bags Required = Volume Needed / Volume Per Bag Number of Bags Required = 1.1 cubic feet / 0.25 cubic feet per bag Number of Bags Required = 4.3 bags Number of Bags Required = 5 bags Cost of Mulch = Number of Bags * Cost Per Bag Cost of Mulch = 5 Bags * $4.75 per bag Cost of Mulch = $23.75 ANSWER: 5 BAGS REQUIRED COSTING $23.75

5.HOW MANY BAGS OF MULCH ARE NEEDED? HOW MUCH WILL THEY COST BEFORE TAXES? A.8 BAGS; $ BAGS; $24.00 B.16 BAGS; $ BAGS; $56.00 C.14 BAGS; $ BAGS; $42.00 D.4 BAGS; $ BAGS; $12.00

NEXT YOU HAVE AGAIN CORRECTLY ANSWERED THE PROBLEM. YOU AND YOUR FRIENDS ARE MAKING THE HOUSE LOOK GREAT! YOU HAVE EARNED YOUR 5 TH POINT, SO PLEASE RECORD IT ON YOUR WORKSHEET. KEEP UP THE GREAT WORK AND CONTINUE PLAYING!

QUIZ REVIEW I AM SORRY, BUT YOU HAVE ANSWERED THE QUESTION INCORRECTLY. HERE ARE THINGS TO CHECK: MATH MISTAKES DID YOU FORGET THE UNIT CONVERSION? DID YOU FORGET THE MULCH IS 2” THICK? DID YOU USE THE FORMULA FOR AREA INSTEAD OF VOLUME? EITHER REVIEW OR TRY AGAIN.

MATERIALCOST (INCLUDES DISCOUNT) Paint (1 gallon covers 300 square feet with no primer required) $42.00 PER GALLON Mulch (1 bag covers 0.5 cubic feet)$3.00 PER BAG Mailbox (includes all hardware)$45.00 Mailbox Post (cedar)$35.00 Mailbox Numbers$2.00/each Bag of Fast Drying Concrete$5.00/each Cleaning Supplies (Window Cleaner, Paper Towel, etc.) $30.00 State Sales Tax7% NEXT

6.WAS $ ENOUGH TO FINISH THE PROJECT WITH THE COSTS FROM PARTS A & B? A.YES, I HAD $ LEFT OVERYES, I HAD $ LEFT OVER B.NO, I WAS $42.91 SHORTNO, I WAS $42.91 SHORT C.NO, I WAS $0.93 SHORTNO, I WAS $0.93 SHORT D.MAYBE, BUT I’M NOT GOOD AT MATHMAYBE, BUT I’M NOT GOOD AT MATH TABLE

NEXT YOU HAVE AGAIN CORRECTLY ANSWERED THE PROBLEM. YOU AND YOUR FRIENDS SHOULD TRY TO DO MORE OR GIVE YOUR NEIGHBOR WHAT IS LEFT OVER. YOU HAVE EARNED YOUR 6 TH POINT, SO PLEASE RECORD IT ON YOUR WORKSHEET. KEEP UP THE GREAT WORK AND CONTINUE PLAYING!

NEXT Volume = 1.1 cubic feet Number of Bags Required = Volume Needed / Volume Per Bag Number of Bags Required = 1.1 cubic feet / 0.25 cubic feet per bag Number of Bags Required = 4.3 bags Number of Bags Required = 5 bags Cost of Mulch = Number of Bags * Cost Per Bag Cost of Mulch = 5 Bags * $4.75 per bag Cost of Mulch = $23.75 ANSWER: 5 BAGS REQUIRED COSTING $23.75

QUIZ MAYBE IS NOT AN ANSWER FOR THIS PROBLEM. YOU HAVE BEEN GIVEN ALL THE INFORMATION THAT YOU NEED TO SOLVE IT. PLEASE REVIEW YOUR WORK AND TRY AGAIN. NICE TRY, BUT I KNEW YOU WOULD GUESS. REVIEW

QUIZ REVIEW I AM SORRY, BUT YOU HAVE ANSWERED THE QUESTION INCORRECTLY. HERE ARE THINGS TO CHECK: MATH MISTAKES DID YOU FORGET SALES TAX? (Sales Tax = Cost * Tax Rate) DID YOU ROUND AT THE END OR AFTER EACH PROBLEM? EITHER REVIEW OR TRY AGAIN.

