Born to Run

Which one is the radius...

and which one is the diameter?

I remember the radius as the one that starts in the 

middle...

...and then RUNS to the outside.

The diameter crosses the entire diagram.

That's it. Work smart, not hard.

Is it Prime (Or is it Memorex)?

A prime number is a natural number greater than 1, that has no positive divisors (factors) other than 1 and itself.

If you think of this definition in pictures of rectangles...

2 - ᥆᥆
3- ᥆᥆᥆
4 - ᥆᥆᥆᥆ or  ᥆᥆
                       ᥆᥆
5 - ᥆᥆᥆᥆᥆
6 - ᥆᥆᥆᥆᥆᥆  or ᥆᥆᥆
                             ᥆᥆᥆

Any number that can ONLY be represented by a straight line is prime.

Straight line is prime.

Math Doctor Video - New Version

See Math Doctor Link for the new Math Doctor Video - write out a 10 by 10 multiplication in under 1.5 minutes.

Circumference

Formula for Circumference?

Well - if you eat a pie a day, you will get a big circumference. (Distance around your middle.)

 

C = ∏   x  D    (diameter)

Find the diameter (or double the radius if the radius is given), multiply by pi and you will get the circumference.












Work Smart, Not Hard!

Do you know "Y" you were intercepted Part Deux

OK - so maybe the last post was a bit easy.

Perhaps there might be a harder question on the GED test?

A quick review... Which line has the equation

 

 y = x + 6

 

 

First of all, image you have been driving along and are suddenly "intercepted" by the police.

"Do you know "y" you were intercepted?" is probably the question you will be asked.

 

The key to this question is the "y" intercept, or the location at which the line crosses (intercepts) the "y" or vertical axis. (For some reason, nobody really cares about the poor old "x" axis. As with all "ex's", they are best left forgotten.)

 

y = x + 6 

 

The free floating number here is the 6. The only line that crosses/intercepts the "y"axis at 6 is line 5. Job done. You are finished.

 

                                 

 

OK, but what about...

 

 

 

 

 

 

Looks like 2 lines intercepting the "y" axis at 6. (Lines 5 and 7) So how now, brown cow?

 

Well, the next clue is the slope of the line. The free floating number corresponds with the intercept while the value associated with the "X" determines the slope. In this case, the slope is positive 1.

 

How can that be? (In algebra, values of positive 1 are dropped, being "understood" to be positive 1.) The formula for this line could have been written as y = 1x + 6

 

So we now need to find which line has a slope of positive 1.

 

By convention, lines that "rise" from the lower left to the upper right are considered to have a positive slope, Lines that "fall" from the upper left to the lower right have negative slopes. That rules out line 7.

 

 

Work SMART, not HARD!

Congruent! Gruesome! Grew Some!

Teacher: "Chris, use the word 'gruesome' in a sentence."
Chris: "A prisoner didn't shave for a week and grew some whiskers."

 

What's this got to do with congruency?

"Congruent" - definition: geometric figures of the same shape and the same size

Note: The figures don't have to be facing in the same direction to be congruent. Think of it as...

"If I cut one shape out, I can rotate it, place it over the top of another shape  and the two shapes will match up exactly."

What if our prisoner above (our con) had a twin brothers who also grew some whiskers....

 

 

Even though con #2 is facing in another direction, he and con #1 are, indeed, congruent.

10% Rule Part Deux - Using 1%

The 10% Rule RULES! Part Two

A quick review...

 

You can calculate any percentage using the 10% rule.

 

 

 

Example 1: What is 15% of 40?

 

 

Start by finding 10%.

 

To find 10%, think of 40 as 40.0

 

Move your decimal ONE place to the left and you have...

 

 

 

4.0  or 4

 

 

5% is half of 10%. Half of 4 is 2, so you need another

 

2

 

4 + 2 = 6

 

 

 

 

DONE! Work SMART not HARD

 

 

 

 

The 1% rule is just an extension of the 10% rule. 

 

 

Example 2: What is 16% of 40?

 

 

16% is just 10% plus 5 % plus 1%

 

 

 

Start by finding 10%.

 

To find 10%, think of 40 as 40.0

 

Move your decimal ONE place to the left and you have...

 

 

4.0  or 4

 

 

5% is half of 10%. Half of 4 is 2, so you need another

 

2

 

4 + 2 = 6

 

Now you just need that last 1%.

 

To find 1%, think of 40 as 40.0

 

Move your decimal TWO places to the left and you have...

 

 

.4

 

4 + 2 + .4 = 6.4

 

 

DONE! Work SMART not HARD

Quick Calculations - Use Half and Double

 

 

                                           X        


Work smart, not hard!

Double the...

... to...

 and halve the ...
 
 
 

... to...

 

 

100 X 8 = 800. Done!

 

Use "7" as your "Key"

Try this trick for multiplying two 2 digit numbers under 20. For example...

First off, make sure the larger number is on top.

Then think of the number 7. Well, the shape of it, anyway.

Now ADD 13 and 2 and stick a zero on the end.

Now cover up everything in the left (or 10's) column.

Now ADD 150 and 6 and you get 156

Done!

Percent Video (Type 4)

Percent Video (Type 4)

Percent Video (Type 4)

I have identified at least 5 distinct types of percent questions. (There may be more...) These include...

