*Contributor: Erika Wargo. Lesson ID: 12825*

Do you feel like a square when it comes to multiplication? Don't squares have to do with geometry? You'll learn how to find the perfect square while "rooting" through interactives and a fun project!

categories

subject

Math

learning style

Auditory, Visual

personality style

Otter

Grade Level

Middle School (6-8)

Lesson Type

Skill Sharpener

- What do the numbers 1, 4, 9, 16, 25, and 36 all have in common?
- What makes a perfect square?

What makes a square so special and perfect?

*Squares*are special shapes where all four sides are*congruent*, or have equal measure.- A
*perfect square*is a number that has a square root that is a whole number. - A
*square root*is when we find the number that, when multiplied by itself, equals the original number. - When the square root of a number is equal to a
*whole number*, it is called a perfect square. - A number is a perfect square when you can take unit squares and form them into a larger square. A
*unit square*is a square that has a length of 1 and a width of 1.

The first four perfect squares are 1, 4, 9, and 16, as shown below:

- Do you see how the multiplication fact relates to the square?

The number that multiplies by itself to create the perfect square, is also the length and width of the square.

- What would be the fifth perfect square?
- How would the square be drawn?
- Discuss with a parent or teacher.

Perfect squares follow a sequence of numbers that increase by odd numbers. 1, 4, 9, 16, 25 are the first five perfect squares. Look at the diagram below:

Notice the sequence formed between the perfect squares.

- If you follow that pattern, what would the next perfect square be?

The next odd number after 9 is 11, so 25 + 11 = 36. The square root of 36 is 6, so 36 is a perfect square.

- What number would come next?

Take a look at an example of a number and determine if it is a perfect square:

5 unit squares cannot be arranged to form a square. Remember that a square has a length and width that are the same measure. You can see in the two figures above that a square is not formed. Five is not a perfect square and its square root would be a decimal number.

Discuss with a parent or teacher how to determine if a number is a perfect square.

You can be better at math if you can quickly recall the first ten perfect squares. Listen to the *Square Numbers Song*, by Schoolbeatz, two times to practice the first ten perfect squares:

Now that you have learned about what a perfect square is and how to identify a perfect square, you will practice with games and interactive practice in the *Got It?* section.