Presented by Holly Thomas, Reiannan Costello and Lauren Hagebols.

Presented by Holly Thomas, Reiannan Costello and Lauren Hagebols

Scatter PlotsScatter plots are a graphic representation of collated biviariate data

via a mathematical diagram using Cartesian coordinates.

The data is presented as a series of dots arranged on the horizontal and vertical axis. The presentation of this data communicates how much one variable is affected by another.

The relationship between the two variables is referred to as the correlation.

Scatter plots are employed as the scatter of these dots communicates where a relationship is likely to exist between the variables

(Booker, Bond, Sparrow & Swan, 2004).

Metalanguage to be revised and developed

Variables:

1: a quantity that can change or carry, taking on different values.

2: a letter or symbol representing a varying quantity, for example n in 10 + n

Bivariate data:

Data that involves two variables.

Correlation:

A casual, complementary, parallel, or reciprocal relationship, especially a structural, functional, or qualitative

correspondence

between two comparable entities.

Positive correlation:

A correlation in which large values of one variable are associated with large values of the other and small with small: the

correlation coefficient is between 0 and +1.

Negative correlation:

A correlation in which large values of one variable are associated with small values of the other, the correlation

coefficient is

between 0 and -1.

Metalanguage to be revised and developed

Coefficient:

A number or symbol multiplied with a variable or an unknown quantity in an algebraic term.

Cartesian Coordinates:

A system of representing points in space in terms of their distance from a given origin measured

along a set of mutually perpendicular axes.

X axis:

The horizontal axis of a graph.

Y axis:

The vertical axis of a graph.

Cluster:

Numbers which tend to crowd around a particular point in a set of values.

Plot:

To represent data graphically on a chart.

Trend line:

A line of best fit (a line on a graph indicating a statistical trend.

Assumed Prior Knowledge

Students will have carried out an extensive

amount of graph work throughout their schooling and will therefore be familiar

with the processes of collating data, how to construct the 'frame' of the graph and how

to label the appropriate axis.

Australian curriculum - Mathematics; data representation and interpretation.

Use scatter plots to investigate and comment on relationships between two continuous variables.

- using authentic data to construct scatter plots, make comparisons and draw conclusions.

Declarative & Procedural KnowledgeDeclarative Knowledge

(will know)Procedural Knowledge

(be able to)

D1: The sequential processes required

to construct a scatter plot.

D2: The importance of accurate data

collation.

D3: How to determine whether a

scatter plot is an appropriate way to

represent that particular set of data.

D4: The features of a scatter plots.

D5: Appropriate terminology for this

topic.

P1: Collate and analyse data for a pair

of variables.

P2: Use a line of best fit to identify if

there is a positive or negative

relationship between the two variables.

P3: Explore the characteristics and

users of scatter plots.

P4: Interpret bivariate data in tables

and graphs.

P5: Choose axes and scales while

constructing a scatter plot.

P6: Enter personal data for a statistical

investigation.

P7: Use patterns in scatter plots to

draw conclusions.

Learning Federation Resource

Key Question

“Do you think there is a relationship between the length of a person’s foot and the span of

their hand from their little finger to their thumb?”

Data TableNumber of People Foot Length’s (in cm) Hand Span’s (in cm)

1 23 20

2 24 19

3 24 18

4 27 21

5 23 22

6 28 22

7 26 18

8 25 22

9 28 22

10 29 24

Minimum and maximumlengths

Number of People Foot Length’s (in cm) Hand Span’s (in cm)

1 23 20

2 24 19

3 24 18

4 27 21

5 23 22

6 28 22

7 26 18

8 25 22

9 28 22

10 29 24

An example of a Positive Relationship

An example of a Negative Relationship

An example of no relationship between two variables

What is the relationship in you scatter plot?

Discuss amongst yourselves the type of relationship the variables have in your

graph.

What relationship did you come up with?

