February 23: Scientific Notation

Today we started the final segment in this unit: Scientific Notation.  Scientific Notation is another way to represent REALLY BIG or really small numbers, like the numbers that are typically seen in science.

For example, the distance from Earth to the Sun is 

92,960,000 miles.

In Scientific Notation, this number is written as    9.296 x 10⁷

Scientific Notation gives us a way to compare magnitude of very large or very small numbers.  We found that it was easier to understand Scientific Notation when we actually did a few examples.  The more we tried to explain the concept, the more confusing it got! So here are the notes we took in class- we did several examples going both from Standard Form to Scientific Notation, and then Scientific Notation to Standard Form.  

Click here to download today's homework.  

February 19: More with Negative Exponents

Today we looked at a few more complex expressions and simplified them.  The idea was to get rid of the negatives by dividing.  Mrs. Corkins and Mr. Alexander both gave different notes, so both are attached to this post in the hopes that if you were still a bit confused after today's lesson, maybe seeing some additional notes from the other class will help!

Here are the notes that Mrs. Corkins gave. 

These are the notes from Mr. Alexander.

Click here for today's homework.

February 18: Negative Exponents

Today we learned about negative exponents.  Yesterday when we discussed zero exponents, we discovered that if the exponent is decreased, we divide by the base.  This pattern continues down from zero into the negatives!  So if a base is raised to a negative, it does not give a negative number, but it continues to divide by the base!

Rule:

x ^-m  =    1  

            x ^m

for any value x other than zero

Click here to download today's homework. 

February 17: Properties of Exponents

YAY FOR 3-DAY WEEKENDS!

We jumped right back into exponents today with looking at zero powers.  The rule is: 

ANY value raised to the zero power will ALWAYS equal ONE (except zero)

Funny that zero is the only exception to the zero exponent rule- hopefully that will make it that much easier to remember!

Here are the notes we took in class- they are pretty short, but they show why anything raised to the zero power is 1: as the exponents increase, we know that means to multiply the base by itself that many times. The greater the exponent, the more times we multiply.  The opposite is also true: as the exponents decrease, we determined that tells us that we need to divide by the base. This will be true for any and every value except zero.

For homework tonight, we have a review worksheet. Click here to download today's homework.   Tomorrow we will learn about negative exponents... think about how we went from 5¹ to 5⁰.  What did we do?  What do you think will happen when we go from 5⁰ to 5^-1 ? Then 5^-2 ?

February 13: Power of a Power

Today we learned how to simplify terms with exponents to a power (Power of a Power).  In this case, the rule we determined is shown below:

We then took a quiz on Exponent rules we've been working on this week.  If you were absent today, make sure to study over the weekend, and be ready to take this in class on Tuesday!

Remember, no school on Monday, February 16!  Happy President's Day!

February 12: Quotient of Exponents

Today we learned how to divide terms with exponents.

Quotient of Powers Rule:    

SUBTRACT the exponents and the base stays the same

 

ex: x ^m ÷ x ⁿ =  x ^m−n

We took notes in class and practiced dividing numbers and variables with different exponents. 

Click here to download today's homework.

February 11: Product of Powers

Product of Powers, or multiplying terms with exponents, was the focus for today.  The best strategy for this new concept is to start by writing each term out in expanded form. Then determine the number of factors and simplify!  Sounds easy, right?  Wait... it gets even easier!

Once we did a few examples together, many of us noticed a pattern- all we have to do is add the exponents!  See?  Told you it was even easier!

Product of Powers Rule:    

Add the exponents and the base stays the same

ex: x ^{m .} x ⁿ =  x ^m+n

Click here for today's homework.

February 10: Properties of Exponents

Today we had a guest teacher, so we reviewed what we covered yesterday: going from expanded notation to exponent notation and the converse.  There were no new notes.



Click here for today's homework.

February 9: Exponents

Today we begin our Unit 6: Exponents and Scientific Notation.  This is a 3 week long unit: the first 2 weeks will be devoted to learning the laws and properties of exponents, and the last week will be scientific notation followed by the Unit test on Friday, February 27.

Today's notes were an introduction to what exponents are, and we learned a few new terms: Exponent, Base, and Expanded Form.

The exponent of a number says how many times to use that number in a multiplication.

It is written as a small number to the right and above the base number.

We also did an in class activity that is attached to the homework (first 2 pages) instead of taking a lot of notes.  Everyone found it much easier to work examples together rather than take traditional notes. 


Click here for today's homework and in class activity.