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1P 3 day 6 graphing calculator and correlation.notebook November 09, 2015
Looking for Relationships using
the Graphing Calculator
Learning Goals
review correlation learn how to make a line of best fit learn to draw graphs on the graphing calculator
The plotted points ...
The relationship ... The graph ...
Reveal one graph at a time. Match the graph with a description from each column. Click again to cover.
Minds On ... (best viewed at 100% zoom)pg 314
1P 3 day 6 graphing calculator and correlation.notebook November 09, 2015
Action!
Scatter Plots Types of correlation
Correlation helps to describe the relationship between 2 quantities in a graph.
Correlation can be described as positive or negative, strong, weak, moderate or none.
A scatter plot shows a correlation when the pattern rises up to the right.
This means the two quantities increase together.
A scatter plot shows a correlation when the pattern falls down to the right.
This means that as one quantity increases the other decreases.
Positive or Negative CorrelationUse the eraser to reveal the answers
BLM
Distribute BLM 3.2.1 to students
pg 315
If the points nearly form a line, then the correlation is
To visualize this, enclose the plotted points in an oval. If the oval is narrow, then the correlation is
If the points are dispersed more widely, but still form a rough line, then the correlation is moderate.
Strong or Weak CorrelationUse the eraser to reveal the answers
If the points are dispersed even more widely, but still form a rough pattern of a line, then the correlation is
If the oval is wide, then the correlation is
pg 15
1P 3 day 6 graphing calculator and correlation.notebook November 09, 2015
A scatter plot shows correlation when no pattern appears.
Hint: If the points are roughly enclosed by a circle, then there is correlation.
No Correlation
pg 315
Graphing using the Graphing Calculator
1. Make a table of values
2. Make graph
3. Find correlation
4. Add a line of best fit
Line of best fit is a line that goes through the points does not have to touch any points approximately half the points above and half below
represents correlation can be used to make predictions
1P 3 day 6 graphing calculator and correlation.notebook November 09, 2015
Graph
Handout #2 Golf Shots
This is done by hand, let's do it with the calculator.
Using the Graphing Calculator
Make a table of values new document List and Spreadsheet
Making a graph Add (on top) Data and Stats Choose the labels for x and yaxis
Making a line of best fit
analyze Add movable line
Checking if the line is a good one
show residual squares (turn it on) move line and look for the smallest sum
1P 3 day 6 graphing calculator and correlation.notebook November 09, 2015
Creating a Line of Best Fit
To be able to make predictions, we need to model the data with a line or a curve of best fit.
Rules for drawing a line of best fit:
1. The line must follow the ___________.
2. The line should ________ through as many points as possible.
3. There should be _______________ of points above and below the line.
4. The line should pass through points all along the line, not just at the ends.
BLM
Distribute BLM 3.2.2 to students
pg 316
Use the information below to draw a scatter plot. Describe the correlation and draw the line of best fit.
The teachers at Holy Mary high school took a survey in their classes to determine if there is a relationship between the student’s mark on a test and the number of hours watching T.V. the night before.
Mark % 75 70 68 73 59 57 80 65 63 55 85 70 55
Number of Hours 1 2 3 2 4 4.5 1 3 3.5 4 1 2.5 4
pg 316
1P 3 day 6 graphing calculator and correlation.notebook November 09, 2015
Home Activity Practice
For each of the graphs below:1) Draw a line of best fit if possible. If a straight line can be drawn, label the graph as linear.
If a straight line cannot be drawn, label the graph as nonlinear.2) Label each graph as showing a relationship or no relationship. 3) The following instructions are for the linear graphs only.
a) Describe the correlation of each scatter plot as positive or negative.b) Describe the correlation as strong, moderate, or weak.
linear
nonlinear
relationship
no relationship
positive
negative
strongmoderate
weak
Drag the key terms to describe each graph
a b c
BLM
Distribute BLM 3.2.4 to students
pg 317
linearrelationshipnegativestrong
nonlinearno relationship
linearpositiveweak
Home Activity Practice
linear
nonlinear
relationship
no relationship
positive
negative
strongmoderate
weak
Drag the key terms to describe each graph
d e f
g h i
pg 17
linear
linear
linear
nonlinear
nonlinear
linear
relationship relationship
relationshiprelationship
positive
positivepositive
negative
no relationship
strongweak
strong
strong
1P 3 day 6 graphing calculator and correlation.notebook November 09, 2015
Attachments
BLM 3.2.4.pdf
BLM 3.2.1.doc
BLM 3.2.1.pdf
BLM 3.2.2.doc
BLM 3.2.2.pdf
BLM 3.2.3.doc
BLM 3.2.3.pdf
BLM 3.2.4.doc
Word Wall 3.2.pdf
1P 3.2 TIPS Lesson.doc
1P 3.2 TIPS Lesson.pdf
Word Wall 3.2.doc
3.2.4: Practice
For each of the graphs below: 1) Draw a line of best fit if possible. If a straight line can be drawn, label the graph as linear.
