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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 48 #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


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

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176

178

180

182

Height vs. Foot Length

184

186

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foot length (cm)

190

192

194


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.


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


Question to Ponder - Will everyone draw exactly the same line of best fit? If not, who is right?


heig

ht (c

m)

19 20 21 22 23 24 25 26 27 28 29 30 31

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184

186

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foot length (cm)

190

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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.


heig

ht (c

m)


foot length (cm)


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.


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)


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 - 3 #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.


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...


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


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.


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.


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


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!

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