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.

We're Not Gonna Take It!

"We've got the right to choose it
There ain't no way we'll lose it." (Twisted Sister)



O.K. - I found these tips from- Basic mathematics.com

And it makes sense. Why take the question the way it is given to us?

Why not twist or rearrange things to our advantage?

Examples of additive compensation

Add 97 + 64

It may not be easy to add 97 and 64 mentally. However, one small adjustment

such as rewriting the problem as 97 + 3 + 61 can help us to get an answer quickly

97 + 3 + 61 = 100 + 61 = 161

Add 25, 27 , and 18

It is not easy to do any of these additions mentally.

25 + 27            25 + 18         27 + 18                             

However, if we take 2 from 27 and add that to 18, the problem becomes

25 + 25 + 20 and this is very easy to do mentally since 25 + 25 = 50 and 50 + 20 = 70

Examples of equal additions method

 The equal additions method is a compensation used when doing subtractions.

Subtract 39 from 57.

57 - 39 can be thought of as  58 - 40

58 - 40 = 18

To make the subtraction 58 - 40, we added 1 to 57 and 39 so that we still have the same subtraction problem.  

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.

Integer Football Game

I came across this cool way to explain integers. Integer football. See for yourself at...

Integer Football

Khan Academy 200 Videos

The Florida Literacy Coalition 

has put together a playlist of   200

math instruction videos from the
Khan Academy. 



Here's the link...


Press here

Don't Call it Algebra (And Nobody Will Know!)

The word Algebra can be intimidating to GED students.

Many people have this conception of Algebra...

I always tell my students that they did algebra back in Grade 2 but they just didn't know it.

Grade 1 -    1 + 1 = ▭

We followed the directions and added the 2 numbers together and wrote "2" in the box.

1 + 1 = 2

Grade 2  Day 1

1 + 1 = ▭

We followed the directions and added the 2 numbers together and wrote "2" in the box.

Grade 2  Day 2

1 + ▭ = 4

We followed the directions and added the 2 numbers together and wrote "5" in the box.

1 + 5 = 4

It looked wrong, and we knew it was wrong, but we followed the directions that said we had to add the two numbers together and put the answer in the box.

After a leap in our thinking, we were able to say that...

1 + "something" = 4

That "something" is 3. 

1 + 3 = 4

1 + ▭ = 4        The ▭ = 3

So how about 1 + x = 4?

"x" is just a ▭                  x = 3

I tell my students that they did Algebra in Grade 2 so they can certainly do it now in GED study.

Hot Dog! It is the Top Dog! Speed Distance Time Triangles

Any question involving Speed Distance Time 

can be solved with this triangle...

and... your thumb

Oh, and a bit of multiplication and division...

But let`s worry about the 

first.

They key here is COVER. You COVER the letter of the element that you are looking for.

1) Here's a sample question...

You drive at a speed of 50 km per hour for 2.5 hours. What distance will you have driven? 

Let's get that thumb out!

You COVER the letter of the element that you are looking for. (Distance) The S and T are next to each other, so you need to multiply the values.

You drive at a speed of 50 km per hour for 2.5 hours. What distance will you have driven? 

50 X 2.5 = 125  What distance will you have driven? 125 km.

2) Here's another sample question...

You drive a distance of 125 miles at a speed of 50 km per hour. How much time will it take you? 

Let's get that thumb out!

You COVER the letter of the element that you are looking for. (Time)  The D is on top of the S, so you need to divide.  

You drive a distance of 125 miles at a speed of 50 km per hour. How much time will it take you? 

125 divided by 50 = 2.5   2.5 hours.

3)  Here's a third sample question...

You drive a distance of 125 miles in 2.5 hours. What was your average speed? 

Let's get that thumb out!

You COVER the letter of the element that you are looking for. (Speed) 

The D is on top of the T, so you need to divide.  

You drive a distance of 125 miles in 2.5 hours. What was your average speed? 

125 divided by 2.5 = 50    50 mph.

So how do you remember which letter goes where on this triangle? Which, by the way, is worth its weight in gold....

Easy... just thing of the Top Dog...

and guess what? The order of the S and T doesn't really matter. You'll get the same answer if the S and T are reversed. The important thing is to keep that DOG on top. 

Work SMART and not HARD

Purr Cent

What Does "Percent" Mean? 

I always say it means "for every hundred."   

Per = for 

cent (dollar, century) = 100.

Percent – think of Purr – Cent.    

One Hundred Cats. 

