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Learning Math Home
Patterns, Functions, and Algebra
Session 5 Part A Part B Part C Part D Part E Homework
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Session 5 Materials:



Notes for Session 5, Part A

Note 2

This section begins with a variation of the toothpick problem from Session 2, allowing us to explore the concept of linearity in a familiar context.

Groups: It's likely that people will have varying degrees of comfort and familiarity with spreadsheets, so working in groups may be helpful. Work on Problems A1-A3, completing the table and coming up with the rules. You may want to share rules before moving to the computers to work on the rest of Part A.

<< back to Part A: Linear Relationships in Patterns


Note 3

The first use of the spreadsheet in Problem A4 requires only the entry of data. To draw the graph for Problem A5, select the data, and then select the graphing tool (this is called the Chart Wizard if you're using Excel). The type of graph or chart for representing a functional relationship is an XY graph, or scatterplot. Some of the scatterplots will display only points, like this:

Others will connect the points with a line:

Groups: After creating the graphs, pause to discuss which graph was chosen to represent the function. Some may say that the points should not be connected because, in this context, the function makes sense only for whole numbers. For example, it may not make sense to talk about how many squares 4.5 toothpicks can make. It is often useful, however, to connect the points on a graph like this so that we can see the shape of the function (in this case, a straight line) more clearly. This is often done by indicating the actual data points by large dots or diamonds and then connecting them with a narrower line.

<< back to Part A: Linear Relationships in Patterns


Note 4

An important feature of spreadsheet programs is the ability to transfer formulas from one cell to another, updating cell references appropriately. This is called "filling," and it is done most easily in Excel by selecting "Fill" and then "Down" from the Edit menu. Some may also know how to do this by dragging the formula from one cell to another. This method also works, but is hard to learn at first.

Once all four columns are filled, the spreadsheet should look something like this:

note 4

It's worth noting some pitfalls in working with spreadsheets:


Forgetting the "=" at the beginning of a formula


Beginning to type data before selecting a cell


Expressing the cell coordinates in the wrong order -- the letter for the column must precede the number for the row


Forgetting to use the "*" for multiplication

End Part A by printing copies of the toothpick graphs or copying the graphs onto graph paper.

<< back to Part A: Linear Relationships in Patterns


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