ShillerMath Book 4 Test Answers

ShillerMath Book 4 Test Answers LESSON 4-44 REVIEW TEST #4-1 ANSWERS HOW KIDS LEARN MATH Grading instructions: compare the answers here to the student s answers. For each correct answer, add the appropriate number of points, which the student may enter, and compute the total score. After the test has been graded, do the lesson(s) for each incorrect response. Now together we will grade your answers. Enter the start time: Enter the finish time: 1. Score 2 points for each correct answer (maximum score: 4) [Lessons 4-1, 4-2] a. 1 point each: quarter to five; four forty-five b. 2 points: 4:45 2. Score 1 point for each correct answer (maximum score: 5) [Lessons 4-5, 4-6, 4-41] a. true b. false c. true d. false e. true 3. Score 1 point for each correct answer (maximum score: 4) [Lessons 4-7, 4-8, 4-12, 4-19, 4-20, 4-21] Name at least one unit of measurement for each of the following: a. time: seconds, minutes, hours, days, weeks, months, years, centuries, millennia b. height: inches, feet, yards, miles, light-years, millimeters, centimeters, meters, kilometers c. mass: ounces, pounds, tons, milligrams, grams, kilograms d. volume: tablespoons, ounces, cups, pints, quarts, gallons, milliliters, centiliters, liters 4. Maximum score: 6 [Lessons 4-9, 4-10] a. 2 points for getting them all correct; 0 points otherwise: $1, $5, $10, $20, $50, $100 b. 2 points for completing the table correctly; 2 points for identifying that a fifty dollar bill cannot be exchanged for just twenty dollar bills. Book 4 Test Answers Page 1 ShillerMath All Rights Reserved

ShillerMath Book 4 Test Answers HOW KIDS LEARN MATH 1 5 10 20 50 100 1 1 5 10 20 50 100 5 1 2 4 10 20 10 1 2 5 10 20 1 NO 5 50 1 2 100 1 5. Score 1 point for each correct answer (maximum score: 7) [Lessons 4-14, 4-15, 4-16] a. Earth e. false; a polygon s sides must all be straight line segments b. measure f. true c. many g. true d. angle 6. Score 2 points for each correct answer (maximum score: 8) [Lesson 4-18] a. true c. false: if A = 8 and C = 5 then A + C = 13 (not 12) b. true d. true 7. Score 2 point for each correct answer (maximum score: 6) [Lessons 4-12, 4-13, 4-19] a. 2 inches b. horizontal; like the horizon c. 3½ 1½ = 2 Book 4 Test Answers Page 2 ShillerMath All Rights Reserved

ShillerMath Book 4 Test Answers 8. Score 1 point for each correct answer (maximum score: 8) [Lessons 4-20, 4-21] a. 16 e. 2 HOW KIDS LEARN MATH b. 2,000 c. 8 f. 4 g. 128 d. 2 h. 1 gallon = 4 quarts. 1 quart = 32 ounces. So 1 gallon = 4 quarts 32 ounces per quart = 128 ounces 9. Score 1 point for each correct answer (maximum score: 7) [Lessons 4-11, 4-17, 4-22, 4-23] a. false; 10 is also an even number between 1 and 10 inclusive b. true c. false; 9 is an odd number too d. false; 9 is a perfect square that is odd e. true f. divide by 5 g. Score 1 point if all correct, 0 points otherwise: 1,100: One thousand one hundred 2,350: Two thousand three hundred fifty 500: Five hundred 245: Two hundred forty-five 5: Five 65: Sixty-five 220: Two hundred twenty 470: Four hundred seventy 100: One hundred 49: Forty-nine 1: One 13: Thirteen 10. Score 1 point for each correct answer (maximum score: 7) [Lessons 4-25, 4-35, 4-40] a. 3, 12, 21,30 e. 69, 78, 87, 96 b. 6, 15, 24, 33, 42, 51, 60 c. 9, 18, 27, 36, 45, 54, 63, 72, 81, 90 f. 99 g. 33 d. 39, 48, 57, 66, 75, 84, 93 Book 4 Test Answers Page 3 ShillerMath All Rights Reserved

