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Grade 7:  The Learning Equation Math

11.01 Powers and Exponents

Number Concepts

Refresher pp 2-3

Learning Outcomes:

The student will:

 

Use this calculator to check the pattern for Powers of 10 shown in the next chart.  Enter the Exponent and Base values then click on for the standard name.  The exponent on this calculator must be less than 600.

Directions:

Exponential Form (baseexponent)

Standard Name

Enter the Exponent:

()

=

Enter the Base:

 

Study the pattern for powers of 10.

 Exponential Notation (Powers of 10)

Exponential Form (Power) Expanded Form/Repeated Multiplication Standard Name
106 10x10x10x10x10x10 1000000
105 10x10x10x10x10 100000
104 10x10x10x10 10000
103 10x10x10 1000
102 10x10 100
101 10 10
100 1 1
10-1 1/10 0.1
10-2 1/10 x 1/10 0.01
10-3 1/10 x 1/10 x 1/10   0.001

 

You can calculate a power on a scientific calculator.  Use this calculator to check the chart above, then try it out for yourself. 

Press Reload/Refresh if the calculator does not show properly.

Power Calculator Imput

wpeBD.jpg (813 bytes) = baseexponent

Standard Name
20 2 wpeBD.jpg (813 bytes) 0 equal.jpg (782 bytes) 1
21 2 wpeBD.jpg (813 bytes) 1 equal.jpg (782 bytes) 2
22 2 wpeBD.jpg (813 bytes) 2 equal.jpg (782 bytes) 4
23 2 wpeBD.jpg (813 bytes) 3 equal.jpg (782 bytes) 8
24 2 wpeBD.jpg (813 bytes) 4 equal.jpg (782 bytes) 16
25 2 wpeBD.jpg (813 bytes) 5 equal.jpg (782 bytes) 32
26 2 wpeBD.jpg (813 bytes) 6 equal.jpg (782 bytes) 64
27 2 wpeBD.jpg (813 bytes) 7 equal.jpg (782 bytes) 128

 

 

Review:
Concept/Term Example(s) Definition/Explanation
power 81 is the fourth power of 3, because:

3 x 3 x 3 x 3 = 81

34 is another way of writing this power

the answer from multiplying a number by itself one or more times.

A power has two parts:

baseexponent = 3

and can be written/read in several ways:

  • the fourth power of three
  • three exponent four
  • three to the fourth power

32

33

Exponents 2 and 3 can also be written/read another way:
  • 32  is read three squared
  • 33  is read three cubed
base

In 34 , the base is 3.

the number being multiplied in a power
exponent In 34 , the exponent is 4. the number of times a number is being multiplied by itself in a power

Powers can be expressed in exponential, expanded, or standard from.

Exponential Form (Power) Expanded Form/Repeated Multiplication Standard Form (Standard Name)

34

3 x 3 x 3 x 3

81

33

3 x 3 x 3 27
32 3 x 3 9
31 3 3
30 no expanded form 1

Lesson on Exponents

 

Enrichment:

Math Forum: BEATCALC - tricks for squaring numbers

 

expression, power, base, exponent, standard form, factor, squared, cubed

Prerequisite Skills:
multiple Repeated addition of a number.

Multiples and Common Multiples - cool

5, 10, 15, and 20 are multiples of 5.
factor a number multiplied to produce a product

Prime and Composite Numbers - cool

1, 2, 3, 4, 6, and 12 are factors of 12.
prime natural numbers (or positive integers) with exactly two factors, 1 and itself

Prime and Composite Numbers - cool

Prime and Composite Numbers Practice

2, 3, 5, 7, 11, 13, 17...
composite numbers with more than 2 factors.

Prime and Composite Numbers - cool

Prime and Composite Numbers Practice

4, 6, 8, 9, 10, 12, 14,15, 16, ...
neither prime nor composite 1 has only one factor

0 is not a natural number (or positive integer)

0, 1

 

Factoring Calculator

Input Output:


 

Prime Number Checker

Please enter a number to see if it's prime:

 

Prime Factorization

Formula to :

This formula may be an integer, a rational number, a polynomial or a rational function. How to type formulas: here are elementary or more advanced examples.

Form Source:  Factoris

 

Prime Number Test

[ Sorry, you cannot see the applet because your browser does not support Java applets ]

source:  Prime Numbers

 

Sieve of Eratosthenes

Purpose:  Learn to identify the prime numbers.  (It may take a few seconds to start up or reset.)

To eliminate all multiples of 2 (except 2 itself), press 2.  Three will not be eliminated, since it is not a multiple of 2.   Press 3 and the Sieve of Eratosthenes will eliminate all of the multiples of 3 (except 3 itself).   Likewise, to eliminate all multiples of a number (except itself), press its button. Do not hesitate to experiment.  If you follow the directions correctly, the numbers left will be the prime numbers.

Press the Reset button to start over. You can select a new size (upto 250) for the table by setting the Size: field, and then pressing Reset.

Explaining the Sieve of Eratosthenes

Apparently your web browser does not run Java applets. Oops.

Source:  Sieve of Eratosthenes

Prime Number Generator

Primes

 

 

Magic Square's Applet

Area of  Rectangles

Area of a Rectangle Applet

Understanding Squares of Numbers

 

 

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