MAT0018C - Instructor

Lab Manual for MAT0018C Instructor’s Manual

Table of Contents Topic (Learning Outcomes) Type Page Decimals & Percent I (MDECL7, 8) Don’t let the decimal point get lost! Activity 1 Million Dollar Ransom Activity 2−3 How much shade can you get from a box? Activity 4 Decimal Review Review 5 Matching Triangles Game 6 Decimals & Percent II (MDECL17, 18) Credit Card Headaches Activity 7−9 Word Problems using Percentages Review 10 The Game of Life Game 11−13 Evaluating Expressions ( MDECL24, 25) Pan Balance - Evaluating Expressions Activity 14−15 Evaluating Expressions Review 16 Relay Race Game 17−18 Fractions (MDECL5, 6) Where is that last piece of pie? Activity 19−20 Fraction Puzzle Activity 21−22 Building a divider for my room! Activity 23−25 Fractions Review Review 26 Complex Fractions Review Review 27 Word problems using Fractions Review 28 Fractions To Go Game 29 Geometry (MDECL9, 19) Find the sum of the interior angles of a triangle Activity 30−31 Units of Measurement Activity 32 Geometry Review Review 33 Unit Conversion Review Review 33 Graphing Inequalities (MDECL26) Linear Inequalities Review 34−35 Inequalities Rummy/Matching Cards Game 36 Integers (MDECL4, 15, 16) Yes, I know that I owe you $13 Activity 37−38 Where can I get an EASY button? Activity 39−40 There’s magic in those squares! Activity 41 Integer Review Review 42 Absolute Value Review Review 43 Integer Operation Fever Game 44 Linear Equations (MDECL20, 21) The World Runs on Equations Activity 45−47 Words to Math and Math to Words Activity 48−49 Equation Review Review 50 Relay Race Game 51−52 Simplifying Expressions ( MDECL22, 23) Do you speak the language of Mathematics Activity 53−54 The cross-number polynomial puzzle Activity 55 Polynomials Review Review 56 JEOPARDY! Game 74 Whole Numbers I (MDECL1, 2, 14) Building a Practice Football Field Activity 57−61

The Sieve of Eratosthenes Activity 62 This Puzzle Won’t Cross Me Up Activity 63 Should I put on my shoes or socks first? Activity 64−65 Getting the numbers in the right square! Activity 66 Who is the Winner?! Activity 67−69 Word problems using whole numbers Review 70 The 24 Game Game 71 Whole Numbers II (MDECL3, 10, 11, 12, 13) Where’s the magic in a magic square? Activity 72 Evaluating Exponential Expressions Review 73 Review Materials JEOPARDY! Game 74−77 Clue Game 78−81 Final Exam Review Game Game 82−83

COMP ID MATHEMATICS CATEGORY MATHEMATICS COMPETENCIES ‐ LOWER

MDECL1 Whole Numbers Perform operations on whole numbers (with applications, including area and perimeter)

MDECL2 Whole Numbers Perform order of operations including absolute values

MDECL3 Whole Numbers Evaluate exponents with whole numbers

MDECL4 Integers Perform operations with integers (with applications)

MDECL5 Fractions Perform operations with fractions (with applications)

MDECL6 Fractions Simplify fractions

MDECL7 Decimals & Percent Perform operations with decimals (with applications)

MDECL8 Decimals & Percent Convert among percent, fractions, and decimals

MDECL9 Geometry Solve application problems involving geometry (circumference of circle, perimeter of polygons, area of a

triangle, parallelograms, circle)

MDECL10 Whole Numbers Compare magnitude of real numbers

MDECL11 Whole Numbers Classify sets of numbers

MDECL12 Whole Numbers Identify and apply the properties of real numbers

MDECL13 Whole Numbers Identify place value and round whole numbers

MDECL14 Whole Numbers Write the prime factorization of a number

MDECL15 Integers Evaluate exponents with integers

MDECL16 Integers Evaluate absolute value expressions

MDECL17 Decimals Identify place value and round decimals

MDECL18 Decimals & Percent Solve percent equations with applications

MDECL19 Geometry Convert units of measurement within same measurement system

MDECL20 Pre-Algebra Set up and solve ratios and proportions with simple algebraic expressions

MDECL21 Pre-Algebra Solve linear equations involving the addition and multiplication property of equalities

MDECL22 Pre-Algebra Define variables and write an expression to represent a quantity in a problem

MDECL23 Pre-Algebra Simplify algebraic expressions involving one variable (2x + 5x)

MDECL24 Pre-Algebra Evaluate algebraic expressions (e.g., find value of 3x when x=2)

MDECL25 Pre-Algebra Solve formulas with given values

MDECL26 Pre-Algebra Graph an inequality on a number line

Instructor's KeyDecimals

Don't let the decimal point get lost!!!

. 1 5 6 4 7 8 . 49 . 9 1 8 8 5 4 .1 6 . 2 3 . 9 1 83 2 7 . 4 1 . 5 45 3 5 1 .

8 1 . 1 24 8 . 2 3 9 1 1 .5 . 8 6 . 0 7 5 4

. 9 3 1 1 . 5 7 63 6 8 . 9 5 7 . 2

Note: Each decimal point is in a box by itself.

1 2 3 4 5 6 7 8 9

10 11

12 13

14 15

16

17 18 19 20 21

22 23 24 25 26

30

31 32

27 28

29

© Valencia College MAT0018C - Instructor's Manual 1

Instructor’s Key: Finding the volume of a rectangular solid.

Million Dollar Ransom Tiger Woods was unfortunately kidnapped by an unknown gang that calls itself "The 3-Putt Crew". Nike received a ransom note that demanded one million dollars in $20 bills for his safe release. When the representatives from Nike showed up at the "drop zone" with a single briefcase, the kidnapper turned and ran. Nike got another phone call for a second drop and this time they had better not mess anything up or else. They also received a Tiger club head cover with "X's" over the eyes. Why did the kidnappers run the first time? Did they know something that the representatives from Nike did not? Let us examine a few things. The key question that must be examined is can you stuff one million dollars in $20's into the typical briefcase? It is always done in movies that way, so let’s see. 1. We must first figure out the volume of a $20 bill. Measure the length and width of a

$20 bill in inches (nearest eighth of an inch). a. Hint: All bills are the same size!

2. The thickness of a dollar bill is harder to measure. Using a micrometer or caliper

would be a good way. Can you think of any others? Using a micrometer, the thickness was measured to be 0.0045 inches. Convert the decimal into a fraction.

Measure the height of 100 bills stacked together and then divide this value by 100. 0.0045 = 9

2000�

618 " × 2

58 "


3. The volume of a rectangular solid is given by:

Volume Length Width Height Calculate the volume of a single bill (include units). 4. How many $20 bills are in one million dollars? 5. If the volume of a single bill is known, and the number of $20 bills in one million

dollars is known, then find the total volume of all the bills (include units). 6. Would this fit in the typical attaché case that measures 5" x 18" x 14"? Find the

volume of the attaché case to compare. 7. How many attaché cases would it take for Nike to deliver the money as

requested?

618

258

92000

498∙218∙

92000

9261128000

cubicinches

50,000

9261128000

∙500001

36173764

cubicinches

Volume of attaché is 1260 cubic inches. No, the money would not fit in one attaché case. 3 attaché cases


Instructor’s Key: Area using decimals

How much shade can you get from a box? Find the area (including appropriate units) of each shaded region. 1. Area = ____________________ 2. Area = ______________________ 7.3 inch square 8.2 cm 15.7 cm 3. Area = ____________________ 4. Area = ______________________ 10.5 feet 15.9 cm 11.05 feet 8.2 cm 12.1 cm 5. Area = ____________________ 6. Area = ______________________

Base of 7 cm 13.23 inches 19 cm 12 cm 10.64 inches 8.9 inches

18.8 inches 22 cm

7.4 feet 4.4 feet

53.29 in2 128.74 cm2

83.465 ft2 257.58 cm2

201.376 in2 167 cm2


Decimal Review

Answers: 1. 5.7 32. 65.901 63. 10.34 2. 6.13 33. 116.395 64. 20.847 3. 55.81 34. 0.312 65. 93.405 4. 4.4 35. 26.712 66. 9340.5 5. 8.92 36. 18.66 67. 26470 6. 40.39 37. 6.82 68. 1.2114 7. 5.236 38. 47.38 69. 28 8. 8.95 39. 3.4716 70. 50 9. 69.73 40. 15.867 71. 3.005 10. 61.6 41. 14.72 72. 305 11. 15.54 42. 4.374 73. 4006 12. 29.55 43. 17.388 74. 180 13. 104.07 44. 1.215 75. 37.576 14. 8.468 45. 0.1394 76. 0.006 15. 33.76 46. 81.51 77. 5000.05 16. 149.89 47. 0.0327 78. 250 17. 126.0958 48. 50.82 79. 10.0101 18. 134.01 49. 209.3356 80. 359000 19. 780.74 50. 36.8344 81. 1.354 20. 3.88 51. 253.38 82. 68.36 21. 190.95 52. 0.00832 83. 15.5 22. 9.29 53. 0.23 84. 5.679 23. 8.864 54. 0.0072 85. 82.954 24. 26.767 55. 220.42 86. 20.68 25. 0.902 56. 5.95 87. 0.544 26. 25.2 57. 39.68 88. 0.03 27. 43.105 58. 1.728 89. 16.39 28. 608.2 59. 39.9 90. 17.376 29. 5.535 60. 228.9 91. 1550 30. 6.25 61. 104.12

31. 2.31 62. 1587.03


Instructor Information Sheet Fraction to Percentage and Percentage to Fraction Matching Triangles Game! Material needed: 8 sets of Percentage Fraction Triangles. Each set has 24 tiles. Classroom setup: Groups of 3 or 4 students. Each group will get a set of Triangles Rules of the game: Each group tries to put down tiles that have matching values

on sides that touch. Fraction-to-fraction or percent-to-percent matches are not acceptable.

Scoring: Winners: Group with the highest score. Suggest to a group that they can try to better their score by

starting again, if time is available.

30 points 80 points 60 points 120 points 180 points


Instructor’s Key: Decimals, Percent

Credit Card Headaches Part I. You have just received a credit card bill. This is what the first page shows:

CREDIT CARD STATEMENT ACCOUNT NUMBER: NAME: STATEMENT DATE: PAYMENT DUE DATE: 1234-567-891 JOHN DOE 2/13/20XX 3/09/20XX CREDIT LINE: CREDIT AVAILABLE: NEW BALANCE: MINIMUM PAYMENT DUE: $2500.00 $546.00 $1954.00 $58.62 INTEREST APR % MINIMUM BANK PRINCIPAL PAYMENT % 24% 1%

Using the information from above, you will be asked to go through two different scenarios. Determine the correct answers for each scenario. Scenario 1: Pay the whole amount by the due date. Month Payment made ($) Interest paid ($) Principal Paid($) Balance payment($)

1 $1954.00 $0 $1954.00 $0 Scenario 2: Pay the minimum amount. The payments are calculated as follows: To calculate the interest paid, take the APR (Annual Percentage Rate) and divide by 12 (months in

a year) to find the interest charged each month. Interest per month: ______%

Multiply the beginning balance of each month by this interest rate to obtain the interest amount.

To calculate the Principal to pay, multiply the balance by the 1% set by the bank.

The minimum payment is found by adding these two amounts. (interest paid + principal paid)

To determine the new balance after a payment has been made, subtract the Principal Paid from the

previous balance.

