8 th Grade Honors Name: Chapter 2 Examples of Rigor Learning Target #: I am learning to compare tables, equations, and graphs to model and solve linear & nonlinear situations. Success Criteria I know I am success when I can. 2. Identify Dependent and Independent Quantities and Write an Expression 2. Determine the Unit Rate of Change 2. Determine the Solution to a Linear Equation Using Function Notation 2. Determine the Solution to a Linear Equation on a Graph Using an Intersection Point 2.2 Identify the Parts of a Linear Function 2.2 Describe the Parts of a Linear Function 2.2 Compare Tables, Equations, and Graphs to Model and Solve Linear Situations 2.3 Represent inequalities on a coordinate plane 2.6 Determine solutions for nonlinear functions graphically using intersection points. Caroline earns $25 per week babysitting after school. She deposits half of this amount into her savings account every Saturday. The table shows amount of money she has saved after so many weeks of babysitting. A. Complete the table. In the last row, write an expression that represents the amount of money Caroline has saved for an arbitrary time w week. B. Use function notation to express the amount of money saved as a function of time. C. To which function family does the function you wrote in part B belong? Units Expression D. Use function notation to determine the amount of money saved after Caroline has babysat for 2 weeks. E. How many weeks will it take Caroline to save $32.50? Independent Dependent 2. Malik received a $250 gift card from his grandparents and is using it only to pay for his karate lessons, which cost $25 per month. A. Write a function that describes the dollar amount of money d, on the card after t months. 0 2 w 62.50 25.00 B. Graph the function that you wrote in part A. Be sure to label your axes. C. Identify the slope and y-intercept of the graph. Describe what each means in terms of this problem situation. D. Use your graph to estimate how much money Malik will have on his gift card after 9 weeks.
3. Elena works a part-time job after school to earn money for a summer vacation. She is paid a constant rate for each hour she works. The table shows the amounts of money that Elena earned for various amounts of time that she worked. A. What are the dependent and independent quantities in this problem situation? Explain your reasoning. B. Determine the unit rate of change for the problem situation. C. Complete the table. Write an expression that represents the amount of money Elena earns for an arbitrary time worked of t hours. D. Use function notation to express the amount of money as a function of time. E. To which function family does the function you wrote in part D belong? F. Use function notation to determine the amount of money that Elena earns for working 7.5 hours.
4. Lea is walking to school at a rate of 250 feet per minute. Her school is 5000 feet from her home. The function f(x) = 250x represents the distance Lea walks. A. How many minutes have passed if Lea still has more than 2000 feet to walk? 5. Julian is cutting lengths of rope for a class project. Each rope length should be 0 inches long. The specifications allow for a difference of inch. The function f(x) = x - 0 represents the difference between the rope lengths cut and the specifications. A. Graph the function. Indicate on the graph what rope lengths meet the specifications. B. Write and solve an absolute value inequality that describes the acceptable rope lengths. 6. Jonah bought a rare collectible for $50 that is supposed to gain one-fifth of its value each year. A. Which equation represents this situation? a. f( x) x 50 5 b. f( x) x 50 5 c. fx ( ) 50(.2) x B. Graph this situation. C. Jonah plans to sell his collectible when it s worth at least $500. When should he sell his collectible?
Learning Target #2: I am learning to solve linear & absolute value equations and inequalities, compound inequalities, & absolute value inequalities. Success Criteria Solve each equation. I know I am success when I can. 2. Solve linear equations 2.3 Write and Solving 2.3 Represent on a Number Linear 2.3 Represent on a Coordinate Plane 2.4 Write Compound 2.4 Represent the Solutions to Compound on a Number Line 2.4 Solve Compound 7. 4(x 7) + 2 = 20 8. 4x 3 = 9x + x 9. 5 9 0. 4x 2(3x + 5) = -2x 7 7. 3 x 8 9 2. -3(2x + 4) = 6(-x 3) + 6 5 Solve each inequality and graph the solution on a number line. 3. 950 9.25x 398 4. 5 9x 2 Graph each compound inequality on the number line. Then, write the final solution that represents each graph. 5. x 4and x 6. x 3or x 2 7. x 3and x 8. x -2 or x 6
9. Create an example of a compound inequality that has infinitely many solutions. Then, graph your solution on the number line. Solve each compound inequality and graph the solution on the number line. 20. - < 4x 3 5 2. x 4 < -2 or -0x 7 < -57 2