ShillerMath Book 4 Test Answers 11. Score 2 points for each correct answer (maximum score: 8) [Lessons 4-26, 4-42] HOW KIDS LEARN MATH a. DCCCVII b. 990 c. 500 d. 7: IVXLCDM 12. Maximum score: 10. [Lessons 4-28, 4-29, 4-31] a. Score 1 point for each correct answer (maximum 3 points): The name of the set is S. The curly braces enclose the members of the set. This set has 3 members. b. Score 2 points for set equations that use all 16 elements exactly once: [Note: there are many possible ways to break down this set into three subsets; other answers may be correct if the set equations, the rule, and the set members all properly answer the question.] A = { 3, 5, 7, 11, 13, 15 } B = { 2, 6, 8, 10, 12, 14 } C = { 1, 4, 9, 16 } Score 1 point each for rule that match the sets (maximum 3 points): A: odd numbers but not perfect squares; B: even numbers but not perfect squares; C: perfect squares c. Score 1 point for each correct answer (maximum 3 points): i. 0 B ii. 3,913 E iii. 20,000 E 13. Maximum score: 10 [Lessons 4-30, 4-33, 4-34] Score one point each for the division expression and the fraction: a. 50 100 50 100 Book 4 Test Answers Page 4 ShillerMath All Rights Reserved

ShillerMath Book 4 Test Answers b. 3 100 3 100 HOW KIDS LEARN MATH c. 100 100 100 100 d. 200 100 200 100 e. 1,000 100 14. Score 1 point for each correct answer (maximum score: 5) [Lesson 4-36] a. A38C2 b. 1559D c. 979855695 d. First cross out all numbers that are not between 5 and 9 inclusive. Then write the remaining numbers. Then write them backwards. e. AC 1,000 100 15. Score 1 point for each correct answer (maximum score: 9) [Lessons 4-27, 4-37, 4-38] a. 50 f. 1,000 b. 80 c. 60 d. 50 g. 1,000 h. 800 i. 2495, 2496, 2497, 2498, 2499 e. 100 16. Score 2 points for each correct answer (maximum score: 6) [Lesson 4-39] a: 1915; b: 1942; c: 1980 17. Score 1 point for each correct answer (maximum score: 9) [Lessons 4-32, 4-42] Score one point for getting all three terms of each sequence and score two points for getting the rule. a. I, X, XIX, XXVIII, XXXVII, XLVI, LV Rule: add 9 b. 20, 40, 80, 160, 320, 640, 1280 Rule: times 2 c. 1, 4, 9, 16, 25, 36, 49 Rule: perfect squares Book 4 Test Answers Page 5 ShillerMath All Rights Reserved

18. Score 1 point for each correct answer (maximum score: 6) [Lesson 4-43] a. 189, 246 (other answers are possible) b. 489, 621 (other answers are possible) c. 198, 246 (other answers are possible) d. 829,641 (other answers are possible) e. 189, 246 (other answers are possible) f. 189, 246 (other answers are possible) 19. Score 1 point for each correct answer (maximum score: 6) [Lesson 4-24] Expression Words Numbers Value Two thousand three (2 x 1,000) + (3 x 1) 2,003 Three thousand two (3 x 1,000) + (2 x 1) 3,002 Nine million four hundred thirtyseven thousand one hundred ninetyfour Twenty million three thousand fourteen (9 x 1,000,000) + (4 x 100,000) + (3 x 10,000) + (7 x 1,000) + (1 x 100) + (9 x 10) + (4 x 1) (20 x 10,000,000) + (3 x 1,000) + (1 x 10) + (4 x 1) 1,437,194 20,003,014 TOTAL SCORE (MAXIMUM 131). Enter a new line onto the Review Test Scoresheet in the Completed Work Binder and fill out all but the last column, including lesson number(s) for any incorrect responses in the Lesson #s to revisit column. After you write in your initials ask the student to do so as well so we can record your accomplishment. If the student got a perfect score, you got everything right! Your math is excellent. Otherwise, you did very well. Now we have the opportunity to look at some of these lessons. Repeat the appropriate lessons and questions until the student achieves a perfect score, each time entering a new line onto the Review Test Scoresheet. Consumable Lessons including review tests are available at http://www.shillermath.com. END OF REVIEW TEST #4-1 ANSWERS Book 4 Test Answers Page 6 ShillerMath All Rights Reserved

