Math for Elementary Teachers one

Wednesday, March 9, 2011

Wrap up

Addition/Subtraction
Line the decimals up!!

you can use:
-decimals squares/base ten
http://nlvm.usu.edu/en/nav/frames_asid_264_g_1_t_1.html

- Pencil & Paper

Add capthttp://www.coolmath.com/prealgebra/02-decimals/07-decimals-subtracting-01.htmion

Multiplication
-Repeated addition: whole number times decimals
     4x0.3=0.3+0.3+0.3+0.3=1.2
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Ratios

Part/whole or Part/part

Ratios can be written two different ways 6:14 OR 6/14 and just like fractions you should reduce a ratio so for 6/14 and 6:14, the number 2 can be divided into each so the simplified answer would be 3/7 or 3:7.

Now how rations appear in the real world is known as proportions, which is comparing two different ratios.
                      a/b=c/d

Example:
if a car gets 30 miles to the gallon of gas, How many gallons would it take for a trip of 420 miles?

you would lay it out as:

30 miles = 420 miles
--------      -----------
1 GAL            X                so you would cross multiply 30 times X to get 30X
                                         and 420 times 1 which would give you 420

Then:

30X=420          and solve as a regular problem to get X alone

x= 420/30

x=14

Using the other way to write ratios:

30:1
420:___

so you would figure out how many times 30 goes into 420 which would be 14.

A little extra practice:

http://www.arcademicskillbuilders.com/games/dirt-bike-proportions/dirt-bike-proportions.html
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These blogs were very time consuming so I am gladly saying this is my last one =)
I will say though it helped me memorize what we were learning because I had to keep applying it, in class, then on the homework, then the lesson plans and the blogs.

Sunday, March 6, 2011

Decimals and Rounding Galore

Decimals:
can be defined as any number written in base-ten positional numeration.
Expanded:expanded notation/ expanded form:the number written out by numbers multiplied by their "columns."

Say the number is 123.45
1(100)+2(10)+3(1)+4(1/10)+5(1/100)

expanded exponential notation:
1(10^2)+2(10^1)+3(10^0)+4(10^ -1)+5(10^ -2)

**^and a number mean it would be written smaller in exponential form

Place Values
573.9634

9 -> tenth
6 -> hundredths
3 -> thousandths
4 -> ten thousandths

Image Source Page: http://www.blurtit.com/q9963737.html

Practicing Place Values:
http://www.aaamath.com/plc51b-placevalues.html

Writing out the decimal

245.639 -> two hundred forty-five and six hundred thirty-nine thousandths

being able to write out your numbers with decimals will come in handy when you are in an adult and writing checks.

Image Source Page: http://www.fnbrockies.com/checkimaging/examplechecks.cfm

from: http://www.fnbrockies.com/checkimaging/examplechecks.cfm

Practices writing out the decimals:
http://www.aaamath.com/dec44a-w2nthsndths.html

Converting fractions to decimals

Image Source Page: http://cnx.org/content/m30506/latest/

42/100 = 0.42
the way you covert the fraction to a decimals is count how many zeros there are in the fraction and that's how many numbers you count where you put the decimals

64193/10000=6.4193

Inequality of Decimals

0.19, 0.036, 0.195, 0.2

add a zero to make all the decimals the same length

0.190, 0.036, 0.195, 0.200
now look at the first number which is the biggest?
0.200
now look at the second number which is the next biggest?
0.190 and 0.195
so now you look at the third number
0.195
and then of course
0.190
and the smallest
0.036

Biggest to Smallest
0.2, 0.195, 0.19, 0.036

A fun game for practice:
http://themathgames.com/our-games/decimal-games/place-value/decimal-place-value-math-game

Fracions

Fractions:

is a part of portion of a whole.

For me I am terrible with fractions, I am not a fan of using them. Some uses make more sense then others for me, like the fraction stripes are kind of hard but as i used them they became more understandable for me. I wish I was taught some of these ways in elementary and junior high because i think i would have understood math more and not struggled as much.

Models

there are many different examples in every day life you use fractions and some you may not even realize your using them.

- when measuring things:
- a whole pizza
-when you eat part how much is left?
-writing a check
-how much change out of 100
- measuring cup

Image Source Page: http://rhbdesigns.blogspot.com/2010_07_01_archive.html

Equal Sizes

a part of unit

Examples:

-Shade Region

2/3 is shaded

- Finite Set

5/6 which means 5 out of 6 of the bubbles are shaded.

- Fraction Strip

Image Source Page: http://ed101.bu.edu/StudentDoc/current/ED101fa09/mikemiro/

- Number Line Model

A little extra help with fractions:
http://www.kidsolr.com/math/fractions.html

Division Concept

any number a & b with b not equaling 0

Examples

Dividing Circles

3/2 = 1 1/2 OR 3/2

Cuisenaire Rods

Ratio

Practice up on your fractions =)

http://www.mrnussbaum.com/tonyfraction.htm

Saturday, March 5, 2011

Positive and Negative Numbers

Multiplying
You can look at multiply decimals by debts and credits:
     3 bills for $2 -> 3(-2)= -6 so that means you would take $-6 dollars from your bank account.
     You return 5 items $1 each ->(-5)(-7)= $35 so that means you have $35 more in your bank account

You can also look at multiplying decimals by time and temperature:
   it's 2 degrees if the temperature is rising by 2 degrees per hour
     what temperature will it be in 3 hours ago?

Rules for Multiplying:
    forward x forward = forward
      (+)     x   (+)     =   (+)

   backward x forward = backward
     (-)          x   (-)      = (-)

   forward x backward = backward
     (+)    x   (-)          = (-)

   backward x backward = forward
      (-)       x    (-)          =   (+)

Friendly Reminder:

Division

Sharing -> -6/3=2

Measurement -> -8/-2=4

Debt & Credits-> A group of 6 has a debit of $24
                            How much does each pay?
                              24/6=$4
Rules for Division:
positive / positive = positive

negative / negative = negative

positive / negative = negative

negative / positive = negative

Practice:
http://www.math-play.com/multiplying-and-dividing-integers-game.html