Calculate the first 5 payments. Partial information has been provided for payments 3, 4, and 5. Month Payment made ($) Interest paid ($) Principal Paid($) Balance payment($)

1 $58.62 $39.08 $19.54 $1934.46 2 $58.03 $38.69 $19.34 $1915.12 3 $57.45 $38.30 $19.15 $1895.97 4 $56.88 $37.92 $18.96 $1877.01 5 $56.31 $37.54 $18.77 $1858.24

2


Complete the table showing balance information regarding your bill after 5 months: Number of months Total amount paid Amount balance is reduced by Interest paid

5 $287.29 $95.76 $191.53 Part II. You have a different credit card bill which reads:

CREDIT CARD STATEMENT ACCOUNT NUMBER: NAME: STATEMENT DATE: PAYMENT DUE DATE: 1234-567-891 JOHN DOE 6/15/20XX 7/08/20XX CREDIT LINE: CREDIT AVAILABLE: NEW BALANCE: MINIMUM PAYMENT DUE: $2500.00 $1138.00 $1362.00 $40.86 INTEREST APR % MINIMUM BANK PRINCIPAL PAYMENT % 24% 1%

You decide to pay $500 for the first month and 30% of the bill each month thereafter, but never paying less than $250 per month until the bill is paid. Be sure to calculate interest in the final month’s payment. Complete the table: Month Payment made ($) Interest paid ($) Principal Paid($) Balance payment($)

1 $500.00 $27.24 $472.76 $889.24 2 $266.77 $17.78 $248.99 $640.25 3 $250.00 $12.81 $237.19 $403.06 4 $250.00 $8.06 $241.94 $161.12 5 $164.34 $3.22 $161.12 $0 Number of months Total interest paid Total amount you paid

5 $69.11 $1431.11 Go to the website: www.bankrate.com . Click on Credit Cards. Under Credit Card Calculators, click on “The true cost of paying minimum”. The credit card calculator should appear. Go back to the first bill used in Scenarios 1 & 2. Enter the charged amount, APR, and check minimum payments. Fill in the table for this credit card bill.

Number of months Total interest paid Total amount paid 192 $3240.09 $5194.09


http://www.bankrate.com/

Using the website, complete the table below: Credit card balance APR Number of months Total interest paid Total amount paid

$354.97 18% 30 $86.77 $441.74

$5385.10 22% 289 $9232.49 $14,617.59

$146.32 19% 11 $13.89 $160.21

$1970.90 21% 187 $2823.81 $4794.71

From the data collected, what conclusions can you draw concerning credit card payments? The best option is to pay in full each month. The worst option is to pay minimum payments ever! However, if you can be disciplined with making reasonable payments, and you need to make a purchase that you cannot afford to pay in full, the credit card option may not be too expensive and yet convenient.


Word Problems using Percentages!!!

Answers: 1. 8% of $56 is $4.48.

2. 0.5% of $2080 is $10.40.

3. 160% of $40 is $64.

4. With tax included the jacket would cost $47.70.

5. The tax on the washing machine will be $18.24.

6. The room at Disney including tax will be $145.80.

7. The total bill with tip included will be $43.56.

8. Your commission for selling the home will be $13,280.

9. The mortgage company will loan you $31,250.

10. The reduced price of the lawn mower will be $435.50.

11. The final cost of the item will be $10.49.

12. The percentage of decrease will be 31.25%.

13. The percentage of increase will be 175%.

14. Your interest for the 3 years will be $345.

15. Your interest for the 6 months will be $4691.25.

16. You will have to pay $68 per month.


The Game of Life Directions:

Set up stations before students arrive. All Students must start at Station 1. Then students may choose to go to any of Stations #2-5. (Not Station #6) After each station, students must get lab instructor to initial their team paper. (All students must complete their own papers, but only one team paper must be initialed at each station.)

Once all of the stations have been completed, students will fill in the tally sheet at the end. They may use a calculator for this part of the game only. The highest score wins!

Station #1 Calculate your Salary

Materials Needed: (1) Die

Team representative rolls the die and records value. Students return to desks to complete salary calculations.

Station #2 Interest Problem and Percent Problem

Materials Needed: (1) Die , 6 Picture Cards

Cards with pictures of houses are spread out.

Station #3 Distance Problem and Practice Multiplication with two digit number

Materials Needed: 6 Baby Photo Cards with information on back, (1) Die

Roll die to select baby.

Station # 4: Percent Problem

Materials Needed: Tax Bracket Chart

Calculate the income tax you will pay each year.

Station #5: Interest Problem with Deposit


Roll Die. Choose card and record interest rate.

Station #6 Percent of Increase Problem


Team Representative rolls die and records number.


Station 1

Die Roll Annual Salary Monthly Salary 1 36000 $3,000.00 2 46000 $3,833.33 3 56000 $4,666.67 4 66000 $5,500.00 5 76000 $6,333.33 6 86000 $7,166.67

Station 2 Price Down Payment Loan Interest Monthly Payment House 1 282000 56400 225600 203040 1190.67 House 2 400000 80000 320000 288000 1688.89 House 3 120000 24000 96000 86400 506.67 House 4 210000 42000 168000 151200 886.67 House 5 140000 28000 112000 100800 591.11 House 6 230000 46000 184000 165600 971.11

Monthly Salary Recommended Monthly Payment @28%

$3,000.00 $840.00 $3,833.33 $1,073.33 $4,666.67 $1,306.67 $5,500.00 $1,540.00 $6,333.33 $1,773.33 $7,166.67 $2,006.67

Salary 1 Salary 2 Salary 3 Salary 4 Salary 5 Salary 6 House 1 -$350.67 -$117.34 $116.00 $349.33 $582.66 $816.00 House 2 -$848.89 -$615.56 -$382.22 -$148.89 $84.44 $317.78 House 3 $333.33 $566.66 $800.00 $1,033.33 $1,266.66 $1,500.00 House 4 -$46.67 $186.66 $420.00 $653.33 $886.66 $1,120.00 House 5 $248.89 $482.22 $715.56 $948.89 $1,182.22 $1,415.56 House 6 -$131.11 $102.22 $335.56 $568.89 $802.22 $1,035.56 Station 3 Roll of Die Distance Hours

1 390 6 2 325 5 3 520 8 4 975 15 5 975 15

Yearly cost of raising a child = $12355.56

WORKSHEET SOLUTIONS


Station 4 Annual Salary $ Tax Bracket % Taxes After Tax Salary

36000 15 $5,400.00 $30,600.00 46000 15 $6,900.00 $39,100.00 56000 15 $8,400.00 $47,600.00 66000 15 $9,900.00 $56,100.00 76000 25 $11,400.00 $64,600.00 86000 25 $12,900.00 $73,100.00

Station 5

Die Number Investment (Monthly Salary) 1 2 3 4 5 6 $3,000.00 $12.00 $13.50 $150.00 $180.00 $945.00 $1,080.00 $3,833.33 $15.33 $17.25 $191.67 $230.00 $1,207.50 $1,380.00 $4,666.67 $18.67 $21.00 $233.33 $280.00 $1,470.00 $1,680.00 $5,500.00 $22.00 $24.75 $275.00 $330.00 $1,732.50 $1,980.00 $6,333.33 $25.33 $28.50 $316.67 $380.00 $1,995.00 $2,280.00 $7,166.67 $28.67 $32.25 $358.33 $430.00 $2,257.50 $2,580.00

Station 6 Die Number Old House Price 1 2 3 4 5 6

282000 -75 -50 -26 -1 24 49 400000 -83 -65 -48 -30 -13 5 120000 -42 17 75 133 192 250 210000 -67 -33 0 33 67 100 140000 -50 0 50 100 150 200 230000 -70 -39 -9 22 52 83


Instructor’s Key:

Evaluating Expressions Following the Standard Order of Operations Using your favorite internet browser, go to http://illuminations.nctm.org/ActivityDetail.aspx?ID=26. Alternatively, perform a search for the following terms: “illumination pan balance numbers”. It should be the first option. Instructions The applet on the site should show a pan balance where you will input expressions. Your goal for the activity is to determine the appropriate steps that you should take to correctly evaluate the following numerical expressions. Try it out: Evaluate: 22(5) 9+

a) Type (or click) the expression into the left pan balance. Above the balance, the value of the expression should be shown. The value is 59. (Press the ‘x2’ key for the exponent)

b) Following the order of operations, the first part of the expression that should be evaluated is the 2(5) , and that is 25. So, now type (or click) 2(25) 9+ into the right pan balance. The two pans should be balanced, and the correct balanced equation will be shown in the table to the right of the balance.

c) Following the order of operations, the next part of the expression that should be evaluated is

the 2(25) , and that is 50. So, now type 50 9+ into the right pan balance. The two pans should again be balanced, and (again) the correct balanced equation will be shown in the table to the right of the balance.

d) Finally, we can add the terms, giving the expression’s value as 59. Type 59 into the right

pan balance. Again, the pans will balance, and the balanced equation will be shown in the table on the right.

Your “written” work for this example would be the three balanced equations that are shown in the table to the right of the pan balance. Written work for the example:

22(5) 9 2(25) 9 50 9 59

+ = += +=

How do I know I am doing it correctly? Take the previous example: 22(5) 9+ . If we go against the accepted order of operations and multiply the 2(5) before evaluating the exponent, then we would input 2(10) 9+ . Type (or press) that expression into the right pan. You should notice that the pans do not balance and that nothing is added to the table. When you are ready for a new exercise, press “Reset Balance” and “Reset Table.”


http://illuminations.nctm.org/ActivityDetail.aspx?ID=26

Evaluate the following expressions using a similar procedure as shown above. Note that you will be graded for the procedure, not for the numerical answer.

A. 23(5 2) 12+ −

135

B. 24 2 3 6 10÷ ⋅ − + 40

C. 34 2(8 5) 7+ − − 51

D. 2

3

4 3 62 4⋅ ++

(type as 2 3(4*3 6 ) / (2 4)+ + )

4

E. 23(5) 4(5) 7+ +

102

F. 28 2 5 4 8+ ⋅ ⋅ ÷ 28

G. 25 4(7 2) 3+ − +

48

H. 2(4 9) 6(3 4)− + + 49

I. 3 2(26 2) (7 6) 5÷ + − +

39

J. 23(6 2 ) 15 5+ ÷ + 7

K. 2 313 6 (26 2 ) 9 ÷ − +

143

L. 3 2

20 ( 8)( 5)2 2+ − −

+

5


Evaluating Expressions Review Evaluate for 4, 2, 1x y z= − = = −

Answers:

1) 10− 10) 0 19) 64

2) 8

11) 38− 20) 24

3) 31− 12) 97 21) 23

4) 40

13) 48 22) 14

5) 4

14) 6 23) 127−

6) 1− 15) 7 24) 17

7) 24− 16) 12 25) 35−

8) 78− 17) 12− 26) 140−

9) 19− 18) 127 27) 32


Instructor’s Information Sheet

Math Relay Instructions

1. Divide students into groups of four.

2. In each team, the four team members must be seated in order from front to back, (i.e. student 2 behind student 1, etc.)

3. Student 1 performs the predetermined math function and writes the answers on

their answer sheet.

4. When they have the answer on their sheet, student 1 then hands their sheet to the person behind them.

5. The next student (student 2) repeats the process, until the final member of the

group completes their question.

6. The fourth member of the group then raises their hand and waits for the lab instructor to check the groups’ work.

7. If the answers are correct, the team gets a point. If the answers are incorrect, the

team starts from the beginning and repeats the race again. (Note to instructor: do not tell the group which of their answers is incorrect)

8. At the end of the round, the team with the most points is declared the winner.


Team Answer Sheet – Math Relay

Round 1 Round 2 Round 3 Round 4

Student #1

Student #2

Student #3

Student #4

2 2 1

−80

14

20

6

135 21 72

195 7 1

159 0 12


Instructor’s Key: Fractions

Where is that last piece of pie?

On Saturday morning Sonja’s mom made one apple pie, one banana pie, one cherry pie, and one pumpkin pie. These are to be dessert at the slumber party for Sonja and 9 of her friends that evening. As the pies cooled her mother cut each of them into 6 equal pieces. After dinner Sonja asked each friend what type of pie she would like. 4 of the girls wanted apple pie (one of the girls was Sonja). 3 of the girls wanted pumpkin pie. 2 of the girls wanted cherry pie. 1 of the girls wanted banana pie.

All fractions must be in lowest terms and proper!

Types of pies Number of pieces eaten? (Info above)

What fraction of pie was eaten?

Number of pieces left over?

What fraction of pie was left?

Apple 4 23

2 13

Pumpkin 3 12

3 12

Cherry 2 13

4 23

Banana 1 16

5 56

Pie totals 10 pieces 213

14 123


Sonja’s big brother and a few of his friends came home after a football game that evening and pigged out on half of the remaining desserts.