If a straight line cannot be drawn, label the graph as non-linear. 2) Label each graph as showing a relationship or no relationship. 3) The following instructions are for the linear graphs only.
a) Describe the correlation of each scatter plot as positive or negative. b) Describe the correlation as strong, moderate, or weak.
Linear / Non-linear Relationship / No Relationship
Positive / Negative Strong / Moderate / Weak
a Linear / Non-linear
Relationship / No Relationship Positive / Negative
Strong / Moderate / Weak
b Linear / Non-linear
Relationship / No Relationship Positive / Negative
Strong / Moderate / Weak
c
Linear / Non-linear Relationship / No Relationship
Positive / Negative Strong / Moderate / Weak
d Linear / Non-linear
Relationship / No Relationship Positive / Negative
Strong / Moderate / Weak
e Linear / Non-linear
Relationship / No Relationship Positive / Negative
Strong / Moderate / Weak
f
Linear / Non-linear Relationship / No Relationship
Positive / Negative Strong / Moderate / Weak
g Linear / Non-linear
Relationship / No Relationship Positive / Negative
Strong / Moderate / Weak
h Linear / Non-linear
Relationship / No Relationship Positive / Negative
Strong / Moderate / Weak
i
SMART Notebook
3.2.1: Scatter Plots - Types of Correlation
Correlation helps to describe the relationship between 2 quantities in a graph. Correlation can be described as positive or negative, strong, weak, moderate or none.
Positive or Negative Correlation
A scatter plot shows a ______________ correlation when the pattern rises up to the right.
This means that the two quantities increase together.
A scatter plot shows a ______________ correlation when the pattern falls down to the right.
This means that as one quantity increases the other decreases.
Strong or Weak Correlation
If the points nearly form a line, then the correlation is
____________________.
To visualize this, enclose the plotted points in an oval. If the oval is
narrow, then the correlation is ____________________.
If the points are dispersed more widely, but still form a rough line,
then the correlation is _____________________.
If the points are dispersed even more widely, but still form a rough
pattern of a line, then the correlation is ___________________.
If the oval is wide, then the correlation is ____________________..
No Correlation
A scatter plot shows ________ correlation when no pattern appears.
Hint:
If the points are roughly enclosed by a circle, then there is _______ correlation.
SMART Notebook
3.2.1: Scatter Plots - Types of Correlation Correlation helps to describe the relationship between 2 quantities in a graph.
Correlation can be described as positive or negative, strong, weak, moderate or none.
Positive or Negative Correlation
A scatter plot shows a ______________ correlation when the pattern rises up to the right. This means that the two quantities increase together.
A scatter plot shows a ______________ correlation when the pattern falls down to the right. This means that as one quantity increases the other decreases.
Strong or Weak Correlation
If the points nearly form a line, then the correlation is ____________________. To visualize this, enclose the plotted points in an oval. If the oval is narrow, then the correlation is ____________________.
If the points are dispersed more widely, but still form a rough line, then the correlation is _____________________.
If the points are dispersed even more widely, but still form a rough pattern of a line, then the correlation is ___________________. If the oval is wide, then the correlation is ____________________..
No Correlation
A scatter plot shows ________ correlation when no pattern appears. Hint: If the points are roughly enclosed by a circle, then there is _______ correlation.
SMART Notebook
3.2.2: Line of Best Fit
Line of Best Fit
To be able to make predictions, we need to model the data with a line or a curve of best fit.
Use the information below to draw a scatter plot. Describe the correlation and draw the line of best fit.
The teachers at Holy Mary high school took a survey in their classes to determine if there is a relationship between the student’s mark on a test and the number of hours watching T.V. the night before.
Mark %
75
70
68
73
59
57
80
65
63
55
85
70
55
Number of Hours
1
2
3
2
4
4.5
1
3
3.5
4
1
2.5
4
Rules for drawing a line of best fit:
1.The line must follow the _____________________.
2.The line should __________ through as many points as possible.
3.There should be ____________________________ of points above and below the line.
4.The line should pass through points all along the line, not just at the ends.
