GRADE 8 ANSWER KEY Note: For more information on particular vocabulary, refer to Kindergarten to Grade 8 Mathematics Glossary (Manitoba Education). NUMBER 1. Squares and Square Roots (8.N.1) Level of Question 1 Type of Question Short Answer 1 mark for correct answer in a). 1 mark for correct answer in b). a) 196 b) 15 2. Estimating Square Roots (8.N.2) Level of Question 3 Type of Question Short Answer 0.5 marks for identifying 23 as being placed incorrectly. 0.5 marks for identifying 50 as being placed incorrectly. 0.5 marks for correctly placing 23. 0.5 marks for correctly placing 50. 23 is 4.79 and should be closer to 5. 50 is 7.07 and should be closer to 7. Page 1 of 24
NUMBER 3. Problem Solving with Square Roots (8.N.1) 1 mark for appropriate work. 1 mark for correct answer. In order to find the length of one side of the field, you need to take the square root of the area. 28900 = 170 m for one side of the field. 170 4 = 680 m is once around the field. Note The students ran 1360 m or 1.36 km. Deduct 0.5 marks if the answer is not in a sentence. Deduct 0.5 of a mark if the final answer is missing units. 4. Understanding Percent (8.N.3) Level of Question 2 Type of Question Short Answer Student receives a total of 1 mark. 0.5 marks for appropriate work. 0.5 marks for correct answer. Possible solutions: 48 0.25 12 = 48 12 4 = 12 boys signed up for the fiddle jam. s may vary. Note Deduct 0.5 marks if the answer is not in a sentence. Page 2 of 24
NUMBER 5. Ratios in Context (8.N.4) Level of Question 1 Type of Question Short Answer 0.5 marks for correct ratio in a). 0.5 marks for correct simplified ratio in a). 0.5 marks for correct ratio in b). 0.5 marks for correct simplified ratio in b). a) b) Ratio Simplified Ratio 8:32 1:4 Ratio Simplified Ratio 24:8 3:1 6. Finding the Rate (8.N.5) Level of Question 1 Type of Question Short Answer 1 mark for correct rate for a). 1 mark for correct rate for b). a) 55 km/h b) 10.09 m/s Page 3 of 24
NUMBER 7. Rate of Pay (8.N.5) 0.5 marks for calculating Gina s rate of pay. 0.5 marks for calculating Aaron s rate of pay. 1 mark for stating that Gina has a greater rate of pay. Gina $78 6h = $13/h Gina has a greater hourly rate of pay. Aaron $129.50 14h = $9.25/h Note Deduct 0.5 marks if the answer is not in a sentence. 8. Problem Solving: Ratio (8.N.5) Note 1 mark for appropriate work. 1 mark for correct answer. 72 8 = 9 players on each team. 9 x 2 = 18 players on two teams. Deduct 0.5 marks if the answer is not in a sentence. Page 4 of 24
NUMBER 9. Multiplying Fractions (8.N.6) Student receives a total of 4 marks. 1 mark for an appropriate picture in a). 1 mark for a correct fraction in lowest terms in a). 1 mark for an appropriate picture in b). 1 mark for a correct fraction in lowest terms in b). a) 6 1 = 12 2 b) 3 8 Note(s) Deduct 0.5 of a mark if the fraction is not in lowest terms in a). 10. Quotient of a Fraction on a Number Line (8.N.6) 1 mark for appropriate work. 1 mark for correct answer. 6 1 3 = 18 Page 5 of 24
NUMBER 11. Fraction Division (8.N.6) 1 mark for appropriate work. 1 mark for correct answer. 1 1 5 = or 3 15 Marc uses 1 15 of a tank each day. Note Deduct 0.5 marks if the answer is not in a sentence. 12. Integer Multiplication (8.N.7) Student receives a total of 4 marks. 1 mark for an appropriate picture in a). 1 mark for a correct answer in a). 1 mark for an appropriate picture in b). 1 mark for a correct answer in b). a) Take away 7 groups of +4. b) Take away 3 groups of -2. I am left with +6. I am left with -28. Page 6 of 24
