5.2E Lesson: Proportions in Tables and Graphs*
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1 5.2E Lesson: Proportions in Tables and Graphs* Name: Period: 1. Use Graph A below to fill in the table relating calories to snacks. Number Number of Ordered Write a complete sentence describing the meaning of this of Snacks Calories Pair point on the graph. (0, 0) Zero snacks have zero calories (1,110) One snack has 110 calories (2,220) Two snacks have 220 calories (3,330) Three snacks have 330 calories. 0 (,0) Four snacks have 0 calories. This task should help students solidif the connections between points on a graph, ordered pairs, unit rates, equations and tables. Note, this is the first ordered pair notation used in this course. Most students saw this in 6 th grade. a. Does the graph show a proportional relationship? Wh or wh not? Yes, it is a straight line going through the origin. Graph A b. What is the unit rate (include labels). How do ou know? 110 calories per snack. Each time a snack is added the calories increase b 110 c. What is the proportional constant? 110 d. Write the equation for the number of calories related to number of snacks. 110
2 2. Use Graph B to fill in the table relating cost to cab-ride distance. Miles Cost Ordered Pair Write a complete sentence describing the meaning of this point on the graph. 0 $ (0,) The cab ride costs $ just to start. 1 $5 (1,5) The cab ride costs $5 after 1 mile. 2 $6 (2,6) The cab ride costs $6 after 2 miles. 3 $7 (3,7) The cab ride costs $7 after 3 miles. $8 (,8) The cab ride costs $8 dollars after miles. Graph B a. Does the graph show a proportional relationship? Wh or wh not? No, it does not start at (0,0) 9 8 b. Looking at the graph, describe what s happening to the cost as miles increase. The cost increases $1 for ever mile. c. Is there a unit rate? If so, what is the unit rate (include labels)? No Cost in Dollars d. Is the rate consistent for the entire graph? Eplain. The unit rate is not consistent for the entire graph Miles e. Challenge: Write the equation relating cost to cab-ride distance. Eplain the equation in words. It costs $ just to hail the cab, and the $1 for ever mile ou go. Again, ou are not tring to teach
3 3. Eamine the graphs below and do the following for each problem: (1) Complete the table. (2) Determine if the situation represents a proportional relationship. (3) State the constant of proportionalit. () Write the equation that relates to. a. b Constant of proportionalit (unit rate): 2 Equation: 2 Constant of proportionalit (unit rate): 1.5 or Equation: 1.5 or c. d Constant of proportionalit (unit rate): 1 Equation: 1 Constant of proportionalit (unit rate): 3 Equation: 3. Graph each relationship from above on the grid below. Label each line a, b, c, or d. For each value in the relationship above, state the corresponding value: a. If = 1, = 2 b. If = 1, = 1.5 c. If = 1, = 1 d. If = 1, = 3 What do ou notice about the relationship between the graphs and the proportional constant? The bigger the proportional constant the steeper the line. The proportional constant and unit rate are the same. Note: in 8 th grade the proportional constant and slope are the same in a proportional relationship. If the relationship is linear but not proportional, we sa that the rate of change is the same as the slope.
4 Converting Units - Quarts related to Gallons: Fill in the missing amounts of quarts and gallons. Then find the ratio for the number of quarts () to the number of gallons (). Gal () Quarts () Ratio What does the ratio tell us? There are quarts in a gallon Write an equation to show how to find the number of quarts in an number of gallons. 7. Make a graph of the relationship between quarts and gallons. Be sure to label our aes and put gallons on the horizontal ais. 8. What does the graph tell us about the relationship of quarts to gallons? It is proportional. 9. Use the line on our graph to fill in the missing -values for the following coordinate points: A (0, 0 ) B (1, ) C (3, 12 ) D (, 16 ) 10. Plot the points and label them A, B, C, and D on the graph. 11. Describe how ou move on the grid from one point to the net (ou must sta on the grid lines to move from A to B, B to C, C to D). Use words like up, down, right, left, vertical, horizontal. It moves up units for ever 1 unit it moves to the right. 12. How does this moving relate to rate? Unit rate is, up over 1 same numbers.
5 13. Would the ordered pair (6, 26) lie on the graph? Wh or Wh not? No. 1. How would our ratio change if quarts was to become the independent variable? There are gallons in a quart. 15. Write the new equation using quarts as the independent variable Graph the new relationship below. Label our aes. Number of gallons Number of quarts 17. When comparing both graphs, what do ou notice? Still a straight line through the origin, and it has a proportional relationship. This line is much less steep. Converting Units - Centimeters related to inches: Fill in the missing data. Inches () Centimeters () Ratio What is the unit rate? How did ou find it? 2.5 centimeters per inch
6 19. What did ou do to find the number of centimeters in a given number of inches? Write an equation to find the number of centimeters in a given number of inches. There are 2.5 centimeters in an inch Predict the movement between points on a graph. Eplain (use words like up, down, right, left, vertical, horizontal). It moves up 2.5 units for ever 1 unit it moves to the right. 21. Graph the relationship.
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