There are eighteen third grade printable exponents worksheets on this page.
Squares and cubes are easy!
They teach raising a base number to different powers like the squares and cubes from different perspectives.
You can teach kids to memorize the squares and cubes, to learn the powers of ten as a base, and how to simplify exponents.
Definition of an exponent from our Math Dictionary:
This little number is a superscript. The exponent worksheets on this page introduce the visual element of the square of a base number (n2) which is the basis of learning square roots and also cubes (n3).
Learning the squares is also the basis for how to figure square footage - simply multiply - the simplest math area formula.
Side x Side = Area = Square Footage
The square root of a number is a number that multiplies itself to solve exponents equations:
s x s = s2
2 x 2 = 4
By multiplying the expression 2 x 2 the factors can be expressed as 22 or 4.
Use this first worksheet for memory work to memorize the square exponents and use the other two as quizzes.
The bottom left exponent activity is way too difficult for some children to draw the lines, yet trying the first few can help them comprehend making a number square.
This is the page to use while teaching the children to memorize the multiplication squares and to write the square superscript 2. (52, 62, 72).
It is an easy practice quiz preparation, too.
This page has the answer missing for an actual quiz.
Use this page when older kids do not comprehend. It's actually quite a large project to draw all the lines, so allow plenty of time. I wouldn't use this worksheet with small children.
Use this page to show the relation between squares and the square roots. Ask "What squared equals one? What squared equals four? It's really a matter of asking the equation differently.
You can use these worksheets with Crewton Ramone's excellent video below. See also a link to his site where he explains the basics at the bottom of this page.
He has worked for over twenty-five years as a professional math tutor, and has put his successful tutoring videos online. See his video below our printables for easy ways to teach square numbers using base ten blocks for exponents and multiplication.
Kids "see" squares and cubes "at-a-glance".
Having a squares chart seems to be the only real square root formula.
If you memorize the squares (the doubles in multiplication), you'll recognize the factors when you are asked for the roots and you'll know most of the squares table for the elementary school grades.
These worksheets can be skipped if your kids understand that square roots "undo" or invert the square equation like division is the inverse of multiplication, like products and quotients.
SPECIAL NOTE: The radicand symbol is simply the division symbol with the left entry crossed out. No need to write it as it is the same number.
Every natural number has an exponent or power of one.
If we multiply a number by itself we add the exponents the number of times we multiply. You can see this at a glance in the printable exponents charts below. Children often understand easily when they see the chart for squares and cubes.
Squares are numbers multiplied to the second power, so the expanded form expression is
31 x 31 = 32 = 9
In English this equation reads as
"Three times three are three squared or nine".
This principle is so helpful for showing that the area of a square uses the same math facts as multiplication and the formula for making squares.
s x s = Area
It is similar for cubes. Cubes are numbers multiplied to the third power, so in expanded form
31 x 31 x 31 = 33 = 27
In English this equation reads as:
"Three times three times three are three cubed or twenty-seven."
The three 1 exponents are added to equal an exponent of 3.
This proves that the volume of a cube uses the same factors as multiplication and the formula for making cubes.
s x s x s = Cube
Exponent addition is so much easier to see with the following printable charts.
This is really so simple when you realize that any number n,
n2 x n3 is n5.
It's one of the laws of exponents.
Have you ever tried finding an exponent chart? Or needed a square root table?
They can be hard to find, so
Use these exponents worksheets to practice the multiplication facts necessary to find the squares and cubes.
Cube worksheets are below and use the same chart as these square worksheets. The charts go as high as the fourth power, n4.
The next printable exponent chart has four of the first one and can be cut to use as a bookmark in a math book or kept in a desk, binder, or taped in a math textbook.
The formula for square roots is the inverse of the formula of a square, or the area of a square; yet in reverse like dividing.
Using an exponents chart makes the powers easy to see.
One of the rules of exponents:
Keep this printable exponents chart in your binder or on the wall next to your desk. It covers the exponentional powers to 4.
The columns show the powers and the rows show the bases. A common base is base ten. That means that the base number is ten to the power of 2, 3, or 4, etc.
If you have the children memorize the 2s, 5s and 10s, those squares, cubes, and square roots will be easy to solve in basic math class and simplifying expressions with exponents in 5th and 6th grade or pre-algebra where they will have to evaluate expressions that have exponents.
Over time kids will begin to see patterns.
These printable exponents charts print four-up for classroom handouts or math bookmarks. Make several copies to share.
I gave one to each child to tape to the inside of their math books for easy reference. Super helpful with square roots!
These first two worksheets are great practice because the exponential equations are right on the page.
The final answer can be written as a superscript or the multiplied answer.
Again, practice the equation which can be copied from the equations on the page. These worksheets spell out the square and cube relationships directly.
These two printable exponent worksheets can help a child visualize the words that we use to talk about the cube roots. Use the square root table above to find the cube root since both are on the table. A cube's volume is simply the height times the width times the base sides.
h x w x b = Volume
If the cube is a square cube, the sides are all equal and when multiplied give the volume of a cube.
s x s x s = Volume
It is a giant help to show young children what a cube looks like with Math manipulatives or a Rubics cube.
Use these exponent worksheets for square cubes.
Also teach that the real exponent for the first number is 1, so the exponents add up to 3 for cubes: 1+2=3.
First, make certain that your students are relatively handy with multiplication and division. The better your students know their math facts, the easier it will be for them to learn exponents.
If your students aren't handy and need practice, use our fun multiplication worksheets, then come back to this page.
Exponents are simply multiplication, and square roots are tricky division. It helps to have a chart for the roots which is why we include the charts in the worksheets above.
Exponents come second in the order of operations for Pre-Algebra. Use this phrase to remember the order: "Please excuse my dear Aunt Sara." or use the phrase PEMDAS and pronounce it as a word, Pemdas.
Negative exponents mean the reciprocal of the base raised to the power of the exponent. They wind up being fractions or division.
Practice is necessary to gain speed using exponents. Knowing how to use and find exponents well makes learning math and science so much easier! See our Order of Operations Worksheets to offer practice using PEMDAS.
You might also like our handy geometry formula sheet.
See more excellent videos on Square Numbers at Crewton Ramone's House Of Math square numbers. He's one tutor that's got a wonderful talent for teaching Math. Sign up for his Password to see more info.
The basic exponent laws are:
MathsIsFun has a great explanation of the laws of exponents.
You will love Maria Miller's Math Mammoth worktexts and worksheets. She explains everything in order and super well.
Find Math Mammoth at Amazon.
We have hundreds of practice math worksheets.
See related pages for more free elementary school and homeschooling ideas by grade:
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