NUMBER 13. Integer Division (8.N.7) Level of Question 2 Type of Question Short Answer 1 mark for correct division expression with integers. 1 mark for correct answer. a) ( 63) ( 9) = 7 b) Cheryl borrowed money for 7 days. Note Deduct 0.5 marks if the answer is not in a sentence. Deduct 0.5 marks if the expression contains only positive integers. 14. Order of Operations (8.N.7) Level of Question 3 Type of Question Long Answer Student receives a total of 3 marks. 1 mark for correct answer in a). 1 mark for correct answer in b). 1 mark for correct justification. a) 12 (2 3) 2 b) 12 2 (3 2) 12 6 2 12 2 1 2 2 6 1 0 6 The answers are different because the brackets are placed in different locations and you have to use BEDMAS. Student responses may vary. Page 7 of 24
15. Using Fractions in Context (8.N.8) 1 mark for appropriate work. 1 mark for correct answer. Students may use any method to solve. Sample solutions: Half of 6 is 3. 1 6 3 1 6= = = 1 1 Half of that is 1 4 4 2 2 2 Janelle needs 1 1 2 cups of flour. Note Deduct 0.5 marks if the answer is not in a sentence. Page 8 of 24
PATTERNS & RELATIONS 1. Model and Solve Linear Equations (8.PR.2) Student receives a total of 3 marks. 1 mark for creating an appropriate equation. 1 mark for correctly solve the equation. 1 mark for a drawing to represent the equation. 3n = 15 3n 15 = 3 3 n = 5 Example pictures: 2. Creating an Equation (8.PR.2) Level of Question 2 Type of Question Short Answer 1 mark for creating an appropriate equation in a). 1 mark for creating an appropriate equation in b). a) 8= 6+ 2x b) 3x + 4 = 12 Page 9 of 24
PATTERNS & RELATIONS 3. Solving Equations: Correcting an Error (8.PR.2) Level of Question 3 Type of Question Long Answer Student receives a total of 3 marks. 1 mark for correctly identifying error. 1 mark for correcting that step. 1 mark for correct solution. Finding the Error: Correct : 4 x + 5 = 40 ( ) 4x 20 = 40 4x 20 40 = 4 4 4 x + 5 = 10 x + 5 5 = 10 5 x = 15 4. Linear Equations Missing Value (8.PR.2) Level of Question 1 Type of Question Short Answer Student receives a total of 1 marks. 1 mark for correct solution and appropriate work y= 4x 9 1= 4x 9 1+ 9= 4x 9+ 9 8= 4x 8 4x = 4 4 2 = x Note(s) If no work shown but correct answer, award 0.5 marks. Page 10 of 24
PATTERNS & RELATIONS 5. Solving Linear Equations (8.PR.2) Level of Question 1 Type of Question Short Answer Student receives a total of 4 marks. 1 mark for appropriate work for a). 1 mark for correct answer for a). 1 mark for appropriate work for b). 1 mark for correct answer for b). a) 6( n + 3) = 18 6n 18 = 18 6n 18 + 18 = 18 + 18 6n = 36 6n 36 = 6 6 n = 6 b) x 6= + 3 4 x 6 3= + 3 3 4 x 3 = 4 x 3 4= 4 4 12 = x ( ) 6. Graphing Linear Equations (8.PR.1) 1 mark for creating correct table of values. 1 mark for graphing linear function. a) h t 1 1 2-1 3-3 4-5 5-7 b) Note(s) If a student makes an error in the table of values but correctly plots coordinates, award 1 mark for b). Page 11 of 24
PATTERNS & RELATIONS 7. Linear Relations in Context (8.PR.1) Level of Question 3 Type of Question Long Answer Student receives a total of 3 marks. 1 mark for describing the relation in a). 1 mark for creating an equation in b). 1 mark for correctly finding the cost in c). a) Answers must include numbers to describe the relationship. A pizza with no toppings cost $9. For every additional topping you pay $2 more. b) c) t=toppings 9+ 2t= y 9+ 2t= y 9 + 2( 10) = y 9 + 20 = y 29 = y A pizza with 10 toppings would cost $29.00. Page 12 of 24
SHAPE & SPACE 1. Identifying the Hypotenuse (8.SS.1) Level of Question 1 Type of Question Short Answer Student receives a total of 1 mark. 1 marks for correct explanation p is the hypotenuse. Two explanations are possible and accepted: p is the hypotenuse because it is the longest side of the triangle. p is the hypotenuse because it is across of the 90 o angle. Note Please note that if there is no explanation, no marks are awarded. 2. Finding the Hypotenuse (8.SS.1) Student receives a total of 1 mark. 1 marks for the appropriate work and correct answer. 21.59 cm Note(s) a + b = c 2 2 2 21 + 5 = c 2 2 2 441+ 25 = c 446 = c 446 = 2 2 c 2 21.59 = c Deduct 0.5 of a mark if the units are not included in the final answer. Page 13 of 24
