Squares: Hot, Cold, and Otherwise

[size=150][color=#0000ff][size=200]Find the square root of a number by [br]using a square as a visual model. [/size][/color][/size]

Let's make some squares! Keep trying a NEW PROBLEM until you feel comfortable answering the next two questions

Based on what you saw above, what does it mean to square a number?

And what does it mean to find the square root of a number?

You've only seen perfect squares so far in this activity. What do you think will happen when you square a number that isn't so perfect.

Let's see what happens here...

Let's try that again! Actually TRY ANOTHER until you feel like you're understanding what is going on.

Did you see how there are a few different correct answers if you move the point very carefully? (If not, go back and see if you can.) Why do you think that is?

Write down some of the different answers you get for one of the square roots above.

What [i]is[/i] going on here?! How are these different from the perfect squares at the beginning of the activity?

One last time...

Challenge questions!

[i]See if you can figure these out on your own, to see if you're ready for assessment[/i]

Takota wants to create a square with an approximate area of [math]\textsf{60 units^2}[/math]. Is 10 a reasonable side length for it? Why or why not?

Takota says that [math]\sqrt{70}[/math] has to be between [math]8[/math] and [math]9[/math]. How can they be so sure?