NEXT LET’S REVIEW WHAT WE HAVE DONE AND WHAT WE LEARNED:  AREA = LENGTH * WIDTH  VOLUME = LENGTH * WIDTH * HEIGHT  SALES TAX = $ BEFORE TAX + ($ BEFORE TAX * TAX RATE) WHAT WAS SPECIAL ABOUT THIS PROBLEM:  UNITS OF MEASUREMENT MUST BE EQUAL BEFORE CALCULATING.  UNITS OF MEASUREMENT DESCRIBE WHAT YOU WANT OR ARE DOING.  ROUND THE PROBLEM AT THE END TO PREVENT ERRORS.  ROUND THE ANSWER BASED ON HOW PRODUCTS ARE SOLD. LENGTH WIDTH LENGTH WIDTH HEIGHT

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In this section, students will be exposed to the harsh realities of life on a budget. The example given here will be a very idealized version, as the expenses are fixed and little interpretation is possible. If more extensive study of this area is warranted or student’s comprehension level warrants it, simulations such as Spent will expose students to these realities in a more interactive and adaptable way. APPLIED CONCEPTS:  Monetary Computation  Critical Thinking PLAY SPENT

NEXT PROBLEM: YOU HAVE JUST GRADUATED FROM SCHOOL EARLY, THANKS IN PART TO YOUR EXCELLENT SCHOOLWORK. YOU ARE GOING COLLEGE AND HAVE EARNED A SCHOLARSHIP THAT PAYS TUITION, BUT YOU HAVE TO WORK TO PAY FOR OTHER EXPENSES. PLEASE LISTEN TO THE PROBLEM BEFORE CONTINUING.

This is the problem again, in written form: GIVEN: YOUR FIRST JOB PAYS $14 PER HOUR. YOU WORK 40 HOURS PER WEEK AND PAID WEEKLY. HEALTH INSURANCE COSTS $104 PER WEEK BEFORE TAXES. YOU PAY 24% IN TAXES. THE REST OF YOUR EXPENSES ARE IN THE TABLE BELOW. NEXT EXPENSES:COST PER TIME PERIOD Rent$ PER MONTH UTILITIES (GAS, ELECTRICITY, CABLE, WATER & SEWER, WASTE DISPOSAL) $ PER MONTH PHONE$75.00 PER MONTH GROCERIES$50.00 PER WEEK GAS, INSURANCE, CAR MAINTENANCE$ PER MONTH ENTERTAINMENT (Movies, Dates, Eating Out, etc.) $ PER MONTH

ASSUMPTIONS:  EXPENSES ARE ALL THAT YOU WILL HAVE. THERE WILL BE NO EMERGENCIES (NOTE: THIS NORMALLY DOES NOT HAPPEN).  YOU HAVE NO OTHER SOURCE OF MONEY  YOU CANNOT BORROW MONEY. FIND: CAN YOU LIVE FOR ONE MONTH ON WHAT YOU HAVE AND PAY FOR ALL OF YOUR EXPENSES? NEXT EXPENSESCOST PER TIME UNIT EMERGENCY FUND$ PER MONTH MISCELLANEOUS$50.00 PER MONTH

NEXT GIVEN: YOU MAKE $10 PER HOUR AND WORK 40 HOURS PER WEEK. INSURANCE IS $50 PER WEEK BEFORE TAXES, WHICH ARE 24%. RENT, INCLUDING UTILITIES COSTS $750 PER MONTH. GROCERIES USUALLY COST $80 PER WEEK. FIND: DO YOU MAKE ENOUGH TO LIVE FOR A MONTH? SOLUTION: STEP 1: FIND INCOME INCOME = PAY RATE ($) * HOURS WORKED INCOME = $10.00 * 40 HOURS HOURWEEK INCOME = $ PER WEEK STEP 2: CALCULATE TAXES AND INSURANCE TAXED INCOME ($) = (INCOME PER WEEK - INSURANCE) * (1 - TAX RATE) TAXED INCOME ($) = ($ $50.00) * (1 – 0.24) TAXED INCOME ($) = ($350.00) * (0.76) TAXED INCOME ($) = $ PER WEEK

