Decimal-icious!

Hi everyone! Just wanted to take a minute to recap what we've learned so far in Chapter 4.

We first discussed the method for multiplying a decimal by a whole number. *Remember, you should not line up the decimals when you are multiplying - only when you're adding or subtracting.*

1) Set the problem up as though you were dealing with plain ol' whole numbers.
2) Solve (ignore the decimals for now - remember, we're pretending they are both whole numbers).
3) To place the decimal in your answer:
    First, count how many numbers after the decimal in the original problem.
    Then, going from right to left in your answer, count that many spaces over and put your decimal there.

Example:

      4.23   ---> There are two numbers after the decimal here. 
   x      6
    2538    ---> Now, going from right to left, put the decimal two places from the end.

Answer: 25.38

Today we talked about multiplying one decimal by another. *Remember, don't line up the decimals since we're multiplying!*

This method is exactly the same as the method for multiplying a decimal by a whole number.

1) Set the problem up.
2) Solve just like they're whole numbers (ignore the decimal).
3)  How many numbers (TOTAL) are there after all the decimals in your problem? Count them up, and then
     place the decimal that many places over in your answer.

Example:

     3.65   ---> There are two numbers after the decimal here. 
x     2.5   ---> There is one number after the decimal here. 
   9125    ---> Now, going from right to left, put the decimal three places from the end, since we counted
                       3 numbers total after decimal points in our problem.

Answer: 9.125

Try checking your answers with a calculator when doing your homework.

Extra Credit Question (you must show all work to receive credit):

         4.42
   x      9.8

It's been a while!

Here's a summary of the concepts we've covered so far in our decimal unit. This is just a quick review of what you already have in your notes:

3-1 Representing Decimals

Use your place value chart to write a decimal in word or expanded form (and vice versa). Example:
Write 6.23 in word and expanded form. (Image: math.tutorvista.com)

    
Word form: "Six AND twenty- three hundredths"

Expanded form: (6 x 1) + (2 x 0.1) + (3 x 0.01) ---> How'd we get that? We multiplied each digit by the number that represents the place value it's in. For example, since the 2 is in the "tenths" place, and one tenth is represented by "0.1," we multiplied them together to get the 2 tenths we need.

3-2 Comparing & Ordering Decimals

1) Line the decimals up
2) Annex zeros if neccessary
3) Go down each column and compare the numbers in each place value with each other
*See p.109 in your textbook for a great picture of this

3-3 Rounding Decimals

To round:
1) Underline the digit to be rounded (if you need to round to the nearest tenth, underline the digit that's in the tenths place)
2) Look at the number to the right - "5 and above, give it a shove; 4 and below, let it go" - so the digit that's being rounded goes up one if a 5 or above is to the right, and stays the same if a 4 or below is to the right.
3) Drop the rest of the numbers. Your new number should end at the place value you needed to round to.

Example: Round 7.35 to the nearest tenth.
First, underline the digit in the tenths place:  7.35
Now, look @ the number to the right:           7.35
It's 5 or above, so we give the 3 a shove:       7.4 (notice that the new number ends at the spot we had to round to)

3-4 Estimating Sums & Differences

I know this section is a little confusing, but keep in mind we're learning how to round just so we can check our real answers to see if they're reasonable.

Estimation Methods
Rounding: Estimate by rounding each decimal to the nearest whole number that's easy for you to add or subtract mentally.
Front-End Estimation: Add or subtract the front digits. Then add or subtract the next digits.
Clustering: Round a group of close numbers to the same number.
*Once you've rounded the decimals, don't forget to add or subtract!!!

3-5 Adding and Subtracting Decimals

1) Line up the decimal points and carry the decimal down.
2) Add or subtract just like with whole numbers.
*Remember to add zeros if you need to.

Here's an example from edu320.pbworks.com. In the second problem, we could add zeros to 4.1 if it makes it easier to add/subtract. It would then look like "4.100".



