CURRICULUM WRITING PROJECT
Program: Bio Tech
Unit:
Lesson Title: Linear Regression
Duration: 2 days (?)
Course:
Course #:
Lesson _____ of _____
Written by: Kathy English
STANDARD & MEASUREMENT CRITERIA
BIOSCIENCE, 41.0100.0
STANDARD 3.0 – DEMONSTRATE CRITICAL THINKING AND SCIENTIFIC PROBLEMSOLVING SKILL IN SCIENTIFIC INQUIRY
3.6 Collect, record, and analyze appropriate data
Common Core State Standards – Math
• HS.S-ID.6. Represent data on two quantitative variables on a scatter plot, and describe
how the variables are related.
a) Fit a function to the data; use functions fitted to data to solve problems in the
context of the data.
c) Fit a linear function for a scatter plot that suggests a linear association.
• HS.S-ID.7. Interpret the slope (rate of change) and the intercept (constant term) of a
linear model in the context of the data.
OBJECTIVES
MPS OBJECTIVE
Written in student-friendly terms to post
Students will be able to apply a linear
regression formula to paired data to find the
equation of the trend line and use the equation
to predict values.
Topic:
Do: Find the line of best fit
Level of thinking: Applying
TERMINOLOGY – Must include up to six key terms or concepts
with definitions
Linear Regression – a line of best fit, found by using a mathematical algorithm, which describes the
linear trend of two-variable data.
INTRODUCTION
(First Slide) Use as a bell-work or warm up:
Think of a time when you made a prediction based on events that had already happened.
What was the risk involved? How sure were you? How do you think analysts make their
predictions about things like gas prices, the stock market, or Black Friday sales?
[This may be too “Marketing-like” adjust as necessary.]
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MPS CTE: LESSON PLAN
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TEACHER ACTIONS
CONTENT
STUDENT ACTIONS
(Objectives reflected here)
Call on a non-volunteer to hear responses for
the introduction. After the first student has had
a chance to give their answer, let him/her call
on the next non-volunteer. 3 or 4 will probably
be all you will have time for.
Briefly discuss the terms on “Collecting Data.”
Bi-variate data simply means values for two
variables, usually an x and y. Show slide
“Visual Aid” and ask students to guess a
scenario to go with the graph.
After being called on to give a response to
the introduction, choose the next person to
respond.
Slide “So…What do You KNOW?” is an
assessment of pre-requisite math. Give
students a chance to do the problems
individually, and then compare with an elbow
partner.
Hopefully, these examples will be super easy,
but if a student feels as if they never ‘got’ this
before, they need to brush up before they try
the rest of this lesson.
There are two slides titled “y = mx + b” and
the next one is “Coincidence…” These slides
reinforce the slide for assessing the math
skills. Hopefully students will remember better
after seeing these.
Take the time to go over the next 4 slides,
“Linear Function,” “Linear Regression…by
hand,” “Fitting a line to data,” and
“Interesting Fact” step by step because there
are symbols and ideas that are most likely new
to the students.
“Make a table” slide is crucial to the
mathematical success of the lesson! Remind
the students that ‘x bar’ and ‘y bar’ means the
average values.
Unless students know (or remember) the
basics of writing an equation of a line, this
lesson may be really hard.
Work these 5 problems alone, and then
when your teacher says to, compare with
your elbow partner.
“Try an example…” sets up the table with
data. Step through the information so that
students can follow along on the notes.
Students need a moment to calculate the
means. “X-bar” and “Y-bar” are the first
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MPS CTE: LESSON PLAN
Students look at “visual aid” slide. They
may confer with a partner to try to imagine
a real-life situation that might be
represented by the scattered data and the
line. If that is difficult, perhaps try to guess
the equation of the line. See note with the
slide.
Using the note-taker, fill in the blanks.
Write questions that you need answered.
Talk to an elbow partner to make sure both
of you understands the concepts up to this
point.
Ask questions as needed.
On the note-taker, students need to write in
their own words what values are
represented in each column, and examine
the slope value formula.
Be sure to write down the formula for slope
and that you understand every part of it.
You will not be expected to memorize this
formula!
Students will plot the points on the graph
provided on the note-taker.
Calculate the average x and average y.
Fill in the first row of values as the teacher
explains and check the answers.
Updated 4/4/12
values to find.
Next, have students calculate the first value in
the (x – x-bar) column. X-bar is the same all
the way down, but X changes on each row.
Next, skip over to the column where you
square that answer. Square it while it is in the
calculator, it will just save time.
Let students fill in those two columns, then
click (each value will fly in on a click) through
the answers to be sure everyone is on the right
track.
Next do the same thing with (y – y-bar) and
square. Click to check the first value in those
columns.
But don’t show answers until students have
tried to do it on their own.
“Here’s where it all comes together…” is where
the ‘big’ calculations come in! Have students
find the slope using the formula and click to fly
in the answer when everyone is ready.
Next, have the students fill in the values to
write the equation of the line.
This is not difficult math, especially if you have
a calculator to help! But…keep in mind that it
takes time!
Continue filling in the calculated values.
Check answers with the teacher and make
corrections if necessary.
Don’t just copy if you don’t get it! Ask for
help from an elbow-partner or the teacher.
Sum the green column and the next-to-last
column. These are the answers you need
for the slope.
“Extrapolate values…” Once the linear model
has been established, the equation can be
used to estimate ‘missing’ values, ones
between the ones we were given originally.
If you wanted to find the y-value that might
have belonged with a given x-value, simply
substitute in the known x and solve for y.
If you wish to know where, along the x-axis, a
certain y-value is likely to have occurred, the
solving is just a little more involved, but not
much harder to do.
“Predict values…” Use the linear model to go
beyond the given data. What happens beyond
the known is tricky and mysterious. Caution
should be used and you should always consider
the actual experiment parameters when
‘predicting’ the future. As far as the algebra is
concerned, using the equation is simple math!
Students need to understand that if there is
not a linear ‘trend’ to the data, then this
method will not work.
Students have to get to work here! Any
time you have a point and a slope, you can
write the equation of the line. Use the
slope-intercept formula and fill in the values
that you know. You know the ‘m’ and you
know an (x, y) point. Substitute in to solve
for ‘b’ the y-intercept.
Examples on the notes-sheet are provided
for extra practice.
Examples on the notes-sheet are provided
for extra practice.
CLOSURE
1. What role does algebra play in analyzing this type of data?
2. Compare the level of accuracy obtained in using the algebra to what could be done by just
estimating a trend line.
3. Think about the time it took to do the calculations for 5 data points. What would a
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MPS CTE: LESSON PLAN
Updated 4/4/12
business analyst do with hundreds of data points?
FORMATIVE ASSESSMENT
CONNECTIONS
Typically in Algebra II, there is not enough time to go through the steps of the linear
regression algorithm (although this may not be universally true). Math students are often
asked to estimate the line of best fit…with no explanation of what makes it the best. It isn’t
always portrayed as something that has application beyond the math classroom. The
formulas are not essential to memorize because the technology available makes hand
calculations unnecessary.
SAMPLE END OF PROGRAM ASSESSMENT QUESTIONS
Must be two or three multiple choice questions with answers highlighted.
EQUIPMENT
RESOURCES
MATERIALS
SUPPLIES
(Everything
that needs to
be prepared
and available
in order to
teach this
lesson)
ACCOMMODATIONS
Citations from web sites referenced:
ATTACHMENTS / HANDOUTS / POWER POINT
Power Point
Notes Sheet
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MPS CTE: LESSON PLAN
Updated 4/4/12