LESSON 4-82 REVIEW TEST #4-2 ANSWERS Grading instructions: compare the answers here to the student s answers. For each correct answer, add the appropriate number of points, which the student may enter, and compute the total score. After the test has been graded, do the lesson(s) for each incorrect response. Now together we will grade your answers. Enter the start time: Enter the finish time: 1. Score 1 point for each correct answer (maximum score: 6) [Lesson 4-45] a. 550 d. 1,000 b. 1,000 c. 920 e. 4,430 f. 4,000 2. Score 1 point for each correct answer (maximum score: 3) [Lessons 4-46, 4-47] a. false b. false c. true 3. Score 2 points for each correct answer (maximum score: 6) [Lessons 4-47, 4-48] a. 1 point each: 12; 16 b. 2 points for either $15 or $15.00 c. 1 point each: $0.50; 50 4. Score 2 points for each correct answer (maximum score: 10) [Lessons 4-49, 4-50, 4-51, 4-52] a. $49.57 d. $1,322.29 b. $246.90 e. $1,392.59 c. $74.11 5. Score 2 points for each correct answer (maximum score: 4) [Lesson 4-53] a. 930 b. 900 6. Score 1 point for each correct answer (maximum score: 3) [Lesson 4-54] a. 20 b. 200 c. 2000 7. Score 2 points for each correct answer (maximum score: 8) [Lesson 4-55] a. 3 c. 2 b. 3 d. 0 Book 4 Test Answers Page 7 ShillerMath All Rights Reserved

8. Score 1 point for each correct answer (maximum score: 8) [Lessons 4-55, 4-56, 4-57] a. ii; b. iii; c. i; d. v; e. vii; f. vi; g. viii; h. x 9. Score 1 point if ALL are correct (maximum score: 1) [Lesson 4-58] oz ozs lb lbs 10. Score 2 points for each correct answer (maximum score: 10) [Lesson 4-59] a. 48 d. 4000 b. 2000 e. 4 c. 3 11. Score 1 point for each correct answer (maximum score: 2) [Lesson 4-60] a. ii b. 4 inches 12. Score 1 point for each correct answer (entire row must be correct) (maximum score: 12) [Lessons 4-61, 4-62, 4-63] Expression Number of operations Operators 4 x 5-4 2 x - 48 12 x 6 + 3 3 x + 7 x 7 x 3 + 3 3 x x + 250 25-7 + 9 3 - + First number Operation Second number Equals Answer Six Addition Three = 9 Six Subtraction Three = 3 Six Multiplication Three = 18 Six Division Three = 2 First number Operand Second number Equals Answer 5 + 4 = 9 4 or - 2 = 2 6-3 = 3 2 x 4 = 8 Book 4 Test Answers Page 8 ShillerMath All Rights Reserved

13. Score 2 points for each correct answer (maximum score: 12) [Lessons 4-64, 4-65, 4-67, 4-78] a. 47 b. 190 c. 294 d. 160 e. 77 f. 480 14. Score 1 point for each correct answer (maximum score: 9) [Lessons 4-66, 4-69] a. i. 15 ii. 30 iii. 0 iv. 45 b. i. > ii. < iii. > iv. < v. = 15. Score 1 point for each correct answer (maximum score: 7) [Lessons 4-68, 4-70, 4-71, 4-72] a. False b. True c. True d. False e. False f. False g. True 16. Score 1 point for each correct answer (maximum score: 3) [Lessons 4-73] a. number b. true or false c. object 17. Score 1 point for each correct answer (maximum score: 5) [Lessons 4-71, 4-74, 4-75, 4-76] a. The length of the rectangle is twice the width (1 point); The perimeter is 36 feet (1 point) b. The perimeter of a rectangle is twice the length plus twice the width (1 point) c. The length is 12 feet (1 point) and the width is 6 feet (1 point) 18. Score 2 points for each correct answer (maximum score: 6) [Lessons 4-77, 4-78] a. 10 b. 18 c. 96 Book 4 Test Answers Page 9 ShillerMath All Rights Reserved

