## Sunday, December 13, 2009

### Triangle Detective

This game is a variation of a variation of a game. There's a terrific game called Polygon Capture which originally came from a Mathematics Teaching in the Middle School article (Oct 98, William M. Carroll). The idea is to turn over a sides property card and an angle property card and capture the polygons that fit the description. For my classes I'm on about version 3 of it, and it's a solid middle school game. (Contact me if you want my copy.) At one point a class was interested in adapting it to triangles, so we did a version of the game that focused on them.

Michigan has moved a lot of the triangle identification objectives down to 4th grade, though, so I thought I should adapt that to be a 4th grade game, and that's what I'm posting today. Mrs. Bruckbauer's students decided it should be Triangle Detective, because you inspect the triangles to see if they fit the card. They are so right. As usual. They also suggested the three points per triangle scoring, and preferred it to the 'most triangles wins' rule.

Triangle Detective

Rules
• Put the triangles into the middle and shuffle or mix up the cards.
• On a player's turn they flip over a card. They catch a triangle if they can find a triangle that matches the card's description. All players have to agree it fits the description.
• Master Cards are special challenges. Are you a triangle master?
• STEAL cards are the only way to take a triangle someone else has captured.
• Play until the deck is empty. Players get three points for each triangle, and the most points wins.

Remember:
Two things are congruent in geometry if they are exactly the same size and shape.

An angle is right if its sides are perpendicular, like the corner of a square.
An angle is obtuse if it is bigger than a right angle.
An angle is acute if it is smaller than a right angle.

A triangle is acute if it has ALL acute angles.
A triangle is right if it has ONE right angle.
A triangle is obtuse if it has ONE obtuse angle.

A triangle is equilateral if it has THREE congruent sides.
A triangle is isosceles if it has TWO congruent sides.
A triangle is scalene if it has NO congruent sides.

Cards:

 ObtuseTriangle Has anobtuse angle Has NOcongruent sides ScaleneTriangle RightTriangle Has two or moreacute angles Has two or morecongruent sides IsoscelesTriangle AcuteTriangle Has aright angle Has threecongruent sides EquilateralTriangle Has at least twocongruent angles Has threeacute angles Has threesides Has a line ofsymmetry Master CardTake a triangle IFyou can nameits side type ANDits angle type Master CardTake a triangle IFyou can explainthe type of eachangle in thetriangle STEAL!If you can findsomeone with anacute scalenetriangle. STEAL!If you can findsomeone with aright isoscelestriangle.

Triangles: (Click for full size image) (3 of each type... including some borderline cases.)

Teaching Notes: The game worked really well for review. The students were engaged and asking good questions. Students were motivated to ask about vocabulary they didn't know, got to see other people apply vocabulary, and see triangles in many different orientations. The statements on the cards led to them thinking about alternative ways to say the same thing, and to think about properties in combination.

Acute triangles are an issue, because it seems to them that one acute angle should be enough. Which is actually nice parallel reasoning from how right and obtuse triangles are explained. We talked about how each angle has a type and each triangle has one angle type. So if it's not obtuse nor right...

We used square and triangle pattern blocks to help check the triangles angles, and talked about how equilateral triangles have all the same angle as well, and that's a way to check them.

The students got quite expert at checking side lengths, and quickly weren't satisfied with 'they look the same.'

They were generally quite helpful to each other, to the point where one student asked them to stop helping because she wanted to find her own.

Good luck to if you try it. And, of course, I'd love to hear how it goes!