---

Four Square Problem Solving Method

1. Understand

READ THE PROBLEM with feeling

What is the question? (Restatement)

What is your job?

Underline / Cross out

List Key facts

 

2. Plan

Select a useful strategy:

Draw a model/picture/diagram

Make a table/pattern

Use a formula/equation

Work Backwartds

SImpler Problem

Guess/Check/Revise

3. SOLVE

4. CHECK

Does your answer MU?

Make sense

Units are given

---

   

Powers of Ten

 

(Exponent tells you how many times you multiply ten by itself.  Also tells the number of zeros.)

 

10¹ = 10 = 10

 

10² = 10 X 10 = 100

 

10³ = 10 X 10 X 10 = 1000

 

10⁴ = 10 X 10 X 10 X 10 = 10,000

 

10⁵ = 10 X 10 X 10 X 10 X 10  = 100, 000

 

10⁶ = 10 X 10 X 10 X 10 X 10 X 10  = 1, 000, 000

 

 

 

Decimal (Negative)  Powers of Ten

 

(Exponent tells how many times you multiply 1/10 by itself and how many zeros including the ones place zero)

 

10^-1 = 1    = 0.1

          10

 

10^-2 = 1   X 1     = 0.01

          10    10

 

10^-3 = 1   X 1   X 1     = 0.001

          10    10     10

 

10^-4 = 1   X 1   X 1   X 1      = 0.0001

          10     10    10    10

 

10^-5 = 1   X 1   X  1   X 1   X  1      = 0.00001

          10    10      10    10      10

 

10^-6 = 1   X 1   X 1   X 1   X 1   X 1     = 0.000001

          10    10     10    10    10     10

---

Multiplying by Powers of Ten

 

                                                     

 

When you multiply a number by a power of 10 (i.e. 10, 100, 1000, etc),

the number becomes greater in value!

 

The digits or order do not change, just the position of the decimal point changes.

 

The decimal point moves to the RIGHT:

 

     Give your Number Might  (in other words, make it larger)                         

     Move the decimal to the Right

 

        

The number of ‘jumps’ that the decimal point makes = the number of 0s.

 

Multiplying by 10 makes the decimal point ‘jump’ one place to the right. Multiplying by 100   involves 2 ‘jumps’.

Multiplying by 1000 involves 3 ‘jumps’.

 

It is often a good idea to add some 0s after the decimal point of your number so that it is easier to see where the decimal point can jump to.

 

For example 26.3=26.3000… 150.609=150.609000…

 

Also, if a number has NO decimal, add .00 to the end.

83  =  83.00

 

 

 Look at these examples:

 

 

0.013  X  1000 = 13.0          1.24  X 10  =  12.4

 

 

 

 

Multiplying by Decimal Powers of Ten

 

*When you multiply a number by a decimal power of 10 (i.e. 0.1, 0.01, 0.001..), the number becomes less in value

 

The digits or order do not change, just the position of the decimal point changes.

 

 

The decimal point moves to the LEFT:

                          

Make your number less

Move the decimal to the left

        

The number of ‘jumps’ that the decimal point makes = the number of decimal places.

 

Multiplying by 0.1    makes the decimal point ‘jump’ one place to the left.

Multiplying by 0.01   involves 2 ‘jumps’.

Multiplying by 0.001 involves 3 ‘jumps’.

 

It is often a good idea to add some 0s before the decimal point of your number so that it is easier to see where the decimal point can jump to.

 

For example 2.63=002.63     50.609=0050.609

 

Also, if a number has NO decimal, add .00 to the end.

 

83  =  83.00

 

Check out these:

 

 

1.3  X  0.01 = 0.013          124  X 0.1  =  124.0 X 0.1 = 12.4 or 12.40

 

 

---

Landmarks

 

 

 

MEAN:  also called the average                        ADD all numbers,  DIVIDE the SUM by the number of numbers you added.

 

   (Hint:  It’s MEAN to make us average the numbers by adding and dividing!!)

 

 

 

 

 

MODE: the number that appears the MOST       Find which number is repeated the MOST times

 

 

 

 

 

MEDIAN:  the MIDDLE number                       LINE UP numbers in order, cross out from both ends

                                                                   If two numbers are in the middle, average them (see MEAN)

 

 

 

 

RANGE:  the difference between                      Maximum- Minimum

              the high and low number

 

 

 

Probability:

 

1.  Know how to find probability:

 

 

What you want to get    =    successful outcomes

 

What is possible to get  =    possible outcomes

 

 

Example:    I want to get an even number from a roll of the number cube.

 

The even numbers on a number cube are 2, 4, 6. 

 

I have three choices that I want to get. (successful outcomes)  This number goes on top.

 

 

There are 6 different possible choices on the number cube: 

1, 2, 3, 4, 5, 6  (possible outcomes)  This number goes on the bottom.

 

3          We read this as 3 out of 6.  It is also 1 out of 2 because I can simplify to 1/2.

 

6

 

 

 

2.  A game is fair is the probability is the SAME!

 

A game is unfair if the probability is different!

 

Getting an odd number is 3 / 6.   Getting an even number is 3  / 6.  They are fair.

 

Getting a number more than 5 is 1 / 6.  Getting a number less than 3 is 2 / 6.  Unfair!

 

 

 

 

3.  Fundamental Counting Principal:

 

Choice 1  *  Choice 2  * Choice 3

 

 

Three choices for pizza:  small or large size, thin or thick crust, peppers, onions or cheese

                                                     2               *               2            *       3         =   12 choices

 

---

Graphs

Line graphs: show changes over time

Bar graphs: use when data can be counted and you want to make comparisons

Circle graphs: use when you want to show data as a part of the whole

Pictographs: use when data are multiples of a number (5, 10, 15, 20, 25...)

Great site for making your own graphs!

http://nces.ed.gov/nceskids/createagraph/

If you want to practice with percents on circle graphs, try this site: http://www.shodor.org/interactivate/activities/CircleGraph/

---