Extension QuestionHow did you discover the kind of relationship

that your graph has? And how does this information relate back to the Key Question of:

“Do you think there is a relationship between the length of a person’s foot and the span of their hand from their little finger to their thumb?”

A Final PointThe Australian Education Council (1991, p. 168)believe that

“Although children need to learn that data can be displayed in a variety of ways and come to terms with many of these representations, it is equally important that they understand that the choice of display depends on the question being asked of the data.“

Australian Education Council (1991). A national statement onmathematics for Australian schools. Melbourne: Curriculum Corporation.

Youtube: Scatter Plot

SWOT Analysis

 A digital resource to assist in the teaching of scatter plots within a mathematical context. This digital resource is a Youtube clip that provides auditory and visual representation of what a scatter plot consists of and instructional information on how to construct a scatter plot.

Weaknesses:This digital resource -

•Did not outline the importance of accurate data collection.•Failed to cover is which situation it is appropriate to pick a scatter plot to display data. •Only briefly covered what an axis is and which way they are positioned. •Did not illustrate how to plot data onto the scatter plot, this was an assumed skill. •Had one major weakness which was that its focus was purely instructional, teaching people how to construct a scatter plot. It omitted any kind of interpretation of the data. There was no evidence of evaluation, predicting or analysis of the data and information that was displayed. This demonstrates that there was no higher order thinking required to complete this activity.

Comments:

Strengths: This digital resource -

•Clearly outlined what are the sequential processes that are required to successfully construct a scatter plot graph.•Outlined the basic features of a scatter plot.•Highlighted some of the appropriate terminology and provided definitions for those words.•Demonstrated in depth what the ‘line of best fit’ is, how it is found and how to draw it, as well as how this line indicates what type of correlation is found within the graph. •Provided real life examples to help convey meaning.•Provided opportunities to check learning through asking the viewer to answer questions. •Contained visual images of content being taught to assist visual learners.

Comments:

Opportunities:

•It would be beneficial to all to include at least one activity that requires the viewer to engage in higher order thinking. This could be evident in questioning about the data that is being represented in the scatter plot. As a conclusion at the end of the resource there could be a statement requiring the viewer to analyse or draw conclusion about the data. •A tool that could be incorporated to improve this resource could be including a greater variety of words within the glossary.•Demonstrating what an axis is and how to plot data would also improve the overall teaching ability of this digital resource.

Threats:

•The most obvious threat to this digital resource is the age of the target audience. Through the interpretation of the vocabulary, colour choices and pacing of this digital resource it is evident that it is aimed at younger students. This might be detrimental in that even though the information presented is valuable some of the older students might interpret it as a resource for younger students and disengage from the learning.

Math Cracker

SWOT Analysis

A digital resource used to enhance the teaching of scatter plots within a mathematical context is an online resource from Math Cracker – Scatter Plot Tool. This digital resource provides a visual representation of the features of a scatter plot, allowing the learners to enter authentic data into correct fields of axes.

Strengths: This digital resource –

• Easy and simple to navigate

•Demonstrates appropriate terminology for this topic

•Includes the correct however basic features of a scatter plot

•Exercises a line of best fit

•Learners are able to print the completed scatter plot to draw conclusions as to the relationship of the variables

•Allows students to enter personal data for a statistical investigation.

Comments:

Weaknesses: This digital resource –

•Does not encourage higher order thinking•Does not outline the importance of accurate and authentic data collation• Does not allow for the learner to manually plot the points of data on the scatter plot•Provides no explanation as to what an axis is and which way they are positioned. •Does not allow for the learner to manually draw a line of best fit on the scatter plot• The resource acts as only a template for the learners to personalise through their data

From a visual aspect, year 10 students may interpret the resource for a younger audience and become disengaged. The website itself is called ‘Kids’ Zone’, and the coloured fonts and images are obviously incorporated to engage younger audiences. However the terminology and features throughout the process of this resource should stimulate the students throughout the construction of a scatter plot.