SHAPE & SPACE 3. Using the Pythagorean Theorem (8.SS.1) Level of Question 3 Type of Question Long Answer Student receives a total of 3 marks. 1 marks for an accurate picture 1 marks for using the Pythagorean Theorem 1 marks for an appropriate explanation o Deduct 0.5 marks if they do not answer in a sentence. s will vary. Students can solve for any part of a right triangle, however, these walls do not meet at a right angle. 14 9 12 a + b = c 2 2 2 12 + 9 = c 2 2 2 144 + 81 = c 225 = c 2 2 225 = c 15 = c 2 The angle can t be 90 o because if it was, the hypotenuse would be 15 m. Page 14 of 24
SHAPE & SPACE 4. Viewing a 3-D Object (8.SS.2) Level of Question 2 Type of Question Short Answer Student receives a total of 4 marks. 1 mark for top view 1 mark for bottom view 1 mark for left view 1 mark for right view Top: Front: Left: Right: 5. Identifying Tessellations (8.SS.6) Level of Question 3 Type of Question Short Answer 1 mark for correct justification in a). 1 mark for correct justification in b). a) No. The shape does not tessellate. There are spaces/gaps. b) Yes. The shape is able to cover an area without spaces. Page 15 of 24
SHAPE & SPACE 6. Tessellation Search (8.SS.6) Level of Question 1 Type of Question Short Answer Student receives a total of 3 marks. 1 mark for recognizing a translation. 1 mark for recognizing a reflection. 1 mark for recognizing a rotation. a) E b) D c) Answer could be C, D, J, G 7. Volume of a Cylinder (8.SS.4) 1 mark for appropriate work. 1 mark for correct answer. Area of the Base: 2 π r 3.14 3 3 28.26 Volume = Area of Base x Height = 28.26 12 = 339.12 cm 3 for the full can The volume of half a can is 169.56 cm 3. Note(s) Deduct 0.5 of a mark if missing or incorrect units. Page 16 of 24
SHAPE & SPACE 8. Vocabulary for Pythagorean Theorem (8.SS.1 & 8.N.1) Level of Question 1 Type of Question Short Answer 0.5 marks for each correct response perfect square legs Pythagorean theorem hypotenuse 9. Drawing a Net (8.SS.2) Level of Question 1 Type of Question Short Answer 1 mark for drawing a net that would create a cylinder. 1 mark for labelling measurements correctly. Sample Answer: Page 17 of 24
SHAPE & SPACE 10. Right Rectangular Prism (8.SS.3 & 8.SS.4) Student receives a total of 4 marks. 1 mark for appropriate work for a). 1 mark for correct answer for a). 1 mark for appropriate work for b). 1 mark for correct answer for b). a) Area of the front/back rectangles 10 2 = 20 m 2 Area of the side rectangles 12 2 = 24 m 2 Area of the top/bottom rectangles 10 12 = 120 m 2 Total Surface Area 20 + 20 + 24 + 24 + 120 + 120 = 328 m 2 b) Volume = Area of Base x Height = 120 x 2 = 240 m 3 s may vary. Note(s) Deduct 0.5 of a mark for missing or incorrect units on the final answer. Page 18 of 24
SHAPE & SPACE 11. Right Triangular Prism (8.SS.3 & 8.SS.4) Level of Question a) 1 b) 2 c) 2 Type of Question Long Answer Note(s) Student receives a total of 5 marks. 1 mark for constructing the 3-D object. 1 mark for appropriate work for b). 1 mark for correct answer for b). 1 mark for appropriate work for c). 1 mark for correct answer for c). a) Object should look like a right-triangular prism. b) Area of the side rectangles 5 6 = 30 cm 2 Area of the triangles 5 4.3 = 10.75 cm 2 2 Total Surface Area 30 + 30 + 30 + 10.75+ 10.75 = 111.50 cm 2 c) Volume = Area of Base x Height = 10.75 x 6 = 64.50 cm 3 Deduct 0.5 of a mark for missing or incorrect units on the final answer. Page 19 of 24
