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:

Fable: The Cat and the Mouse

Charlie and Tenley act out the story of The Cat and the Mouse. Try to guess the moral before it is revealed at the end.

Fable: The Fox and the Crane

Kenley, Will, and Heather act out the story of The Fox and the Crane. Try to guess the moral before it is revealed at the end.

Will's Podcast

View our Podcasts! (finally)

Nine of our Pocasts are finally up on the web!

Here's the link where you can find them:

http://schoolcenter.k12albemarle.org/education/components/docmgr/default.php?sectiondetailid=90315&catfilter=13745#showDoc

All you have to do is click on the Podcast you'd like to watch. A small screen will appear for you to watch. You should also be able to download them if needed.

Liam, Hannah, and Heather will be finishing up a few things on Thursday and soon their Podcasts will be added to this list!

4,000 minutes

How in the world are going to make up all the snow days we've missed? No one wants to have a shorter summer, so in math we explored the possibility of adding a little extra time on to each day. Here was the math invitation:

Making up our Snow Days 

Our last day of school was supposed to be June 10th but now we must add our missed days to the end of the year. Some people still want to end on June 10th, and rather than having extra days at the end of the year they want to add extra minutes to each day to make up the lost time. Our school day begins at 7:45 and ends at 2:25. So far we have missed 10 days due to snow or rain. How much time have we missed so far? 

What if we added on a little time to each day? How many extra minutes would we need to add each day? What time would school get over? You should plan it so that equal minutes are added on to each day. The earliest the extra time could begin is March 1st. 

You should come up with at least 2 different plans to present to the School Board. You may use a calculator, but make sure that your mathematical thinking is clear for each plan using words, pictures, and numbers. 

To begin, students worked on the first part of the problem trying to figure out how much time we had missed so far. This brought out a variety of strategies and some heated discussions.

Carly used a number line (which we recently used to solve difference problems) to find the number of hours and minutes in one day. Here is her work:

Charlie didn't start by using a number line. He first wrote down 24 x 10. He said this was because there were 24 hours in one day and we missed 10 days. I asked, "Do we go to school for 24 hours a day?" This brought out the eraser. You can see that he then took on more of the number line approach (without the line). He began at 7:45 and added minutes and hours until he arrived at 2:25. He added 15 + 25 to find that it equaled 40 minutes plus the additional five hours and one hour he’d already added on. He then wrote down 5 x 60 and entered it on his calculator. That’s…. 300. Now I need to add 60 more minutes on for the other hour. Ok, 360 minutes plus the 40 minutes equals 400 minutes times 10 days equals 4,000 minutes.

And there you have it! We need to make up 4,000 minutes. Wondering what our plan is?

Here is Clare's plan: (click to make larger)

Take a look at the following album to find nine of our plans.

http://picasaweb.google.com/thirdgradestonypoint/SnowPlans#

Let us know which plan you think sounds like the best.

Pottery tells stories

After using our own resources to learn some basics about Ancient Greek pottery, we met with Mary Lou to look more closely at the designs and shapes that were common. The shape we saw most often was a large jug with two handles. This style is called an amphora and was used to transport and store grapes, olive oil, wine, oil, olives, grain, and fish. Mary Lou led us through a series of steps to help us “see” the shapes and patterns more clearly. Students worked to create the outline of their pots and repeating patterns near the top (lip) and bottom (foot) but were instructed to keep the middle part empty. We learned that many Greek pots tell a story or a myth in the middle section using pictures. A few days later the students were invited to design the middle part based on the myth we had recently read:

The Naming of Athens 

“According to the legend, the gods Athena and Poseidon quarreled over the naming of the greatest town in Greece. Poseidon thrust his trident into a rock on the Acropolis. Sea water gushed out, and Poseidon promised the people riches through sea trade if they named the city after him. 

Athena planted an olive tree as her gift to the people. It was decided that she had given the more valuable gift and the city was called Athens in her honor. Athena’s sacred olive tree was burnt when the city was sacked by the Persians, but when it later threw out green shoots it brought new hope to the Athenians.” 

Below you can see how Clare tried to tell this particular story through pictures on her pot. Can you recognize Poseidon (trident) and Athena (spear and shield)?

Check out our artwork in this album:
http://picasaweb.google.com/thirdgradestonypoint/GreekPottery#

Or view them in a slideshow:
http://picasaweb.google.com/thirdgradestonypoint/GreekPottery#slideshow/5447097123240698914