NEXT STEP 3: CALCULATE TOTAL INCOME TOTAL INCOME ($) = INCOME PER WEEK ($) * 4 (# OF WEEKS IN A MONTH) TOTAL INCOME ($) = $ PER WEEK * 4 WEEKS PER MONTH TOTAL INCOME ($) = $1, PER MONTH STEP 4: CALCULATE TOTAL BILLS TOTAL BILLS ($) = SUM OF ALL BILLS ($) TOTAL BILLS ($) = $ (RENT) + ($80.00 PER WEEK * 4 WEEKS PER MONTH) (GROCERIES) TOTAL BILLS ($) = $1, PER MONTH STEP 5: DID YOU HAVE ENOUGH MONEY? $ LEFTOVER = TOTAL INCOME ($) – TOTAL BILLS ($) $ LEFTOVER = $1, $1, $ LEFTOVER = -$6.00 ANSWER: NO, I WAS $6.00 SHORT OF MY MONTHLY EXPENSES.

7.DID YOU HAVE ENOUGH MONEY TO SURVIVE FOR A MONTH? HOW MUCH DID YOU HAVE LEFT OVER OR WERE SHORT? A.YES, I SURVIVED FOR A MONTH AND HAD $ LEFT OVER.YES, I SURVIVED FOR A MONTH AND HAD $ LEFT OVER. B.NO, I DID NOT HAVE ENOUGH AND WAS $63.76 SHORT.NO, I DID NOT HAVE ENOUGH AND WAS $63.76 SHORT. C.NO, I DID NOT HAVE ENOUGH AND WAS $ SHORT.NO, I DID NOT HAVE ENOUGH AND WAS $ SHORT. D.YES, I SURVIVED FOR A MONTH AND HAD $86.24 LEFT OVER.YES, I SURVIVED FOR A MONTH AND HAD $86.24 LEFT OVER.

NEXT YOU HAVE AGAIN CORRECTLY ANSWERED THE PROBLEM. IT IS HARD TO LIVE ON A BUDGET, IS IT NOT? YOU HAVE EARNED YOUR 7 TH POINT, SO PLEASE RECORD IT ON YOUR WORKSHEET. KEEP UP THE GREAT WORK AND CONTINUE PLAYING!

QUIZ REVIEW I AM SORRY, BUT YOU HAVE ANSWERED THE QUESTION INCORRECTLY. HERE ARE THINGS TO CHECK: MATH MISTAKES DID YOU FORGET INCOME TAX? (INCOME TAX = PAY RATE PER WEEK * (1 – TAX RATE)) DID YOU TAKE OUT INSURANCE AFTER TAXES? DID YOU ROUND AT THE END OR AFTER EACH PROBLEM? EITHER REVIEW OR TRY AGAIN.

NEXT LET’S REVIEW WHAT WE HAVE DONE AND WHAT WE LEARNED:  INCOME = WAGE ($) * HOURS WORKED  TAXABLE WAGE = (INCOME – PRETAX EXPENSES) * (1 – TAX RATE % ) WHAT WAS SPECIAL ABOUT THIS PROBLEM:  YOU SAW HOW EASY IT IS TO OVERSPEND ON A MONTHLY BASIS, EVEN WHEN YOU THINK YOU MAKE ENOUGH MONEY.  AS AN ADULT, YOU PRIORITIZE YOUR EXPENSES AND CHOOSE WHAT YOU CAN AFFORD. I DID NOT LET YOU CHOOSE.

In the final exercise, students will be given a list of materials for a simple outdoor tool shed that they are planning to build for a raffle at school. They will be given a cut list of some of the materials, and then read some of the others from a tape measure. They will estimate the cost and determine if they can build one for less money than a company has offered to supply one for the raffle. The exercise encompasses each of the skills to which they have been exposed, as well as reinforces their critical thinking skills. They will not fully build the shed, but will complete a portion of the work. No blueprints are involved due to the comprehension required to read them, as well as the teaching standard does not exist to support this need. APPLIED CONCEPTS:  Measurements from tape (fractional – 1/16” increments)  Area = Length * Width  Unit Conversions (12 inches per foot)  Monetary computation  Reinforces skills from each of the past 3 exercises.

