Shares

Sharing can be so difficult, especially when it isn't 50:50. Does this question look familiar?


Chris and Pat paint a house. Chris works for 5 hours and Pat works for 3. They are paid $240.00. How much should each get paid?

Of course Pat would say $120.00 but that is not the answer. 

The key to solving is looking at the 2 numbers that AREN'T the total - in this case the 5 and 3. These are the "shares", and they add up to 8. 

If you divide the $240.00 by 8, you will get $30.00. Each share is worth $30.00. Chris worked 5 shares, so will be paid 
$30.00 x 5 - $150.00. 

Pat worked 3 shares, so will be paid $30.00 x 3 - $90.00. 

If you add $150.00 and $90.00, you will get $240.00

Note! Be careful with these types of questions on multiple choice tests. The question might ask, "How much more does Chris earn than Pat?" or something similar. 

Up in the Sky! It's a "Y"

Which is the "x" axis and which is the "y"?

1) Well, "y" is the sky, so it is the vertical axis.

2) A pirate ship is sailing ACROSS the ocean to look for treasure. The captain sees an island on the horizon."X" marks the spot on the treasure map. "X" is the horizontal axis.

Age Problems - Method 2 - Substitution

Chris is 3 times as old as Pat.               Together their ages add up to 32.                          How old is each of them?

Method 2 - "Game Show" Higher or Lower Method

a) Pat is your "reference" or starting point. Look for the word "as" or "than". (The first sentence could have been written "Chris is 3 times older than Pat.") The word associated with "as" or "than" becomes your reference. 

b) Pick 1 to represent Pat's age. 

c) If Pat is 1, then Chris has to be 3 because "Chris is 3 times as old as Pat."

d) "Together their ages add up to 32..." so...
1 + 3 will not work, as it doesn't = 32. The answer is too low. Pick a higher number to represent Pat's age. 

e) Pick 10 to represent Pat's age. 

f) If Pat is 10, then Chris has to be 30 because "Chris is 3 times as old as Pat."

g) "Together their ages add up to 32..." so...

10 + 30 will not work, as it doesn't = 32. The answer is too high. Pick a lower number to represent Pat's age. 


h) Eventually, by going higher and lower, you'll figure out that Pat is 8. Chris is 24 because Chris is 3 times older than Pat.

i) Check! Always check! "Together their ages add up to 32."       8 + 24 = 32.

Classic "Age" Problems - A couple of ways to solve these questions - Method 1

Chris is 3 times as old as Pat.               Together their ages add up to 32.                          How old is each of them?

Method 1 - 

a) Create an equation. Pat is your "reference" or starting point. Look for the word "as" or "than". (The first sentence could have been written "Chris is 3 times older than Pat.") The word associated with "as" or "than" becomes your reference. 

b) Pick a letter to represent Pat's age. We'll use "x".

c) If Pat is "x", then Chris has to be 3x.

d) "Together their ages add up to 32..." so...
x + 3x = 32

e) Combine your x's. (That's a lot of alimony). 
4x = 32

f) This means 4 times "something" = 32. The answer is 8. One "x" = 8

g) Pat is 8, because Pat is one "x". Chris is 24 because Chris is 3 times older than Pat.

h) Check! Always check! "Together their ages add up to 32."       8 + 24 = 32.

Complementary? Supplementary?

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.

Quadrilateral Song

Quadrilateral song!
see here

Mean, Median, Mode Rap

Love it or hate it, rap sticks in your brain. Here's one for mean, median and mode...

Press here

Have a Nice Day!

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.

Multiplication Tables in under 2 minutes - Back by Popular Demand

Can you write out the multiplication table to 10 by 10 in under 2 minutes...

We're nearly up to 1400 hits on this video. I have had all kinds of praise for the content. The video itself was done on a budget of about 59 cents and the "special effects" need upgrading but the ideas are certainly worth sharing. See...

Math Doctor

Positive and Negative Numbers

Here's a useful video to help with positive and negative numbers.

Positive and Negative Numbers Video

Dividing Fractions

The first dividing fractions video can be found here...  video

84 - You're never too old to get your GED

Graduate Harry Schildroth of Port Elgin, Ontario, Canada, pictured here with Liz Sandals, Ontario's Minister of Education. You'll find the complete

story here

"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 MUADO - 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 MUADO, and get yourself the right answer.

Solving Triangle Questions That Don't Really Look Like Triangle Questions

The GED exam may well have one word question involving a hiker, a boat or an airplane travelling so far in one direction, turning then travelling so far in a second direction.


There may also be a question with a grid, where you are asked to find the distance between two given points.

Believe it or not, these are triangle questions.

Example. A hiker walks 3 km due south, then turns and walks 4 km due east. How far is the hiker from the starting point? (The boat and airplane questions are similarly worded.) You might be tempted to answer "7", which would be incorrect.

How to solve? Draw a picture. Of a right-angled triangle.

You now have a Pythagorean question, where you have the two short legs and you are looking for the hypotenuse (long side.) You may also recognise this as a 3/4/5 triangle, where the hypotenuse is 5. There's your answer - 5.