1) One number expressed as a % of another

2) Finding a certain % of a given number

3) (For want of a better title) The good old "650 is 15 % of what number" type of question.

4) Percent change

5) Increasing or decreasing a number by a given percentage

 

Here's the link for the 4th of 5 videos in a series on percent questions.

Percent Video (Type 3)

Percent Video (Type 3)

I have identified at least 5 distinct types of percent questions. (There may be more...) These include...

1) One number expressed as a % of another

2) Finding a certain % of a given number

3) (For want of a better title) The good old "650 is 15 % of what number" type of question.

4) Percent change

5) Increasing or decreasing a number by a given percentage

 

Here's the link for the 3rd of 5 videos in a series on percent questions.

Percent Video (Type 1)

I have identified at least 5 distinct types of percent questions. (There may be more...) These include...

1) One number expressed as a % of another

2) Finding a certain % of a given number

3) (For want of a better title) The good old "650 is 15 % of what number" type of question.

4) Percent change

5) Increasing or decreasing a number by a given percentage

 

Here's the link for the first of 5 videos in a series on percent questions.

 



Complementary? Supplementary? Part Deux

For some updates, look below the angle pictures for some further hints. In the original post, I suggested that...


My students often can't remember which angles are complementary and which ones are supplementary. I always tell them to think of a really cheap wedding, where the complementary (free) drinks are limited to 90. Complementary angles add up to 90 degrees. "C" for "cheap" and "c" for complementary. A "superb" wedding (supplementary) would offer 180 free drinks. Supplementary angles add up to 180 degrees. "S" for "superb" and "s" for supplementary. Failing that, I tell them that "c" comes before "s" in the alphabet and 90 comes before 180.

 

complementary

supplementaryfrom ClipArt, etc.

 

 

Further Ideas!

 

1. Complementary makes a Corner

Supplementary makes a Straight Line

 

2. Bodybuilders who take vitamin supplements get bigger muscles. 180 is bigger than 90, so supplementary is 180.

 

 

Key Math Words - "English" words versus "Math" words

 

12 and 5...  What is the difference between these two numbers?

Well, you might say that 12 has two digits and 5 has only one. You might say that the digits in 12 are gold and the 5 is blue.

In the mathematical world, difference means subtraction. The difference, in this case, is 7.

Some key subtraction terms are...

reduce

minus

diminish

decrease

dropped      and...

fell

Some key addition terms are...

sum

total

raise

combine    and...

additional

Some key multiplication terms are...

product

per

Some key division terms are...

quotient

split   and...

shared

Knowing these terms can help with word questions, when you are trying to figure out which operation to perform.

Solving Equations - Think "Hockey Trades"

Look familiar?  

x + 31 = 64            

Solve for "x"




Think of these problems as hockey trades. Good old #31...

...likes playing for team "x". (They are in first place in the league.) We know that "x" is happy because there is a plus/positive sign to the left of his number. Think of the equation as...

x /+ 31/ = 64   

However, hockey being hockey, sometimes players get traded. Good old /+ 31/ is being sent down the lines (=) to the last place team. Do you think he will be happy when he gets there. No... (note the incredible graphics here at the RUGS Blog) He's now not happy and, therefore, is now negative /-31/. The equation will now look like this...

x = 64  /- 31/

64 - (minus, take away, etc.) 31 = 33

Therefore x = 33





You can also have some grumpy, negative players on the last place team who are suddenly traded to the top team. 



x /- 15/ = 64            

Solve for "x"


When grumpy (negative) #15 gets sent down the lines (=) to the new team, he becomes very happy (positive).

x = 64  /+ 15/

x = 79

Angle Properties Song

Angle Properties - Interior, exterior, corresponding...

Which is which? See...here for more info. (And another great song.)

Angles Song

Angles - Obtuse? Acute, Right? Reflex? 

Which is which? See...here for more info. (And a great song.)

Double/Double or Double/Double/Double

Are you multiplying by 4 or 8? 


Dividing by 4 or 8?


If you are multiplying by 4, think double/double.

So... 6 X 4? 

(No expense spared here at the RUGS Blog for our state of the art graphics.)

Double 6 = 12 and double 12 = 24. 

So 6 x 4 = 24.

4 x 8?

If you are multiplying by 8, think double/double/double.

Double 4 = 8 and double 8 = 16 and double 16 = 32. 

So 4 x 8 = 32.

If you are dividing by 4, think half/half.

So... 24 divided by 4? 

half of 24 is 12 and half of 12 is 6 

24 divided by 4 is 6

If you are dividing by 8, think half/half/half.

So... 24 divided by 8? 

half of 24 is 12 and half of 12 is 6 and half of 6 is 3

24 divided by 8 is 3

Adding/Subtracting Positive and Negative Numbers

There are a couple of visual/concrete models used to help student to add and subtract positive and negative numbers.

There's the thermometer...

...and the elevator...

...and the diver...

A diver rises and falls below the surface of the water. A diver can also climb out of the water on a set of stairs...

The water level is "0". So, imagine...

(-3) + (+4)

(-3) is the STARTING position of the diver. 3 steps below the water level.

+ means "and" or "then"

+ is the direction of travel.          + means up

4 is the distance of travel, in this case 4 steps up

So, think of the diver starting at 3 steps below the water surface. The diver then travels up 4 steps. The diver will emerge from the water and be one step above the water surface.

(-3) + 4 = 1 (or +1)