1P  3  day 7  Scatter plots.notebook November 10, 2015

Learning goals    will draw a graph including all features

 axis labels (with units) title scale points

  will draw line of best fit (by hand and by technology)

  will describe patterns and relationships in the data

  make predictions about the data

Creating Scatter Plots and Lines of Best Fit

The following graph shows the number of Canadian pregnancies over time.  

What predictions can be made from this graph?

Minds On...

1P  3  day 7  Scatter plots.notebook November 10, 2015

Test the hypothesis:  The older you are, the more money you earn.

Plot the data on the scatter plot below, choosing appropriate scales and labels.

pg 331

Note:  The symbol _____ is used to signal a "break" in the axis when the scale does not start at zero to avoid a large empty space in one corner of the graph.

1)  Draw a line of best fit.  Describe the trend in the data.

2)  Does the data support the hypothesis?  Give reasons to support your answer.

3)  Explain why the data for ages over 65 do not correspond with the hypothesis.

4) Explain what the point (41, 35 000) represents.

pg 331

1P  3  day 7  Scatter plots.notebook November 10, 2015

Anthropologists and forensic scientists use data to determine information about people. Scientists can make predictions about the height, age, and sex of the person they are examining by looking for relationships in large amounts of data.

1)  Construct a graph of the length of the humerus bone vs. the length of the radius bone.

pg 332Use the Graphing Calculator to Graph

Copy your graph here

from the calculator

2) Trace the point on the graph that represents the data for a radius that is 21.9 cm long.  

     How long is the humerus?

3) Trace the point on the graph that represents the data for a humerus that is 27.1 cm long.

     How long is the radius?

4) Describe the trend (pattern).

pg 32

1P  3  day 7  Scatter plots.notebook November 10, 2015

5) Describe the relationship:  As the length of the radius gets longer, the humerus _____________________  ____________________________________________________________________________________

6.  a) Draw a line of best fit.

b)  Use the line of best fit to predict the length of the humerus if the radius is 24.5 cm long. 

     Did you interpolate or extrapolate?

c) Use the line of best fit to predict the length of the radius if the humerus is 25cm long.  

     Did you interpolate or extrapolate?

pg 32

Assignment   Tomorrow 

1P  3  day 7  Scatter plots.notebook November 10, 2015

Attachments

BLM 3.4.4.doc

BLM 3.4.4.pdf

BLM3.4.2.doc

BLM3.4.2.pdf

BLM3.4.3.doc

TIPS Lesson Unit 3 Lesson 4.doc

TIPS Lesson Unit 3 Lesson 4.pdf

BLM3.4.3.pdf

BLM 3.4.1.doc

BLM 3.4.1.pdf

3.4.4: Journal Activity

Write a response to:

What have you learned about how scientists use data in their jobs?

SMART Notebook

3.4.4: Journal Activity

Write a response to:

What have you learned about how scientists use data in their jobs?

SMART Notebook

3.4.2: Creating Scatter Plots and Lines of Best Fit

Test the hypothesis: The older you are, the more money you earn.

Plot the data on the scatter plot below, choosing appropriate scales and labels.

Age

Earnings ($)

25

22 000

30

26 500

35

29 500

37

29 000

38

30 000

40

32 000

41

35 000

45

36 000

55

41 000

60

41 000

62

42 500

65

43 000

70

37 000

75

37 500

Note: The symbol _______ is used to signal a “break” in the axis when the scale does not start at zero to avoid a large empty space in one corner of the graph.

1)Draw a line of best fit. Describe the trend in the data.

2)Does the data support the hypothesis? Give reasons to support your answer. (Refer to the scatter plot.)

3)Explain why the data for ages over 65 do not correspond with the hypothesis.

4)Explain what the point (41, 35000) represents.

SMART Notebook

3.4.2: Creating Scatter Plots and Lines of Best Fit Test the hypothesis: The older you are, the more money you earn. Plot the data on the scatter plot below, choosing appropriate scales and labels.