Multiplying Fractions - What if my answer is an "improper" fraction?

What is the easiest way to deal with an answer that is in the form of an improper fraction? As the video says, have a drink! Unsure what this means? Well...       

see here

"Area of a Triangle" Song

For a song explaining how to calculate the area of a triangle, press...
here

Mixed Drinks - Mixed Fractions

You would probably rather have a mixed drink than have to multiply mixed fractions. However, if you HAVE to multiply the fractions, try this video    It may help.

Mean, Mean and Mode Dance

Mean? Median? Mode? Which is which? See

here

for the answer to your question.

Slope of a Line

What is the mathematical formula behind the slope of any line?

See... here

Multiplying Fractions Part 3 - Cancellation

Multiplying Fractions Part 3 - Cancellation. Find the ....

Video Here

Multiplying Fractions Part 2

Press...

here

for the video for Multiplying Fractions Part 2

Multiplying Fractions Part 1

Press...

Here

for  the link to the video for Multiplying Fractions - Part1.

Fractions into Decimals Rap

If you are turning fractions into decimals, look...

Here

for the Fractions into Decimals Rap

GED Pep Talk Part 2

Pep Talk Part 2  This video will help GED students on the days of the exam. The small issues surrounding writing an exam can contribute to failure. If these issues are planned for, reduced or eliminated, success will be more likely.

GED Pep Talk Part 1

This video will help GED students on the days leading up to the exam, as well as on the days of the exam. Some times the small issues surrounding writing an exam can contribute to failure. If these issues are planned for, reduced or eliminated, success will be more likely.



GED Pep Talk - Part 1

Rounding Numbers with the "Rounding Rap"

Here's the link for the "Rounding Rap" on You Tube.

Link

Fractions Video 6 - The Magical List and Lowest Terms

Fractions Video 6 - The Magical List. How to use the list to help put fractions into lowest terms. See...Link

Pythagoras Rap

I guess, strictly, we should have a right-angle triangle in the picture. Here's the Link
for the Pythagoras Rap.

Fractions Video 5 - Introduction to Lowest Terms

The video for Introduction to Lowest Terms can be found in the link below...

 

 

Video 5

Fractions Part 4 - Finding A Common Denominator

Fractionss Part 4. Common Denominator. See the video...   Turning Cats and Dogs into Pets

Square Numbers with Elvis Video

See this video Elvis Squares for ideas on square numbers.

GED Pep Talk - Tips for passing the exam.

A.  Mindset

1.       The FACT that you have made it as far as registering means you are likely to PASS

 

B. Practical Issues Before the Exam - Reducing Stress

1.      Go to the test site ahead of time. Time the trip so you know how long it will take to get there. Check out the parking. Do you have to pay? Do you need change/tokens? Are you going by bus? If so, know the bus schedule.

2.      Find out where the room is so you are not wasting time on the day looking for it.

3.      Sort out overnight accommodation if you are not going to go home on the Friday night.

4.      Clear your schedule for Friday afternoon and all day Saturday. Make sure somebody else is covering your chores/duties/childcare, etc.

5.      Plan a “treat” event (shopping, restaurant, etc.) that you will do immediately after the exam as a reward for all your hard work.

6.      Make a cheat-sheet of all the things you are afraid you might forget (tips and tricks you have learned, definitions, times tables, etc.) and study this sheet.

7.      Get a good night’s sleep on the Thursday night before the exam. Make sure you have arranged things so you will get a good night’s sleep on the Friday night as well. Stay away from alcohol.

 

C.   On Exam Day

1.      Arrive at least ½ hour early so you are not feeling rushed or panicked. Give yourself extra time on your journey to handle things like detours, construction, accidents, etc.

2.      Dress in layers and take a hat. MOST PLACES HAVE 2 TEMPERATURES - TOO HOT or TOO COLD. The air conditioning might be cranked up or the heating might not be working properly. Being uncomfortable will be a mjor distraction to you.

3.      Do not eat a big meal before the exam. This might make you sleepy. Instead, eat a small meal of energy foods like pasta. Take along some energy bars or trail mix to snack on.

4.      Sip on water to help you stay awake and to keep you hydrated. No coffee is allowed in the exam room so keep your supply outside in an insulated container. Caffeine can improve concentration in some people.

5.      If you prefer to sit in a particular part of the room, ask to do so. Sitting at the back reduces the number of people around you who may distract you with coughing, paper shuffling, etc.

6.      Study your cheat sheet until the last moment.

 

D.The Friday Exam

1.      Immediately write down everything you can remember from your cheat sheet onto the blank paper that is given to you. Take a deep breath and start the exam knowing that you will pass.

2.      Look at your watch and determine when your time will be half up. When you get to this time, make sure you have completed at least half the questions. If you haven’t, you need to speed up. If you have completed more than half the questions, you can slow down a bit.

