looking for relationships using the graphing...

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


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

PDF

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


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


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


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


PDF

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


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


PDF

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

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



c



d Linear / Non-linear



e Linear / Non-linear



f



g Linear / Non-linear



h Linear / Non-linear



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


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


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


a

Linear / Non-linear


Positive / Negative


b

Linear / Non-linear


Positive / Negative


c

Linear / Non-linear


Positive / Negative


d

Linear / Non-linear


Positive / Negative


e

Linear / Non-linear


Positive / Negative


f

Linear / Non-linear


Positive / Negative


g

Linear / Non-linear


Positive / Negative


h

Linear / Non-linear


Positive / Negative


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


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).


The variable in a relation whose value you choose.

QuickTime™ and a

decompressor


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


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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