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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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Algebra Site Map
Session 7 Materials:
Notes
Solutions
Video

Session 7, Part C:
Figurate Numbers

In This Part: Square Numbers | Triangular Numbers

"Triangular numbers" describe the number of dots needed to make triangles like the ones below. The first triangular number is 1, the second is 3, and so on.

triangle

Problem C5

Solution  

Draw the next two triangles in this pattern.


 

Problem C6

  

Fill in the table below:

Number of dots on side of triangle

 

Total number of dots (triangular number)

1

 

1

2

 

3

3

 

4

 

5

 

6

 

 

45

 

190

 

show answers

 

Number of dots on side of triangle

 

Total number of dots (triangular number)

1

 

1

2

 

3

3

 

6

4

 

10

5

 

15

6

 

21

9

 

45

19

 

190

 

hide answers


 

Problem C7

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?


 

Problem C8

Solution  

Describe a rule relating the number of dots on the side of a triangle (the independent variable) and the total number of dots (the dependent variable).


 

Problem C9

Solution  

Describe any similarities and differences between your rules and graphs for the square and triangular numbers. In a way, they both have the same kind of rule. How would you describe it? Note 11


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
Think about how you would go from one output to the next. What changes? Can you describe these changes with a rule?   Close Tip

 
 

You can create "figurate numbers" for any polygon shape. Below are pictures of the first few pentagonal and hexagonal numbers.

pentagon

hexagon

The growth of figurate numbers is an example of a quadratic function. A quadratic function's formula will always involve squaring the input number: y = 3x2 + 5 is a quadratic function, and y = 3x + 5 is not. In Part D, we will explore the formulas and properties of quadratic functions in more detail.


Next > Part D: Quadratic Functions

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