Annotated Answer Key. Name. Grade 8, Unit 7, Lesson 2: Building blocks: proportional and non-proportional linear relationships

Transcription

1 Complete the questions about linear below. 1. (a) Use the steps provided to determine a pattern, then fill in the two missing steps with the correct number of squares. 2. (a) Use the steps provided to determine a pattern, then fill in the two missing steps with the correct number of stars. Step 0 No squares in Step 0 Step 0 Step 1 Step 1 Step 2 Step 2 Step 3 Step 3 Step 4 Step 4

2 1. (b) Fill out the table below using your work from part (a) above. 2. (b) Fill out the table below using your work from part (a) above. Step Number of Squares Step Number of Stars (c) Fill in the blanks to complete the written description of how the number of squares [from parts (a) and (b) above] is changing with each step, then use this description to come up with an algebraic rule to describe this relationship. Written description: Initially there are _ 0 _ squares, and the number of squares increases at a rate of _ 5 squares per step _. Algebraic rule: 2. (c) Give a written description of how the number of stars [from parts (a) and (b) above] is changing with each step, then use this description to come up with a symbolic formula to describe this relationship. Written description: Initially _ there is 1 star _, and _ the number of stars increases at a rate of 3 stars every step. Symbolic formula: x = step number _ x = step number y = _ number of squares _ y = number of stars Equation: y = 5 x y = 3 x + 1

3 1. (d) Draw a graph to represent the relationship between the step and the number of squares. 2. (d) Draw a graph to represent the relationship between the step and the number of stars. NOTE: Students may be tempted to draw the line connecting these points, so this might provide an opportunity to address domain, and discrete vs. continuous. 1. (e) Circle the correct word to complete 2. (e) Circle the correct word to complete 3. (a) Susan is buying cupcakes for a party she is hosting. If each cupcake costs $1.50, write an equation to calculate the total cost. (Make sure to define your variables!) x = number of cupcakes purchased y = total cost y = 1.5x 3. (b) Circle the correct word to complete 4. (a) Susan also wants to rent a karaoke machine for the party. It costs $50 to have it delivered, and an additional $20 for each hour you use the machine. Write an equation to calculate the total cost. (Make sure to define your variables!) x = number of hours machine is used y = total cost of renting the machine y = 20x (b) Circle the correct word to complete

4 5. (a) Write an equation to represent the relationship shown in the table below. 6. (a) Write an equation to represent the relationship shown in the table below. x y x y y = 3.25x NOTE: An empty row was left at the beginning of this table so that students can work back to x = 0 to find the initial value to help them to see that this is a proportional relationship. They might simply divide each y -value by the corresponding x -value to identify it as proportional; however, in which case that row might not be necessary. y = 2 x + 12 NOTE: The empty row was not included here, in the hopes that students will apply the scaffolding from the previous problem to this problem, but if they do not do this on their own, you may want to make the suggestion of adding in that extra row. 5. (b) Circle the correct word to complete 6. (b) Circle the correct word to complete

5 7. (a) Write an equation to match the graph below. 8. (a) Draw a graph of the line whose 3 equation is y = 4 x 6. 3 Equation: y = 2 x 7. (b) Circle the correct word to complete 8. (b) Circle the correct word to complete NOTE: As students have probably seen many more proportional with a positive constant of proportionality, they might be thrown off by the negative slope of this graph. 9. Write a few sentences explaining how to tell the difference between proportional

6 linear and non-proportional linear. (You may include observations about the tables, about the graphs, about the equations, about the written descriptions, or any general observations!) Tables: Proportional include the pair (0,0). When you divide each y -value by its corresponding x- value the result is the same for all pairs. Non-proportional do not include the pair (0,0). Graphs: Proportional pass through the origin. Non-proportional do not pass through the origin. Equations: Proportional do not have a constant term in the equation. (Form: y = mx) Non-proportional do have a constant term in the equation. (Form: y = mx + b, b 0) Verbal: Description of proportional (first column) only requires a unit rate. Description of non-proportional (second column) requires a rate and an initial value.