1 cat = 1 PurrCent.

1  / 

1/100 is...                1 %

9/100      is          9 %

18/100  is 18 %

        

I have to shut our 100 cats in the basement at night because they makes too much noise. 

Remembering that we put ALWAYS put cats in the basement...

So here's a question...

What is 18% of 25?

 18   X 25   

100 (basement)

18 x 25 = 450

Now divide 450 by those 100 pesky cats down in that basement!

450 divided by 100 = 4.5

 Answer - 18% of 25 is 4.5

Work SMART, not HARD

Nice Day Updated

Which one is the numerator and which one is the denominator? A common question, answered easily by "Have a Nice Day." N, D - Nice Day, Numerator, Denominator.

Here are a few more... ND - No Date

ND - No Dice

ND - Nice Dog

ND - North Dakota

ND - Nice Dangle (Hockey players will get this one.)

Dividing Fractions #%$^&*() Don't choke!!!!!!!!!!!!!!!!!

Dividing fractions? Don't choke!!!!!!!!!!!!!!!!!

Isn't one of the fractions supposed to be flipped around or something? I can never remember which one...

Here's the easy way to remember the process...

(Note - you are under no obligation to use this simple and easy to remember explanation. You can use any unnecessarily long and convoluted method you wish to help explain it.)

So what is 6/31  divided by 2/3?

Here's dad and son. Dad is 6 feet tall and aged 31. Dad is first in age so he's the first fraction.

Son is 2 feet tall and aged 3 months. Son is second.

Son starts to choke...

Dad, being dad, starts to swear. (He never swore much before the had children.) Swearing is bad (apparently), so we cross this out. Son gets turned upside down and becomes 3/2. Choking stopped!


So now we have 6/31  X   3/2

Solve as you would a normal fraction multiplication question. Remember....

Leave the first fraction alone. The guy is trying to save his son's life, here, people, so leave him alone to get on with the job. Please disperse. Back away from the man. Go about your business.

Turn the 2nd fraction upside down.

Put an X between your two fractions.

Solve as you would a normal fraction multiplication question.



Work smart, not hard.

Exponent Secrets

See this link           http://www.mathsisfun.com/activity/secret-safe-exponentially.html  for a great explanation of exponents.

! #@$%&#@#

Ever wonder what that...

or...

                                                                                                                                                                                  

           

               

                                                           X

...key is for on your calculator? Well...

That's your gold plated 

short cut to solving those "arrangement"-type questions. 

You know (and love) the ones - "You have one red, one green, one blue and one yellow circle. How many ways can you arrange these 4 circles?"

So you might set out to make a grid or chart, starting with red. 

1) ০০০০

2) ০০০০

3) ০০০০

etc., etc., until your crayons and patience are worn out.

Or you could just enter 4 on your calculator and then press the factorial (x!) key (you might have to press shift first, depending on your calculator.) Bang. Done. Work smart, not hard.

"3 out of 4" Questions - Rate and Proportion

This is a modification from an earlier post. I realised there might be a few Heavy Metal fans out there...fans of the band MUAADON.

"3 out of 4" Questions - Rate and Proportion

Look or sound familiar? 



"A 10 metre flag pole casts a shadow of 6 metres. A 12 metre pole would cast a shadow that is ______ metres in length."

"A motorcyclist rides 125 miles in 3 hours. At this rate, how much distance will be covered in 5 hours?"

A factory produces 3000 widgets every 45 minutes. How many widgets will be produced in 7 hours?


These questions, I like to call, are "3 out of 4" questions. You are given 3 numbers and you need to find the 4th. How to solve? Make yourself a 4-way relationship box. 


Let's look at question 1 again. 

"A 10 metre flag pole casts a shadow of 6 metres. A 12 metre pole would cast a shadow that is ______ metres in length."

Your two "measurements" are height (H) and shadow length (SL).

H           SL
10            6
12            ?

Remember MUAADON - Multiply Up And Across, Divide by the Other Number.

12 x 6 = 72
72/10 = 7.2

You could have set your box up another way.

H      10    12
SL     6      ?

6 x 12 = 72
72/10 = 7.2

Same answer...


Tricks to watch out for!

In question 3, the two "measurements" are time and widgets. However, the first "time" is in minutes and the second one is in hours. You need to either convert the 45 minutes to .75 hours, or convert the 7 hours to 420 minutes. Then set up your box, remember MUAADON, and get yourself the right answer. Rock on!

Mean Median Mode Range - from www.showme.com

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!

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.