Teaching Algebra with Manipulatives

Investigating Polygons and Patterns
Materials:
NAME ______________________________________________ DATE
Algebra Activity Recording Sheet
(Use with the Lesson 1-2 Follow-Up Activity on page 19 in the Student Edition.)
ruler
Collect the Data
1. Record your results in the table below.
Diagonals From
Figure Name Sides (n) Diagonals One Vertex
triangle 3 0 0
quadrilateral 4 2 1
pentagon 5
hexagon 6
heptagon 7
octagon 8
____________ PERIOD ____
Algebra 2—Chapter 1
Analyze the Data
2. Describe the pattern shown by the number of diagonals in the table
above.
3. Complete the last column in the table above.
4. Write an expression in terms of n that relates the number of diagonals
from one vertex to the number of sides for each polygon.
5. If a polygon has n sides, how many vertices does it have?
6. How many vertices does one diagonal connect?
Make a Conjecture
7. Write a formula in terms of n for the number of diagonals of a polygon
of n sides. (Hint: Consider your answers to Exercises 2, 3, and 4.)
8. Draw a polygon on the back of this sheet with 10 sides. Test your
formula for the decagon.
9. Explain how your formula relates to the number of vertices of the
polygon and the number of diagonals that can be drawn
from each vertex. Use the back of this sheet for more space.
Extend the Activity
10. Use the back of this sheet for your drawings.
11. Complete the table at the right.
12. Use any method to find a formula that relates the number
of dots, x, to the number of lines, y.
13. Explain why the formula works.
Dots (x)
Connection
Lines (y)
3 3
© Glencoe/McGraw-Hill 213 Teaching Algebra with Manipulatives
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