NEXT PROBLEM: TO RAISE MONEY FOR THE SCHOOL, YOUR ENGINEERING CLUB IS BUILDING A SHED FOR A RAFFLE. THE TEACHER HAS DRAWN A SIMPLE PLAN SO YOU CAN SEE HOW IT WILL LOOK.

NEXT GIVEN: THE SHED IS 10 FEET LONG, 8 FEET WIDE AND 96 INCHES TALL. THE DOOR MEASURES 4 FEET WIDE AND 72 INCHES TALL. THE MATERIALS YOU NEED ARE IN THE TABLE BELOW. MATERIALDESCRIPTIONCOST ($) 2 X 4 X 8’ STUDUsed to build wall frame$3.00/ea. 2 X 6 X 10’ #1&2Used to build floor and roof frame $4.50/ea. 4 X 4 X 10’ PTUsed for floor to ground support $18.00/ea. Roofing MaterialsShingles, Nails, Supplies$4.50/ square foot 5/8” X 4’ X 8’ SHEATHINGUsed for floor and roof$22.00/sheet SidingUsed to cover walls$15.00/sheet HardwareNails, Door, etc.$ ” 8’ 10’ SHED DIMENSIONS 4’ 72” DOOR DIMENSIONS

NEXT ASSUMPTIONS: NONE REQUIRED FIND: A.THE LENGTH OF THE WALL STUD FROM A GIVEN MEASUREMENT FROM A PICTURE. B.HOW MANY UNITS OF ROOFING MATERIALS ARE REQUIRED? C.WHAT IS THE COST FOR SHED? IS CHEAPER TO BUILD IT OR PURCHASE ONE FROM A DONOR? REVIEW THE SHORT VIDEO ON READING A TAPE MEASURE IF NEEDED:

NEXT GIVEN: YOU HAVE DECIDED TO BUILD SIMPLE SHELVES TO PUT INTO YOUR SHED. YOU WANT THE SHELVES TO BE 8 FEET WIDE. YOU BUILD A RECTANGULAR FRAME FROM 2 X 4’S AND COVER THE SHELVES WITH ½” THICK PLYWOOD, WHICH YOU HAVE TO MEASURE. FIND: A.DETERMINE DEPTH OF SHELF SUPPORT. B.DETERMINE HOW MUCH PLYWOOD YOU NEED IF YOU BUILD 5 SHELVES. C.IF 2 X 4’S ARE $2/EACH, PLYWOOD IS $10/SHEET (4’ X 8’), AND OTHER EXPENSES ARE $10, APPROXIMATELY HOW MUCH WILL THIS COST? SOLUTION: A.GIVEN MEASUREMENT: 4” 8’ x”

NEXT SOLUTION: A.READING (BLACK TO TIP OF ARROW): 20 INCHES + 5 MARKS (EACH IS 1/16”) 20 INCHES + 5 * 1/16” LENGTH = 20 5/16 INCHES B.AREA = LENGTH * WIDTH AREA = 8 FEET * ( 20 5/16 INCHES * (1 FOOT/12 INCHES) (NOTE UNIT CONVERSION) AREA = 8 FEET * 1.7 FEET AREA = SQ. FEET TOTAL AREA = AREA * NUMBER OF SHELVES TOTAL AREA = SQ. FEET * 5 SHELVES TOTAL AREA = SQ. FEET TOTAL AREA = 68 SQ. FEET 20 5/16” 8’

NEXT SOLUTION: B. TOTAL AREA = 68 SQ. FEET TOTAL MATERIAL REQUIRED = TOTAL AREA / AREA PER PIECE TOTAL MATERIAL REQUIRED = 68 SQUARE FEET / 32 SQUARE FEET (NOTE 4*8) TOTAL MATERIAL REQUIRED = 2.12 SHEETS (NO PARTIALS) TOTAL MATERIAL REQUIRED = 3 SHEETS OF PLYWOOD C.YOU DETERMINED THAT YOU NEED 13 PIECES OF 2 X 4. COST = (COST 2 X 4 * #) + (COST PLYWOOD * #) + (EXPENSES) COST = ($2.00 * 13) + ($10.00 * 3) + $10.00 COST = $ $ $10.00 COST = $66.00 PLUS TAX

