Tangram Puzzles

Tangrams are a Chinese dissection puzzle consisting of seven flat shapes, called tans, which are put together to form shapes. The objective of the puzzle is to form a specific shape (given only in outline or silhouette) using all seven pieces, which may not overlap.

Check out the Tangram math tasks we've been working on:

Mr. Infin Ity, a mathematician, is in love with tangrams. He wants to use tangram shaped tiles to decorate the floor of his office. If one small triangle tile costs $0.75, how much would you infer the other shapes cost? How much would it cost to fill the square with small triangles? Explain your thinking use words, pictures, and numbers. Remember to use evidence to justify your inferences.

Here is Anna Grace's work:

The second part to the problem:
At a second store, Mr. Infin Ity found the large triangle tile costs $1.40. How much would you infer the other shapes cost? How much would it cost to fill the square with large triangles? Explain your thinking use words, pictures, and numbers. Remember to use evidence to justify your inferences.

The third part to the problem:

At a third store, Mr. Infin Ity found the parallelogram tile costs $0.96. How much would you infer the other shapes cost? Explain your thinking use words, pictures, and numbers. Remember to use evidence to justify your inferences.

Take a look at how Anna Grace's recording has changed from the first task. Now she is generalizing about the relationship between the shapes, rather than simply focusing on the cost. Her recording reminds me of a geometry proof:

THE CHALLENGE:

Mr. Infin Ity has calculated that at the final store all the pieces needed to form the large square would cost $8.00. How much does each piece cost?

Henry uses "guess and check" to solve the first time:

To get Henry thinking more algebraically, I asked, "Is there a more efficient strategy than using guess and check? What if you were given any cost for the entire square? What would your strategy be?

Charlie's thinking at first:

To get Charlie thinking more algebraically, I asked, "What if you were given any cost for the entire square? How could record a series of steps that would work for any whole square?" Notice how Charlie uses abbreviations to communicate his thinking:

H=Whole squaure

BT=Big triangle

MT=Medium triangle

SQ=Square

P= Parallelogram
ST=Small triangle

Here's Liam's recording to explain what he discovered about the relationship between the area of the square, parallelogram, and medium triangle:

Watch a video of Liam explain his thinking and recording: