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MFM 1P Foundations of Mathematics
Grade 9 Applied Mitchell District High School
Unit 3 Graphing Relations 6 Videos, 7 Lessons
Allow no more than 12 class days for this unit!
This includes time for review and to write the test. This does NOT include time for days absent, including snow days.
You must make sure you catch up on class days missed.
Lesson # Lesson Title Practice Questions Date Completed
1 Interpreting Scatter Plots Page 148 #1-5
2 Lines of Best Fit Page 153 #1, 4, 9
3 Lines of Best Fit with a Graphing Calculator
4.0 Curves of Best Fit Page 163 #3, 4, 5
4.1
No Video - Curves of Best Fit with the Graphing Calculator
Work through Page 164-166 in your text. It shows you step by step instructions on how to use the
graphing calculator for these kinds of question
Page 166 #1, 2
5 Graphing Linear Relations Page 171 #1, 2, 4-7
6
No Video - instead you are performing a "lab" to discover a relationship that is non-linear.
This is to be HANDED in for marks.
7 Interpreting Graphs Page 182 #1-5
Review
No-Video Complete text book questions and be sure to speak with
me about any difficulties you are having.
Page 188 - Chapter Test Page 186 #1-7 with emphasis
on WORD PROBLEMS!
Test Written on : _______________________________________
MFM1P U3L1 Interpretin Scatter Plots
Interpreting a Scatter Plots
Topic : scatter plots
Goal : I know how to make a scatter plot and how to use it to make meaning of data
To make a scatter plot, you need to gather (or have gathered for you) a whole bunch of individual points of data. The following some information gathered from a previous class. Use it to complete the graph on the next page
24 86
23 16427.5
8397 178
21 71
23 93 170
27 72
23 69 165
26 92
26.5
181
90 176
28 185.5
21 57 149
24 94 169
26 96 173
26 60 165
158169
90
163
22 84 166
23 83 16323 88 169
21 84 150
27 96 185
CarterTomTereasaLizzyBarryAllisonMaryJohnBillCarlRickGlenCarol
BethDarylJudySofiaAndreaDale
MFM1P U3L1 Interpretin Scatter Plots
heig
ht (c
m)
19 20 21 22 23 24 25 26 27 28 29 30 31
152
154
156
158
160
162
164
166
168
170
172
174
176
178
180
182
Height vs. Foot Length
184
186
188
foot length (cm)
190
192
194
MFM1P U3L1 Interpretin Scatter Plots
Definitions
Axis :
Scatter Plot :
Dependant Variable :
Independent Variable :
Outlier :
the vertical and horizontal lines that divide up the 4 quadrants on a plane. The vertical axis is the y-axis or dependent axis. The horizontal axis is the x-axis or independent axis
a graph of plotted points that show a relationship between two sets of data.
a variable (characteristic) whose value depends on another. It is often called the y-value and plotted on the vertical axis in a graph
a variable (characteristic) whose value isdepended upon by another. We usually know or set these values and calculate can calculate the dependant variable based on them. It is often called the x-value and is plotted on the horizontal axis on a graph.
a piece of collected data that appears far outside the trend of the other data. Outliers are often deemed to be a mistake, or unusual and disregarded during the analysis of the data.
MFM1P U3L1 Interpretin Scatter Plots
Questions
1. Does the Scatter plot you created show any kind of relationship (trend) between foot length and height?
2. Is the relationship a weak, moderate or strong relationship?
3. One person has a height of 173 cm what is their foot length?
4. One person has a foot length of 22 cm what is their height?
5. Are there any points that stand out from the rest?
Practice Questions - Page 148 #1-5
MFM1P U3L2 Lines of Best Fit
Lines of Best FitOnce you see a pattern or trend in your scatter plot, you can create a line or curve of best fit to model your data.
������������ ����� ��� • used to show the general trend in a scatter plot.• it can help you make predictions• there are many different types:
������������
If there is no pattern or trend in your data, a model should not be created.
������� ��������
How to create a ������ ��������� by hand:
• there should be an even split of data points above or below your line
• the line must follow the general trend/direction of the points
Topic : Lines of Best Fit
Goal : I can recognize when a line of best fit is appropriate for data, I can fit it to the data and can use the line to make predictions.
Once you see a pattern or trend in your scatter plot, you can create a line or curve of best fit to model your data.
• it may actually pass through very few (or even no) actually data points
MFM1P U3L2 Lines of Best Fit
Question to Ponder - Will everyone draw exactly the same line of best fit? If not, who is right?
MFM1P U3L2 Lines of Best Fit
heig
ht (c
m)
19 20 21 22 23 24 25 26 27 28 29 30 31
152
154
156
158
160
162
164
166
168
170
172
174
176
178
180
182
Height vs. Foot Length
184
186
188
foot length (cm)
190
192
194
MFM1P U3L2 Lines of Best Fit
1. Describe the trend line on the graph from yesterday.
2. Use your line of best fit to estimate how tall you would expect someone to be if their foot measured 30 cm.
3. How big would you expect the foot of someone who is 166 cm tall
4. Mrs. Caldwell is 153 cm tall, how big do you think her foot should be?
5. Mrs. Caldwell's foot is actually 23cm how does this fit with the trend line.
6. Use the attached sheet of graph paper to make a scatter plot for Height vs. Arm Length and fit a line to your scatter plot. Create 3 questions like the ones above that relate to your graph.
MFM1P U3L2 Lines of Best Fit
heig
ht (c
m)
Height vs. Foot Length
foot length (cm)
MFM1P U3L2 Lines of Best Fit
Question 1.
Question 2.
Question 3.
Height vs. Armspan
Practice Questions - 153 #1, 4, 9
MFM1P U3L3 Using a Graphing Calculator for Line of Best Fit
Topic : graphing relations
Goal : I can draw a line of best fit through data using a graphing calculator.
Using a Graphing Calculator for a Line of Best FitExample 1. Use a graphing calculator to plot the points in the following chart and use it to answer the given questions.
a) Does there appear to be a relationship between the temperature and ice cream sales? If so, describe it.
b) If there is a relationship - we say that the two values have a correlation. If both values are increasing it has a positive correlation. If one value increases while the other decreases, it is said to have a negative correlation. Is this POSITIVE or NEGATIVE correlation?
c) Use the graphing calculator to find a line of best fit for the data. How many ice cream sales would you expect if the temperature reached 30o. This number is OUTSIDE the information you are given. Going beyond your given information is called extrapolation
d)Using the line of best to find the ice cream sales you might expect if the temperature was 20o. This is inside your data, but not one of the points given. Finding information inside your data is called interpolation.
MFM1P U3L3 Using a Graphing Calculator for Line of Best Fit
Clear the Memory when you first turn on the calculator
Enter an equationto graph
Adjust the amount of a graph you see
Zoom in or out of the graph
View the graph you have plotted or
entered
Turn on the scatter
plot settings
Adjust your plot
Enter your
scatter plot
points
Put independent (horizontal) variable in L1 and dependant
(vertical) in L2
Make it find a line of best fit.
Put the line on the graph
statistics
Adjust the Window
xmin xmax
ymax
ymin
xmin Set a little smaller than your smallest independent value (horizontal)
xmax Set a little bigger than your largest independent value (horizontal)
ymin Set a little smaller than your smallest dependent value (vertical)
ymax Set a little bigger than your largest dependent value (vertical)
MFM1P U3L3 Using a Graphing Calculator for Line of Best Fit
Men's world Speed Skating records
Practice Questions - Page 154-155 #4, 6, 9
MFM1P U3L4 Curve of Best Fit
Topic : curves of best fit
Goal : I know what a graph looks like when a curve of best fit is more appropriate than a line of best fit.
Curve of Best Fit
Not all data that you can find will give you a linear pattern. If the data is quite obviously NOT in a line, it is inappropriate to fit a line to it. Instead you should use a curve of best fit.
MFM1P U3L4 Curve of Best Fit
Daylight 9.09.911.212.814.215.215.414.513.211.710.39.2
Month123456789
101112
Graph the following information and draw on a curve of best fit.
Day
light
Hou
rs
Month
Note: You don't just play connect the dots. Draw the smoothest curve possible in the pattern it implies. If you CAN play connect the dots to get a smooth curve, it is a
PERFECT relationship. The closer the dots are to your line, the stronger the relationship.
Practice Questions - Page 163 #3, 4, 5
When you have these completed, work on Page 164 - 166 in the text book where it shows you how to find a curve of best fit with the graphing calculator.
MFM1P U3L5 Graphing Linear Relations
Topic : Relationships
Goal : I can collect data and determine if it represents a linear or non-linear relationship.
Graphing Linear RelationsWhenever you graph information, and the graph turns out to be a straight line, we say that there is a linear relation. If the points are in a perfect straight line, it is a mathematically linear relationship.