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8.USING THE PICTURE GIVEN, WHAT IS THE LENGTH OF THE WALL FRAMING? A.93 5/8 INCHES93 5/8 INCHES B.92 10/16 INCHES92 10/16 INCHES C.92 5/8 INCHES92 5/8 INCHES D.92 ½ INCHES92 ½ INCHES

NEXT YOU HAVE AGAIN CORRECTLY ANSWERED THE PROBLEM. YOU DID A GREAT JOB READING THE TAPE MEASURE AND REMEMBERED TO SIMPLIFY THE FRACTION. YOU HAVE EARNED YOUR 8 TH POINT, SO PLEASE RECORD IT ON YOUR WORKSHEET. KEEP UP THE GREAT WORK AND CONTINUE PLAYING!

NEXT YOU ARE CORRECT THAT THE TAPE MEASURE SHOWS 92 10/16 INCHES. HOWEVER, FRACTIONS ARE ALWAYS SHOWN IN SIMPLEST FORM: 10 / / 2=8 I WILL AWARD YOU AN A FOR EFFORT AND ½ OF A POINT. PLEASE RECORD ON YOUR WORKSHEET AND CONTINUE WITH THE PROBLEM.

QUIZ REVIEW I AM SORRY, BUT YOU HAVE ANSWERED THE QUESTION INCORRECTLY. HERE ARE THINGS TO CHECK: DID YOU MISREAD THE TAPE MEASURE? REMEMBER: 2 WAYS TO READ THE TAPE MEASURE 1.) COUNT EACH TICK MARK AS 1/16, THEN SIMPLIFY. 2.) READ FROM LEFT TO RIGHT : 0, 1/16, 1/8, 3/16, ¼, 5/16, 3/8, 7/16, ½, 9/16, 5/8, 11/16, ¾, 13/16, 7/8, 15/16 3.) THE NUMBER IN FRONT OF THE FRACTION IS THE FIRST NUMBER EITHER REVIEW OR TRY AGAIN.

NEXT SOLUTION: A.READING (BLACK TO TIP OF ARROW): 20 INCHES + 5 MARKS (EACH IS 1/16”) 20 INCHES + 5 * 1/16” LENGTH = 20 5/16 INCHES B.AREA = LENGTH * WIDTH AREA = 8 FEET * ( 20 5/16 INCHES * (1 FOOT/12 INCHES) (NOTE UNIT CONVERSION) AREA = 8 FEET * 1.7 FEET AREA = SQ. FEET TOTAL AREA = AREA * NUMBER OF SHELVES TOTAL AREA = SQ. FEET * 5 SHELVES TOTAL AREA = SQ. FEET TOTAL AREA = 68 SQ. FEET 20 5/16” 8’

QUIZ SOLUTION: B. TOTAL AREA = 68 SQ. FEET TOTAL MATERIAL REQUIRED = TOTAL AREA / AREA PER PIECE TOTAL MATERIAL REQUIRED = 68 SQUARE FEET / 32 SQUARE FEET (NOTE 4*8) TOTAL MATERIAL REQUIRED = 2.12 SHEETS (NO PARTIALS) TOTAL MATERIAL REQUIRED = 3 SHEETS OF PLYWOOD C.YOU DETERMINED THAT YOU NEED 13 PIECES OF 2 X 4. COST = (COST 2 X 4 * #) + (COST PLYWOOD * #) + (EXPENSES) COST = ($2.00 * 13) + ($10.00 * 3) + $10.00 COST = $ $ $10.00 COST = $66.00 PLUS TAX

9.USING THE PLAN DRAWN, THE INSTRUCTOR TELLS YOU THAT THE ROOF MEASURES 11 FEET X 54 1/8 INCHES. FROM THE PROBLEM, YOU WERE GIVEN THAT A SQUARE FOOT OF ROOFING COSTS $4.50. HOW MANY SQUARE FEET OF ROOFING WILL BE REQUIRED? A.100 SQUARE FEET100 SQUARE FEET B.9 SQUARE FEET9 SQUARE FEET C.50 SQUARE FEET50 SQUARE FEET D.200 SQUARE FEET200 SQUARE FEET 54 1/8” 11’

NEXT YOU HAVE AGAIN CORRECTLY ANSWERED THE PROBLEM. YOU DID A GREAT JOB WITH AREA AND REMEMBERED TO CHECK THE UNITS BEFORE STARTING. YOU HAVE EARNED YOUR 9 TH POINT, SO PLEASE RECORD IT ON YOUR WORKSHEET. KEEP UP THE GREAT WORK AND CONTINUE PLAYING!

