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Course: Math 8
Unit: 4 Data: Representation and Interpretation
Unit Length: 20 Days (50 Minute Class)
Unit Overview:
During this unit, you will be collecting data, making conjectures, and investigating real-world situations
leading to the creation of scatter plots. Then, you will use the concept of scatter plots to graph best fit
lines, explore unit rates, initial value, and understand all of these in their context. Finally, you will create
linear functions, identify the important quantities, and interpret their meaning to make predictions and
justify conclusions.
Next Generation Content Standards and Objectives:
Math.8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph.
Compare two different proportional relationships represented in different ways. For example,
compare a distance-time graph to a distance-time equation to determine which of two moving
objects has greater speed.
Math.8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct
points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through
the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
Math.8.F.4 Construct a function to model a linear relationship between two quantities. Determine
the rate of change and initial value of the function from a description of a relationship or from two
(x, y) values, including reading these from a table or from a graph. Interpret the rate of change and
initial value of a linear function in terms of the situation it models, and in terms of its graph or a
table of values.
Math.8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing
a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph
that exhibits the qualitative features of a function that has been described verbally.
Math.8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate
patterns of association between two quantities. Describe patterns such as clustering, outliers,
positive or negative association, linear association and nonlinear association.
Math.8.SP.2 Know that straight lines are widely used to model relationships between two
quantitative variables. For scatter plots that suggest a linear association, informally fit a straight
line and informally assess the model fit by judging the closeness of the data points to the line.
Math.8.SP.3 Use the equation of a linear model to solve problems in the context of bivariate
measurement data, interpreting the slope and intercept. For example, in a linear model for a
biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight
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each day is associated with an additional 1.5 cm in mature plant height.
Math.8.SP.4 Understand that patterns of association can also be seen in bivariate categorical data
by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a
two-way table summarizing data on two categorical variables collected from the same subjects. Use
relative frequencies calculated for rows or columns to describe possible association between the
two variables.
Standards for Mathematical Practices:
1
Make sense of problems and persevere in solving them.
2
Reason abstractly and quantitatively.
3
Construct viable arguments and critique the reasoning of others.
4
Model with mathematics.
5
Use appropriate tools strategically.
6
Attend to precision.
7
Look for and make use of structure.
8
Look for and express regularity in repeated reasoning
Driving question:
1. How can the same mathematical idea be represented in a different way? Why would that be
useful?
2. How does collecting, modeling, and interpreting the relationship between two quantities
help make sense of data?
Overview script:
Math 8 Unit 4 Overview
Data: Representation and Interpretation
Script
Display
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Math 8
Text:
Unit 4 Overview
●
●
Text
Data: Representation and Interpretation

Unit 4 is based upon 2 driving questions:


How can the same
mathematical idea be
represented in a different way?
Why would that be useful?
How does collecting, modeling,
and interpreting the
relationship between two
quantities help make sense of
data?
Math 8
Unit 4 Overview
Data: Representation and Interpretation
Text

How can the same mathematical idea be represented in a
different way? Why would that be useful?
 How does collecting, modeling, and interpreting the
relationship between two quantities help make sense of
data?
Maybe Graphics of Equations, Tables, Linear Graphs and Survey
Questions in the background
In this unit you will build on the work you
have already done with linear functions and
relationships.
Linear functions show a relationship
between two variables. The points of a
linear function lie along a straight line.
A linear relationship is a relationship in
which there is a constant rate of change
between two variables; for each interval
increase in one variable, there is a constant
change in the other variable. For example:
Joe wants to buy a video game that costs
$60. He has $15 in savings. He earns $5 for
shoveling snow off of each driveway. How
many driveways must Joe clear in order to
Please take full liberty in using your imagination
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have enough money to buy the video game?
Represent this problem situation using a
table, graph and equation.
Next, you will analyze non-linear graphs
for different rates of change. You will use
the context of the graph to explain the
changes in variables.
Bivariate is a fancy word for two
variables. Chances are you have already
worked with equations containing two
variables like y=2x or y=3x + 4. Now you
will use that knowledge to work with two
variable data that has been collected.
Two-way frequency tables and
scatterplots are often used to organize
data that is classified by two quantitative
variables and can be used to explore if a
relationship exists between the quantities.
Need a graph (or animation) to display John walking to school. Need
varying rates of change i.e. walking at steady pace, stopping at
crosswalk, running, arriving at school. Distance vs. Time Graph.
Something like this:
http://www.mathwarehouse.com/classroom/worksheets/distancevs-time/distance-vs-time-graph-worksheet.pdf
Absences
Math
Scores
3
65
5
50
1
95
1
90
3
80
6
40
5
70
3
75
0
100
Have this chart and a scatter plot of the data. Animate a line of best fit
being drawn through the scatter plot
8th Grade Students
Patterns of association can also be seen in
categorical data that is displayed in a twoway table. Relative frequencies calculated
Male
Female
Total
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for rows or columns may be used to
describe possible links between two
variables.
Why do I have to learn this? When am I
ever going to use this in real life? To be
well equipped for the career options of
your future, understanding that the way
information is collected and represented
can be critical to your ability to make
reasonable decisions. These skills will
help you in the field of Marketing, Finance,
Hospitality and Tourism, Health, and
Forestry/Natural Resources.
The key performance tasks for this unit
are to:









Make conjectures
Collect data and interpret meaning
to justify conclusions
Investigate real-world situations
Identify important quantities
Make Scatter plots
Determine the line of best fit
Construct Two-way tables for
quantitative and categorical data
Understand unit rates and how
they relate to slope
Convert information from a table,
graph, and equation
The students will know:
Extracurricular
Activities
23
20
43
No Extracurricular
Activities
12
25
37
Total
35
45
80
Pictures that relate to each of the listed careers.
The key performance tasks for this unit are to:









Make conjectures
Collect data and interpret meaning to justify conclusions
Investigate real-world situations
Identify important quantities
Make Scatter plots
Determine the line of best fit
Construct Two-way tables for quantitative and categorical
data
Understand unit rates and how they relate to slope
Convert information from a table, graph, and equation
WVU K12 Partnerships Unit Overview Construction Tool



vocabulary as related to the context
how to describe data relationships
characteristics of linear equations
The students will do:





create two-way tables
make scatter plots
fit lines to data
calculate slope/unit rate and initial value
interpret linear equations in context of situation