MPM1D – Unit 4: Relationships – Lesson 5 Date:___________ Learning goal: how to interpret and analyze graphs.

Interpreting Graphs WARM UP

1) What is happening between points A and B? 2) What is happening between points B and C? 3) What is happening between points C and D? 4) What is happening between points D and E? 5) What is happening between points E and F? 6) Tell a story that describes what is happening in the graph.

Interpreting Graphs Example 1: Suppose tap water, flowing from a faucet at a constant rate is used to fill each of these containers. Match each of the following graphs with the appropriate container. Justify your choice.

Example 2: Adrian and Joseph decided to race one another. The graph shows their motion during the race.

a) Over what distance was the race run? Who won?

b) Who got a head start? How many seconds was the head start?

c) Who ran faster during the race?

d) For how many seconds had Adrian been running when he was overtaken by Joseph?

e) How far from the start did Joseph overtake Adrian?

Example 3: Chris runs each day as part of his daily exercise. The graph shows his distance from home as he runs his route. a) Which segment is Chris travelling the fastest/slowest? b) The formula to calculate speed is c) Calculate his rate of change (speed) for each segment of the graph. Example 4: The graph represent the distance between a squirrel and a tree, d, in metres, as a function of time, t, in seconds. Calculate the speed of each section of the graph. Show your work

Assignment 4.5: Interpreting Graphs 1. Ian and his friends were sitting on a deck and eating sunflower seeds. Each person had a bowl with the

same amount of seeds. The graphs below all show the amount of sunflower seeds remaining in the person’s bowl over a period of time. Write sentences that describe what may have happened for each person.

a) b) c) d)

2. Indicate which graph matches the statement. Give reasons for your answer.

a) A bicycle valve’s distance from the ground as a boy rides at a constant speed.

a) b) c) d)

b) A child swings on a swing, as a parent watches from the front of the swing.

3. Liquid is poured at a steady rate into the bottle

shown in the diagram. As the bottle is filled, the height, h, of the liquid in the bottle changes. Which of the five graphs below shows this change? Give a reason for your choice.

h

h

h

h

h

Time

Time

Time

Time

Time

Graph A

Graph C

Graph B

Graph D

Graph E

4. 11 o’clock, Micha’s mother sends him to the corner store for milk and tells him to be back in 30 minutes. Examine the graph.

a) Why are some line segments on the graph steeper than

others? b) Calculate the rate of change (speed) of each of the line

segments: c) Over what interval(s) of time is Micha travelling the

fastest? Compare steepness, not direction. d) Over what interval(s) of time is Micha travelling the

slowest? Compare steepness, not direction. e) How long did it take Micha to reach the store? How do you

know? f) How long did Micha stay at the store? g) How long did it take Micha to get home from the store? h) How can you use the graph to tell which direction Micha is

travelling? i) Did Micha make it home in 30 minutes? How do you

know? 5. The tortoise and the hare run a race against each other. The distance time graph for their race is shown

below. The motion of the tortoise is shown by the line AB. The motion of the hare is shown by the line CDEF.

a) Over what distance was the race run? b) What is the speed of the tortoise? c) How many seconds of a head start did the tortoise have over the hare? d) Describe what the hare was doing between the points C and D, D and E, E and F. e) What is the speed of the hare between the points C and D, D and E, E and F f) How long has the tortoise been moving when it was overtaken by the fare? g) Who won the race and why?

6. The information shown in a graph does not have to represent distance from a CBR. For each of the following, choose the description that most closely matches the graph.

(a) (i) The elevator starts on the second floor, goes to

the fifth floor where it takes on passengers and then goes to the seventh floor.

(b)

(ii) Sarah takes half an hour to get dressed in the morning, hurries to her friend’s house so they can walk to the bus stop to catch the bus to work.

(c) (iii) As the weather cools in the autumn, sales at Matt’s ice cream shop have been decreasing. During one rainy week only the regulars who work in the same building purchased their usual snacks. When Matt introduces a new product, sales begin to improve.

(d) (iv) Daniel’s company assets decrease during the

months when he is preparing his new store but

improve dramatically when the store opens. When a

competitor opens a nearby store, Daniel’s fortunes

take a down turn.

(e) (v) Sandy has been saving a regular amount each

week. When she joins her family on a vacation she

spends part of her savings but resumes her saving

habit when she returns.

(f)

(vi) Jeff’s strength training program calls for him to add time to his workout gradually. After a few weeks Jeff decides to suddenly increase the time he is spending but finds he can maintain but not increase the new level for several weeks. Then he is able to gradually increase the workout time again.