Note: The symbol _______ is used to signal a “break” in the axis when the scale does not start

at zero to avoid a large empty space in one corner of the graph. 1) Draw a line of best fit. Describe the trend in the data. 2) Does the data support the hypothesis? Give reasons to support your answer.

(Refer to the scatter plot.) 3) Explain why the data for ages over 65 do not correspond with the hypothesis. 4) Explain what the point (41, 35000) represents.

Age Earnings ($)

25 22000

30 26500

35 29500

37 29000

38 30000

40 32000

41 35000

45 36000

55 41000

60 41000

62 42500

65 43000

70 37000

75 37500

SMART Notebook

3.4.3: Forensic Analysis

Anthropologists and forensic scientists use data to determine information about people. Scientists can make predictions about the height, age, and sex of the person they are examining by looking for relationships in large amounts of data.

1.Construct a graph of the length of the humerus bone vs. the length of the radius bone.

Length of Radius (cm)

Length of Humerus (cm)

25.0

29.7

22.0

26.5

23.5

27.1

22.5

26.0

23.0

28.0

22.6

25.2

21.4

24.0

21.9

23.8

23.5

26.7

24.3

29.0

24.0

27.0

2.Circle the point on the graph that represents the data for a radius that is 21.9 cm long. How long is the humerus? _____________.

3.Put a box around the point on the graph that represents the data for a humerus that is 27.1 cm long. How long is the radius? ______________.

4.Describe the trend.

5.Describe the relationship: As the length of the radius gets longer, the humerus ____________________________.

6.a)Draw a line of best fit.

b)Use the line of best fit to predict the length of the humerus, if the radius is 24.5 cm long. Did you interpolate or extrapolate?

c)Use the line of best fit to predict the length of the radius, if the humerus is 25 cm long. Did you interpolate or extrapolate?

SMART Notebook

Unit 3: Day 4: Is There a Relationship? (Part 2)

Grade 9 Applied

75 min

Math Learning Goals

· Identify the trend and correlation of a scatter plot.

· Describe the relationship between the variables.

· Make a prediction about a linear relationship using a line of best fit.

· Use technology to graph scatter plots.

Materials

· BLM 3.4.1, 3.4.2, 3.4.3, 3.4.4.

· TI-83/84 graphing calculators or TI-Nspire calculators or Fathom software

Individual ( Practice

SMART Board Addition: Begin the lesson with an open question that asks students to make predictions from a given graph. Tell them to refer to BLM 3.3.4 question #4. If a student is having difficulty with the question, some possible question prompts are:

· What does the graph tell you about the number of pregnancies?

· What trends do you see in the graph?

· Could you extrapolate to predict what may happen in a later year?

(adapted from More Good Questions by Marian Small & Amy Lin)

Whole Class ( Discussion

Review student’s work from Day 3. Take up some of the Home Activity responses on the SMART Board.

Minds On…

Pairs ( Investigation

Students complete the investigation from the previous day.

Individual ( Investigation

Students finish completing BLM 3.3.3.

Curriculum Expectations/Performance Task/Rubric: Students submit BLM 3.3.3 for assessment. Use BLM 3.4.1 to assess the student’s work.

For students who finish the investigation early: Assign BLM 3.4.2 and BLM 3.4.3

Assessment of learning (student achievement).

Action!

Whole Class ( Discussion

When all students are finished the investigation: To consolidate, invite students to the SMART Board to reproduce each of the four scatter plots. Students’ can record their answers to the inferring and concluding questions on the second page of BLM 3.3.3 on the SMART Board.

Use the following prompts to debrief the activity, Could I Be a Forensic Scientist?

· Describe the relationships in the graphs

· Which graph showed the strongest correlation?

· Do any of the graphs show no relationship?

How did you determine the height of the skeleton?

Distribute BLM 3.4.2 and BLM 3.4.3 to students who don’t already have a copy. If time permits, the SMART Board can be used to take up the answers.