Tomorrow we'll practice adding and subtracting.

Frequency Tables

Hey guys! Everyone seems to be doing well with frequency tables. Just remember that your interval needs to be consistent. Here's a frequency table from mathsteacher.com.au. Notice that the interval is 5, not 4 - even though when you look at "40-44" it seems like there are four numbers there, there are actually five numbers because all of the following are included in that set: 40, 41, 42, 43, 44. Also, notice that each interval is the same each time (5).



I had a blast today with Ms. H. as our teacher! :) She did a great job collecting the data by taking a survey and showing the data by placing the information into a frequency table.

So... who's excited for Blackrock?! :)

P.S.

(See below for your homework post)

I wanted to share this cool photo from N.W.'s math notes for Area:

I can just hear L and W shouting "Multiply us!"

Interested in extra credit? I took this photo at the game last night and thought, hmm... this is perfect for an area question! Calculate (please show your work) the dimensions of an NFL football field. The overall length of an NFL field is 360 ft, and the width is 160 ft (we will use feet since the measurement using yards includes a decimal). Turn it in on Monday with your HW for an extra point. Have a splendiferous weekend!

Weekend Homework 9/28

Nice job today on your assessments! I was very impressed - many of you have greatly improved with Order of Operations and Exponents after workshop. Keep up the good work!!!

You have one question for this weekend. Please show all of your work, step-by step.

A room has a length of:

7 x 3 – 55 ÷ 5  (ft)

It has a width of:

2³ + 712 – 710  (ft)

What is the Area of the room?

Hint: You will first have to use Order of Operations to find out the length/width of the room.

Assignment 9/27

Hola, estudiantes! Please find the area for the following:

1) A room that is 12ft long and 10ft wide.

2) A field that is 100m long and 60m wide.

3) A random piece of space debris that just so happened to land in Ms. Johnson's yard, and contains
    the secrets to the universe, and was possibly placed there by the same aliens who get really fussy
    about exponents, that is 5ft long and 4 ft wide.

Remember, A = l x w. Also, don't forget to include "units squared"!

Just for fun...

This super-cool flash drive robot thingy that came to class today would like to share a video with you. 

Check out this cool rap song about Order of Operations. :)

WoRkShOp

Hello to all of my wonderful, brilliant, hard-working Math students!

I know workshop can be pretty intense, but I need to make sure each and every one of you know how to do the problems that were on Friday's quiz correctly. Make sure you have your Math notebook and a pencil out and ready to go if you are in workshop. Aunt Sally can't wait to be excused :)



Some of the things I'm noticing:

While many of you are doing great with remembering your Order of Operations, some of you are forgetting to copy the rest of the problem down exactly the way it is after you complete one operation. This is an example of doing the first operation in the right order, but then copying the rest of the problem incorrectly:

See how the 9 got brought down because mulitplication comes before addition, and so we assumed that we multiplied whatever we had already solved by 9... and then we just randomly added that 4? Be SURE to copy the rest of the problem down EXACTLY how it appears after performing every operation:

This is correct. First, we did division (because Multiplication and Division are on the same level, and should be performed from left to right). Right after that, we copied the rest of the problem exactly how it appears above. Then we multiplied 4x9 to get 36 - but notice that, again, we brought the rest of the problem down with it exactly how it appears above. Then we added for our final answer.


Something else I noticed on your quizzes was some confusion about variables:
Remember that a number right next to a variable means MULTIPLY! :)

Example:
Solve 2x + 3, if x = 5.
Notice the "2x" part? Don't just plug 5 in for x. Remember, 2x means 2 times x. So:
2 x 5 + 3
10 + 3
= 13.

See you tomorrow for more workshop.

Just a few reminders...

Open-note quiz tomorrow on 1-4 through 1-7b!

