Tangrams: Lessons in Logical Thinking

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Playing with tangrams can be a lot of fun, but not too many students have looked at them in a systematic way. The seven shapes can give students practice in problem solving and logical thinking and are captivating enough to keep them working at it for a long while. We first began by reading some books about tangrams (see above.)

This graph is from Family Math

 Have them make a graph with basic shapes on one side and numbers along another. See if they can figure out how to make the shapes with different amounts of the seven possible shapes. When they figure out how to make the wanted shape out of the prescribed amount of shapes, have them sketch it in the square. Better yet, make a wall sized graph and have them trace over the tangram shapes, cut them out in one piece and glue onto the graph. This is a great family, multi-aged project, saving the easier columns for the younger students and the multi-shape columns for the older students. This is a project that can be done a little bit at a time over a period of days or weeks, as part of their math or during free time.

Another fun way to explore tangrams is to make cookies with them!

I rolled out some sugar cookie dough and I used my wooden tangram pieces for a template...

cut out the seven magic shapes.

I then let them decide what cookie picture they wanted to make and place the shapes correctly.

They added some chocolate or caramel pieces for decorative features.
They baked into large one-piece cookies but you could still see the lines where the tangram shapes fit together.

source: 

• Mathematics; a Way of Thinking, Bob Baratta-Lorton
• Cookie Tangrams at Almost Unschoolers 

Mayans and Toltecs (500-1500) and Base 20 Math

The Maya people lived in small kingdoms in the rainforests and plains of Central America. Their temples were pyramids and they played a fast-moving ball game. They had a very accurate 365 day calendar.

Around 1160 fierce tribes began invading, scattering both the Toltecs and the Mayas.
Around 850m most of the Maya had moved north into the area known as the Yucatan. Meanwhile, in Mexico the Toltecs became powerful. In the 1100's invadig tribes drove the Toltecs out of Mexican and into the Yucatan, where it seems as if they worked together peacefully.

Remember the fun we had with base 6 math? The Mayan's math system was a base 20 system.

So, I got out the counters and we decided to have some fun with Mayan Math.

First we made up a name for the numbers from 10- 20, because it was easier to understand the place value if we used differnt names for the digits that we have in our base 10 that would not also be in base 20. So, our ten became bleep...11 became cheep...12 became seep and so on to 20.

 Then we went through the same games as we had gone through with our base 6 math.
It was confusing and fun and we laughed and got frustrated. I was so busy I forgot to take photos. 

We looked again for patterns.

We tried adding and subtracting using base 20. I was hard but fun.

Place value is beginning to take on new meaning.

 In 1542 the Mayans surrendered to Francisco de Montejo.

More Activities

Another great Mayan activity to do is this Jade Mask at Academia Celestia.
Makita has a lot of great links there, too.
You could also make Mayan worry dolls from the tutorial at Child in Harmony which are still made in Guatemala.

 

"The Lost Button" or Buttons of All Sorts

Buttons can be a great math manipulative. To make a literature-math connection, read "The Lost Button" in Frog and Toad Are Friends. Using buttons, either real ones or paper ones, for props for each of the buttons he finds is a great interactive way of reading the story.

Then you can further explore various types of buttons. Have each student pick out their favorite button and play a game in which you announce an attribute and have them raise their hand if their button has that attribute. This can get really fast-paced.

Then hide a button and play a hide and seek type game using "warmer" and "colder" for indicators as to how close the seeker is.

Another early reader that features the concept of sorting and buttons is 3 Little Fire Fighters. In this story three small fire fighters need to get dressed for a parade, but are all missing their buttons. They mix and match the buttons several times until they can find a way for them all to have matching buttons. We then sorted our buttons in all kinds of ways such as by color and by size.

Sometimes sorting is not as easy as one would think. As my son Sam said, "Sometimes it is hard to tell where one leaves off and another begins."

Then play a game in which your students pick buttons, but do not let them tell what criteria they have sorted them by. Then you and the rest of your students have to guess in what way each student has sorted! Sorting can get more sophisticated and can involve shades of color and number of button holes.

Your students can now make their own paper buttons, designing them any way they want. Once they are completed, you can begin graphing them in several ways, using different criteria. Use a piece of posterboard or a dry erase board to make your graph and they can place their buttons on where it is appropriate. First you can graph them according to how many holes they have and then you can graph them according to what shape they are, continuing on for as long as you want. This a great beginning graphing experience and you can later move on to more symbolic bar graphing.