Sunday, October 13, 2013

Preparing for our Absolute Value unit

We start our Absolute Value Unit in a week.  I've been working on my Day 1 lesson plan.  Our algebra team typically does a "fire station" problem published by some state resources.  I checked out the MTBoS, and found that Kate at http://function-of-time.blogspot.com/ has published three awesome blogs on absolute value.  I put those together to create this lesson plan.  I'd love your feedback ... I have a week to tweak the plan!

Absolute Value Function:  Day 1

Introduction:

Cut apart fire station map and tape locations on individual construction paper.  Have volunteer students line up in front of room … holding a location.  The fire station person stays put.  The person holding the first building walks forward the number of blocks representing distance from fire station.  Continue … until several buildings are represented.  Note the shape of the human graph.  (See references at the end)


CANDY CORN Activity
(Note:  I used a picture of a bag of candy corn, put it in a google form, and sent it to our school staff, my parents, and my students.  All were invited to guess how many candy corns are in the bag!  I’ve collected the data in a google spreadsheet and in excel.)

I notice, I wonder
Use laptops and distribute excel file. Give students time to write “I notice; I wonder” based on their examination of the data.
What can you predict or infer from this data?
Ask students to circle (or highlight) the comments they wrote that can be solved mathematically.
Ask students to share one of their thoughts.

Show bag of candy … ask them for their guesses.  Reveal the total number of candies in the bag.

Ask students to examine their excel data to answer these questions.  Note, teacher data is in “sheet 1;” parent data is in “sheet 2;” student data is in “sheet 3.”
How many people participated in our guessing game?
Rank the guesses.  How?  Highlight the list of guesses.  On the Home ribbon, on the far right; select Sort and Filter; select “smallest to largest”
How many guesses were more than the number of candy corn?  How many guesses were less than the number of candy corn?
Calculate the percent error for each guess.  Why is the percent of error significant?
How does the teacher, parent, and student data compare?  How is the data different?
Now that you have studied the data a bit more, what can you predict or infer from the data?
Discuss students’ discoveries thus far.

Continue with Analysis
On average how good were the guesses?
How can we use the guessing data to represent distance from the correct guess?
Find the distance each guess is from the correct number of candy corn.
How might you reorganize this data to create a visual illustration of the guessing?
On graph paper, graph 13 pieces of data.  Use 6 guesses below the correct number, the actual number, and 6 guesses above the correct number.  The x axis represents the guesses.  The y axis represents the distance the guesses are from the correct number of candy corn.
Use excel to create a graph online.
Highlight 2 columns of data:  the guesses and the distance each guess is from the correct number of candy corn.
Select Insert; Select Scatterplot; Label your axes.
Write an equation from the data and the graph.

Display graphs & equation, discuss results. 

Note: Francis Galton found that the mean of every person's guesses is consistently better than any one person's guess.  What is the mean of the guesses?  Would that have been a good guess?

Assign the following problem:

The Public Library is located on E Main Street and has buildings at every block to the right and to the left.  Investigate the relationship between the address number on each building and its distance from the library.  The library’s address is 400 E Main Street.  The Star Co Coffee Shop is at 500 E Main Street, the Visitor’s Center is at 200 E Main Street, and the Main Street CafĂ© is at 300 E Main Street, and the Union State Bank is at 700 E Main Street.

Collect the data and illustrate it on a number line.
Create a table showing the locations of each building and its distance from the Public Library.
Graph the information in your table.  Be sure to scale your graph and label the axes appropriately.
State the reasonable domain and range for the problem situation.   Use set notation.
Using the data given, find the absolute value equation that best fits the data.
How does the reasonable domain and range for the problem situation differ from the domain and range for the function found in “e”?

Write an explanation of how the first station introduction, the candy corn exploration, and the public library problem are related.  Your written response should be in paragraph form, and include appropriate expository elements.


References
Fire Station Problem (this is the typical problem used in my school world)
Kate’s amazing blogs on Absolute Value:

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