Thinking With Mathematical Models 

Thinking With Mathematical Models  Working together using this wiki Problem 1.1 Testing Paper Bridges Problem 1.2 Drawing Graph Models Problem 1.3 Finding Equation Models Problem 1.4 Problem 1.5 Resources

 

Working together using this wiki

 

Think of this wiki as a shared online whiteboard. As we progress through this unit from the CMP program, we will add our progress and hopefully comments from teachers and students.  Play around with this wiki: Notice how you can add comments to a page, see what people have changed, and edit all the text.

 

Problem 1.1 Testing Paper Bridges

11/30/07 - entry by Mr. Cioffi

We tested paper bridges today.  We had to set up the 11" bridges on two stacks of books.  We then added one penny at a time to a paper cup placed in the middle of the bridge. 

 

    

We kept adding pennies until the bridge collapsed. 

 

We made a table of data and then graphed it.  We also combined our data with the whole class.  We made predictions for bridges that have 6, 7, 2.5, 3.5 layers. 

 

 

 

Problem 1.2 Drawing Graph Models

12/4/07 - Entry by Jake T.

 

We made our own graph models today using the data from yesterdays experiment.

 

Graph model - a straight line or curve that shows the trend in a set of data

 

We also learned that when you make a graph model, you follow the graph model, not the numbers on it.

 

 

Here is an example of a graph model: 

                                                                                                                      Published via My Scanner...

 

 

Image Courtesy of Jake T.

 

 

Problem 1.3 Finding Equation Models

12/5/07 - Entry by Evan

 

in 1.3 we used the equation y=mx+b

 

The m in this equation is the slope.

The b is the y-intercept.

slope is the rise over the run in a given line.

the y-intercept is where the line croses over the y axis.

we continued to talk about the info from 1.1.

we used graphing Calculators to make a table and graph

 

 

Problem 1.4

12-6-07 - by Michael

 

Today we learned about how the price of hats affects the number of students willing to pay for them. We found out that as the price of hats increases the the number of students who will buy them decreases.Also an equation that we found for this problem was y=-75=475.

 

 

Problem 1.5

12/12/07 - By Samm D

 

One 12/10 we did problem 1.5. We learned that Linear realtionships can be shown in all different situations.

 

In this problem we had two kids mowing lawns, one for 5$ a week and another for 3$ a week plus 20$ that he started with.

We had to come up with eaquations to match the graph above and the decription, We also had to figure out which graph model goeswith each person.

We found out that  the orange,lighter graph belongs to Johnah, the one that started out with 20$ and got 3$ a week.

With That we knew the darker graph belongs to Denis the one who was paid 5$ a week. We came up with the eaqations of...

Denis- Y=5x

Jonah- Y=3x + 20

we are still using the equation Y=mx+b

 

today

Today we did a check up, like a test to see where we are at in the unit, it went over a bunch of the stuff we had been doing and we had to solve some problems and/or

tell which equations,tables and graphs were linear.

 

 

Resources

I will include some of the resources you will need for this unit right here.  Just click on the file you want and it should open and you can print it off to use at home or in school. 

Vocabulary.pdf 

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