SMART Notebook
3.2.2: Line of Best Fit
Line of Best Fit To be able to make predictions, we need to model the data with a line or a curve of best fit.
Use the information below to draw a scatter plot. Describe the correlation and draw the line of best fit. The teachers at Holy Mary high school took a survey in their classes to determine if there is a relationship between the student’s mark on a test and the number of hours watching T.V. the night before. Mark % 75 70 68 73 59 57 80 65 63 55 85 70 55 Number
of Hours
1 2 3 2 4 4.5 1 3 3.5 4 1 2.5 4
Rules for drawing a line of best fit:
1. The line must follow the _____________________.
2. The line should __________ through as many points as possible.
3. There should be ____________________________ of points above and below the line.
4. The line should pass through points all along the line, not just at the ends.
SMART Notebook
3.2.3: Relationships Summary
A scatter plot is a graph that shows the _______________________ between two variables.
The points in a scatter plot often show a pattern, or ____________.
From the pattern or trend you can describe the ________________.
Example:
Julie gathered information about her age and height from the markings on the wall in her house.
Age (years)
1
2
3
4
5
6
7
8
Height (cm)
70
82
93
98
106
118
127
135
a)Label the vertical axis.
b)Describe the trend in the data.
c)Describe the relationship.
Variables
The independent variable is located on the ___________ axis.
Note:
The independent variable comes first in the table of values.
This variable does not depend on the other variable.
The dependent variable is located on the ____________ axis.
This variable depends on the other variable.
Independent variable: _______________
Dependent variable: _____________
3.2.3: Relationships Summary (continued)
Making Predictions
Use your line of best fit to estimate the following:
Question
Answer
Method of Prediction
How tall was Julie when she was 5 years old?
How tall will Julie be when she is 9 years old?
How old was Julie at 100 cm tall?
How tall was Julie when she was born?
Interpolate
When you interpolate, you are making a prediction __________ the data.
Hint:
You are interpolating when the value you are finding is somewhere between the first point and the last point.
These predictions are usually _________.
Extrapolate
You are extrapolating when the value you are finding is before the first point or after the last point. This means you may need to extend the line.
When you extrapolate, you are making a prediction _____________ the data.
It often requires you to ____________the line.
These predictions are less reliable.
SMART Notebook
3.2.3: Relationships Summary A scatter plot is a graph that shows the _______________________ between two variables. The points in a scatter plot often show a pattern, or ____________.
From the pattern or trend you can describe the ________________. Example: Julie gathered information about her age and height from the markings on the wall in her house.
Age (years) 1 2 3 4 5 6 7 8
Height (cm) 70 82 93 98 106 118 127 135
a) Label the vertical axis. b) Describe the trend in the data. c) Describe the relationship.
Variables The independent variable is located on the ___________ axis.
This variable does not depend on the other variable.
The dependent variable is located on the ____________ axis.
This variable depends on the other variable.
Independent variable: _______________ Dependent variable: _____________
Note: The independent variable comes first in the table of values.
3.2.3: Relationships Summary (continued) Making Predictions Use your line of best fit to estimate the following:
Question Answer Method of Prediction
How tall was Julie when she was 5 years old?
How tall will Julie be when she is 9 years old?
How old was Julie at 100 cm tall?
How tall was Julie when she was born?
Interpolate When you interpolate, you are making a prediction __________ the data.
These predictions are usually _________. Extrapolate When you extrapolate, you are making a prediction _____________ the data.
It often requires you to ____________the line. These predictions are less reliable.
Hint: You are interpolating when the value you are finding is somewhere between the first point and the last point.
You are extrapolating when the value you are finding is before the first point or after the last point. This means you may need to extend the line.
SMART Notebook
3.2.4: Practice
For each of the graphs below:
1) Draw a line of best fit if possible. If a straight line can be drawn, label the graph as linear.
If a straight line cannot be drawn, label the graph as non-linear.
2) Label each graph as showing a relationship or no relationship.
3) The following instructions are for the linear graphs only.
a) Describe the correlation of each scatter plot as positive or negative.
b) Describe the correlation as strong, moderate, or weak.