How many pieces of pie are now left? 7 What is the total of pies now left in the refrigerator (mixed number)? 𝟏 𝟏 𝟔�

The following weekend Sonja and her mom were going to bake some more pies for a bake sale. They were to make 2 cherry pies and 3 apple pies. After her mom found the recipe, they sat down together to make a list of how much of each ingredient they would need. Fill in the required ingredients for the following:

Ingredients Amount of each

ingredient for one (1) pie

Amount needed for 2 cherry pies

Amount needed for 3 apple pies

Total needed for all 5 pies

Flour 124

cups 142

364

1114

Sugar 34

cup 112

124

334

Milk 112

cups 3 142

172

Apples/Cherries 233

cups 173

11 1183

Eggs 2 4 6 10

Vanilla 13

teaspoon 23

1 213

Cinnamon 12

teaspoon 1 112

122


Instructor’s Key: Fraction Puzzle Work out the following fraction problems. On the next page is a letter key that you will use to decode the message. Match up the letter with its answer on this page with that same answer on the second page. Remember, all your fractional answers must be reduced, but when matching them they may be written as improper fractions or as mixed numbers. Have fun!

R. 1 1 12 3 4+ +

1 13= 1 or

12 12

D. 23 3

2 4 −

1 3= 1 or 2 2

B. 7 5 35 6 4• •

7 8

=

A. 3 514 8−

1 9= 1 or 8 8

Q. 2 73 15 10−

7 17= 1 or

10 10

U. 3 11 25 2÷

16= 25

H. 3 77 3−

19 40= 1 or 21 21

− −

E. 21 2

2 5 +

13= 20

P. 3 1 32 5 4+ −

19= 20

W. 15 2

3−

2 8= 2 or 3 3

L. 4 12 35 3÷

21= 25

N. 7 2 110 5 2

− −

1= 5

−

T. 3 7 110 3 2

• +

1 6= 1 or 5 5

S. 1 32 4−

1= 4

−

C. 3 12 24 2

− +

1 5= 1 or 4 4

− −

M. 4 63 7

+ −

10= 21

Y. 2 3 53 4 6− −

11= 12

−

O. 2 41 13 5

− −

7 52= 3 or 15 15

− −

F. 5 3

12 20−

4=

15

I. 2 13 25 16 3

+

−

1 7= 2 or 3 3

Attach your neat work sheet for full credit.


Albert Einstein said this about work ethic, math, and the world... ____ ____ ____ ____ ____ ____ ___ ____ ____ ____ ____ ____ 11

5 40

21− 13

20 7

8 7

3 11

5 6

5 13

20 13

12 9

8 1

5− 3

2

____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ 6

5 40

21− 13

20 1

4− 8

3 13

20 13

20 11

5 5

4− 52

15− 10

21 13

20

____ ____ ____ ____ ____ ____ ____ 4

15 11

12 52

15− 10

21 11

5 191

21− 13

20

____ ____ ____ ____ ____ ____ ____ , ____ ____ ____

7315

− 1625

65

14

− 73

112

1320

65

19121

− 1320

____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____, 4021

− 118

1312

32

415

1112

7315

− 1021

223

123

65

4021

− 73

15

−

____ ____ ____ ____ ____ ____ ____ ' ____ ____ ____ ____

415

1312

7315

− 1021

5215

− 15

− 1320

14

− 5215

− 83

15

−

____ ____ ____ ____ ____ ____ ____ .

1320

415

415

5215

− 1312

65

14

−

T H E B I T T E R A N D

T H E S W E E T C O M E

F R O M T H E

H A R D F R O M W I T H I N

O U T S I D E T H E

F R O M O N E S O W N

E F F O R T S


Instructor’s Key: Fractions, Money, Perimeter, Area

Building a divider for my room Before you head over to Home Depot for some lumber and nails to build your divider, it is important that we make a drawing with appropriate sizes.

Actual size of a 2x4 board is 114

x 213 inches.

Each board, as seen in the drawing below, has a width of 114

inches.

16 inches (Measurement from the beginning of one stud to beginning of next one.) More studs go in this area!!! Vertical stud Note: You are looking at the edge 90 1/4 inches of the 2x4s (1 1/4 inches). Fire blocks 16 feet 1. How long should we cut each of the vertical studs? __________ 2. How much will we cut off of an 8-foot board to get this length? __________ 3. How many vertical studs should we cut to build this wall? __________

Suggestion: Draw a sketch of your wall with studs.

87 34

inches

8 14

inches

13


4. We will need to put in fire blocks between the vertical studs.

What length should we cut these fire blocks? __________ 5. How many of the fire blocks will we need to cut? __________ 6. How many total inches of lumber do we need for the fire blocks? __________ 7. How many feet of lumber will be needed to make the fire blocks? __________ Costs of 2x4 boards: 8 foot: $1.93 16 foot: $4.36 8. Considering the costs would you buy 8′ or 16′ boards for fire blocks? _____ Why? 9. What is the total number of 8-foot boards needed to build this wall? _____ 10. How many 16-foot boards are needed to build this wall? __________ 11. How much will all the lumber cost for this wall? __________

Now we need to cover one side with drywall. We buy drywall in sheets that are 4 feet wide and 8 feet long and cost $5.48 each.

12. How many sheets of drywall will we need? __________ 13. How much will all of the drywall cost? __________

14 34

inches

12

177 inches

14 34

feet

8 foot

Because 2 – 8 footers are cheaper than 1 – 16 footer

15

2

$37.67

4

$21.92


Now that we have our drywall nailed to the wall we need to paint it. In order to find the amount of paint needed we will have to find the area of the wall. Each quart of paint will cover 50 square feet of wall and costs $6.35. 14. What is the area of our wall using inches (include units)? __________ 15. How many square inches are there in a square foot? __________ 16. Convert the area of our wall to square feet (include units)? __________ 17. How many quarts of paint will we need for our wall? __________ 18. How much will we pay for the paint? __________

Our last job will be to put a border around the edge of the wall. Border material as shown in the example comes in 25 feet rolls at a cost of $17.40 each. 19. How many rolls of border material will we need for our wall? __________ 20. How much will we have to pay for the border material? __________ If you total up all the costs for the wall, it should be $113.44. If you did not get the same total, check your work or get assistance.

17328 sq. in

144

120 13

sq. ft

3

$19.05

2

$34.80


Fraction Review Answers:

1. 21 32

2. 6 35

3. 4 45

4. 21 40

5. 10 21

6. 5 8

7. 10 21

8. 4 9

9. 7 15

10. 9 20

11. 2 3

12. 3 5

13. 1 15

14. 2 25

15. 5 36

16. 8 15

17. 5 6

18. 15 16

19. 16 5

20. 16 49

21. 1 2

22. 2

23. 1

24. 9 16

25. 3 2

26. 4 7

27. 7 9

28. 9 8

29. 10 11

30. 12 7

31. 13 12

32. 16 15

33. 13 14

34. 49 30

35. 17 21

36. 3 2

37. 13 10

38. 19 18

39. 19 20

40. 25 24

41. 1 5

42. 5 9

43. 1 3

44. 2 3

45. 1 4

46. 1 12

47. 1 10

48. 8 21

49. 2 15

50. 5 21

51. 7 10

52. 1 2

53. 11 18

54. 1 20

55. 17 21

56. 1 30

57. 1

58. 5 8

59. 1 3

60. 1 10


Complex Fraction Review

Answers

1. 3 2

6. 16 x 35

11. 45 − 18x 5x

2. 55 54

7. 19 y 21

12. − 1 3

3. 6

8. 31 42

13. 27 15x − 20

4. 7 y − 42 15

9. 2

14. 3 5

5. 5x 6

10. 23 34

15. x 6


Word Problems using Fractions!!!

Answers: 1. After I cut a pizza into 8 equal pieces, I ate 5 of them.

2. Having picked up 2 pizzas I cut each of them into 5 equal pieces. I fed 8 of

the pieces to my kids.

3. There are 290 votes needed to meet this requirement.

4. The height of the last rebound is 2 inches.

5. The area of the earth’s surface that is covered by water is 150 million square

miles.

6. The runner would have to complete 104 laps.

7. The technician can cut 56 slices from the rod.

8. The amount of space that is lost is 15/12 inches.

9. The order of wrenches from smallest to largest is: 5/32, 3/16, 1/4, 3/8.

10. The difference in horsepower is 1/6 horsepower.

11. No, the truck could not haul this load to the site in one trip.

12. She will have to collect 150 signatures to make $60 a day.



Adding and multiplying fractions

Fractions To Go! Material needed: Fraction dice (numerators are not all the same). Classroom setup: Groups of 4 students (3 if necessary). Divided into 2 teams. Procedure to start: Each group will be given 3 dice. *To increase difficulty of game, use 4 dice* Rules of the game: All answers MUST be reduced. One team will roll the dice.

If the “1” value comes up, then roll that die again. This team will now add and also multiply all the values on the dice with a time limit of 2 minutes. The opposing team will then have 1 minute to find an error in the answers.

Scoring: If no error can be found then the first team is awarded a point.

If the opposing team finds an error in the work, they will be awarded the one point.

Continuation: The second team will now get a chance to receive a point by

the same rules that the first group had. Each group will rotate as to who rolls the dice and tries to win more points.

Winners: Group with most points.


Instructor’s Key:

Geometric Proof and Discovery

Finding the sum of the interior angles of a triangle. If you add all of the angles together, what number will you get? _________ 5. The sum of the interior angles of ANY triangle is _______. 6. Mathematically find the measurements of the unknown (?? °) angles below. Write your answers next to the ??°. 34° 92° 65° 23° 79° 67 °

47° 22° 38°

116° 42 ° 95°

A

B

C

180

180°


7. Now that you know the total measure of all the interior angles of any triangle, use this knowledge to set up and solve the following algebra problem. Algebraically find the measure of each angle in the picture below. (3x)° (x +15) ° x° Hint: Add the expressions for the 3 given angles and set them equal to the sum of the

interior angles for a triangle. Solve for x. 8. The value of each of the 3 angles is: _______ _______ _______ 9. The angles in an equilateral triangle are always ____________. Therefore the value

of each of the three (3) angles is ________. 10. Algebraically find the value of the angles of the following triangle: (2x + 5)° (5x)° (7x + 35)° Hint: Add the expressions for the 3 given angles and set them equal to the sum of the

interior angles for a triangle. Solve for x. 11. The value of each of the 3 angles is: _______ _______ _______

(3x) + (x + 15) + x = 180 5x + 15 = 180 x = 33

33° 48° 99° equal

60°

(2x + 5) + (7x + 35) + 5x = 180 14x + 40 = 180 x = 10

25° 50° 105°


Units of Measurement Instructor’s Directions:

1. The class will be divided into groups of 2 to 4, depending on attendance. 2. The lab instructor will hand out a packet of wooden dowels, post-it notes, rulers, and a template

of the 4 shapes to each group. 3. Upon completion of the lab, each group will turn in one paper.

Objectives: Learn the kinds of units used to express length/distance (linear units)

Real-World: Answer questions like "How much fencing do I need?" Learn the kinds of units used to express area (square units)

Real-World: Answer questions like "How much carpet do I need?" Definitions: Perimeter – The total distance around an object. Area - A measure of the amount of surface enclosed by the perimeter. Measurements: The length of one wooden dowel is "1 linear unit" (it is shaped like a line) or just "1 unit." This is a measure of distance. To measure area, we must create a surface. Let's say that a square with a length of 1 unit and a width of 1 unit has an area of "1 square unit." Notice that each post-it is a square and has an area of 1 square unit. Instructions: Place the wooden dowels around shape A to measure its perimeter. Write its perimeter (including the correct units) in the left side of the table below. Place post-its inside shape A to measure its area. Each time you use a post-it, label it "one square unit" with large letters so that it fills the whole surface of the post-it. If you use only a portion of the post-it note, label it accordingly. Write its area (including the correct units) in the left side of the table below. Repeat this for shapes B, C, and D. Complete only the first two columns for now.

