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Learning Math Home
Patterns, Functions, and Algebra
 
Session 7 Part A Part B Part C Part D Homework
 
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Session 7 Materials:
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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

square numbers

Problem C1

Solution  

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

 

show answers

 

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

Solution  

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?


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
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

 

Problem C4

Solution  

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).


Next > Part C (Continued): Triangular Numbers

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