Order of Operations and Exponents

We went over a LOT in class today!  Review the notes and examples below.  Homework is also posted below.

Homework:

Have a good night!

-Miss K  :)

From Purple Math:

Exponents are shorthand for repeated multiplication of the same thing by itself. For instance, the shorthand for multiplying three copies of the number 5 is shown on the right-hand side of the "equals" sign in (5)(5)(5) = 5³. The "exponent", being 3 in this example, stands for however many times the value is being multiplied. The thing that's being multiplied, being5 in this example, is called the "base".

This process of using exponents is called "raising to a power", where the exponent is the "power". The expression "5³" is pronounced as "five, raised to the third power" or "five to the third". There are two specially-named powers: "to the second power" is generally pronounced as "squared", and "to the third power" is generally pronounced as "cubed". So "5³" is commonly pronounced as "five cubed".

When we deal with numbers, we usually just simplify; we'd rather deal with "27" than with "3³". But with variables, we need the exponents, because we'd rather deal with "x⁶" than with "xxxxxx".

From Math is Fun:

Exponents

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

In 8² the "2" says to use 8 twice in a multiplication,
so 8² = 8 × 8 = 64

In words: 8² could be called "8 to the power 2" or "8 to the second power", or simply "8 squared"

Exponents are also called Powers or Indices.

Some more examples:

Example: 5³ = 5 × 5 × 5 = 125

• In words: 5³ could be called "5 to the third power", "5 to the power 3" or simply "5 cubed"

Example: 2⁴ = 2 × 2 × 2 × 2 = 16

• In words: 2⁴ could be called "2 to the fourth power" or "2 to the power 4" or simply "2 to the 4th"

Exponents make it easier to write and use many multiplications

Example: 9⁶ is easier to write and read than 9 × 9 × 9 × 9 × 9 × 9

You can multiply any number by itself as many times as you want using exponents.

Tonight's homework is worksheet 2-4.  Feel free to use a calculator!

-Miss K  :)

Fun times today!

Thanks for being so great as we finished our 100 box reward!  Back to learning tomorrow!  We're going to do exponents!  Interested in exponents right now?  Watch the video below!

-Miss K  :)

Playing with exponents, folding, halving, and theoretical math!

So we first reviewed the pink paper problem from yesterday!  Option B was the better choice, but over time we found out that option A becomes the best choice on the 13th week. Take a look at your potential earnings over 25 weeks (about half the year) below!

We talked about halving and folding and practiced doing so in various mediums!

We also played an exponent game!  Try it at home...  What gets you closest to 300,000??

Tonight's homework is to complete 2 X 10 + 7 - 3^3 problems!  (^ means that the number that follows it is an exponent)

See you tomorrow!

-Miss K  :)

More exponents!

Examples from class:

Watch this old Faberge ad first...

Some videos about exponential growth with paper folding!





Tonight's homework:

Good luck on the homework!  Just one problem, so take the time to do it out and do it right!

-Miss K  :)

Exciting Exponent Exploration!!!

Today we started working with exponents!  Here are some notes from class...

Tonight's homework is worksheet 2-4 all problems.

Good luck on the homework!  See you tomorrow when we get to get a little bit silly with exponents!

-Miss K  :)

Allowance Problem

For those of you that are curious, I used excel to go to 25 weeks in the allowance problem...

Things I noticed:

• Through 12 weeks, Option B is the better choice.
• At week 13, Option A will have paid out more in total than Option B.
• It will take 100 weeks to earn $1000 with Method B, but only 16 weeks with Method A.
• By the time you earn $250 with Method B, you will have already raked in way more than a half million dollars with Option A and will earn over $300,000 in that week alone!

Did you notice any thing else that you found interesting?

-Miss K  :)

More exponents!

Nice work on last night's homework!  I also appreciate the hard work that you put in today in class.  If you missed class or want a reminder, check out these screen shots from class:

Tonight's homework problem:  (or at least the start of it!)

You just need to finish the allowance problem for homework tonight!  Tomorrow we start Order of Operations!

-Miss K  :)

Exponents

Today we began working with exponents.

Some notes/examples from class:

Other things to help...

I've had trouble finding videos on the topic, but here's a cool one that I posted a few weeks ago that used exponents!

Do a little bit of research or logical thinking to figure out this picture.  

What is any number to the zero power equal to?  Leave your answer in the comments!

-Miss K  :)