3.      You will likely pass the GED exam if you use the 4-step method.

a)      Scan the exam and complete the questions that are the easiest. Skip over any questions that you don't know. Aim to do half the questions. If you answer each of these questions correctly, you will already have passed.

b)      Go back and go over the questions you skipped. Chances are you may have suddenly remembered how to do a question or another question will have triggered your memory. Continue to skip questions that you don't know.

c)      Look at each question you skipped. If they are multiple choice, scratch off 3 of the 5 answers that you feel are obviously wrong. Pick one of the two remaining answers. Chances are your first guess will be right.

d)     With any remaining questions, GUESS! You have a 1 in 5 chance of being right, which is better than the 0 in 5 chance you have by not answering.

4.      Stay until the very end of every exam section unless you are absolutely sure you have passed. Do not be pressured by others who are leaving early. DO NOT be pressured by the examiner looking at the clock, shuffling papers, etc., trying to hurry you up. Keep your head down and stay focussed.

5.      For the section with the Essay and Grammar, write the essay first. You do not want to be thinking about how you will write your essay while trying to complete the grammar multiple choice questions.

 

E.   After The Friday Night Exam

1.      Go straight home or to where you are going to stay the night. Do not discuss the exam questions with anyone. This will only make you more worried.

2.      Stay away from alcohol

3.      Go straight to bed when you get home.

 

 

F.   Saturday Morning

1.      Get up early. Eat a decent breakfast.

2.      Pack a healthy lunch. You do not want to worry about having to look for a cafeteria, restaurant, etc. at lunch, especially if you have to leave the site.

3.      Arrive at least ½ hour early so you are not feeling rushed or panicked. Give yourself extra time on your journey to handle things like detours, construction, accidents, etc.

4.      Dress in layers and take a hat.

 

G. The Saturday Exam

1.      Keep sipping water and snacking on energy bars throughout the morning.

2.      Find a place to eat lunch by yourself. If you sit with others, you will likely talk about the finished parts of the exam and lose your focus. You cannot change your answers, so talking about them will serve no purpose other than to worry you.

3.      Follow the same advice for the Friday night exam. Complete all questions using the 4 step method and use the entire time period for each section.

 

H. After the Exam

1.      Go on your treat activity and forget about your exam.

Fed Up With Fractions - Part 3. Adding Cats and Dogs

Fed Up With Fractions Part 3

Darth Vader Explains Pythagoras

Darth Vader
explains Pythagoras...

Multiplying Binomials - FOIL Rap

First Outer Inner Last. See the Binomial Rap Link Below.

FOIL Rap video

Fractions Solved Part 2 - Cats and Dogs

The video for Fractions Solved Part 2 is linked here.

How To Fill In the Standard Grid

See this video for help in filling in the Standard Grid

Fed Up With Fractions Introduction

See the link below for the first in a series of fractions videos...

Fed Up With Fractions Introduction

Percent Type Five

The Percent Type 5 video is ready!

Type 4 Percent (Percent Change)

See the video for Type #4 Type 4 Percent Video

Percent Type 3 Video

The Percent Type 3 Video is now available. See   Percent Type 3 Video

Percent Type 2 - Video

Percent Type 2 is now a YouTube Video. See...Percent type 2

Percent Type 1 - Powtoon Video

I've completed an explanation of Percent Type 1 using Powtoon Video. The YouTube Link is...Type 1 video

Multiplication Tables in 2 Minutes

You aren't allowed  to take multiplication tables into a GED exam. But what if there was a strategy that would allow you to write them out once the exam had started? In under 2 minutes, no less. Use the multiplication tables then for multiplying, dividing, putting fractions in lowest terms, finding roots and finding square numbers. In under 2 minutes? Impossible you say. See here for the strategy.

Type 5

% Solved!

Type #5

4)    Increasing or decreasing a number by a given %

I have:  1 number

 I have: A given % increase or decrease

I need to find: The new value, after the % change has been applied.

Example:    a) What is $640.00 decreased by 10%?

                   b) What is $200.00 increased by 20%?

Key to Solving:

These questions are not much different from a type 2 question. You just need to think of the % as a new value.

a)     What is $640.00 decreased by 10%?

Step 1 – a 10% decrease is equal to 90% of the original value

Step 2 –       90    X  640.00 = $576.00  

                   100

b)    What is $200.00 increased by 20%?

Step 1 – a 20% increase is equal to 120% of the original value

Step 2 –       120    X  200.00 = $240.00  

                   100

Tricks to look out for.

Watch out for fractional percents like 3  1 %

                                                                  2

a) What is $360.00 increased by 3  1 %  ?

                                                                  2

Step 1 – a 3  1 %  increase is equal to 103.5% of the original value

                     2

Step 2 –       103.5   X  $360.00 = $372.60  

                   100

b)      What is 12 increased by 1 %  ?

    4

Note – a  1 %  increase is equal to 100.25% of the original value. It is a

                4    

                       quarter of a percent, not a quarter.

ý  Wrong! 125   X  $12 = $15.00   

                   100

þ Right!   100.25   X  $12 = $12.03