Math Final

Hello all. Just wanted to give you a run-down of what's going to be on your final. Remember, we'll be taking a practice final next week as we review.

Please review the following in your notes (also, remember to use Glencoe's online Self-Check Quizzes to test your knowledge of each section in the book):

- Prime factorization
- Powers and exponents
- Order of operations
- Variables and expressions
- Area

- Graphing (Bar/Line graphs)
- Frequency tables & Stem and Leaf plots
- Measures of central tendency (Mean, Median, Mode, Range)

- Rounding, adding, subtracting, multiplying, and dividing decimals

- Adding, subtracting, multiplying, and dividing fractions
- GCF/LCM
- Turning fractions into decimals
- Turning decimals into fractions

- Comparing/ordering fractions and decimals

- Adding, subtracting, multiplying, and dividing integers
- The Coordinate Plane

Adding Integers

Hello all,
Just wanted to post a quick review for your assessment Tuesday. We'll be checking the practice quiz Monday so please remember to bring it with you to class for workshop.

On this assessment, we'll be covering 8-1 through 8-3 (adding/subtracting integers). For subtraction, please review the previous post about the KFC method. Remember, Keep, Flip, Change!!! :)

For addition:

First, remember that a negative plus a negative will always equal a negative. If you lose five bucks and then you lose three more, you've LOST a total of 8 bucks, and a loss is represented by a negative, so you'd have -8 dollars.

-5 + -3 = -8

The tricky part comes in when you need to add a negative and a positive together.

Let's review the 3 methods we can use to add negative and positive integers:

1. Use a number line. From your starting point, move to the right if adding a positive integer; move to the left if adding a negative integer.

2. Use the method you have in your notes:
     1. Ignore the signs. What numbers do you have?
     2. Find the difference of those two numbers.
     3. For your answer, keep the sign of the biggest number.
     
     -7 + 4 -----> What numbers do I have if I ignore the signs? 7 and 4.
       7 - 4 ----->  Now, I take the difference of the two numbers.
       = 3   -----> Since the number with the greatest absolute value was -7, the answer becomes negative.
       = - 3

3. Use counters! Place negative and positive symbols inside a shape of your choosing. Cancel out whatever you can. What you're left with is your answer. Example:

The following picture represents 4 + (-5):

Since 1 positive is cancelled out by one negative, we are left with this, which represents -1:

And voila! You have your answer :)

If you're having a hard time adding integers in your head, any of these 3 methods will help you out. Happy adding!

Subtraction and... Fried Chicken?!!

Scared of subtraction involving negative integers? Don't be - remember, it's just addition in disguise!

The rule for subtraction is:

Add the OpPoSiTe!


Who likes fried chicken? It's one of my all-time favorites. :)

Img: thebittenword.com

So... what does fried chicken have to do with subtracting integers? Check out this cool chart from passyworldofmathematics.com:


Then, solve your problem as an addition problem. Here are a few examples:

-5 - 3 = ?
-5 + (-3) = -8  ---> Both numbers are the same sign, so we can add like normal and keep the sign.

7 - (-2) = ?
7 + 2 = 9   ---> Again, both numbers are the same sign, so we can add like normal and keep the sign.

4 - 8 = ?
4 + (-8) = ?  ---> Now we've got addition with two different signs, so remember to use your absolute values!
The absolute values are 4 and 8. The difference between 4 and 8 is 4. Now, is it negative or positive? Look at the original number that had the greatest absolute value: -8. Since it's negative, we know the answer is -4.



1) a. -5
    b. -1
    c. -3

2) a. -4
    b. -6
    c. 5

3) a. 35
    b. -106
    c. -46

HaPpY SuBtRaCtInG!

3rd Quarter Extra Credit Option

Create a blog post for next year's Math class focusing on one concept from Chapter 6. (For example, multiplying fractions.)

Your blog post must:
1. Teach students how to perform the particular math operation you're focusing on
2. Include both words and graphics

You can send this to me digitally or hand me a hard copy.

Due date: Friday, 3/28

This extra credit assignment will be worth one homework grade (it will take the place of a homework assignment if you've missed one) or three points added to your lowest test/quiz grade.

Logic Puzzles Day! 3/20

Hello friends. For today's assignment, we'll be getting away from fractions for a bit and using the logic to solve some puzzles. :)

Please break up into groups of 3.

Each group will choose a set of questions to answer (please let the rest of the class know which puzzles you choose, so no one chooses the same puzzles).

