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. :)