 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum  MENU          Session 7, Part C:
Figurate Numbers (45 minutes)

In This Part: Square Numbers | Triangular Numbers

 Now that we have a basic understanding of exponential functions, let's move on to another kind of relationship. As you work through the following problems, try to get a sense of how these relationships are different from both linear and exponential functions. "Square numbers" describe the number of dots needed to make squares like the ones below. The first square number is 1, the second is 4, and so on. Note 9   Problem C1 Draw the next two squares in this pattern. Note 10 Problem C2

Fill in the table below:

 Number of dots on side of square Total number of dots (square number)  1 1 2 4 3 4 5 6 100 169 Number of dots on side of square Total number of dots (square number)  1 1 2 4 3 9 4 16 5 25 6 36 10 100 13 169

hide answers Problem C3 Graph the data in your table using graph paper or a spreadsheet, then describe your graph. How is it different from the linear and exponential graphs you've seen?  Try to be specific about how this graph is different from an exponential graph. What is the key property of an exponential graph?   Close Tip Try to be specific about how this graph is different from an exponential graph. What is the key property of an exponential graph? Problem C4 Describe a rule relating the number of dots on the side of a square (the independent variable) and the total number of dots (the dependent variable).   Session 7: Index | Notes | Solutions | Video

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