Linear / Non-linear
Relationship / No Relationship
Positive / Negative
Strong / Moderate / Weak
a
Linear / Non-linear
Relationship / No Relationship
Positive / Negative
Strong / Moderate / Weak
b
Linear / Non-linear
Relationship / No Relationship
Positive / Negative
Strong / Moderate / Weak
c
Linear / Non-linear
Relationship / No Relationship
Positive / Negative
Strong / Moderate / Weak
d
Linear / Non-linear
Relationship / No Relationship
Positive / Negative
Strong / Moderate / Weak
e
Linear / Non-linear
Relationship / No Relationship
Positive / Negative
Strong / Moderate / Weak
f
Linear / Non-linear
Relationship / No Relationship
Positive / Negative
Strong / Moderate / Weak
g
Linear / Non-linear
Relationship / No Relationship
Positive / Negative
Strong / Moderate / Weak
h
Linear / Non-linear
Relationship / No Relationship
Positive / Negative
Strong / Moderate / Weak
i
SMART Notebook
Dependent Variable
The variable in a relation whose value
depends on the value of the
independent variable.
Ex. Doing a science lab where you are
comparing how far a car goes over
time, time stays constant (so it is the
independent variable) while distance
changes over time (so it is the
dependent variable).
Independent Variable
The variable in a relation whose value
you choose.
Ex. A CBR activity where you are
comparing how far someone walks over
time. In this case, time stays contant
(independent variable) and the
distance changes over time (dependent
variable).
TM
Extrapolate
To estimate values lying outside the
range of a given data. To extrapolate
from a graph means to estimate
coordinates of points beyond those that
are plotted.
The population has
continued to
increase each year.
From 1961 to 2001,
the population
increased about 3
million every 10 years.
Since there has been continued growth within
Canada at a fairly steady rate, we can make a
prediction that Canada’s population in 2011 will
be approximately 34 million.
Ex.
Interpolate To estimate values lying between
elements of given data.
To interpolate from a graph means to
estimate coordinates of points between
those that are plotted.
Ex:
QuickTime™ and a decompressor
are needed to see this picture.
You now know that you have earned $12.00 for
working 3.5 hours.
Suppose you work for
3.5 hours at $4.00 per
hour. Using the graph,
you can predict your
earnings.
On the x-axis, create a
vertical line to meet
with the line of best fit.
Then, extend a
horizontal line, from this
point, to the y-axis.
Line of Best Fit
A straight line drawn through as much
data as possible on a scatterplot.
Ex:
Curve of Best Fit
The curve that best describes the
distribution of points in a scatter plot.
Ex. Similar to the Line of Best Fit with the
only difference being that the line is
now curved.
Outlier
A point that does not follow the pattern
shown on a graph. It does not follow the
line of best fit.
Ex.
In this graph, the green point is an outlier.
It does not follow the line of best fit.
Excerpt from:
Grade 9 & 10 Math Glossary Most definitions are taken from Ministry of Education
Grades 7, 8, 9, & 10 Revised Math Curriculums
All diagrams were created by Linda LoFaro (OCSB).
SMART Notebook
Unit 3: Day 2: Looking for Relationships (Part 2)
Grade 9 Applied
75 min
Math Learning Goals
· Investigate a relationship between measures by constructing a scatter plot.
· Describe the trend seen in the plotted points.
· Create a line of best fit to represent linear data
Materials
· BLM 3.2.1, 3.2.2, 3.2.3, 3.2.4
Whole Class ( Matching Activity
Students select statements to describe a scatter plot, focusing on the pattern in the scatter plot, and providing a rationale for their choice of statement. Discuss responses with the whole class.
Minds On…
Whole Class ( Discussion
Introduce correlation by presenting the information on BLM 3.2.1. Student can practice using the vortex activity
Whole Class/Individual ( Demonstration
Discuss the need for a line of best fit to make predictions. Outline four rules for line of best fit.
Students practice creating a line of best fit using the Gizmos activity: Lines of Best Fit Using Least Squares - Activity A http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=144 & Activity B http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=68
If you do not have access to gizmos, two alternate websites are available: Interactivate http://www.shodor.org/interactivate/activities/Regression/ and NLVM http://nlvm.usu.edu/en/nav/frames_asid_144_g_3_t_5.html?open=activities&from=category_g_3_t_5.html These manipulatives requires the user to enter their own data; the first allows students to create their own line of best fit first before viewing the solution.
Have students complete BLM 3.2.2 individually.
Action!
Whole Class ( Discussion
Complete Relationship Summary as a class BLM 3.2.3.
Ask: Based on the data, what would Julie’s height be at age 10? age 12? How do you know?
Discuss the need for a line of best fit to make predictions [interpolation, extrapolation].
Discuss the limitations of extrapolation too far away from the collected data, e.g., when Julie is age 30.
