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.

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

 

 

 

 

 

 

 

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 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.

Slope - Wake Up First!

Have you been asked to calculate the slope of a line?

Think of jogging. If you want to go for a run up a slope in the morning, you must rise first before you run.

So...    to calculate the slope of a line...
use the formula...             slope = rise
                                                        run
Rise is the vertical distance between two points on a slope. Run is the horizontal distance between two points on a slope.

In this case, the rise is 2 and the run is 6.

slope = rise
             run   so...

2            1
6      =   3

Convention says that lines that "fall" as they move to the right have negative slopes and lines that "rise" as they move to the right have positive slopes. I guess it depends on your point of view - are you going up or down the hill?

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

Beer saves the day - again. Improper Fractions

21   What do I do with this improper fraction?

 8

You need to change it into a mixed fraction. How do you do this? Well, think of beer. You have 21 bottles but can only carry 8 bottles at a time...

You will make 1 full trip, carrying 8 bottles.

You will make a 2nd full trip carrying another 8 bottles.

You have 5 bottles left.  They do not represent a "full" trip. Your 2 "full trips" become the whole number component of the mixed fraction. 

Your 5 bottles that are "left over" go on the top shelf of the fridge. (That is where all left overs go." Your denominator was 8, so let's keep it at 8. You now have...

2  5

     8    

For a video explanation, start 2 minutes into the video here

Backwards Backwards

         5
-    - 3

What is this?  

1) 5 take away minus 3?

2) 5 minus minus 3?
3) 5 plus 3?

In effect, this is 5 plus 3. Why? Firstly, despite what your mother told you, two wrongs do make a right. Well, in math they do. In this case, the 2 negatives (wrongs) become a right (positive).

Think of the motion of the woman in the photograph. She is moving to the right and we generally think of a right movement in math as positive. A left motion in mathematics is considered negative. Left, in history, was considered evil or sinister.

If we ask the woman to turn around and walk backwards, or asked her to walk "backwards backwards", she'd still be moving to the right. (Just facing the other way but we don't worry about this - just the direction of travel.) 

Your two "minus" signs are your backwards backwards. They become a positive. Try walking backwards backwards for yourself. 

Call a spade... something else

a)  5x + 3
+  2x + 6   =      ??????

b) 3x²  +  4x

+ 4x²  +  5x =      ??????

Some of my past students seemed to want to add the "x's" together, getting answers such as...

a)  5x + 3
+  2x + 6   =          7x² + 9        or....

b) 3x² + 4x

+ 4x² + 5x =              7x⁴ + 9 x²

My advice, always, is not to call a spade "a spade", but to use the good old cat and dog to help us. (Or any other animal you might choose.) For question a)...

Restate the question as 5 cats and 3 dogs ADDED to 2 more cats and 6 more dogs. You'll get 7 cats and 9 dogs. None of those cats gets squared or changed to a super cat, nuclear powered cat, robo-cat or anything else.  So your answer is...

7x + 9 

For question b) ... you'll simply have 3 elephants and 4 cats ADDED to 4 elephants and 5 cats. Your answer is...

7x² + 9 x

It is easy to get blinded by all the exponents when you get questions such as...

 7x² + 2y + 9x⁴  +  8x² + 3y + 3x⁴ 

It is much easier to imagine 15 elephants, 5 giraffes and 12 monkeys.