19. Score 1 point for each correctly placed dot (maximum score: 6) [Lessons 4-79] Wake up time 9am - - 8am - - 7am - - 6am - - ---- ---- ---- ---- ---- ---- ---- 1 2 3 4 5 6 7 Day 20. Score 3 points if worked correctly (maximum score: 3) [Lessons 4-80, 4-81] 16 x 14 = (10 + 6) x (10 + 4) = 10 x 10 + 10 x 4 + 6 x 10 + 6 x 4 = 100 + 40 + 60 + 24 = 224 TOTAL SCORE (MAXIMUM 124). Enter a new line onto the Review Test Scoresheet in the Completed Work Binder and fill out all but the last column, including lesson number(s) for any incorrect responses in the Lesson #s to revisit column. After you write in your initials ask the student to do so as well so we can record your accomplishment. If the student got a perfect score, you got everything right! Your math is excellent. Otherwise, you did very well. Now we have the opportunity to look at some of these lessons. Repeat the appropriate lessons and questions until the student achieves a perfect score, each time entering a new line onto the Review Test Scoresheet. Consumable Lessons including review tests are available at http://www.shillermath.com. END OF REVIEW TEST #4-2 ANSWERS Book 4 Test Answers Page 10 ShillerMath All Rights Reserved

LESSON 4-111 REVIEW TEST #4-3 ANSWERS Grading instructions: compare the answers here to the student s answers. For each correct answer, add the appropriate number of points, which the student may enter, and compute the total score. After the test has been graded, do the lesson(s) for each incorrect response. Now together we will grade your answers. Enter the start time: Enter the finish time: 1. Score 2 points for each correct answer (maximum score: 6) [Lesson 4-83] a. 7 b. 9 pm c. 9pm 2. Score 1 point for each correct answer (maximum score: 3) [Lessons 4-84, 4-85, 4-86, 4-87, 4-89] a. false b. true c. true 3. Score 2 points for each correct answer (maximum score: 6) [Lessons 4-84, 4-85, 4-86, 4-87, 4-89] a. -1 b. -5 c. -6 4. Score 1 point for each correct answer (maximum score: 6) [Lesson 4-88] a. i. 30 minute ii. 47 minutes iii. 14 minutes b. i. 34 minutes ii. 4 minutes iii. 57 minutes 5. Maximum score: 9 [Lessons 4-90, 4-91] a. 1 point each i. < ii. > iii. > b. 2 points each. i. -2 ii. -1 iii. -8 6. Score 2 points for each correct answer (maximum score: 6) [Lesson 4-92] Book 4 Test Answers Page 11 ShillerMath All Rights Reserved

Item Estimated Measured Variance Length (inches) Length (inches) 1. television 36 40-4 2. sofa 70 72-2 3. bookshelf 38 32 6 7. Score 2 point for each correct answer (maximum score: 8) [Lessons 4-93, 4-94] a. -1 b. -4 c. -1 d. -5 8. Score 1 point for each correct answer (maximum score: 3) [Lesson 4-95] a. 5 b. 6 c. 0 9. Maximum score: 11 [Lessons 4-96, 4-97] a. 1 point each i. false ii. true iii. true b. 2 points each i. 65 o ii. 37 o c. 2 points each 10. Maximum score: 12 [Lessons 4-98, 4-100, 4-101, 4-102] a. True-False (1 point each) i. true ii. false b. How many inches are in 4'2"? (2 points) Book 4 Test Answers Page 12 ShillerMath All Rights Reserved

