### Answers to Problems

Nothing is worse than working a problem, and not knowing if your answer
is right or not. This page is to reveal the answers to the various
problems that appear in different postings on this blog.

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May 1, 2014 - Magic Squares

This is one possible solution.

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January 30, 2014 - Learn By Heart

1) Heart Burn

2) Hearty

3) Heartless

4) Cross My Heart
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January 24, 2013

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December 26, 2012

1) Jeans Problem -  A Story or Word Problem

\$40.00 - 22.95 = \$17.05No, I do not enough money to buy a shirt.
2) Checkerboard - A Process Problem
Although this investigation seems quite simple, it requires a methodical approach if the correct answer is to be attained.  The investigation involves finding out how many different squares there are on a checkerboard. You might think that there are only 64, but you would be wrong.

The diagram below shows that there are indeed 64 squares, but there are also some more.

Don't forget the one large square (shown in red here).

And, also the 16 two-by-two squares shown below (although these aren't the only 2 x 2 squares!)

There are many more different-sized squares on the checkerboard.
The complete list of answers is shown below:
 1, 8x8 square 4, 7x7 squares 9, 6x6 squares 16, 5x5 squares 25, 4x4 squares 36, 3x3 squares 49, 2x2 squares 64, 1x1 squares

Therefore, there are actually 64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 squares on a checkerboard!
(204 in all).  If the students manage to find all of them, ask them if they can see
a pattern in the results (i.e. the square numbers in the table).

3)  Marcus and His Free Throws - A Word or Story Problem

If you divide 30 by 5, you get an answer of 6 sets of five shots.  That is the total number of
shotsMarcus attempts.  If he makes 4 out of every 5 then 6 x 4 = 24 free throws.

4)  Soup for Lunch - A Word or Story Problem

42 students - the 28 who had sandwiches = 14 students who ate soup
5)  T-Shirts - A Process Problem
The answers are 11, 13, 18, 31, 33, 38, 81, 83 and 88.  Mathematically you can find the
answer by multiplying the numbers of digits (3) by the number of places (2) which equals 6,
but then you must add three because the digits can be repeated.  So 3 x 2 + 3 = 9 different numbers.
6)  Ostriches and Horses - A Process Problem
Draw 50 sticks to represent the animals' legs.  By guessing and checking, the students cirlce four legs for the horses and two legs for the ostriches.  The trick is to have 17 animals when all of the the legs are circled.

The answer is:  8 horses (32 legs) and 9 ostriches (18 legs)

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November 29, 2012

Drew and Addie are playing a game. At the end of each game, the loser gives the winner a chip. When they are done playing several games, Drew has won three games, but Addie has three more chips than she had when the game began. How many games did Drew and Addie play?

The answer is: Drew and Addie played 9 games. The best way to solve this is to get out chips or some other manipulative and work backwards through the process using the strategy of guess and check.

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August 8, 2013

1. I have 8 grandchildren, five of whom are adopted.
2. My husband asked me to marry me on our first date.
3. I am a big KU fan.  (We live in Kansas. KU stands for Kansas University, home of the Jayhawks.)

4. I have been teaching for over 30 years.

Surprise.... it's #3 that is false.  I was born and raised in Ohio and did graduate work at THE Ohio State University.  Go Bucks!!! And, yes, my husband did ask me to marry him on our fist date.  As you can tell, I eventually said, "Yes."
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