Comments:

Opportunities:

•Provides opportunity for analysis of the data

•This online resource could be utilised as an consolidation learning experience

•Summative assessment tool as to the relationships between variables (analysis and explanation)

•This resource provides no scaffolding for learners in the context of scatter plots. To improve this resource an introduction to the purpose and choices of scatter plots employing a range of metalanguage would be beneficial. Features that allow the learners to manually decide on scales, plot data, axis and a line of best fit would provide a more meaningful learning experience.

Threats:

Aesthetically this resource is rather dull and not appealing and learners could easily become disengaged due to the lack of interactive features.

.

Create A Graph!

SWOT AnalysisA digital resource that supports the learning of a Scatter Plot is an online resource from Kids’ Zones Learning with NCES – Create a Graph. This online resource provides a template for students to construct a scatter plot by being able to enter their data into correct fields of axes in an accessible sequence of steps. Strengths: This digital resource –

• Is visually and kinaesthetically engaging for students.• Easy to navigate and follow the sequenced steps.• Follows a sequential process required to construct a scatter plot, e.g. students must enter their data into the correct fields – x axis, y axis, minimum value, maximum value and the values for each point. • Allows for a maximum of 6 groups (variables to compare). • Includes the correct features of a scatter plot.• Included appropriate terminology.• Allows students to enter personal data for a statistical investigation. • Once the scatter plot is created, students are then able to print out their graph and draw conclusions from the patterns in the scatter plot.

Weaknesses: This digital resource –

• Did not outline the importance of accurate data collation.• Does not allow for the learner to manually plot the points of data on the scatter plot, the resources generates the scatter plot for them.• The resource is only a given template to fill in data. It does not explain the importance of using a scatter plot in comparison to another graph to represent data in.• It does not provide a tool to draw a line of best fit to identify if there is a positive or negative relationship between the two variables.

Opportunities:

• An opportunity to improve this digital resource would be for the learner to be able to manually plot the points of data onto the scatter plot.• A feature that would benefit this online resource is to include another step in the process where the learner is able to draw a ‘line of best fit’ and determine the relationship between the variables to promote higher order thinking. • An introduction to explain what a scatter plot is, explore the characteristics and users of scatter plots, and how to determine whether a scatter plot is an appropriate way to represent the learners’ particular set of data. It could include a glossary for the terms used in the resource.

Threats:

• From a visual aspect, year 10 students may interpret the resource for a younger audience and become disengaged. The website itself is called ‘Kids’ Zone’, and the coloured fonts and images are obviously incorporated to engage younger audiences. However the terminology and features throughout the process of this resource should stimulate the students throughout the construction of a scatter plot.

ReferencesAustralian Curriculum, Assessment and Reporting Authority (ACARA). (2011). The Australian

curriculum: Mathematics. Retrieved from http://www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10

 Australian Education Council (1991). A national statement on mathematics for Australian schools.

Melbourne: Curriculum Corporation. Booker, G., Bond, D., Sparrow, L. & Swan P. (2004). Teaching Primary Mathematics. (3rd Ed). French

Forest, NSW. Pearson Education.

BibliographyBull, I., Howes, B., Kimber, K., Nolan, C & Noonan, K. (2006). Maths Dimensions: essential learning.

Melbourne, Vic: Pearson Education Australia Group Wiki. Retrieved from:

http://www.wikispaces.com/user/my/Scatterplots  Kids’ Zone learning with NCES. (n.d). Create a graph. Retrieved from:

http://nces.ed.gov/nceskids/createagraph/default.aspx Math Cracker free math help. (2010). Scatter plot tool. Retrieved from:

http://www.mathcracker.com/scatter_plot.php  Youtube. (2009). Scatter plots by teachertubemath. Retrieved from:

http://www.youtube.com/watch?v=FVZI6t-B2Ik