Write Answers in Terms of "Units" Write Answers in Terms of "Inches"

Shape Perimeter Area Perimeter Area A 10 5 30 in. 45 sq. in. B 4 1 12 in. 9 sq.in. C 8 3 24 in. 27 sq. in. D 7 2 1/2 21 in. 22 ½ sq. in.

Now convert the "units" into "inches", completing the last two columns of the above table. Using a ruler, measure the length of the wooden dowel and then enter the new Perimeter measurements in inches. Now measure the dimensions of the post-it note. Mark each square inch, and forming a grid on the post-it note. Enter the new measurements for area using square inches. Lastly, use a ruler to measure the shapes and verify the measurements you have calculated.


Geometry Review & Unit Conversion Review Answers: (Geometry) Answers: (Unit Conversion)

1. P = 44 in. A = 121 sq. in.

2. P =44 dm

A = 90 sq. dm

3. P = 44 ft. A = 117 sq. ft.

4. C = 12π cm

A = 36π sq. cm.

5. P = 52 A = 112

6. P = 62

A = 148

7. V = 160 cubic meters

8. V = 62.4 cubic inches

9. A = 20

10. A = 33

11. A = 49

12. A = 152

13. 3A (49)4

π= sq. meters

14.A= 184 sq. meters

1. 500000 cm 2. 13500 sq. feet

3. 120 pints

4. 238 pounds (lbs.)

5. 10 quarts

6. 2.2 short tons

7. 120 feet

8. 6 fl. ounces

9. 45760 yards

10. 145 sq. yards


Linear Inequalities Review Solve and graph

1) 2x (−∞, −2]

2) 5 x (−5, ∞)

3) 1x [1, ∞)

4) 3 1x [−3, 1)

5) 12x (12, ∞)

6) 4 2x (−4, 2]

7) x is greater than 7 x > 7 (7, ∞)

8) x is less than or equal to −6 x ≤ −6 (−∞, −6]

9) −5 is greater than or equal to x −5 ≥ x (−∞, −5]


10) 3 4x − < x < 7 (7, ∞)

11) 3 6x ≥ x ≥ 2 [2, ∞)

12) 3 12x− ≥ x ≤ −4 [−4, ∞)

13) 5 7x + > x > 2 (2, ∞)

14) 4 3 11x− + ≤ x ≥ −2 [−2, ∞)

15) 2( 3) 5 3 4x x+ + ≥ − − x ≥ −3 [−3, ∞)

16) 4 12 2 8x x+ < − x < −10 (−∞, −10)

17) 3 less than 5 times a number is less than or equal to 12. 5x – 3 ≤ 12 x ≤ 3 (−∞, 3]

18) 4 times a number minus 10 is greater than or equal to −6 plus 5. x ≥ 9/4 [9/4, ∞)



Linear Inequalities

Inequalities Rummy Material needed: Inequalities Rummy deck (45 cards) Classroom setup: Groups of 4 students (3 if necessary). How to play: Choose a dealer. The dealer shuffles the deck of inequalities

cards, deals 5 cards to each player, and then turns one card face up to create a discard pile. The person to the right of the dealer begins play by either picking the top card on the discard pile or drawing from the deck. The player chooses the card based on any matches that may be in their hand. If the player is able to make a match of 3 cards (linear inequality, line graph, word phrase), they lay these cards out before the other players. The other players will then check to see if the matches are correct. The player then discards a card from his/her hand onto the discard pile. Play proceeds to the next player to the right.

Winner: The game ends when a player is able to lay down all the cards

in his/her hand or the draw deck is depleted, in which case, the winner is the person with the most matches.


Instructor’s Key: Addition of Integers DO NOT USE A CALCULATOR!!! Yes, I know that I owe you $13. Adding positive and/or negative numbers is the same as combining how much money you have or owe.

Positive is money you have

Negative is money you owe Fill in the empty boxes: Math problem Meaning of problem Combined Value 1. 5 + (−2) Have $5 and Owe $2 Have $3 3 2. 6 + (−7) Have $6 and Owe $7 Owe $1 −1 3. −3 + (−5) Owe $3 and also Owe $5 Owe $8 −8 4. −4 + 9 Owe $4 and Have $9 Have $5 5 5. 5 + 6 Have $5 and also Have $6 Have $11 6. −7 + (−6) Owe $7 and also Owe $6 Owe $13 7. 10 + (−2) Have $10 and Owe $2 Have $8 8. −12 + 7 Owe $12 and Have $7 Owe $5 9. 6 + (−1) Have $6 and Owe $1 10. −8 + (−4) Owe $8 and also Owe $4 11. −10 + 6 12. 14 + (−9) 13. −5 + (−8)

Owe $10 and Have $6 Have $14 and Owe $9 Owe $5 and also Owe $8

Have $5 Owe $12 Owe $4 Have $5 Owe $13

11 −13

8 −5 5

−12 −4 5

−13


Work the following addition problems (combine what you have and/or owe): 14. 7 + (−3) = 4 21. 14 + (−12) = 2 28. 50 + (−21) = 29 15. −5 + (−2) = −7 22. (−20) + 7 = −13 29. −33 + (−45) = −78 16. −12 + 9 = −3 23. −15 + (−23) = −38 30. 74 + 49 = 123 17. 11 + 8 = 19 24. 26 + 14 = 40 31. −86 + 100 = 14 18. −9 + (−6) = −15 25. 19 + (−29) = −10 32. −32 + (−75) = −107 19. 7 + (−11) = −4 26. −35 + (−8) = −43 33. 105 + (−37) = 68 20. −8 + 13 = 5 27. 30 + (−12) = 18 34. −92 + 54 = −38

Column #1 total = −1 Column #2 total = −44 Column #3 total = 11 If you did not get these totals, then recheck your work or get assistance! Now let’s look at an addition problem with more than 2 numbers: 7 + (−6) + (−3) + 5 + (−8) + 9 + (−2) = ? Have $2 Have $7 & Owe $6 & Owe $3 & Have $5 & Owe $8 & Have $9 & Owe $2 equals what? Because addition has a commutative property (it allows a change in the order of an addition problem), then an EASIER method of working this problem would be to find the total you have and the total you owe. Then combine these two values.

Rewritten: 7 + 5 + 9 + (−6) + (−3) + (−8) + (−2) = ? Have a total of $21 and Owe a total of $19 Combine to get an answer of Have $2 Answer: 2 Work the following addition problems (combine what you have and owe): 35. −3 + 7 + (−6) + 9 = 7 36. 2 + (−8) + (−3) + 5 = −4 37. −7 + (−3) + 9 + (−5) = −6 38. 6 + 5 + (−4) + (−8) = −1 39. −4 + 9 + 8 + (−2) + 1 = 12 40. −9 + (−4) + (−1) + 10 = −4 41. 5 + 3 + (−6) + (−1) + (−8) = −7 42. −3 + 9 + 2 + (−4) + (−2) + 7 = 9 43. −1 + (−9) + 7 + 3 + (−5) + 8 = 3 44. −11 + (−6) + 9 + 15 + (−7) + 2 = 2 45. 16 + (−9) + (−12) + 4 + 10 + (−8) = 1 46. −15 + (−4) + 17 + 5 + 11 + (−9) + (−8) = −3 47. −20 + 12 + (−8) + 14 + (−6) + (−18) + 1 = −25 48. 4 + 22 + 7 + 9 + 6 + 3 + 8 + 25 + 1 = 85 49. −3 + (−14) + (−28) + (−5) + (−6) + (−17) + (−2) = −75 50. 26 + (−27) + 8 + (−1) + (−16) + 33 + 4 + (−5) = 22 Combine all your answers from #35 thru #50 = 16 If you did not get 16, then recheck your work or get assistance!


Instructor’s Key: Subtraction of Integers

Where can I get an EASY button?

In our early childhood TAKE AWAY (subtraction) was easy!

12 – 8 = 4

Then along came negative numbers and subtraction turned hard. −7 – (−5) = ????

Will subtraction ever be easy again? Yes! Just push the EASY button and watch what happens!

Before you push After you push 9 – (−4) = ? 9 + 4 = 13 −5 – 11 = ? −5 + (−11) = −16 7 – 12 = ? 7 + (−12) = −5 −6 – (−8) = ? −6 + 8 = 2

How it does that: −14 – (−9) = ??? It changes the number that follows the subtraction sign to the opposite value, then the subtraction sign turns into an addition sign. Now it is an easier addition problem.

−14 + 9 Owe $14 and Have $9 = Owe $5

Therefore: −14 – (−9) = −5

Rewrite the following hard subtraction problems as easier addition problems: 1. 5 – (−7) 5. −3 – 4 9. 23 – 40 13. 3 – 9 – 11 Ex. 5 + 7 −3 + (−4) 23 + (−40) 3 + (−9) + (−11) 2. −4 – 8 6. 9 – 12 10. −32 – 120 14. −2 – 4 – (−7)

−4 + (−8) 9 + (−12) −32 + (−120) Ex. −2 + (−4) + 7 3. −5 – (−3) 7. −6 – (−4) 11. 56 – (−411) 15. −28 – (−4) – 9 −5 + 3 −6 + 4 56 + 411 −28 + 4 + (−9) 4. 7 – 15 8. 5 – (−9) 12. −80 – (−49) 16. 78 – 31 – (−100) 7 + (−15) 5 + 9 −80 + 49 78 + (−31) + 100


Steps to making hard subtraction problems into easier addition problems: Step 1: Find the opposite value of the number that follows each subtraction sign and

then write with an addition sign. Step 2: Combine all positives values ($ you have) and all negatives ($ you owe). Step 3. Combine the positive and negative values (amounts you have and owe). Example: −4 – (−8) + 5 – 12 + (−3) = ? Original problem −4 + 8 + 5 + (−12) + (−3) = ? Step 1 13 + (−19) = ? Step 2 −6 Step 3 Simplify the following subtraction problems showing all appropriate steps: 17. 9 – 18 23. −15 – 9 + (−10) 29. −5 – (−15) + 8 – (−3) −9 −34 21 18. −7 – (−5) 24. −7 + 11 – 20 30. 9 – (−25) + (−7) – 13 −2 −16 14 19. −8 – 12 25. 9 – 31 – 6 + 8 31. −23 + 9 – 11 – 3 −20 −20 −28 20. 14 – (−9) 26. −18 – (−8) + 35 32. 31 – 77 –12 – (−5) 23 25 −53 21. −32 – (−12) 27. −28 – (−32) + 4 33. 102 – (−224) + (−208) −20 8 118 22. 9 – (−31) 28. 9 – 20 + 5 – (−2) 34. −432 – 450 – (−1023) 40 −4 141 Column total = 12 Column total = −41 Column total = 213 If your column totals are different, check your work or get assistance.


Instructor’s Key: Evaluating expressions with integers

There’s magic in those squares Evaluate the squares using these values: a = 2, b = −3, c = −5, d = 4, e = −1 Then put your answer in the square. The total of each group of 4 squares that are lined up horizontally, vertically, or diagonally will always be the same.

What is the sum of each column, row, or diagonal? __________

ab ba− 2cde d+ 2c e− a d+

a cd− ( )ac− 4b− 2d

( )bd a− − 2( )c d− − cd− ( )c b− +

bad− b cae+

da

( )( )a d c+ −

0 28 26 6

22 10 12 16

14 18 20 8

24 4 2 30

60


Integer Review

Answers: 1. 2 27. 20 53. 12 2. −11 28. 1 54. −88 3. 7 29. 10 55. −60 4. −17 30. −5 56. −40 5. −5 31. −1 57. 90 6. 7 32. −6 58. −240 7. −45 33. −10 59. 360 8. 77 34. −2 60. 90 9. −24 35. −9 61. 2 10. −90 36. −2 62. −3 11. −16 37. −4 63. 4 12. 2 38. −6 64. −4 13. −19 39. −20 65. 8 14. 8 40. 13 66. −9 15. 5 41. −25 67. −36 16. −1 42. −9 68. 36 17. −4 43. 36 69. 6 18. −11 44. 1 70. −36 19. 1 45. −58 71. −20 20. −63 46. 16 72. 23 21. −4 47. 24 73. 26 22. −11 48. 0 74. 26 23. 9 49. 65 75. −8 24. 6 50. −64 76. 7 25. 22 51. −40 77. −19 26. −20 52. −27


Absolute Value Review Answers:

1) 17 10) 149

2) 123 11) 15

3) 94 12) 0

4) 0 13) 14

5) 6− 14) 160

6) 42− 15) 4−

7) 23 16) 4

8) 18 17) 151

9) 1 18) 33−


Instructor Information Sheet

Integer Operation Fever A high interest game that reinforces the integer operations Number of players 2-4 Materials Needed Integer Operation Fever card deck (52 cards)

To win The player or team that takes the most tricks wins the game!

