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.

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

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.

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

The 10% Rule RULES! Part One

 

You can calculate any percentage using the 10% rule.

 

No need to remember any rules, formulae or part/whole/percent triangles.

 

Example 1: What is 15% of 40?

 

 

Start by finding 10%.

 

To find 10%,

chop off the "0" in 40 and you have...

 

4

 

 

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

 

2

 

4 + 2 = 6

 

 

DONE! Work SMART not HARD

 

 

Example 2: What is 15% of 42?

 

 

There's no zero to chop!

 

Think of 42 as "42 decimal" or "42." Move that decimal one place to the left and you have 4.2

 

This is your 10%.

 

5% is half of 10%. Half of 4.2 is 2.1, so you need another

 

2.1

 

4.2 + 2.1 = 6.3

 

DONE! Work SMART not HARD

 

 

 

 

 

 

Neat Trick for Squares - Well Some of Them

If you are squaring a number that ends in 5, your answer will end in 25.

There's the early Christmas present...

That's the easy part. What about the hard part?

There isn't one...

2

15

 

You know your answer will end in 25...

 

Now, multiply the first digit (the 1 in 15) by ONE larger (2)

 

1 x 2 = 2

 

Stick the 2 in front of the 25 and you have your answer...

 

225

 

Try squaring 25...

 

You know your answer will end in 25...

 

Now, multiply the first digit (the 2 in 25) by ONE larger (3)

 

2 x 3 = 6

 

Stick the 6 in front of the 25 and you have your answer...

 

625

 

Still not convinced?

 

Try squaring 35...

 

You know your answer will end in 25...

 

Now, multiply the first digit (the 3 in 25) by ONE larger (4)

 

3 x 4 = 12

 

Stick the 12 in front of the 25 and you have your answer...

 

1225

 

 

 

 

 

 

 

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 5)

Percent Video (Type 5)

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 5th of 5 videos in a series on percent questions.