Word Wall:
Dependent Variable
Independent Variable
Interpolate
Extrapolate
Line of Best Fit
Curve of Best Fit
Outlier
(included in Smart Notebook file)
Consolidate Debrief
Concept Practice
Exploration
Home Activity or Further Classroom Consolidation
BLM 3.2.4 – students practice identifying characteristics of scatter plots
SMART Notebook
Unit 3: Day 2: Looking for Relationships (Part 2) Grade 9 Applied
75 min
Math Learning Goals • Investigate a relationship between measures by constructing a scatter plot.
• Describe the trend seen in the plotted points.
• Create a line of best fit to represent linear data
Materials • BLM 3.2.1,
3.2.2, 3.2.3, 3.2.4
Whole Class ���� Matching Activity Students select statements to describe a scatter plot, focusing on the pattern in the
scatter plot, and providing a rationale for their choice of statement. Discuss responses
with the whole class.
Minds On…
Whole Class ���� Discussion Introduce correlation by presenting the information on BLM 3.2.1. Student can practice
using the vortex activity
Whole Class/Individual ���� Demonstration Discuss the need for a line of best fit to make predictions. Outline four rules for line of
best fit.
Students practice creating a line of best fit using the Gizmos activity: Lines of Best Fit
Using Least Squares - Activity A http://www.explorelearning.com/index.cfm?
method=cResource.dspView&ResourceID=144 & Activity B http://www.
explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=68
If you do not have access to gizmos, two alternate websites are available: Interactivate
http://www.shodor.org/interactivate/activities/Regression/ and NLVM http://nlvm.
usu.edu/en/nav/frames_asid_144_g_3_t_5.html?open=activities&from=category_g_3_t
_5.html These manipulatives requires the user to enter their own data; the first allows
students to create their own line of best fit first before viewing the solution.
Have students complete BLM 3.2.2 individually.
Action!
Whole Class ���� Discussion Complete Relationship Summary as a class BLM 3.2.3.
Ask: Based on the data, what would Julie’s height be at age 10? age 12?
How do you know?
Discuss the need for a line of best fit to make predictions [interpolation, extrapolation].
Discuss the limitations of extrapolation too far away from the collected data, e.g., when
Julie is age 30.
Word Wall: Dependent Variable Independent Variable Interpolate Extrapolate Line of Best Fit Curve of Best Fit Outlier (included in Smart Notebook file)
Consolidate Debrief
Concept
Practice
Exploration
Home Activity or Further Classroom Consolidation BLM 3.2.4 – students practice identifying characteristics of scatter plots
SMART Notebook
Dependent Variable
The variable in a relation whose value depends on the value of the independent variable.
Ex.Doing a science lab where you are comparing how far a car goes over time, time stays constant (so it is the independent variable) while distance changes over time (so it is the dependent variable).
Independent Variable
The variable in a relation whose value you choose.
QuickTime™ and a
decompressor
are needed to see this picture.
Ex.A CBR activity where you are comparing how far someone walks over time. In this case, time stays contant (independent variable) and the distance changes over time (dependent variable).
Extrapolate
To estimate values lying outside the range of a given data. To extrapolate from a graph means to estimate coordinates of points beyond those that are plotted.
QuickTime™ and a
decompressor
are needed to see this picture.
The population has continued to increase each year.
From 1961 to 2001, the population increased about 3 million every 10 years.
Since there has been continued growth within Canada at a fairly steady rate, we can make a prediction that Canada’s population in 2011 will be approximately 34 million.
Interpolate
To estimate values lying between elements of given data.
To interpolate from a graph means to estimate coordinates of points between those that are plotted.
Ex:
You now know that you have earned $12.00 for working 3.5 hours.
Line of Best Fit
A straight line drawn through as much data as possible on a scatterplot.
Ex:
Curve of Best Fit
The curve that best describes the distribution of points in a scatter plot.
Ex.Similar to the Line of Best Fit with the only difference being that the line is now curved.
Outlier
A point that does not follow the pattern shown on a graph. It does not follow the line of best fit.
Ex.
In this graph, the green point is an outlier.
It does not follow the line of best fit.
Excerpt from:
Grade 9 & 10 Math Glossary
Most definitions are taken from Ministry of Education
Grades 7, 8, 9, & 10 Revised Math Curriculums
All diagrams were created by Linda LoFaro (OCSB).
Ex.
��
TM
Suppose you work for 3.5 hours at $4.00 per hour. Using the graph, you can predict your earnings.
On the x-axis, create a vertical line to meet with the line of best fit.
Then, extend a horizontal line, from this point, to the y-axis.
SMART Notebook
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