Instructions

1) Shuffle the cards and dealer deals out the entire deck of cards to the other players 2) The player to the left of the dealer will place a card from one of the suits (addition, subtraction,

multiplication, or division) in the middle of the table other players must follow suit. The player placing the card with the highest value takes the trick.

3) A player that is not able to follow suit must place a card on the trick but will not be able to take the trick.

4) In case of a tie, the player playing first takes the trick. 5) A point is scored for each trick taken. The winner is the player with the most tricks.

(Example of one round of the game)

Player 1 Player 2 Player 3 Player 4

Player one plays a division card. Other players must

follow suit. (−𝟑𝟔÷−𝟏𝟐 = 𝟑)

Player two follows suit. (𝟏𝟎𝟎÷ 𝟐𝟓 = 𝟒) (−𝟔𝟑÷ −𝟕 = 𝟗) (𝟕𝟐÷ 𝟗 = 𝟖)

Player three plays the highest value card, therefore takes the trick.


Instructor’s Key: Equation Information and practice The World runs on Equations!!! Match the words with the appropriate mathematical expression: Use each answer only once!_____ 1. x is less than 7 _____ 2. sum of x and 7 _____ 3. quotient of x and 7 _____ 4. x more than 7 _____ 5. difference of x and 7 _____ 6. x less than 7 _____ 7. twice x _____ 8. 7 is greater than x _____ 9. half of x _____ 10. product of 7 and x _____ 11. x squared _____ 12. half the difference of 7 and x _____ 13. twice the sum of 7 and x _____ 14. 7 less than the product of 7 and x _____ 15. difference of x and 7 squared

A. 2x B. 7 x C. x 2 D. x – 7 E. 1/2 x F. x + 7 G. x – 72 H. 7 – x J. 7 x – 7 K. x/7 L. 2(7 + x) M. 7 > x N. 7 + x P. x < 7 Q. 1/2 (7 – x)

Use each answer only once!_____ 1. Solving: Step 1 _____ 2. Solving: Step 2 _____ 3. Solving: Step 3 _____ 4. Solving: Step 4

a. Isolate the variable term from the constant b. Simplify the expressions on each side c. Isolate the variable from the coefficient d. Collect variables from both sides into 1 term

Put the 4-steps to SOLVE EQUATIONS into the right order.

P F K N D H A M E B C Q L J G b d a c


From the previous page write down the 4 steps for solving an equation: S1: _________________________ S3: ______________________________ S2: _________________________ S4: ______________________________

Label below which step you are DOing and the RESULTS that you get. 1. 4 3 5x + = 2. Example: 3 2 6 3x x− + = Do 1st S3: 3− 3− Do 1st S1: Simplify left side Results 4 2x = Result s 6 3x + = Do 2nd 4 4 Do 2nd S3: 6− 6−

Results 12

x = Results 3x = −

3. 3 2 2 5x x+ = + 4. 3 25x+ =

Do 1st S2: 2x− 2x− Do 1st S3: 3− 3−

Results 2 5x + = Result s 15x= −

Do 2nd S3: 2− 2− Do 2nd S4: (5) 1(5)5x

= −

Results 3x = Result s 5x = − 5. ( )4 3 2 10x + = 6. 4 5 4x x− = + Do 1st S1: Simplify left side Do 1st S2: x− x− Results 12 8 10x + = Results 3 5 4x − = Do 2nd S3: 8− 8− Do 2nd S3: +5 +5 Results 12 2x = Results 3 9x = Do 3rd S4: 12 12 Do 3rd S4: 3 3 Results 1

6x = Results 3x = 7. ( )3 4 5x x− = 8. 2 3 6 5 2 2x x x− + = − +

Do 1st S1: Simplify left side Do 1st S1: Simplify both sides Results 3 12 5x x− = Results 1 6 2 7x x− + = − + Do 2nd S3: 3x− 3x− Do 2nd S3: 2x+ 2x+ Results 12 2x− = Results 6 7x + = Do 3rd S4: 2 2 Do 3rd S3: 6− 6− Results 6 x− = Results 1x =

Simplify each side Isolate the variable term Collect variables into 1 term Isolate the variable


Match the stories with the appropriate mathematical equation and identify the meaning of the x variable used to write the equation. Use each story only once to match with the equations below: A. A television set costs $900. If tax is 6%, what is the total price? B. Dinner was $30. If I leave a 15% tip, what is the total cost of dinner? C. I have $900 in my savings account. If I get 6% interest on my principal, what will be the

total in my account at the end of 3 years? D. I have $900 in my savings account. If I get $30 interest at the end of 3 years, what

percentage rate is the bank giving? E. The television costs $900. If the store is giving you a 15% discount, how much will the

television cost before they add the tax? F. A 30-foot tree is cut into 2 pieces. If one piece is twice as long as the other piece, how long

is the short piece? G. Your car’s average speed is 30 mph. If you go 300 miles, how long will it take? H. What is your car’s average speed if you go 300 miles in 5 hours? I. I took 2 tests in my math class with a total score of 150 points. If the higher of the two

grades was 30 points above the lower score, what was the lower score? J. The total of 3 consecutive integers is 900. What is the smallest integer? K. Attendance the first day of the car show was excellent. It doubled the second day and tripled

the third day. If the total attendance for all three days was 9000 people, how many attended the first day?

L. Margie and Jack are running for president. Margie received 900 more votes than Jack. If there were a total of 9000 votes, how many votes did Jack receive?

M. Target buys cards for $2 and sells them for $3. What is the percentage of markup? N. The sum of two consecutive odd integers is 300. What is the smaller integer? Note: First word problem above has been completed as an example. E 1.

______________________900 (0.15)(900)

xx== −

C 2. ______________________900 (900)(0.06)(3)

xx== +

L 3. ______________________( 900) 9000

xx x=+ + =

H 4. ______________________

300 (5)x

x==

A 5. 900 (0.06)(900)

x Total priceofTV

x

=

= +

F 6. ______________________2 30

xx x=+ =

B 7. _____________________30 (0.15)(30)

xx== +

___ 8. ______________________( 1) ( 2) 900

xx x x=+ + + + =

___ 9. ______________________

300 30x

x==

___10. ______________________

30 (900) (0.01)(3)x

x==

___ 11. _____________________

(0.01)(2) 1xx=

=

___ 12. _____________________2 3 9000

xx x x=+ + =

___13. ______________________( 30) 150

xx x=+ + =

___14. _____________________

( ) ( 2) 300xx x=+ + =

Discounted cost of TV

Total in account

Votes Jack received

Car’s speed (mph)

Length of short piece

Total cost of dinner

Smallest integer

Number of hours

Percentage rate

Percentage of markup

Attendance on 1st day

Lower score

Smaller integer

M

G

J

K

D

I

N


Instructor’s Key:

Words to Math and Math to Words Part I - Translation Translate the following phrases into algebraic expressions (or vice-a-versa). Challenge yourself to use a variety of words when translating. Do not use the same words or phrases repeatedly.

Words Math

1) Five subtracted from a number 𝑥 − 5

2) The quotient of a number and sixteen 𝑥

16

3) 20 less than 2 times a number 2x – 20

4) Twice a number minus 20 2x – 20

5) Nine less a number 9 − 𝑥

6) 6 less than the product of 2 and a number 2𝑥 − 6

7) 3 less than the product of a number and 5 5x – 3

8) 5 times a number less 3 5x – 3

9) 3 times the sum of a number and 2 3(x + 2)

10) The product of 3 and the sum of a number and 2 3(x + 2)

11) Four times the sum of twice a number and three yields twelve 4(2𝑥 + 3) = 12

12) 1 less than the product of 2 and a number yields the product of 3 and the sum of the same number plus 7 2y – 1 = 3(y + 7)

13) Twice a number less one is the same as the product of 3 and the sum of 7 more than the same number 2y – 1 = 3(y + 7)

14) Twice a number yields 25 less the product of 3 and the same number 2x = 25 – 3x

15) The product of 2 and a number is the same as 3 times the same number subtracted from 25 2x = 25 – 3x


Part II – Solving Equations

Use your answers from Part I of the activity to set up and solve the following linear equations.

A) 𝑥 − 5 = 5𝑥 − 3 Answer from #1 Answer from #7

𝑥 = −12

B) 9− 𝑥 = 2𝑥 − 6 Answer from #5 Answer from #6

𝑥 = 5

C) 2𝑥 − 20 = 3(𝑥 + 2) Answer from #4 Answer from #9

𝑥 = −26

D) x = 0 Answer from #11

E) y = -22 Answer from #12

F) x = 5 Answer from #14


Equation Review

Answers: 1. x = 7

2. x = 14

3. x = 5

4. x = 18

25.

26.

27.

28.

x = 2

x = −1

x = 5

x = 3

47. 48.

x = 17 3

x = 15 2

5. x = −9

6. x = 1

7. x = −6

8. x = −32

9. x = −14

29.

30.

31.

32.

33.

x = 0

x = 12

x = 15

x = −6

x = 35

49. 50.

51.

52.

x = − 5 16

x = 2

x = 4

x = 0 10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

x = −5

x = 5

x = 49

x = −5

x = −8

x = 3

x = −2

x = 2

x = 8

x = 2

x = 2

x = −4

x = 2

x = 2

x = −3

34.

35.

36.

37.

38.

39.

40.

41.

42.

43.

44.

45. 46.

x = −24

x = 10

x = −8

x = 6

x = 20

x = 9

x = 1

x = −1

x = −2

x = 5

x = −1

x = 0

x = − 1 3

53. 54. 55. 56.

57. 58. 59. 60. 61.

x = −6

x = − 9 2

x = 2 5

x = 5

x = −4

x = 11 2

x = 17 8

x = 11 4

x = 1 3



Math Relay Instructions

1. Divide students into groups of four.

2. In each team, the four team members must be seated in order from front to back, (i.e. student 2 behind student 1, etc.)

3. Student 1 performs the predetermined math function and writes the answers on

their answer sheet.

4. When they have the answer on their sheet, student 1 then hands their sheet to the person behind them.

5. The next student (student 2) repeats the process, until the final member of the

group completes their question.

6. The fourth member of the group then raises their hand and waits for the lab instructor to check the groups’ work.

7. If the answers are correct, the team gets a point. If the answers are incorrect, the

team starts from the beginning and repeats the race again. (Note to instructor: do not tell the group which of their answers is incorrect)

8. At the end of the round, the team with the most points is declared the winner.


Team Answer Sheet – Math Relay

Round 1 Round 2 Round 3 Round 4

Student #1

Student #2

Student #3

Student #4

7 6 0.6

2

−4

−4

223

7 0.64 23

3 −2.1 2312

2 1.35 3


Instructor’s Key: Basic Algebra Knowledge Do you speak the Language of Mathematics?

Just like any other foreign language, mathematics has a language of its own.

Memorize the meaning of the words.

Understand the steps to simplifying an expression.