QUIZ REVIEW I AM SORRY, BUT YOU HAVE ANSWERED THE QUESTION INCORRECTLY. HERE ARE THINGS TO CHECK: DID YOU FORGET THERE ARE TWO SIDES OF ROOF? DID YOU FORGET THE UNIT CONVERSION? (12 INCHES = 1 FOOT ) DID YOU ROUND WRONG? EITHER REVIEW OR TRY AGAIN.

QUIZ SOLUTION: B. TOTAL AREA = 68 SQ. FEET TOTAL MATERIAL REQUIRED = TOTAL AREA / AREA PER PIECE TOTAL MATERIAL REQUIRED = 68 SQUARE FEET / 32 SQUARE FEET (NOTE 4*8) TOTAL MATERIAL REQUIRED = 2.12 SHEETS (NO PARTIALS) TOTAL MATERIAL REQUIRED = 3 SHEETS OF PLYWOOD C.YOU DETERMINED THAT YOU NEED 13 PIECES OF 2 X 4. COST = (COST 2 X 4 * #) + (COST PLYWOOD * #) + (EXPENSES) COST = ($2.00 * 13) + ($10.00 * 3) + $10.00 COST = $ $ $10.00 COST = $66.00 PLUS TAX

10. IS IT CHEAPER TO BUILD IT OR BUY ONE FOR $1,900? YOU HAVE THE COST OF ROOFING AND THOSE IN THE TABLE BELOW. A.BUILD IT. YOU SAVE $75.00BUILD IT. YOU SAVE $75.00 B.BUILD IT. YOU SAVE $525.00BUILD IT. YOU SAVE $ C.BUILD IT. YOU SAVE $750.00BUILD IT. YOU SAVE $ D.NO SAVINGS. BUY IT.NO SAVINGS. BUY IT. COMPONENTDESCRIPTIONCOST ($) FRAMING MATERIALS LUMBER, SHEATHING$ ROOFING MATERIALSSHINGLES & SHEATHINGFROM PROBLEM #9 SIDINGINCLUDES TRIM$ HARDWAREDOOR, NAILS, ETC.$300.00

NEXT YOU HAVE AGAIN CORRECTLY ANSWERED THE PROBLEM. SINCE YOU CORRECTLY FIGURED THE ROOF AREA IN PROBLEM 9, THIS ONE WAS PRETTY EASY FOR AN EXPERT LIKE YOU ! YOU HAVE EARNED YOUR 10 TH POINT, SO PLEASE RECORD IT ON YOUR WORKSHEET. KEEP UP THE GREAT WORK AND CONTINUE PLAYING!

QUIZ REVIEW I AM SORRY, BUT YOU HAVE ANSWERED THE QUESTION INCORRECTLY. HERE ARE THINGS TO CHECK: CHECK YOUR ADDITION DID YOU USE THE WRONG ANSWER FROM PROBLEM 9? EITHER REVIEW OR TRY AGAIN.

NEXT LET’S REVIEW WHAT WE HAVE DONE AND WHAT WE LEARNED:  WE HAVE LEARNED HOW TO READ A TAPE MEASURE.  ALWAYS LEAVE FRACTIONS IN SIMPLEST FORM!  WE USED AREA = LENGTH * WIDTH TO COMPUTE MATERIALS FOR THE ROOF, AND ROUNDED ACCORDINGLY.  WE PERFORMED UNIT CONVERSIONS (12 INCHES = 1 FOOT)  WE HAVE WORKED WITH ESTIMATING MATERIAL COSTS. WHAT WAS SPECIAL ABOUT THIS PROBLEM:  IT’S USUALLY CHEAPER TO BUILD THAN TO BUY  YOU USED AND SIMPLIFIED FRACTIONS.  WE CONVERTED UNITS COMMONLY USED.