c. Fill in the blanks in the chart. (2 points each blank) Height in inches Height in feet and inches 36 inches 3 feet 0 inches 63 inches 5 feet 3 inches 57 inches 4 feet 9 inches 33 inches 2 feet 9 inches 11. Maximum score: 3 [Lesson 4-99] The numbers are 8, 4 and 4. 12. Score 1 point for each correct answer (maximum score: 8) [Lessons 4-103, 4-104] Inches Feet Yards 36 3 1 144 12 4 Millimeters Centimeters Meters 2000 200 2 4000 400 4 13. Score 1 point for each correct answer (maximum score: 8) [Lesson 4-105] Seconds Minutes Hours 7200 120 2 10800 180 3 Hours Days Weeks 168 7 1 504 21 3 14. Score 1 point for each correct answer (maximum score: 4) [Lessons 4-106, 4-108] a. "40 minutes after 4" and "20 minutes before 5" b. "10 minutes after 10" and "50 minutes before 11" 15. Maximum score: 3 [Lesson 4-107] W O R M 1 1 1 1 O R M 1 2 3 R M 1 3 Book 4 Test Answers Page 13 ShillerMath All Rights Reserved

M 1 1+3+3+1 = 8 16. Score 2 points for each correct answer (maximum score: 8) [Lesson 4-109] a. 39 days b. 110 hours c. 107 minutes d. 318 seconds 17. Score 3 points if all answers are correct (maximum score: 3) [Lesson 4-110] The multiples of 3 are 30, 33, 36, 39, 42, 45. TOTAL SCORE (MAXIMUM 107). Enter a new line onto the Review Test Scoresheet in the Completed Work Binder and fill out all but the last column, including lesson number(s) for any incorrect responses in the Lesson #s to revisit column. After you write in your initials ask the student to do so as well so we can record your accomplishment. If the student got a perfect score, you got everything right! Your math is excellent. Otherwise, you did very well. Now we have the opportunity to look at some of these lessons. Repeat the appropriate lessons and questions until the student achieves a perfect score, each time entering a new line onto the Review Test Scoresheet. Consumable Lessons including review tests are available at http://www.shillermath.com. END OF REVIEW TEST #4-3 ANSWERS Book 4 Test Answers Page 14 ShillerMath All Rights Reserved

LESSON 4-144 REVIEW TEST #4-4 ANSWERS Grading instructions: compare the answers here to the student s answers. For each correct answer, add the appropriate number of points, which the student may enter, and compute the total score. After the test has been graded, do the lesson(s) for each incorrect response. Now together we will grade your answers. Enter the start time: Enter the finish time: 1. Score 1 point for each correct answer (maximum score: 4) [Lesson 4-112] a. 2 b. 3 c. 5 d. 5 2. Score 2 points for each correct answer (maximum score: 4) [Lessons 4-113, 4-114] a. 21 b. 120 3. Score 1 point for each correct answer (maximum score: 4) [Lessons 4-115, 4-116] a. 100 b. 99 c. 81 d. 64 4. Score 1 point for each correct answer (maximum score: 3) [Lessons 4-116, 4-117] a. thousand b. ten thousand c. million 5. Score 1 point for each correct answer (maximum score: 2) [Lessons 4-116, 4-117] Number Expression 14,203 1 10 4 + 4 10 3 + 2 10 2 + 3 1 1,000,030 1 10 6 + 3 10 6. Score 1 point for each correct answer (maximum score: 7) [Lessons 4-119, 4-120, 4-121, 4-122] a. For each number, tell how many thousands it contains. i. 5 ii. 10 iii. 450 iv. 3,000 b. Give the names for the first three powers of ten where the exponent is a multiple of three. Book 4 Test Answers Page 15 ShillerMath All Rights Reserved

