Stuffing Envelopes
(Task from Illustrative Mathematics)
Anna and Jason have summer jobs stuffing envelopes for two different companies.Anna earns $14 for every 400 envelops she finishes. Jason earns $9 for every 300envelopes he finishes.
a)Draw graphs and write equations that show the earnings, as functions of thenumber of envelopes stuffed, for Anna and Jason.
b)Who makes more from stuffing the same number of envelopes? How can you tellthis from the graph?
c)Suppose Anna has savings of $100 at the beginning of the summer and she saves allher earnings from her job. Graph her savings as a function of the number of envelopes she stuffed, n. How does this graph compare to her previous earnings graph? What isthe meaning of the slope in each case?
Slopes Between Points on a Line
(Task from Illustrative Mathematics)
The slope between two points is calculated by finding the change in -values anddividing by the change in -values. For example, the slope between the points (7, -15)and (-8, 22) can be computed as follows:
The difference in the -values is .
The difference in the -values is .
Dividing these two differences, we find that the slope is .
Eva, Carl, and Maria are computing the slope between pairs of points on the line shownbelow.
Eva finds the slope between the points (0,0) and (3,2). Carl finds the slope between thepoints (3,2) and (6,4). Maria finds the slope between the points (3,2) and (9,6). They haveeach drawn a triangle to help with their calculations (shown below).
i. Which student has drawn which triangle? Finish the slope calculation for eachstudent. How can the differences in the x- and y-values be interpreted geometricallyin the pictures they have drawn?
ii. Consider any two points and on the line shown above. Draw a triangle like the triangles drawn by Eva, Carl, and Maria. What is the slope betweenthese two points? Why should this slope be the same as the slopes calculated by thethree students?
Battery Charging
(Task from Illustrative Mathematics)
Sam wants to take his MP3 player and his video game player on a car trip. An hour before they plan to leave, he realized that he forgot to charge the batteries last night. Atthat point, he plugged in both devices so they can charge as long as possible beforethey leave.
Sam knows that his MP3 player has 40% of its battery life left and that the battery charges by an additional 12 percentage points every 15 minutes.His video game player is new, so Sam doesn’t know how fast it is charging but herecorded the battery charge for the first 30 minutes after he plugged it in.
Time charging (minutes) / 0 / 10 / 20 / 30Video game player battery charge (%) / 20 / 32 / 44 / 56
a)If Sam’s family leaves as planned, what percent of the battery will be charged foreach of the two devices when they leave?
b)How much time would Sam need to charge the battery 100% on both devices?