The quiz will cover:
Exponents
Order of Operations
Algebraic Expressions
Problem-Solving

Be sure to organize your math notes tonight so they're ready and easy to use for tomorrow's quiz.

If you're nervous about exponents, go back to the post about exponents and copy the steps into your notes.

Don't forget about Aunt Sally's operations - Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

*Be sure to READ each question on your quiz - remember that for this chapter, when using variables, you will be given the value of the variable(s) so you can plug that number in. Then, be sure to use the Order of Operations to complete the problem. For example:

Solve the following for x = 2 and y = 3:
5x - (2y + 1) ---> We know x is 2 and y is 3, so plug those numbers in for the variables.
5 x 2 - (2 x 3 + 1) ---> Use Order of Operations to solve.
5 x 2 - (6 + 1)
5 x 2 - 7
10 - 7
= 3

Remember that the online self-check quizzes (Glencoe website stored to the Favorites on your laptop) are a great way to make sure you're ready. See you tomorrow!

Order of Operations!!!

Just a quick message from Dr. Johnson:

Always use PEMDAS to guide you through a numerical equation. Remember "Please Excuse My Dear Aunt Sally." By the way, nice job everyone on your Aunt Sally artwork! :)

Parentheses

Exponents

Multiplication & Division, left to right

Addition & Subtraction, left to right

Here's an example from Coolmath.com:



And another with exponents:

For one point extra credit, solve the following problem and bring your answer to class on Monday. Don't forget to show your work! See your class notes and my previous blog post about exponents if you get stuck.

3 x 2³ + (21-14 ÷ 2)

Expressing Prime Factorization with Exponents

Think back on our activity from class. How did the number of prime factors for each total number of holes relate to the number of holes after we "punched" the paper?

They were the same. Remember when we folded the paper 2 times, the number of holes was 4. The prime factorization of 4 is 2 x 2. That's a total of two prime factors - the same number of folds.

First, let's review how prime factorization works (also known as a factor tree):

Start with a product. Then, break that product down into its factors until you reach ALL PRIME FACTORS at the bottom. That bottom row is your prime factorization.

*Always remember to carry down your prime factors, to put a multiplication sign in between the factors on each row, and to check your answer at the bottom by making sure all the numbers are prime and verifying that, when multiplied together, they equal the product at the top of the tree.*

Example:

                                                                     32

                                                              

                                                             2       x      16

                                                     2       x       4      x      4

                                              2      x         2  x   2  x  2   x  2   ---> This is your answer. 2 x 2 x 2 x 2 x 2.

Remember from class yesterday that you can put this answer together in a nice, neat package by using exponents:

2 x 2 x 2 x 2 x 2 = 2⁵

Exponents

Here is some basic info you can refer to when dealing with exponents. Remember, an exponent is that teeny little number floating above and to the right of a number (the base):


This reads "two to the third power." Remember from our example in class, Aliens are VERY fussy about how their powers are used! :) When you see a number with an exponent like the one above, don't multiply the two numbers together, like this: 2 x 3. Your answer will be incorrect. Instead, the base number is multiplied by itself, and the power tells us how many times. The problem above would be solved by multiplying two by itself, three times:

2 x 2 x 2 = 8

And voila! The aliens are happy :)



Image credits:
wclipart.com
solving-math-problems.com

Online textbook is working! Woohoo!

To access your online textbook:

1. Make sure you are using Internet Explorer as your web browser. The book will not work in Google Chrome.

2. Visit www.glencoe.com/ose

3. In the box that says "Access Code/Class Code" type the following (the letters are all caps and the 0s are zeros):

E8BE080E20

This should take you to your online textook. Use the Table of Contents to navigate through the book.

Glencoe website

Hello all!

Here is the link for the Glencoe website. This will take you to the "Self-Check Quizzes." Click on the chapter and then section you'd like to study.

To access the other features, use the left margin of the website to check out Extra Examples, Study Guides, Practice Tests, and Personal Tutor videos.

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