Example 1. Create a table of values comparing the frame number to the number of tiles in the frame. Graph the data and see if you can find a relationship in the data.
frame#
# oftiles
Can you find a way to determine the number of tiles by just knowing the frame number?
Describe the trend.
MFM1P U3L5 Graphing Linear Relations
Example 2. How are the non-right angles in a right triangle related?
x
y
x y1020304050607080
You should notice a pattern in the table after figuring out a few numbers. As long as I've chosen to have my x-values to go up at a
constant rate, then the y-values will too. Linear relations have a CONSTANT RATE OF CHANGE. If you don't set pick x-values that
have a that constant rate of change you won't see that pattern in the y's until you graph the points.
Pul
lP
ull
Pul
lP
ull
Is it appropriate to draw a line through the points? i.e.
is all the information between the points valid?
Pul
lP
ull
Should we extend the line - make it go on forever by putting
arrows heads on it? Or is it a line segment?
Pul
lP
ull
What are the ends of our line segment? Are the ends
"meaningful"? If yes use a "DOT" , if no use a open circle.
When you graph a relation, ask yourself...
MFM1P U3L5 Graphing Linear Relations
Using words write a rule that shows what you need to do with x, to get y...
Now write that in math symbols...
If the bottom angle (x) in a right triangle were 35o, what is the top angle. Use both your graph and your math equation.
Practice Questions - Page 171 #1, 2, 4-7
MFM1P U3L6 Graphing Non-Linear Relations
Graphing Non-Linear RelationsInvestigation - Motion of a pendulum
Purpose : to see if there is a relationship between the time for a pendulum to swing and the length of a the pendulum string.
Apparatus : string, metal washer, ruler, marker, tape
Method : 1. Attach the washer to the string.2. starting at the washer, use your marker to put a mark
every 10 cm along the length of the string.3. Attach the string to the desk starting first at the 10 cm
mark, so that it may swing freely below the desk.4. Pull the pendulum back and release. Let it swing
freely for a few times then begin timing. Time for 6 full swings (back and forth) and record in the table below. Repeat 2 more times and then take an average time for that length.
5. Repeat step 4 for lengths 20, 30, 40, 50 and 60. Try to pull the washer back at the roughly the same angle each time.
6. Graph on the grid provided. Draw on a best fit / line or curve as appropriate.
Hypothesis :
Topic : linear vs. Non Linear relations
Goal : I can analyze collected data to determine if the relationship is linear or non-linear and I can make predictions using that analysis
MFM1P U3L6 Graphing Non-Linear Relations
Observations :
When%transferring%your%data%to%the%graph%you%must%decide%which%of%length%or%time%is%your%dependent%and%
which%is%you%independent%variables.%%Does%“length%depend%on%time”%or%does%“time%depend%on%length”.%%Remember%the%
vertical%axis%depends%on%the%horizontal%
axis.
MFM1P U3L6 Graphing Non-Linear Relations
Conclusions : Complete the following questions…
Describe the trend. Does this show a linear relationship? How do you know?
Suppose you had made the pendulum 35 cm long, how long do you think it would take to swing 6 times?
What problems did you experience? What other factors may have influenced the swing time? Is there any way you could test out your theory?
Practice Questions - Page 177 #1-3, 5, 6, 10
MFM1P U3L7 Interpreting Graphs
Interpreting GraphsIf the given graph shows the height of water in a bath tub - use it to answer the following questions
What happened from C to D and from F to G that would cause the water level to change, almost instantaneously?
What part of the graph shows the actual bath?
What is happening from A to B?
When did the person pull the plug?
Topic : Graphing Relationships
Goal : to be able to look at a graph and interpret what is happening.
MFM1P U3L7 Interpreting Graphs
How to read a line graph...
Horizontal Lines mean -
Vertical Lines mean -
Straight Lines mean -
Curves mean -
The steeper the line
Practice Questions - Page 182 #1-5
MFM1P U3L7 Interpreting Graphs
The Bicycle TripMary and Carolyn set out for a bicycle trip. The distance-time graph shows their progress as they reach their destination.
Write a story that describes their trip. This could be a play-by-play sportscast.
Details you should include:• times they were together/apart, stopped, or going faster/slower• possible events explaining the different sections of the graphs• references to time and distance• comparisons and contrasts
Write a creative story as you use the information in the graph.
Thinking Task for Graphing RelationsDue - the day your write the Unit 3 test!