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[Timeline]
Grade 7: The Learning Equation Math
11.01 Powers and Exponents


Learning
Outcomes: The student will:
Study the pattern for powers of 10.

Exponential
Form (Power) 
Expanded
Form/Repeated Multiplication 
Standard
Name 
10^{6} 
10x10x10x10x10x10 
1000000 
10^{5} 
10x10x10x10x10 
100000 
10^{4} 
10x10x10x10 
10000 
10^{3} 
10x10x10 
1000 
10^{2} 
10x10 
100 
10^{1} 
10 
10 
10^{0} 
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. 



Review:
Concept/Term 
Example(s) 
Definition/Explanation 
power 
81 is the fourth power of 3, because: 3 x 3 x 3 x 3 = 81
3^{4} is another way of writing this power 
the answer from multiplying a number by itself one or more times. A power
has two parts:
base^{exponent }=
3^{4 }
and can be written/read in several ways:
 the fourth power of three
 three exponent four
 three to the fourth power

3^{2}
3^{3} 
Exponents 2 and 3 can also be written/read another way:
 3^{2} is read three squared
 3^{3} is read three cubed

base 
In 3^{4} , the base is 3. 
the number being multiplied in a power 
exponent 
In 3^{4} , 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) 
3^{4} 
3 x 3 x 3 x 3 
81 
3^{3} 
3 x 3 x 3 
27 
3^{2} 
3 x 3 
9 
3^{1} 
3 
3 
3^{0} 
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 

Prime Number Test
source: Prime
Numbers 
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 

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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[Timeline]
 Started September, 1998. Copyright © 1999, 2000
visitors since September 3, 2000 