Transcript Ch2 Project - TeacherWeb

Algebra 1 – Chapter 2 project
Questions about Perfect Squares
Asking questions
In order to understand the underlying
structure of numbers (which is more
complicated than you would ever think),
mathematicians ask questions about them.
In this project, you will answer questions
about the sums of perfect squares.
Then, you will come up with your own
questions that you think will generate
interesting answers.
Perfect Squares
• Integers that are the squares of integers
• 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, …
• Note: integer: whole numbers, zero, and
negative whole numbers
1. Sums of perfect squares
1 1  2
2
2
1 2 5
2
2
•Can you write EVERY number as a sum of two
nonzero perfect squares?
•If so: tell us how to do so for any number.
•If not: find an integer that you cannot write as a
sum of two nonzero perfect squares.
2. Specific Sums
• Find two perfect squares that are the sums
of two nonzero perfect squares.
3. Multiple Representations
• Are there any integers you can write as
the sum of two nonzero squares in two
different ways?
• *Note: changing the order of the numbers
that you are adding doesn’t count.
Asking good questions
• Replace the italicized words with a new
word.
• Is your new question a good question?
• Why or why not?
4. Are any integers the sum of two nonzero perfect
SQUARES?
5. Are any integers the SUM of two nonzero perfect
squares?
6. Are any integers the sum of THREE nonzero
perfect squares?
7. Extending an idea
You can ask a good question by extending
an idea.
We only asked about positive integers.
Is there a good question we could ask about
negative integers? Explain.
8. Using answers to ask more
questions
• Look at your responses to question 2.
Use your answer to ask a new question.