Consolidate Debrief

Reflection

Home Activity or Further Classroom Consolidation

Individual ( Practice

In your journal, write a response: What have you learned about how scientists use data in their jobs? BLM 3.4.4 can be used for this purpose.

SMART Notebook

Unit 3: Day 4: Is There a Relationship? (Part 2) Grade 9 Applied

75 min

Math Learning Goals • Identify the trend and correlation of a scatter plot.

• Describe the relationship between the variables.

• Make a prediction about a linear relationship using a line of best fit.

• Use technology to graph scatter plots.

Materials • BLM 3.4.1, 3.4.2, 3.4.3,

3.4.4.

• TI-83/84 graphing

calculators or TI-Nspire

calculators or Fathom

software

Individual ���� Practice SMART Board Addition: Begin the lesson with an open question that asks students to

make predictions from a given graph. Tell them to refer to BLM 3.3.4 question #4. If a

student is having difficulty with the question, some possible question prompts are:

- What does the graph tell you about the number of pregnancies? - What trends do you see in the graph? - Could you extrapolate to predict what may happen in a later year?

(adapted from More Good Questions by Marian Small & Amy Lin)

Whole Class ���� Discussion Review student’s work from Day 3. Take up some of the Home Activity responses on

the SMART Board.

Minds On…

Pairs ���� Investigation Students complete the investigation from the previous day.

Individual ���� Investigation Students finish completing BLM 3.3.3.

Curriculum Expectations/Performance Task/Rubric: Students submit BLM 3.3.3 for

assessment. Use BLM 3.4.1 to assess the student’s work.

For students who finish the investigation early: Assign BLM 3.4.2 and BLM 3.4.3

Assessment of

learning

(student

achievement).

Action!

Whole Class ���� Discussion When all students are finished the investigation: To consolidate, invite students to the

SMART Board to reproduce each of the four scatter plots. Students’ can record their

answers to the inferring and concluding questions on the second page of BLM 3.3.3 on

the SMART Board.

Use the following prompts to debrief the activity, Could I Be a Forensic Scientist?

• Describe the relationships in the graphs

• Which graph showed the strongest correlation?

• Do any of the graphs show no relationship?

How did you determine the height of the skeleton?

Distribute BLM 3.4.2 and BLM 3.4.3 to students who don’t already have a copy. If

time permits, the SMART Board can be used to take up the answers.

Consolidate Debrief

Reflection

Home Activity or Further Classroom Consolidation Individual ���� Practice In your journal, write a response: What have you learned about how scientists use data

in their jobs? BLM 3.4.4 can be used for this purpose.

SMART Notebook

3.4.3: Forensic Analysis Anthropologists and forensic scientists use data to determine information about people. Scientists can make predictions about the height, age, and sex of the person they are examining by looking for relationships in large amounts of data. 1. Construct a graph of the length of the humerus bone vs. the length of the radius bone.

2. Circle the point on the graph that represents the data for a radius that is 21.9 cm long.

How long is the humerus? _____________.

3. Put a box around the point on the graph that represents the data for a humerus that

is 27.1 cm long. How long is the radius? ______________.

4. Describe the trend. 5. Describe the relationship: As the length of the radius gets longer, the humerus

____________________________.

6. a) Draw a line of best fit. b) Use the line of best fit to predict the length of the humerus, if the radius is 24.5 cm long.

Did you interpolate or extrapolate? c) Use the line of best fit to predict the length of the radius, if the humerus is 25 cm long.

Did you interpolate or extrapolate?

Length of Radius

(cm)

Length of Humerus

(cm)

25.0 29.7

22.0 26.5

23.5 27.1

22.5 26.0

23.0 28.0

22.6 25.2

21.4 24.0

21.9 23.8

23.5 26.7

24.3 29.0

24.0 27.0

SMART Notebook

3.4.1: Investigation Rubric – Could I Be a Forensic Scientist?