Talk with your group members about the puzzle - put your heads together!!! It may take a while, but I have a feeling you guys can figure these out. :) Summarize your answers on a sheet of paper to be handed in tomorrow. NO cheating - Google-ing the answer isn't the way to go. Here are the riddles:

Set 1

BULBS

This is one of my favorite free printable logic puzzles with a real life solution.
There are three switches downstairs. Each corresponds to one of the three light bulbs in the attic. You can turn the switches on and off and leave them in any position.
How would you identify which switch corresponds to which light bulb, if you are only allowed one trip upstairs?

A PING-PONG BALL IN A HOLE

Your last good ping-pong ball fell down into a narrow metal pipe imbedded in concrete one foot deep.
How can you get it out undamaged, if all the tools you have are your tennis paddle, your shoe-laces, and your plastic water bottle, which does not fit into the pipe?

SET 2

A MAN IN AN ELEVATOR

A man who lives on the tenth floor takes the elevator down to the first floor every morning and goes to work. In the evening, when he comes back; on a rainy day, or if there are other people in the elevator, he goes to his floor directly. Otherwise, he goes to the seventh floor and walks up three flights of stairs to his apartment.
Can you explain why?
(This is one of the more popular and most celebrated of all lateral thinking logic puzzles. It is a true classic. Although there are many possible solutions that fit the conditions, only the canonical answer is truly satisfying.)

THE BALL

How can you throw a ball as hard as you can and have it come back to you, even if it doesn't bounce off anything? There is nothing attached to it, and no one else catches or throws it back to you.

Set 3

THE MAGNET

This logic puzzle was published in Martin Gardner's column in the Scientific American. You are in a room with no metal objects except for two iron rods. Only one of them is a magnet.
How can you identify which one is a magnet?

VIRILE MICROBES

A Petri dish hosts a healthy colony of bacteria. Once a minute every bacterium divides into two. The colony was founded by a single cell at noon. At exactly 12:43 (43 minutes later) the Petri dish was half full.
At what time will the dish be full?

Set 4 - Super challenging!

SHEIKH'S INHERITANCE

An Arab sheikh tells his two sons to race their camels to a distant city to see who will inherit his fortune. The one whose camel is slower wins. After wandering aimlessly for days, the brothers ask a wise man for guidance. Upon receiving the advice, they jump on the camels and race to the city as fast as they can.
What did the wise man say to them?

MASTERS OF LOGIC PUZZLES (DOTS)

Three Masters of Logic wanted to find out who was the wisest amongst them. So they turned to their Grand Master, asking to resolve their dispute.
"Easy," the old sage said. "I will blindfold you and paint either red, or blue dot on each man's forehead. When I take your blindfolds off, if you see at least one red dot, raise your hand. The one, who guesses the color of the dot on his forehead first, wins."
And so it was said, and so it was done. The Grand Master blindfolded the three contestants and painted red dots on every one. When he took their blindfolds off, all three men raised their hands as the rules required, and sat in silence pondering. Finally, one of them said: "I have a red dot on my forehead."
How did he guess?

_______________________________________________________________________________

Once all of your groups are finished discussing and summarizing answers (don't lose that paper!!!), you may work individually on the Chapter 6 Self-Check quizzes from the Glencoe website. This will be silent, independent work. See you tomorrow!

Funky Fractions

Greetings, Mathlings!

Just some review for what we've already learned for adding and subtracting fractions:

When the fractions have the same denominator, simply add or subtract the numerators, keep the denominator the same, and then simplify.

When the fractions have unlike denominators:
1. Find the Least Common Denominator (The LCM of the denominators)
2. Convert to equivalent fractions - "rename" the fractions with the LCD
3. Follow the procedure for adding/subtracting with the same denominator

Remember, we must find the LCD and rename all the fractions when comparing fractions as well.

....but here's a little something extra for you:

The following chart illustrates the "Butterfly Method" we're going to talk about in class today. A lot of people find it easy to use when you're adding or subtracting with two fractions. *Don't forget to simplify!*

Monday, 2/24

Howdy, y'all. Please make sure you bring your "Ten Commandments from Chapters 1-5" to class tomorrow. We will be adding to the list.

One thing I saw on your Assessments that really needed work were decimal operations (adding, subtracting, multiplying, and dividing with decimals). Please review adding and subtracting decimals by watching the personal tutor video from lesson 3-5 on the Glencoe resources site:

http://www.glencoe.com/sec/math/msmath/mac04/course1/personal_tutor/index.php/

Then complete p.123, 12-19. Be sure to show your work.
See you tomorrow!