Match: Use each answer only once! ______ 1. Factors ______ 2. Terms ______ 3. Expression ______ 4. Equation ______ 5. Simplify ______ 6. Solve ______ 7. Natural numbers ______ 8. Integers ______ 9. Prime numbers ______ 10. Add/Subtract terms ______ 11. Trick for remembering

the steps for simplifying an expression

a. What we do to an equation b. Must have same variable(s) and

the same amount of the variable(s) c. Numbers and/or variables that are

multiplied d. Counting numbers e. One or more terms f. ( )( )GE MD AS

g. Separated by add/subtraction signs h. What we do to an expression j. Has only 2 different factors k. Has an expression on the left and

right side of an equals sign m. Positive and negative natural

numbers and zero

Match: Use each answer only once! ______ 1. Simplifying: Step 1 a. Work all implied grouping symbols ______ 2. Simplifying: Step 2 b. Do all addition & subtraction left to right ______ 3. Simplifying: Step 3 c. Do all multiplication & division left to right ______ 4. Simplifying: Step 4 d. Work inside all grouping symbols ______ 5. Simplifying: Step 5 e. Work all indicated exponents

Only LIKES can be added, but ANYTHING can be multiplied.

c g e k h a d m j b f

d a e c b


Match the word with the appropriate mathematical meaning: Use each answer only once!_____ 1. sum _____ 2. difference _____ 3. product _____ 4. quotient _____ 5. squared _____ 6. cubed _____ 7. is _____ 8. perimeter _____ 9. is less than _____ 10. ratio _____ 11. is greater than _____ 12. twice _____ 13. area _____ 14. of _____ 15. percent

A. the word for the exponent 2 B. > (when read from left to right) C. answer for a division problem D. = E. out of 100 F. amount is multiplied by 2 G. answer for an addition problem H. < (when read from left to right) J. number of squares inside of a polygon K. answer for a subtraction problem L. the word for the exponent 3 M. fraction N. multiplication P. answer for a multiplication problem Q. distance around the outside a polygon

Following the Order of Operations find the first 2 or 3 steps of simplifying. #1 and #10 are examples.

1.example 23 5 2x+ + 2. 7( 5) 3x + + 3. 6 2 3 (5)x x+ +

First: 9 5 2x+ + First: ____________ First: _______________ Second: 5 11x + Second: ____________ Second: _______________

4. 5 (7 3)x x− + 5. 25 3 1x− + + 6. 2(3 ) 4(5 )x x+

First: ___________ First: ____________ First: _______________ Second: ___________ Second: ____________ Second: _______________

7. 2 7 5 (4)x y y+ + 8. 5 6(4 3 )y y+ + 9. 7 5 3x x x x− + − First: ___________ First: ____________ First: _______________ Second: ___________ Second: ____________ Second: _______________

10.example 2( 3) 5 (4 3)x x+ − + 11. (2 4 5)3 4(8 2 3)x x x+ + + − − First: 2 6 20 15x x+ − − First: ________________________ Second: 18 6 15x− + − Second: ________________________ Third: 18 9x− − Third: ________________________

12. 22 7 4(3 )x x− + 13. 2 2(3 ) 5(2 3)x x x+ − + First: ___________________ First: ________________________ Second: ___________________ Second: ________________________ Third: ___________________ Third: ________________________

G K P C A L D Q H M B F J N E

7x + 35 + 3 6x + 2 + 15x 7x + 38 21x + 2

5x(4) + x −25 + 3x + 1 6x + 20x 20x + x −24 + 3x 26x

2x + 7y +20y 5 + 6(7y) 2x + 3x − x 2x + 27y 5 + 42y 5x − x

(6x + 5)3 + 4(5 − 2x) 18x + 15 + 20 − 8x 10x + 35

2x − 49 + 4(3x) 9x2 + 5(2x − 3) + x2

2x − 49 + 12x 9x2 + 10x − 15 + x2 14x − 49 10x2 + 10x − 15


Instructor’s key Definitions, Polynomial operations, Order of operations, Exponents

3 6 + 5 X - 1 5 3 1 E2 9 - 6 4 V

+ 1 X - 5 0 Q U O T I E N T1 6 - 2 5 - 6 - N

9 B 3 6 6 2 4X + 6 5 9 9 4- 2 Y 1 Y 1 3 4

2 7 X + 4 5 1 5 + 52 C 1 0 Y + 1 6 X Y - 2 6 Y

- 1 0 - Z 43 2 8 2 5 0 0 2 0 E

X T E R M 0 5 1 0 + 9 0 X- + U 0 0 P5 P 2 9 N Z E R O + OY R 5 D 1 N+ I N T E G E R S 3 5 - 1 5 X + 1 0 E1 M F 2 N6 E I 8 + TZ 9 9 N + 3 3 P 8 3

E 6 XD +

2

Definitions, Order of Operations, and Polynomials crossword puzzle

1 2 3 4

6

7 8 9

10

11

14

5

12 13

15

16 17

18

19

20 21 22

23 24 25

26

27 28 29

30 31 32

33

X2

X2

X2

X2

X2

X2

X3

X2

X2


Polynomials Review Answers: 1) 8 3x + 2) 3 8x −

3) 2x− 4) 22 6 6x x+ −

5) 4 30.8 2 2x x x+ + 6) 3 12x− +

7) 5 2x − 8) 4 2x− −

9) 12 6x− + 10) 90 70x− −

11) 3 18a + 12) 3y− +

13) 3 1x− − 14) 22 2 5x x− +

15) 22 5 3x x− − − 16) 42x

17) 4 25 20y y+ 18) 4 3 23 5 3z z z+ +

19) 5 34 4x x x+ + 20) 215 19 56y y− −

21) 28 38 35y y+ + 22) 216 1x −

23) 2 22x xy y+ + 24) 11 9 712 55 63x x x+ +

25) 4 3 22 15 12 56x x x x+ + − 26) 4 3 27 32 8 32x x x x+ + −

27) 4 3 236 66 35x x x x− − + 28) 8 6 5 4 335 39 65 14 91x x x x x+ + − +

29) 20.21 1.16 1.28x x+ + 30) 210.81 35.17 10.72x x+ +


Instructor’s Key: Whole numbers

Building a Practice Football Field Local high school officials have contracted you to estimate the cost of building a new practice field for their football team and marching band to use. The picture on the last page is the measured drawing for the new field. All the questions in this lab will refer to it.

Part One: The fencing-in of the field. Outside dotted line on drawing. The school officials wish to put a 10-foot high chain link fence encircling the field. Around the field is a 30-foot buffer zone just to give some extra space to running football players. They want the fence to run around the outside of the buffer zone (perimeter). We will use length to describe the longer side of the rectangular field and width to describe the shorter side of the rectangular field. 1. Use the drawing to find the length of the fence. 1. 420 feet 2. Use the drawing to find the width of the fence. 2. 220 feet 3. Use the length and width to find the number of feet of fence required to enclose the field. This is called the perimeter. 3. 1280 feet 4. A fence does not hang in mid-air. You must have support poles to which the fence will be attached. Our support poles will be spaced every twenty feet or the fencing will sag. How many support poles are needed to complete the fencing job? 4. 64 poles

Show your work and put the appropriate units with your answers.


Reminder: Show calculations and include units with your answers.

5. When putting in fencing, one does not just dig a hole, put the post in, and then fill the hole with dirt. There is a little bit more to the process than that. To provide enough support, each pole must have a concrete foundation within the hole it is to be placed. We know that one bag of concrete mix is enough to set 2 of the support poles. How many bags of concrete mix will be needed to complete the job? 5. 32 bags 6. The actual chain link fencing comes in 50-foot rolls. How many rolls will be needed to complete this job?

6. 26 rolls Now use the previous information to figure out the bill for the fencing of the field. Poles......................................... $ 18 each Fencing rolls............................ $ 107 per 50-foot roll Concrete mix........................... $ 2 per bag Labor cost estimate = Double the total cost of the supplies. [Show calculations]

Total cost of poles $ 1152.00 Total cost of fencing rolls $ 2782.00 Total cost of concrete mix $ 64.00 Miscellaneous costs $ 850.00

Subtotal for supplies $ 4848.00 Labor estimate: $ 9696.00 Total cost for fencing the field will be: $ 14,544.00

If your total was different, check your work before continuing!


Part 2: Getting the field green So far you have a lovely fence enclosing a flat dirt rectangle. Of course, you want to put grass down. Grass can be grown, but that takes a long time and is not very easy to do. You will do what most places do; sod the entire field. Sod is grass that has already been grown, and then it is cut from the ground in manageable sizes to be placed over the area that you want covered. Reminder: Show calculations and include units with your answers.

1. You will first need to figure out the area (number of square feet) of the field that you want to sod. Use the calculations for length and width of the field from Part 1 to figure out the area. Remember that this is not just the football field, but the whole field that is to be enclosed. The area (including units) of the field is 92,400 ft2

2. Sod is sold in 2-foot by 2-foot squares. How much area does one of these squares take up?

The area (including units) of 1 piece of sod is 4 square feet Sod to be delivered to the ball field

One truck load holds 40 pallets

One pallet holds 60 pieces of sod

Each piece of sod is 2 feet by 2 feet

Each pallet cost $50

Number of truck loads delivered

Number of pallets Number of sod pieces

Area of sod coverage

Cost of sod

1 truckload 40 pallets 2400 pieces of sod 9600 square feet $2000 2 80 4800 19200 $4000 3 120 7200 28800 $6000 4 160 9600 38400 $8000 5 200 12000 48000 $10000 6 240 14400 57600 $12000 7 280 16800 67200 $14000 8 320 19200 76800 $16000 9 360 21600 86400 $18000

10 400 24000 96000 $20000 11 440 26400 105600 $22000 12 480 28800 115200 $24000

3. According to the table, how many full truckloads of sod need to be ordered? (Note: Any

extra sod will be put around the outside of the fence.) 10 truckloads 4. According to the table, how many pieces of sod will be bought? 24,000 pieces 5. According to the table, how much will it cost for all the sod? $20,000 Using this information let’s figure out the cost for getting the field green. Delivery charge….......................... $ 75 per trip Estimated Labor charge = Double the cost of the sod. Total cost of sod $ 20,000.00 Labor Estimate $ 40,000.00 Delivery charges $ 750.00 Total for putting down sod on the field $ 60,750.00

If your total was different, check your work before continuing!


Part 3: Keeping the field green for years to come We live in a sub-tropic environment that is tough on grass. To keep the practice field green for years to come, it will need an irrigation system and sprinklers. The plan for the irrigation system is on the measured drawing at the end of this lab.

Reminder: Show calculations and include units with your answers.

1. How many sprinkler heads does the plan call for? 1. 13 sprinklers 2. PVC pipe is a polymer pipe used in most homes and irrigation systems today. It is

very durable and extremely easy to work with. Use the drawing to determine how many feet of PVC sprinkler pipe will be needed for the project.

2. 1130 feet 3. At each place where the pipes meet is an irrigation junction box. These help direct

water flow to different zones so parts of the field can be watered at different times. Each junction box is an electrically controlled valve which turns pipes on or off when needed. How many junction boxes will be needed for the plan?

3. 5 boxes 4. When putting in an irrigation system there are many extra items that are required.

The industrial control box (which controls when the sprinklers go on and off) will cost about $350. There are also backflow control valves that allow water to flow only one-way. Each zone will need one and it has been decided that there will be a total of 4 zones. Each backflow control valve costs $75. What is the total cost of all extra or miscellaneous items?

4. $650.00

Key for the measured drawing: Represents sprinkler pipes that are run underground. Represents a sprinkler head.

s


Reminder: Show calculations and include units with your answers. Now use the previous information to figure out the bill for keeping the field green. Sprinkler head ...................................... $ 25 each PVC pipe .............................................. $ 1 per foot Junction Boxes ..................................... $ 50 each Labor Cost Estimate: Double the cost of supplies + $300 Total cost of sprinkler heads $ 325.00 Total cost of PVC pipe $ 1130.00 Total cost of junction boxes $ 250.00 Miscellaneous costs $ 650.00

Subtotal for sprinkler supply costs $ 2355.00 Labor Cost Estimate $ 5010.00

Total for keeping the grass green $ 7,365.00

If your total was different, check your work before continuing! Total from Part 1 (Fencing in the field)………………………..$ 14,544 Total from Part 2 (Getting the field green)…………………….$ 60,750 Total from Part 3 (Keeping the field green)……………………$ 7,365 Total cost of the project ………………………………………..$ 82,659


Instructor’s Key: Finding prime numbers

The Sieve of Eratosthenes

• Cross out 1. It is not a prime number. Why not? • Circle the 2. Cross out every other number after

the 2 up to 100. • Circle the 3. Cross out every third number after

the 3 up to 100, even if it is already crossed out. • The 4 is already crossed out. You don’t have to

check every fourth number after the 4. Why not? • Circle the 5. Cross out every fifth number after

the 5 up to 100, even if it is already crossed out. • The 6 should already be crossed out. You don’t

have to check every sixth number after the 6. Why not?