Criteria

Below Level 1

Level 1

Level 2

Level 3

Level 4

Representing

Constructs table of values, scatter plot, and line of best fit

- the representations do not match the data or each other

- constructs table of values, scatter plot, and line of best fit with limited understanding

- constructs table of values, scatter plot, and line of best fit with some understanding

- constructs table of values, scatter plot, and line of best fit with considerable understanding

- constructs table of values, scatter plot, and line of best fit with thorough understanding

Connecting

Describes the trend, relationship, and correlation of the data

- describes the trend, relationship, and correlation of the data inaccurately or not at all

- describes the trend, relationship, and correlation of the data with limited effectiveness

- describes the trend, relationship, and correlation of the data with some effectiveness

- describes the trend, relationship, and correlation of the data with considerable effectiveness

- describes the trend, relationship, and correlation of the data with a high degree of effectiveness

Reasoning and Proving

Forms conclusions using convincing arguments

- forms conclusions without presenting an argument or arguments are inaccurate

- forms conclusions using arguments with limited effectiveness

- forms conclusions using arguments with some effectiveness

- forms conclusions using arguments with considerable effectiveness

- forms conclusions using arguments with a high degree of effectiveness

Communicating

Expression and organization of ideas and mathematical thinking

- no evidence of ability to express and organize ideas and mathematical thinking

- expresses and organizes ideas and mathematical thinking with limited effectiveness

- expresses and organizes ideas and mathematical thinking with some effectiveness

- expresses and organizes ideas and mathematical thinking with considerable effectiveness

- expresses and organizes ideas and mathematical thinking with a high degree of effectiveness

Use of conventions, vocabulary, and terminology

- uses conventions, vocabulary, and terminology inaccurately or not at all

- uses conventions, vocabulary, and terminology with limited accuracy

- uses conventions, vocabulary, and terminology with some accuracy

- uses conventions, vocabulary, and terminology with considerable accuracy

- uses conventions, vocabulary, and terminology accurately and precisely

SMART Notebook

3.4.1: Investigation Rubric – Could I Be a Forensic Scientist?

Criteria Below Level 1

Level 1 Level 2 Level 3 Level 4

Representing Constructs table of values, scatter plot, and line of best fit

- the representations do not match the data or each other

- constructs table of values, scatter plot, and line of best fit with limited understanding

- constructs table of values, scatter plot, and line of best fit with some understanding

- constructs table of values, scatter plot, and line of best fit with considerable understanding

- constructs table of values, scatter plot, and line of best fit with thorough understanding

Connecting Describes the trend, relationship, and correlation of the data

- describes the trend, relationship, and correlation of the data inaccurately or not at all

- describes the trend, relationship, and correlation of the data with limited effectiveness

- describes the trend, relationship, and correlation of the data with some effectiveness

- describes the trend, relationship, and correlation of the data with considerable effectiveness

- describes the trend, relationship, and correlation of the data with a high degree of effectiveness

Reasoning and Proving Forms conclusions using convincing arguments

- forms conclusions without presenting an argument or arguments are inaccurate

- forms conclusions using arguments with limited effectiveness

- forms conclusions using arguments with some effectiveness

- forms conclusions using arguments with considerable effectiveness

- forms conclusions using arguments with a high degree of effectiveness

Communicating Expression and organization of ideas and mathematical thinking

- no evidence of ability to express and organize ideas and mathematical thinking

- expresses and organizes ideas and mathematical thinking with limited effectiveness

- expresses and organizes ideas and mathematical thinking with some effectiveness

- expresses and organizes ideas and mathematical thinking with considerable effectiveness

- expresses and organizes ideas and mathematical thinking with a high degree of effectiveness

Use of conventions, vocabulary, and terminology

- uses conventions, vocabulary, and terminology inaccurately or not at all

- uses conventions, vocabulary, and terminology with limited accuracy

- uses conventions, vocabulary, and terminology with some accuracy

- uses conventions, vocabulary, and terminology with considerable accuracy

- uses conventions, vocabulary, and terminology accurately and precisely

SMART Notebook

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