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?

Acute? Obtuse? Reflex? Which is Which?

Acute? Obtuse? Reflex? 

Which is Which?

Angles less than 90 degrees are...   Acute

Angles between 90 and 180 are...   Obtuse

Angles between 180 and 360 are...

Reflex

How to remember?

Alphabet! AOR. Fortunately, the angles are in alphabetical order.

A - Acute - up to 90

O - Obtuse - between 90 and 180

R - Reflex - between 180 and 360

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.

TMI? No... Not Enough Information (NEI) or Extraneous Information (EI)?

At a recent sporting event, 25 athletes won one gold medal each. 25 others won a silver medal. 25 won bronze. 40 athletes did not win any medals. How many medals were awarded?

Answers

a) 115
b) Not enough information
c) 75

The answer is "c"

Note: 

You might be tempted to answer... a) (115) because that is 25 x 3 + 40. You see the numbers in the question and you combine them. 

You might be tempted to answer... b) "Not enough information" because the question involves medals awarded to some athletes and then suddenly some athletes aren't getting any medals.

********If you answer "Not enough information" more than twice on a fifty question exam, you should check the questions again. 

Trick Question!

The sum of three consecutive positive odd numbers is 69.

What is the difference between the biggest and smallest of these three numbers?

HINT: Don't work out the three numbers! (They are 21, 23 and 25, by the way). The difference between the largest and smallest of any three given consecutive positive odd numbers is 4. Try it...


1,3,5


3,5,7

etc.

How much precious exam time would you have used up trying to work out that question?

Work SMART, not HARD.