STATISTICS & PROBABILITY 1. Interpreting Data (8.SP.1) Level of Question 3 Type of Question Open Response Student receives a total of 3 marks. 1 mark for appropriate justification in a). 1 mark for appropriate justification in b). 1 mark for appropriate justification in c). a) Answers will vary. Either graph can be appropriate. Sample responses: A, because the months that they had higher sales are on the top of the graph. A, because their bar was stacked first on top of Rick s Marine. B, because the graph is increasing. b) Answers will vary. Sample responses: There was no more snow so no one was buying Skidoos. Nickel City had a sale so people bought from them instead of Rick s Marine. c) Answers will vary. Sample responses: Nickel City had better prices and people went there instead. 2. Displaying Data (8.SP.1) Level of Question 2 Type of Question Short Answer 1 mark for correct answer for a). 1 mark for correct answer for b). a) No, because line graphs show change in data over time. b) c) Sample Answer: A bar graph would have been better to show the data because it would have shown the difference between the data more clearly. Answers will vary. Page 20 of 24
STATISTICS & PROBABILITY 3. Representing Data (8.SP.1) Level of Question 2 Type of Question Short Answer Note Student receives a total of 1 mark. 1 marks for correct explanation Line graph Sample answer: A line graph would be the most appropriate because it shows change over time. Please note that if there is no explanation, no marks are awarded. 4. Misleading Bar Graph Data (8.SP.1) Level of Question 1 Type of Question Short Answer Student receives a total of 1 mark. 1 marks for correct explanation The scale on the vertical axis is misleading. Example answer: His scale is going up by only 1%, but it looks like more. 5. Calculating Probability of Independent Events (8.SP.2) Level of Question 2 Type of Question Short Answer 1 mark for appropriate work. 1 mark for correct answer. Notes Chances of Winning Chances of Winning Chance of Winning X = a Class Prize a School Prize Both Prizes 1 1 1 = = 0.000032 = 0.0032% 24 1300 31200 1 He has a chance of winning both prizes. 31200 Deduct 0.5 marks if they do not answer in a sentence. Answer can be written in fraction, decimal or percent form. Page 21 of 24
STATISTICS & PROBABILITY 6. All Possible Outcomes for Independent Events (8.SP.2) Student receives a total of 4 marks. 1 mark for determining all possible outcomes. 1 mark for all probabilities being correct in the table below. Students must use an appropriate method to find all possible outcomes. Sample solutions: Tree Diagram Table 1 2 3 4 5 6 H H1 H2 H3 H4 H5 H6 T T1 T2 T3 T4 T5 T6 Getting a 3 and a head? An odd and a tail? A 1 or 2 and a head? 1 12 3 6 2 6 Notes Students can write probabilities as fractions, decimals, and percents. 7. Dependent & Independent Events (8.SP.2) Level of Question 1 Type of Question Short Answer 0.5 marks for each correct answer Event Dependent Independent Landing a bottle flip and attending summer school X Roll a die and flipping a coin X Sleep and test scores in history class X Sugar intake and weight gain X Page 22 of 24
STATISTICS & PROBABILITY 8. Outcome of Dependent Events (8.SP.2) Level of Question 3 Type of Question Long Answer 1 mark for correct calculation of winning. 1 mark for explanation. 2 13 26 1 = = = 16.67% 3 52 156 6 or 2 1 = 2 = 1 = 16.67% 3 4 12 6 Answers should include that Cheyenna is incorrect. Sample answer: No, I do not agree because her chances of winning are only 17%, she was way off. Page 23 of 24
NON-CALCULATOR Students cannot have a calculator or scrap paper. o Please have students have a book to silent read if they are done early. Level of Question 1 Type of Question Short Answer Outcomes 8.N.1 8.N.2 8.N.3 8.N.4 8.N.5 8.N.6 8.N.7 Student receives a total of 13 marks. 1 mark for each correct response in questions 1, 3, 4, 5, and 6. 0.5 of a mark for each correct response in question 2. 1a) 5.4-5.9 1b) 8.8-8.9 2. Fraction Decimal Percent a) 0.2 20% 125 b) 1.25 100 345 c) 34.5% 1000 3a) 11 1 24 3b) 7 3 16 4a) 1 7 2 4b) 1 2 12 5a) 63 5b) 80 6a) ( 2) 6b) ( + 9) Page 24 of 24