one thousand, one million, one billion 7. Score 2 points for each correct answer (maximum score: 4) [Lesson 4-123] a. 6 x 10 4 + 5 x 10 3 + 3 x 10 2 + 3 x 10 1 + 1 x 10 0 b. 1 x 10 6 + 1 x 10 3 + 4 x 10 0 8. Maximum score: 2 [Lesson 4-124] The answer is 21. 9. (Maximum score: 10) [Lessons 4-125, 4-126] a. Score 1 point for each correct answer and 1 point for the correct rule i. 13; add 3 ii. 2000; multiply by 10 iii. 81; multiply by 3 b. Score 2 points for each correct answer i. 73 ii. 24 10. Maximum score: 10 [Lessons 4-127, 4-129, 4-130] a. 5 points for getting them all correct; 0 points otherwise: $1 $5 $10 2 0 1 2 2 0 7 1 0 12 0 0 b. 2 points for each method 1st way - 20 minus 6 is 14 so we give the customer $14 (either one $10 bill and four $1 bills or two $5 bills and four $1 bills or one $5 bill and nine $1 bills or fourteen $1 bills). 2nd way - From $6, give four $1 bills to get to $10, then give $10 more (either one $10 bill, two $5 bills, one $5 bill and five $1 bills, or ten $1 bills). c. Four $1 bills and one $10 bill. (1 point) 11. Maximum score: 7 [Lessons 4-131, 4-132, 4-133] a. (1 point) 2, since eight divided by two is four, and four divided by two is two. Book 4 Test Answers Page 16 ShillerMath All Rights Reserved

b. (1 point for each correct entry in the table) Series Next 3 numbers Pattern i. 12, 24, 36, 48, 60, 72 +12 ii. I, 4, VII, 10, XIII, 16 +3 and alternate with Roman numerals c. (2 points) 6 for 28, 35, 42, 49, 56, 63 12. Score 1 point for each correct answer (maximum score: 4) [Lessons 4-134, 4-135] a. many correct answers are possible. (1 point for each correct method) 87 + 45 = 87 + 13 + 32 = 100 + 32 = 132 87 + 45 = 80 + 7 + 20 + 25 = 80 + 20 + 7 + 25 = 100 + 32 = 132 b. many correct answers are possible. (1 point for each correct method) 24 + 16 + 5 = 45 45-21 = 24 13. Score 3 points for each correct answer (maximum score: 15) [Lessons 4-136, 4-137, 4-138] a. 3185 b. 11,032 c. 85,475 d. 832,785 e. 439,956 14. Score 4 points for each correct answer (maximum score: 8) [Lessons 4-139] a. Bob has 14 books. He has twice as many books as Mary so Mary has 7. Mary has two more books than Dave so Dave has 5. Combined they have 14 + 7 + 5 = 26 books. b. Edith rode 5 miles. Ann rode twice as far as Edith so Ann rode 10 miles. Joan rode twice as far as Ann so Joan rode 20 miles. Combined they rode 20 (Joan) + 10 (Ann) + 5 (Edith) = 35 miles. 15. Score 1 point for each correct answer (maximum score: 4) [Lesson 4-141] a. false b. true c. true d. false Book 4 Test Answers Page 17 ShillerMath All Rights Reserved

16. Score 2 points for each correct answer (maximum score: 8) [Lesson 4-118, 4-128, 4-140] a. nine hundredths b. six thousandths c. four tenths d. iii 17. Score 1 point for each correct answer (maximum score: 5) [Lesson 4-142] a. Yes b. No c. No (could have fractional pounds or stones or kilograms) d. Yes e. Yes 18. Score 5 points for the correct answer (maximum score: 5) [Lesson 4-143] 5 feet TOTAL SCORE (MAXIMUM 106). Enter a new line onto the Review Test Scoresheet in the Completed Work Binder and fill out all but the last column, including lesson number(s) for any incorrect responses in the Lesson #s to revisit column. After you write in your initials ask the student to do so as well so we can record your accomplishment. If the student got a perfect score, you got everything right! Your math is excellent. Otherwise, you did very well. Now we have the opportunity to look at some of these lessons. Repeat the appropriate lessons and questions until the student achieves a perfect score, each time entering a new line onto the Review Test Scoresheet. Consumable Lessons including review tests are available at http://www.shillermath.com. END OF REVIEW TEST #4-4 ANSWERS Book 4 Test Answers Page 18 ShillerMath All Rights Reserved