• Circle the 7. Cross out every seventh number after the 7 up to 100, even if it is already crossed out. • The 8 should already be crossed out. You

don’t have to check every eighth number after the 8. • The 9 should already be crossed out. You don’t have to check every ninth number after the 9. • The 10 should already be crossed out. You don’t have to check every tenth number after the 10. • Circle all the remaining numbers up to 100 that are not crossed out already.

You should have circled 25 of the numbers. These circled numbers are the prime numbers less than 100.

1. A prime number has exactly 2 different factors which are the number __one __ and the

number itself 2. Why is 1 not a prime number? Because it does not have 2 different factors 3. The sum of all the prime numbers less than 100 is 1060 4. The prime factorization of the sum from #3 is 2 2 5 53⋅ ⋅ ⋅ 5. Looking at the largest prime factor from #4 the difference of the digits is 2 6. The product of every fifth prime number less than 100 is 103,256,791

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100


Instructor's KeyWhole number operations

This Puzzle Won't Cross Me Up!!!

3 3 1 2 12 5 0 8 1 7 2 84 7 4 8 5 6 5 4 02 3 5 0 0 8 4

5 2 01 4 4

1 4 2 9 2 7 63 9 5 5 3 0 8 0 51 6 9 5 5 4 9 0

2 0 0 5 8

1 2 3 4 5

6 7 8 9

10 11 12

13 14

15

16 117 18

19 20 21 22 23 24

25 26 27

28 29

30 31


Instructor’s Key: Simplifying Expressions using Order of Operations Should I put on my shoes or socks first?

Putting on your socks and then your shoes will get your feet covered.

Or…

You could put on your shoes and then your socks. It will certainly obtain the objective of getting your feet covered, but you will look a little weird to the rest of us!

In the world of math if we are asked to find the value of: 4 5 3+ ⋅ Who is to say what to do first? Add or Multiply???

Being American it may seem logical that we just start on the left and work to the right, like we read. But mathematics is international and other countries do not all go from left to right normally.

So…

Mathematicians UNITE and hereby AGREE to the Order of Operations: First: Do any work inside all grouping symbols:

[ ]( ) FractionParentheses Brackets Absolute value RadicalBar

Second: Work all implied grouping symbols: numbernumber numbernumber

Third: Work all indicated exponents. Fourth: Perform all mult. and/or division as they occur from left to right. Fifth: Perform all addition and/or subtraction as they occur from left to right.

Trick to remembering: ( )( )GE MD AS


Following the order of operations, find only the first 2 steps to be done. Example:

1. 8 5 2 3− − + 2. 7 2 8 4+ − + 3. 4 3 2 6− + − First: 3 2 3− + First: 9 − 8 + 4 First: 1 + 2 − 6 Second: 1 3+ Second: 1 + 4 Second: 3 − 6 4. 3 8 2 4⋅ ÷ ⋅ 5. 6 2 8 4÷ ⋅ ÷ 6. 4 2(5 3)+ − First: 24 ÷ 2 ∙ 4 First: 3 ∙ 8 ÷ 4 First: 4 + 2(2) Second: 12 ∙ 4 Second: 24 ÷ 4 Second: 4 + 4 7. 4(9 2 3) 1− ⋅ + 8. 23 5 2+ ⋅ 9. 35(8 2) 4− + First: 4(9 − 6) + 1 First: 9 + 5 ∙ 2 First: 5(6)3 + 4 Second: 4(3) + 1 Second: 9 + 10 Second: 5(216) + 4

In the following section you may use the

number 3 as many times as needed to make a problem.

Using the order of operations on your problem, obtain the given answer. More than one solution is possible!

Example: Answer: 11 Problem: (3 3) 3 3 3+ ÷ + ⋅ 10. Answer: 2 Problem: 3 − (3 ÷ 3) 11. Answer: 3 Problem: 3(3 ÷ 3) 12. Answer: 4 Problem: 3 + (3 ÷ 3) 13. Answer: 5 Problem: (3 ÷ 3) + (3 ÷ 3) + 3 14. Answer: 7 Problem: 3 + 3 + (3 ÷ 3) 15. Answer: 8 Problem: 3(3) − (3 ÷ 3) 16. Answer: 10 Problem: 3(3) + (3 ÷ 3) 17. Answer: 12 Problem: 3[3 + (3 ÷ 3)] 18. Answer: 13 Problem: 3[3 + (3 ÷ 3)] + (3 ÷ 3) 19. Answer: 15 Problem: 3[(3 ÷ 3) + (3 ÷ 3) + 3] 20. Answer: 50 Problem: [(3 ÷ 3) + (3 ÷ 3) + 3][3(3) + (3 ÷ 3)] 21. Answer: 101 Problem: [3(3) + (3÷3)][3(3) + (3÷3)] + (3÷3) 22. Answer: -1 Problem: 3 − [3 + (3 ÷ 3)] 23. Answer: -2 Problem: (3 ÷ 3) − 3 24. Answer: -10 Problem: −[3(3) + (3÷3)]


Instructor’s Key: Order of operations

Getting the numbers in the right square

Use the numbers 1 through 9 only once to complete the equations below:

5 − 1 + 9 = 13 + ∙ + 7 ∙ 3 + 8 = 29

∙ - / 2 + 6 ∙ 4 = 26

= = = 19 -3 11


Instructor’s Key Voting Methods

Who is the winner??!! Start by ranking the following automobile makers based on your preference (i.e. 1, 2, 3) Cadillac 3 Mercedes 2 Audi 1 As a class, complete the following table by entering in the number of votes for each preference ranking: Number of Votes

3 5 7 8 2 1 Cadillac 1 1 2 2 3 3 Mercedes 2 3 1 3 1 2 Audi 3 2 3 1 2 1 One voting method we can use to find the class preference is the Borda count. A Borda count assigns points to each candidate based on the preference rankings. A candidate gets 3 points for every first-place vote, 2 points for every second-place vote, and 1 point for every third-place vote. i.e. Candidate 1: 3 (sum of first place votes) +2(sum of second placed votes) + 1(sum of third placed votes) = Borda count 1. Perform the Borda count for each automobile maker

a. Cadillac: 3( 3+5 ) + 2( 7+8 ) + 1( 2+1 ) = 57 b. Mercedes: 3( 7+2 ) + 2( 3+1 ) + 1( 5+8 ) = 48 c. Audi: 3( 8+1 ) + 2( 5+2 ) + 1( 3+7 ) = 51

2. Which automobile maker had the highest Borda count? Cadillac Another voting method sometimes used is a runoff vote. In a runoff vote, once the top two candidates are selected, the data is once again calculated. This time, it is a winner take all scenario. Going through above table once again, the candidate with the higher preference rankings gains all the votes in each column. The candidate with the largest total is declared the winner.

Enter values here!


3. Based off of your previous answers, which two automobile makers would qualify for the runoff vote?

Cadillac and Audi

4. Tally up the votes and find the winner of the runoff vote. (complete the table by

copying the data from the previous table, including the number of votes and the preference ranking for the two choices. Show all your work) Number of Votes

3 5 7 8 2 1 Auto Maker 1: Cadillac 1 1 2 2 3 3 Auto Maker 2: Audi 3 2 3 1 2 1

Cadillac – 3+5+7=15 Audi – 8+2+1=11

Cadillac would be the winner. Complete the rest of the activity for the following scenario: Lionel Messi, Cristiano Ronaldo, and Xavi are the finalists for the FIFA World Soccer Player of the Year award. Coaches, captains, and sports journalists from around the world vote to decide who will be crowned the winner. The preference rankings for the 206 votes cast are listed below: Number of Votes

25 18 33 30 41 23 16 20 L. Messi 1 2 1 3 2 3 1 1 C. Ronaldo 2 1 3 1 1 2 3 2 Xavi 3 3 2 2 3 1 2 3 The committee decides to use the Borda count to tally up the votes. Recall; with the Borda count, after votes have been cast, they are tallied as follows: the lowest-ranked candidate is given 1 point, the second lowest is given 2 points, and the top candidate is given 3 points. The number of points given to each candidate is summed up. The candidate with the highest Borda count is the winner. i.e. Candidate 1: 3 (sum of first place votes) +2(sum of second placed votes) + 1(sum of third placed votes) = Borda count 5. Perform the Borda count for each candidate

a. Messi: 3(25+33+16+20) + 2(18+41) + 1(30+23) = 453 b. Ronaldo: 3(18+30+41) + 2(25+23+20) + 1(33+16) = 452 c. Xavi: 3(23) + 2(33+30+16) + 1(25+18+14+41+20) = 331


6. Who would be the winner using Borda’s method? Lionel Messi Since the vote count for the top two candidates was very close, the committee decided to hold a runoff count in order to determine the winner. 7. Which two candidates would qualify for the runoff vote?

Lionel Messi and Cristiano Ronaldo

8. Perform the calculations for the runoff vote and determine the winner. Number of Votes

25 18 33 30 41 23 16 20 L. Messi 1 2 1 3 2 3 1 1 C. Ronaldo 2 1 3 1 1 2 3 2

Messi – 25+33+16+20 = 94 Ronaldo – 18+30+41+23 = 112 The winner would be Cristiano Ronaldo.

9. Suppose in a different scenario, the 206 votes are recast for the three candidates.

After the first 96 votes are tallied the numbers are as follows: Messi 37 Ronaldo 34 Xavi 25 Using the equation below, find the minimum number of votes Xavi would need in order to win the award. (solve for x) 25 37 (110 )x x+ = + − x = 61votes 10. Using the internet, find an organization or country that uses the Borda count method

to assign an award or elect an official. Most Valuable Player – MLB, Heisman Trophy – NCAA, AP Poll – NCAA Football


Word Problems using Whole numbers!!!

Answers:

1. One piece is 8 feet and the other is 12 feet. 2. The husband bought 14 presents and the wife bought 7.

3. The rectangle is 31 inches long and 25 inches wide.

4. The original price of the car was $15,500.

5. The markup is $2.60.

6. You went 441 miles.

7. The shuttle travels 2,898,000 miles in one week.

8. It will take 20 months to pay the loan back.

9. There are 6 minutes of commercials.

10. First day was 1100 people, second day was 2200, and the third day was 3300.

11. Billy Bob received 176 votes and Peggy Sue received 263 votes.

12. The lowest grade was 52 and the highest grade was 90.

13. The grape ivy cost $41.

14. The two consecutive numbers are 7 and 8.

15. Number of laps: Yogi swam 11, Smokey swam 22, and Boo-Boo swam 14.

16. Your average speed was 50 miles per hour.

17. The three consecutive integers are 33, 34, and 35.


Instructor’s Information Sheet Order of Operations using integers 24 Game Equipment needed for this activity: Two (2) sets of single-digit cards. Note: There are enough cards in two packs for 12 different groups. Explanation of Activity: 1. Try to break the class into as many groups of 3 as possible. 2. All members of each group should put their names on the paper from the lab manual

(official score sheet) to be turned in at the end of the period. 3. Give each group a set of cards consisting of 1(1-dot), 2(2-dots), 1(3-dots), for a total

of 4 cards. 4. The group is allowed to use any combination of addition, subtraction, multiplication,

division, and exponents with order of operations and grouping symbols (parentheses or fraction bar) to create a total value of 24.

5. An answer must use all of the four (4) numbers on ONE SIDE of the card and each number can only be used once.

6. The numeral with a RED DOT is a nine (9), not a six (6). 7. Remind them that 5(9 – 2)2 and 2 * 5(9 – 2) are the same and are not to be

considered as different solutions. 8. Each group should turn in the official score sheet at the end of class. 9. Credit should be given according to the number of different solutions that the group

turns in. Instructor’s options:

• Allow each group to make only one trade during the class. This trade will be for another set of four (4) cards.

• No values can be used as exponents. • A tardy student can be added to an existing group of 2. • A tardy student can work alone until (and if) another tardy student arrives.


