Squares, Primes, Etc.:

Square Dance

 

Today's Snack: Eat something that is a square - a peanut butter and jelly sandwich . . . a few pieces of individually-wrapped processed cheese . . . Frosted Mini-Wheats . . . or maybe all of the above, with a glass of orange juice, which is NOT square, but is sure tasty and good for you.

 

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Supplies:

Pencil | ruler | one piece of paper

 

 

Here are some math vocabulary words that are good to know:

 

Integer - pronounced IN tuh jer - that's a whole number, like 0, 1, 2, etc.

 

Square number - an integer times itself; 4 is the square of 2 (2 x 2 = 4)

 

Square root - the integer which, multiplied by itself, equals a square (2 is the square root of 4)

 

Perfect square - another name for a square number

 

 

On your piece of paper, you can make "dot pictures" that help you understand square numbers. Make a series of squares with a number of dots so that you can see how the perfect squares literally take shape.

 

For example, make a dot picture that shows that 4 is the square of 2:

 

.   .

.   .

 

See how there are two dots vertically (up and down) and two dots horizontally (side to side), and the four dots together form a square?

 

Now try it with three dots, to see what is the square of three:

 

.   .   .

.   .   .

.   .   .

 

There are three dots vertically and three dots horizontally, forming a square shape, with a total of nine dots overall.

 

Now how about the square of four:

 

.   .   .   .

.   .   .   .

.   .   .   .

.   .   .   .

 

How many dots vertically? How many dots horizontally? How many dots overall? So what is the square of four?

 

You can continue making dot squares for as long as you'd like, using bigger and bigger integers.

 

It's important to know the squares by heart for at least the integers 1-10 as you move into upper-level math.

 

If you know the squares of various integer, then you also know the square roots of various integers. For example, you know that the square of four is 16, and now you know that the square root of 16 is 4.

 

Now turn over your piece of paper, and let's do a different kind of activity, also using square numbers. Here it is:

 

 

There are 20 integers between 1 and 100 which have the sum of their digits equal to a perfect square. Can you name all 20? (Hint: few of these are actually perfect squares, but their digits add up to perfect squares.)

 

 

The answer is below, but try to solve this by yourself first. Write the 20 integers down on your piece of paper. Good luck!

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(Answers: 1, 4, 9, 13, 18, 22, 27, 31, 36, 40, 45, 54, 63, 72, 79, 81, 88, 90, 97, 100)