Date: Tue, 14 Apr 1998 22:25:13 -0400
Sender: Robin
Subject: Question: Logic and Matirx instruction

Level: Elementary/Middle

I need assistance with instruction strategies to teach the construction of a matrix, solving a logic problem. Providing instruction in the construction of a simple matrix , no problem. However, I stumpted on this one.

Five players were chosen as All Stars at the basketball banquet. Based on the following clues, find the player's name, team, uniform color and number of points scored.

1. The player from the PRIMA DONNAS scored 50 more points than the player who wear a shite uniform.

2. William Worm wears a blue uniform

3. Betty Cooper scored 20 more points than the player from the DARTH INVADERS.

4. The CAT FOLLIES do not wear blue uniforms

5. The player wearing the yuellow uniform scored 170 points.

6. Mark Clark scored 70 fewer points than the player who wears a green uniform.

7. The player from the ITSY BITSY'S SCORED 300 points.

8. Chris Hooper plays for the STICKY WICKETS.

9. The player who wears a white uniform scored 190 points.

10. Anne lester wears a red uniform and scored 220 points.

After constructing 2 matrix I'm stumped. One is players name and color of uniform and the second is team name and uniform color.

I've consulted methodology text and nothing to assist me, I like to provide my students with more challenging problems.

Footnote:
I sat down a third time with the problem and solved it , I found it quite easy. My problem is this , how do I provide instruction using this concept.

R. Booker

Hi Robin

One apporach to these problems is to start with the matrix that has the most information. If you consider the four factors (name, team, uniform color and number of points scored) and count how many times each factor is mentioned in the clues you get:
 Name: mentioned 5 times Team: mentioned 5 times Uniform color: mentioned 7 times Points scored: mentioned 7 times
I wold start with either uniform color or points scored since they are both mentioned in 7 clues. Since one of the "points scored" is unknown I started with uniform color.

ColorNameTeamPoints
Yellow
White
Red
Green
Blue

Reading through the clues the first time I can fill in some information.

ColorNameTeamPoints
Yellow  170
White  190
RedAnne Lester 220
Green
BlueWilliam Worm

Now looking at the clues again, the first implies that the Prima Donnas scored 240 points which is the missing "points scored" value. Now that you know all the values for the points scored variable and the only 70 point difference is between 240 and 170, clue 6 implies that Mark Clark plays for the yellow team and the green team scored 240 points. Thus, together with the seventh and eighth clues we get

ColorNameTeamPoints
YellowMark Clark 170
WhiteChris HooperSticky Wickets190
RedAnne Lester 220
Green Prima Donnas240
BlueWilliam WormItsy Bitsy's300

Clues three and four now fill in the outstanding cells in the matrix.

Cheers,
Harley

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