Instructor’s Key: Exponents

Where’s the magic in a magic square? Work the problems in each of the squares. Then put your answer in the square. The total of each group of 4 squares that are lined up horizontally, vertically, or diagonally will always be the same.

What is the sum of each column, row, or diagonal? __________

6 22 8− 2 36 2−

2 25 1+ 2 14 10−

3 13 5− 3 210 10÷

3 22 2+ 2 54 0+

4 3 210 10 2÷ + 3 23 3−

4 22 2+ 3 82 0−

2 2 18 2 10− ⋅ ?2 16=

10 11 1+ 2(2 3) 5+ +

0 28 26 6

22 10 12 16

14 18 20 8

24 4 2 30

60


Evaluating Exponential Expressions Review

Answers: 1) 17 10) 0 19) 2−

2) 2−

11) 91 20) 27

3) 36− 12) 8− 21) 1

4) 50

13) 9 22) 3

5) 36

14) 40 23) 3

6) 32 15) 16 24) 24−

7) 80 16) 30 25) 3

8) 9− 17) 10− 26) 13

9) 8− 18) 3 27) 16


Instructor Information Sheet Jeopardy! Instructions Materials Needed: Computer, Projector, Clickers (3), Timer Directions: Divide the class into 3 teams

Each team will receive a clicker. Teams will be given 2-4 min. to answer each question

depending on the category. The team who clicks in first will have a chance to

answer the question. If they do not get the correct answer the next team that clicked in will have a chance to answer and receive full credit. There is no penalty for incorrect answers.

The team who gets the correct answer can choose the next category.

If no team gets the correct answer the host will then choose the next category.

The round is over when all questions have been attempted.

There is 1 random daily double question in round 1, and 2 in round 2. Point value of the question is doubled if you get the correct answer.

Everyone will get a chance at Final Jeopardy. Teams will have 5 min to answer final jeopardy. It is worth $2000

Team with the most points wins.


Jeopardy Questions – Round 1 Integers Answers:

$100 110−

$200 3

$300 34−

$400 432

$500 undefined

Fractions Answers:

$100 95

yx

$200 3−

$300 760

$400 12 76x− −

$500 32

Equations Answers:

$100 22x =

$200 57x =

$300 0y =

$400 12x = −

$500 2x =

Whole Numbers Answers:

$100 41017

$200 98784

$300 21

$400 9

$500 12

Feeling Lucky Answers:

$100 2 22 3 11⋅ ⋅

$200 5.8


$300 9

$400 7 420x y

$500 400

Geometry Word Problems Answers:

$100 80m

$200 49in2

$300 78ft2

$400 31.4cm or 10πcm

$500 210m3

Jeopardy Questions – Round 2

English to Math Answers:

$200 5 15x +

$400 78x−

$600 202

xx

−

$800 x 2x 43< +

$1000 ( )2 x 25 6 2x 44+ − = +

Decimals Answers:

$200 18.945

$400 0.1284−

$600 3.5

$800 2.63

$1000 39x =

Compare Numbers Answers:

$200 103 250<

$400 168 20− < −

$600 4 12 116 48 4

= =

$800 0.032 0.320− > −

$1000 4 42%9

− < −


Conversion Answers:

$200 35%

$400 0.0345

$600 58

$800 43 3or 220 20

$1000 0.082−

Simplify Polynomials Answers:

$200 5x

$400 29t t−

$600 6 39x 9x y+

$800 5 5 2 3 5 2 3 4 38x y z 4x y z 32x y z− − +

$1000 2x 44xy 61y− − +

Find the LCD Answers:

$200 16

$400 21

$600 12

$800 48

$1000 108

Jeopardy Questions – Final Jeopardy

Answers:

Final Jeopardy 3


Who did it? Answer these questions to determine who committed the crime!

1. Evaluate 1 114 6−

a. −5 (It was not Bishop Smith)

b. 1912

− (It was not Mrs. Daisy)

c. 1912

(It was Professor Bloom)

d. 5 (It was Bishop Smith)

2. Solve 3 24 3

y= +

a. 57

(It was Major Watts)

b. 112

(It was not Major Watts)

c. 1712

(It was Professor Bloom)

d. 1 (It was not Professor Bloom)

3. Evaluate 7 78 4÷

a. 12

(It was not Bishop Smith)

b. 2 (It was not Mrs. Court) c. 32 (It was Miss Margaret)

d. 4932

(It was Mrs. Daisy)

4. Does 2 1(5 3) (12 5)5 3

x x− − − simplify to: 122

x− −

a. True (It was not Miss Margaret) b. False (It was not Professor Bloom)


Where did it happen? Answer these questions to determine where the crime was committed!

1. Simplify 3 7 411 ( 2 5 )x x x− −

a. 1477x− (In the Theater Room) b. 10 722 55x x+ (In the Foyer) c. 10 722 55x x− − (Not in the Foyer) d. 21 1222 55x x− − (On the Sundeck)

2. Simplify 0.6 0.18xy yx+

a. 0.78xy (Not on the Sundeck)

b. 20.78xy (Not in the Florida Room) c. 0.108xy (Not in the Master Office)

d. 20.108xy (Not in the Guest House)

3. Simplify (3 5) ( 2)x x+ + −

a. 24 3x + (Not in the Guest House) b. 4 3x − (In the Foyer) c. 23 10x − (In the Master Office) d. 4 3x + (Not the Theater Room)

4. Simplify 2 2( 2 5) (7 3 11)x x x− + + + −

a. 25 3 6x x+ − (Not in the Master Office) b. 29 3 6x x− + − (Not in the Florida Room) c. 25 8 11x x+ − (In the Florida Room) d. 29 8 11x x− + − (In the Theater Room)


What was the weapon? Answer these questions to determine what was used to commit the crime!

1. John bought yard of fabric at $4 per yard. How much did he spend?

a. $5.20 (The Saber) b. $1.56 (Not the Rifle) c. $2.50 (Not the Hammer) d. $10.00 (The Rifle)

2. Evaluate 4 3x x when x = −2. a. 8 (The Hammer) b. 24 (Not the Compression Band) c. -8 (Not the Hammer) d. -24 (The Compression Band)

3. Find the area of a triangle with base inches and height inches.

a. sq. in. (Not the Saber)

b. sq. in. (The Rifle)

c. sq. in. (The Cake Plate)

d. sq. in. (Not the Rifle)

4. A hotel room costs $50.00 with a 9.2% tax. What is the total cost of the room?

a. $104.40 (The Martini Shaker) b. $54.60 (Not the Martini Shaker) c. $23.40 (Not the Compression Band) d. $75.66 (The Saber)


Who? With What? Where? Answer these questions LAST to finish!

1. The perimeter of a fence is 48 meters. If the width is two meters less than the length, then

find the width. a. 25 meters (Not Bishop Smith) b. 9 meters (Not Major Watts) c. 13 meters (Not Prof. Bloom) d. 11 meters (Not Mrs. Court)

2. Evaluate 5 3 7 4 4 3+ − + ÷ ⋅

a. 43

(In the Foyer)

b. 4 (Not in the Florida Room) c. -1 (In the Theater Room) d. -2 (In the Florida Room)

3. You are 200 miles from home. If R represents your speed, then write an expression that will determine the amount of time needed to get home.

a. 200 + 𝑅 (With the Compression Band) b. 200𝑅 (Not with the Saber) c. 𝑅

200 (With the Cake Plate)

d. 200𝑅

(With the Saber)


Instructor Information Sheet Final Exam Review Game Instructions

1) Roll the die to determine who goes first. The player rolling the highest number plays first. Play moves counterclockwise.

2) The student who is to play second reads a question from the cards to the first player.

a. If the question is answered correctly, then Player 1 rolls the die and moves his or her marker the resulting number of spaces forward on the playing board.

b. Player 1 then tries to get bonus spaces by rolling the die a second time. If the number on the die matches the number on the playing board where the player’s game piece rests, then Player 1 moves the marker ahead that many spaces.

c. If the question is answered incorrectly, then it is Player 2’s turn. 3) Player 3 next reads the question to Player 2. Play continues in this manner until

one player reaches the finish. 4) To finish, the player must roll the number that exactly matches the number of

spaces left to make it to the finish circle. 5) Place the used cards (questions) on the bottom of the stack. 6) LOSE A TURN: Leave the marker on the “Lose a Turn” space and the player

loses his or her next turn. 7) MOVE AHEAD 3 SPACES: If the marker ends up here, the player can

automatically move ahead 3 spaces right away.

If a player gives the wrong answer, he or she should be shown the correct answer. Players are encouraged to discuss the right answer and how it is obtained.


LOSE A

TURN 4 2 5

2 2

2 3 4 3 5 2 6

1 FINISH

MOVE AHEAD

3 SPACES

LOSE

A TURN

MOVE AHEAD

3 SPACES

3 6 LOSE

A TURN

4 2

START 5 1 2

5 1 4 2 4 5 6 1

2 3

1 3 4 2 5 LOSE

A TURN

MOVE AHEAD

3 SPACES

6 MOVE AHEAD

3 SPACES

6 2 1 3

1 3 4 4 6 5


TRANSLATING KEY WORDS AND PHRASES INTO ALGEBRAIC EXPRESSIONS The table below lists some key words and phrases that are used to describe common mathematical operations. To write algebraic expressions and equations, assign a variable to represent the unknown number. In the table below, the letter “x” is used to represent the unknown. In translation problems, the words sum, total, difference, product and quotient imply at least two parts – use parentheses when a sum or difference is multiplied. For example, the phrase "the sum of three times a number and five" translates to "3x + 5," while the phrase "three times the sum of a number and five" translates to "3(x + 5)."

OPERATION

KEY WORD/PHRASE

EXAMPLE

TRANSLATION

Addition (+ ) plus A number plus three x + 3 more than Ten more than a number x + 10 the sum of The sum of a number and five x + 5 the total of The total of six and some number 6 + x increased by A number increased by two x + 2 added to Eleven added to a number x + 11

Subtraction (− ) minus A number minus seven X – 7 less than Four less than a number X – 4 the difference of The difference of a number and three X – 3 less Nine less a number 9 – X

decreased by A number decreased by twelve X – 12 subtracted from Six subtracted from a number X – 6

Multiplication (× ) times Eight times a number 8x the product of The product of fourteen and a number 14x twice; double Twice a number; double a number 2x multiplied by A number multiplied by negative six −6x

of

Three fourths of a number 3 x

4 Division (÷ )

the quotient of

The quotient of a number and seven

7x

divided by

Ten divided by a number

10x

the ratio of

The ratio of a number to fifteen

15x

Powers ( xn ) the square of;

squared The square of a number; a number squared

x2

the cube of; cubed

The cube of a number; a number cubed

x3

Equals (= ) equals Seven less than a number equals ten. x − 7 = 10 is Three times a number is negative six. 3x = −6 is the same as Eight is the same as twice a number. 8 = 2x yields Twelve added to a number yields five. x + 12 = 5 amounts to Nine less a number amounts to twenty. 9 – x = 20


Specialized Prep Area Who can use: Any prep math student.

Where: Building 4 (downstairs library) - Room 102

When Fall and Spring Hours

Monday - Thursday: 8AM to 10PMFriday: 8AM to 5PM Saturday: 8AM to 4PM

Summer Hours

Monday - Thursday: 7AM to 10PMFriday: 7AM to 12PM Saturday: 8AM to 2PM

Website: www.valenciacollege.edu/east/academicsuccess/spa/

Facebook: www.facebook.com/valencia.spa

Bring your Valencia ID for a quick and easy sign-in experience each time you visit. Upon signing out, we will record your time spent in the SPA. This information will be made available for your instructor. Workshops will be held throughout the semester reviewing specific topics covered in the prep math courses. Please check the website and flyers posted around campus.

Overall Success Rate in East Campus Developmental Math Courses Based on Student Number of Visits to the SPA

50%

58%62% 63%

76%

0%

10%

20%

30%

40%

50%

60%

70%

80%

0 1‐2 3‐5 6‐9 > 10


MAT0018C - Instructor

Documents

Transcript of MAT0018C - Instructor