Transcript rttmsa 1.5 - additional practice with linear relationship concepts.pptx

MSA Investigation 1 – Additional Practice
Learning Target: Added practice with linear relationships
Homework:
1) Complete all pages in the packet.
2) Get a signature on the packet.
Warm Up: (packet pg. 13)
Jose, Mario, Melanie, Mike, and Alicia are on a weeklong cycling trip.
The table below gives the distance Jose, Mario, and Melanie travel for the first
3 hours. Cycling times include only biking time, not time to eat, rest, and so on.
1. Assume that each
person cycles at a
constant rate.
Find the rate at
which each person
travels during the
first 3 hours.
Jose: 5 mph
Mario: 7 mph
Melanie:
9 mph
3. Graph the time and distance data for all three riders on the
same coordinate axes. Use different colors for each person.
10 20 30 40 50 60 70 80 90 100 110
Distance (Miles)
Cycling with Friends
KEY:
Jose
Mario
Melanie
4. Use the graphs
to find the distance
each person travels
in 6 ½ hours.
1
2 3 4 5 6 7
Hours cycled
8 9 10
2. Find the distance each person travels in 7 hours.
y = mx + b
Jose:
35 miles = 5 mph (7hrs)
Mario:
49 miles = 7 mph (7hrs)
Melanie:
63 miles = 9 mph (7hrs)
5. Use the graphs to find the time
it takes each person to travel 70 miles.
KEY:
Jose
Mario
Melanie
10 20 30 40 50 60 70 80 90 100 110
Distance (Miles)
Cycling with Friends
6. How does the
rate at which each
person rides affect
the graph?
1
2 3 4 5 6 7
8 9 10
Hours cycled
7. For each rider, write an equation to calculate the distance
traveled after a given number of hours. y = mx + b
Jose: d = 5t
32.5 = 5(6.5)
Mario: d = 7t
45.5 = 7(6.5)
Melanie: d = 9t
58.5 = 9(6.5)
8. Use your equations from the previous question to
calculate the distance each person travels in 6 ½ hours.
9. How does a person’s cycling rate show up in his or her equation?
y = mx + b
It is the slope or the coefficient.
It is placed before, and multiplied by,
the independent variable.
10. Are any of these proportional relationships? If so, what is the
constant of proportionality?
Yes, they are all proportional
Jose:
5
Mario:
7
Melanie: 9
11. Mike makes the following table of the distances he travels during
the first day of the trip.
a. Suppose Mike continues riding at this rate. Write an equation
for the distance d Mike travels after t hours.
y = mx + b
d = mt
d = 6.5t
b. Sketch a graph of the equation.
5 10 15 20 25 30 35 40 45 50 55 60 65
distance
Mike’s cycling trip
i. How did you choose
the range of values for
the time axis?
ii. How did you choose
the range of values
for the distance axis?
1
2 3 4 5 6 7
8 9 10
time (hours)
c. How can you find the distances Mike travels in 7 hours and 9 ½ hours
using the table?
7
8
9
45.5
52
58.5
10
65
5 10 15 20 25 30 35 40 45 50 55 60 65
distance
Mike’s cycling trip
1
2 3 4 5 6 7
8 9 10
time (hours)
d. How can you find the
distances Mike travels in
7 hours and 9 ½ hours
using the graph?
g. How can you find the number of hours it takes Mike to travel 100
miles and 237 miles using the ________?
TABLE
EQUATION
d = 6.5t
100 = 6.5(15.38)
237 = 6.5(36.5)
GRAPH
300
275
250
225
200
175
150
125
100
75
50
25
5
10
15
20
25
30
35
40
45
50
distance
Mike’s cycling trip
time (hours)
10
15.38
130
36.5
65
100
200
237
i. What are the advantages and disadvantages of using
each model in parts c-h?
Advantages
Table
Graph
Equation
Disadvantages
j. Compare the rate at which Mike rides with the rates at
which Jose, Mario, and Melanie ride. Who rides the fastest?
Mike:
6.5 miles per hour
Jose:
5 miles per hour
Mario:
7 miles per hour
Melanie: 9 miles per hour
i. How can you determine this from the tables?
ii. How can you determine this from the graphs?
10 20 30 40 50 60 70 80 90 100 110
Distance (Miles)
Cycling with Friends
1
2 3 4 5 6 7
8 9 10
Hours cycled
KEY:
Jose
Mario
Melanie
Mike
iii. How can you determine this from the equations?
Mike:
d = 6.5t
Jose:
d = 5t
Mario:
d = 7t
Melanie: d = 9t
12. The distance in miles Alicia travels in t hours is represented by
the equation d = 7.5t.
a. At what rate does Alicia travel? Explain.
7.5 miles per hour
The number of hours she travels
times her travel rate of 7.5 miles per hour
will determine the total hours she will travel.
b. Suppose the graph of Alicia’s distance and time is put on the same
set of axes as Mike’s, Jose’s, Mario’s, and Melanie’s graphs. Where
would it be located in relationship to each of the graphs? Describe
the location without actually making a graph.
Alicia would be
faster than Jose and
Mike, and just barely
faster than Mario.
But Alicia would be
slower than Melanie.
10 20 30 40 50 60 70 80 90 100 110
Distance (Miles)
Cycling with Friends
1
2 3 4 5 6 7
8 9 10
Hours cycled
MSA Investigation 1 – Additional Practice
Did I reach my Learning Target?
Additional practice with linear relationship concepts.
Homework:
1) Complete all pages in the packet.
2) Get a signature on the packet.