By Jerald Murdock, Ellen Kamischke, Eric Kamischke
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Extra info for Discovering Algebra - Investigative Approach
Draw a large square or rectangle on your paper. Number the vertices from 1 to 4 as shown. a. Choose a point anywhere on your figure. This is your starting point. b. In order to choose a vertex to move toward, flip two different coins, such as a nickel and a penny. Use this scheme to determine the vertex: Nickel Penny Vertex number H H 1 H T 2 T H 3 T T 4 Measure the distance between your starting point and the chosen vertex. Mark a new point two-thirds of the distance to the vertex. Use this point and repeat the process at least 20 times.
Plot the first result from your table, and draw an arrow to the next result to show how the value of the expression changes. For example, Step 7 How do the results in your group compare? Step 8 Repeat Steps 1 to 6 with one of the expressions below. Step 9 How do the results in your group compare? Do the results of these expressions differ from the results of your first expression? In this investigation you explored what happens when you recursively evaluate an expression. First you selected a starting number to put into your expression, then you evaluated it.
To investigate these questions, choose positive and negative numbers, zero, and positive and negative fractions to put in the box and evaluate the expressions 3 and 4 You may want to use a table like the one at right to save your results. Why is that? Are there any exceptions? Look again at your results for the expression 3. What would the numerator of the fraction have to be so that is smaller than 3 ? Greater than 3 ? Now do the same thing with Display your results in a table. htm Assessing What You’ve Learned BEGIN A PORTFOLIO If you look up “assess” in a dictionary, you’ll find that it means to estimate or judge the value of something.