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I’M IN A GOOD MOOD, SO I WILL LET YOU GO BACK TO THE LESSON AND TAKE IT AGAIN. NOW, PLEASE GO TO WORK AND PROVE THAT YOU ARE THE EXCELLENT STUDENT THAT I KNOW YOU ARE! BACK TO LESSON

1.WHAT FORMULA DO YOU USE WHEN CALCULATING THE VOLUME OF A SQUARE OR RECTANGULAR-SHAPED OBJECT, SUCH AS A FLOWER BED? A.VOLUME = LENGTH * WIDTHVOLUME = LENGTH * WIDTH B.VOLUME = LENGTH * WIDTH * HEIGHT (ALL UNITS OF MEASUREMENT ARE EQUAL)VOLUME = LENGTH * WIDTH * HEIGHT (ALL UNITS OF MEASUREMENT ARE EQUAL) C.VOLUME = LENGTH * WIDTH * HEIGHT (UNITS OF MEASUREMENT DO NOT MATTER)VOLUME = LENGTH * WIDTH * HEIGHT (UNITS OF MEASUREMENT DO NOT MATTER) D.VOLUME = 2 * LENGTH + 2 * WIDTHVOLUME = 2 * LENGTH + 2 * WIDTH

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2.WHEN WE CALCULATED THE GAS MILEAGE OF THE CAR, WHAT DID MPG STAND FOR? A.MILES PER GALLONMILES PER GALLON B.MILES PER GASOLINEMILES PER GASOLINE C.MY POOR GRANDMAMY POOR GRANDMA D.MAY PURCHASE GASOLINEMAY PURCHASE GASOLINE

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3.HOW MANY INCHES ARE IN 1 FOOT? HOW MANY FEET ARE IN 1 YARD? A.6 INCHES PER FOOT. 1 ½ FEET PER YARD6 INCHES PER FOOT. 1 ½ FEET PER YARD B.UNITS DO NOT MATTER. THEY SAY THE SAME THING.UNITS DO NOT MATTER. THEY SAY THE SAME THING. C.12 INCHES PER FOOT. 3 FEET PER YARD.12 INCHES PER FOOT. 3 FEET PER YARD. D.16 INCHES PER FOOT. 2 ½ FEET PER YARD.16 INCHES PER FOOT. 2 ½ FEET PER YARD.

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4.WHY IS IT SO IMPORTANT TO INCLUDE UNITS OF MEASUREMENT? WHY MUST ALL UNITS BE THE SAME WHEN WORKING WITH THEM? A.UNITS TELL YOU WHAT YOU ARE DEALING WITH. THEY MUST BE THE SAME SO THAT YOU CAN WORK WITH THEM AS IF THEY WERE NUMBERS.UNITS TELL YOU WHAT YOU ARE DEALING WITH. THEY MUST BE THE SAME SO THAT YOU CAN WORK WITH THEM AS IF THEY WERE NUMBERS. B.I DON’T KNOW, BUT KNOW THAT THEY ARE IMPORTANT SO I DON’T GET PAID IN PENNIES.I DON’T KNOW, BUT KNOW THAT THEY ARE IMPORTANT SO I DON’T GET PAID IN PENNIES. C.UNITS ARE NOT IMPORTANT. DON’T WORRY ABOUT THEM.UNITS ARE NOT IMPORTANT. DON’T WORRY ABOUT THEM. D.UNITS ARE JUST THERE AT THE END. I CAN IGNORE THEM TILL THEN.UNITS ARE JUST THERE AT THE END. I CAN IGNORE THEM TILL THEN.

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5.WHEN YOU WORK, WHY IS IT SO EASY TO OVERSPEND? A.THERE IS NEVER ENOUGH MONEY.THERE IS NEVER ENOUGH MONEY. B.YOU CAN NEVER TELL HOW MUCH YOU WILL SPEND.YOU CAN NEVER TELL HOW MUCH YOU WILL SPEND. C.YOU ALWAYS THINK YOU MAKE ENOUGH.YOU ALWAYS THINK YOU MAKE ENOUGH. D.THE MORE YOU WORK, THE LESS YOU MAKE.THE MORE YOU WORK, THE LESS YOU MAKE.

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PLAY AGAINEND GAME