Download Algebra 1 – Making Algebra Connections

Algebra 1 – Making Algebra Connections
Name_________________________
Use your triangle from the Connect-the-Dots Activity to answer the following questions. Be sure to thoroughly
explain your answers!!!
1. What patterns do you notice after each new stage of Sierpinski’s Triangle? (Hint: How are the
downward-facing triangles drawn?)
2. Using your triangle from the Connect-the-Dots Activity, complete Stage 4 of Sierpinski’s Triangle.
(There are no dots to connect this time!!)
3. Take a look at all of the upward-facing triangles in each stage. Complete the table below.
Stage
Number
Number of Upward-
Facing Triangles
0
1
2
3
4
4. Look for a pattern in the Number of Upward-Facing Triangles Column. How is each number related to
the number of triangles in the previous stage?
5. The pattern in #4 can actually be written much simpler by using exponents. An exponent is a
number that is smaller number raised up to the right of a normal number that tells you how many
times to multiple that number by itself. So, 62 means to multiply 6*6 to get 36.
Rewrite your second column in the table in #4 using exponents. Do not erase your numbers, just use
an equal sign!
Homework
(This is not a stopping point!!! You should start on your homework in class if you have extra time – no sitting
around if you finish an activity early!)
Consider the following square that follows a similar pattern to Sierpinski’s Triangle.
Stage 0
Stage 1
Complete two more stages of the square pattern in the square below before completing the table to the right.
(What happens inside each white square?) After you have completed the table, look for a number pattern
using exponents, and add this to the table.
Stage
Number
0
1
2
3
Number of
White Squares