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6th Grade Math Study Guide 1. Emma wrote the opposite of the number −8 . What number did Emma write? 2. Drag (write) each number to its location on the number line. -3.5 3.5 -2 2 3. Erik placed numbers a, b, and c on this number line. Part A Erik incorrectly states that b and c are both opposites of a, because b and c are both on the opposite side of zero from a. Use the drop-down menus to explain why Erik is incorrect. Numbers are opposites when they are in Choose... A number Part B Choose... distances from zero and from zero on a number line. Choose... has more than one opposite. Erik's friend draws a second number line to help him understand opposites. Plot the opposite of b and the opposite of the opposite of c on the number line. 0 4. Write a positive or negative number to represent each situation. Situation Number 50 feet below sea level feet winning $100 in a contest $ a loss of 10 yards yards 20 degrees below 0°F °F 5. Fiona says there is only one number that is its own opposite. Which number is this? −1 −1/2 0 1 6. Graph the ordered pairs on the coordinate plane. Use the Point tool. A(3, 2) D(4, 3) B(–5, 2) E(–4, 0) C(–1, –4) F(2, –4) 7. Use the drop-down menus to describe the signs or values of the x- and y-coordinates of any point at each location on the coordinate grid. x-coordinate y-coordinate Quadrant I Choose... Choose... Choose... Choose... Choose... Choose... Quadrant II Quadrant III Quadrant IV Choose... Choose... Choose... Choose... Choose... Choose... Choose... Choose... x-axis y-axis origin 8. Paul is creating a map of his town on a coordinate plane, where each unit represents 1 block. He will include the following locations on his map. Location Paul's house Store Pond Theater Bank Coordinates (4, 0) (–3, 0) (1, 0) (–3, 1) (–2, –4) Part A Graph each of the locations on the coordinate plane. Use the Point tool. Part B Paul wants to add the town's statue to his map. The statue is located 2 blocks to right of the origin, and 4 blocks down from the origin. What is the location of the statue? (–2, –4) (–2, 4) (2, –4) (2, 4) 9. Look at this list of points. A(3, –4), B(–5, 1), C(0, –4), D(4, 4), E(–2, 0), F(–4, 4) Determine whether each statement about the points is correct. Select True or False for each statement. Point A is located in Quadrant IV. Point C and point F are directly across the x-axis from each other and are the same distance from the x-axis. Point E is located in both Quadrant II and Quadrant III. Point B is located in Quadrant III. Point D and point F are directly across the y-axis from each other and are the same distance from the y-axis. True False True False True False True False True False 10. Shauna wants to give information about the coordinates of two points on a coordinate graph based on descriptions of their locations. Use the drop-down menus to complete an explanation for Shauna. If the points are directly across the x-axis from each other and the same distance from the Choose... , then the Choose... are opposites. If the points are directly across the y-axis from each other and the same distance from the Choose... , then the Choose... are opposites. 11. The deepest that a submarine can go under normal conditions is −1,300 feet. The depth at which water pressure will damage the submarine is −1,950 feet. Which depth is greater? Write an inequality to compare −1,300 and −1,950. 12. The table shows the record low temperatures for five states. State Colorado Hawaii Florida Montana Mississip Temperature (in °F) −61 15 −2 −70 −19 Which list is ordered from greatest to least temperature? −70, −61, −19, −2, 15 15, −2, −19, −61, −70 −70, −61, −19, 15, −2 15, −70, −61, −19, −2 13. The letters r, s, and t represent integers, where t > r, r > s, s < 0, and s > –r. Drag each letter to its correct location on the number line. 0 R S T 14. Elinor and her cousins play a game. They draw cards that have positive and negative numbers on them. Each player starts at 0 . A positive number means to move forward, and a negative number means to move backward. The table shows the cards they drew in three rounds. Josh Cathy Elinor Round 1 −6 −4 6 Round 2 −3 2 −2 Round 3 1 −7 3 Part A Elinor says she moved the farthest from the starting point for Round 1. Use the drop-down menus to explain whether or not Elinor is correct. Elinor is Choose... Elinor moved value is because 6 is Choose... Choose... Choose... on a number line. in Round 1 because |6 is Choose... |−6 and this |−4. Part B After Round 3, Josh has moved a total of −8, Cathy has moved a total of −9, and Elinor has moved a total of 7. Drag the players' names to order them from closest to farthest distance from the starting point after Round 3. Cathy Elinor Josh 15. Jake draws the following cube. Brittany draws a cube with a side length that is 2 units greater than the side length of Jake's cube. Michael draws a cube with a side length that is 1/3 the side length of Brittany's cube. Determine whether each expression represents the volume, in cubic units, of Michael's cube. Select Yes or No for each expression. (1 (4×2)) Yes No 3 2×2×2 Yes No (10) 3 8 Yes No Yes No (4 + 2 ) 3 8 /3 × 8/ 3 × 8/ 3 Yes No Yes No 16. What is the value of (1/3) ? 1/81 1/12 4/12 4/3 17. Kim is studying a bacteria sample that triples its mass every day. At the end of day 1 of her study, the sample has a mass of 3 milligrams. Part A What is the mass of the bacteria sample after 5 days of study? Drag each expression into the correct box of the table. Represents the mass, in milligrams, of the sample after 5 days 3 5 Does not represent the mass, in milligrams, of the sample after 5 days 3x5 18. What is the value of n in the equation 1/3n=9 ? 3x3x3x3x3 n= ___ 5x5x5 19. Myra's older brother, Joe, works part time at a store where he earns $645.60 each month. What expression could be used to find the amount Joe earns working any number of months, m? 20. Jessie and Charlie are walking on a beach. Charlie walks 2.3 kilometers farther than Jessie. Part A Write an equation for the number of kilometers Jessie walks, j , if Charlie walks 4.2 kilometers. Write an equation for the number of kilometers Charlie walks, c , if Jessie walks 3.9 kilometers. Equation for the number of kilometers Jesse walks: _____________________ Equation for the number of kilometers Charlie walks: ___________________ Correct answers: Part B Use the drop-down menus to show the distances Jessie and Charlie walk. If Charlie walks 4.2 kilometers, then Jessie walks Choose... kilometers. If Jessie walks 3.9 kilometers, then Charlie walks Choose... kilometers. 21. Myra's older brother, Joe, works part time at a store where he earns $645.60 each month. What expression could be used to find the amount Joe earns working any number of months, m ? 22. Meiko buys 4 packs of markers that each cost the same price. Each pack of markers is discounted by $0.75. Write an expression that could be used to determine the total amount Meiko spends on markers. Let m represent the original price for one pack of markers. 23. Consider the expression 5(3+6). Which statements are true about this expression? Select all that are correct. One factor is 3. The expression has three factors. One factor is equal to 9. The expression is the product of two factors. One factor has two terms. One factor is the difference between 6 and 3.