Tangrams with Grandfather Tang
Lesson 2 of 4
Objective: The students will be able to create two dimensional shapes based on specified properties.
This lesson is one of my favorites because I can integrate social skills, math and Chinese culture all at one time. It is also a big lesson because I start with reading a book, silently modeling making tangram shapes and then having the students complete a Tangram Challenge. I use this lesson on an early release day and it last the entire day. I love lessons that are integrated and use an entire day.
As my students gather on the carpet to listing to the book Grandfather Tang's Story I ask them to think about any stories that are retold in their families, and then to talk to a partner about it until I ask for attention. This question is meant to help the students make connections from their personal life to the story I am about to read. It also gives the students a chance to share about themselves with other students.
In Grandfather Tang's Story, a grandfather tells his granddaughter a tale of two fox fairies who challenge each other by becoming stronger or faster animals. The story ends with one of the fox fairies near death from their adventures and being nursed back to health by the other. As the grandfather tells the story, he rearranges seven tangram shapes to represent the animals.
Because we are always teaching the College and Career Readiness Anchor Standards for Reading , I tie in Key Ideas and Details because the students need to determine a theme of this tory using details from the text, including how characters in the story respond to challenges. We also compare and contrast the behaviors of the two fox fairies with each other and with our own (positive) behaviors. This was a great way to explore positive friendship skills. We were also able to discuss who the narrator was and how his, the grandfather's, point of view may have influenced how the events were described.
During the discussion one of my students points out that this is a story about how to not treat your friends. I ask them to give me details from the book to explain their thinking. I help them begin by giving a reference, "Turn back to the page where Chou is a dog. He growled and said he wanted to eat Wu Ling." With a toss of the Koosh, I hand the discussion over to the students.
Then I shift the discussion, "Tell a neighbor how the story would be different if it wasn't the grandfather telling the story?" I listen for about 30 seconds before I raise my hand and the class falls silent as each student raises their hand in response - a signal I've used since the first day of school. For my students, this means finish your sentence and then look to me to show attentive listening. We are ready to move forward with the discussion.
To insure my students have been discussing the question, I tell them when I call on them they are to tell me what their partner said about changing the narrator. One of the most interesting responses was that the story would not change with narrators, because it is a traditional story that has been passed down for hundreds of years. Sometimes this student can come off as sarcastic, but I have to hold my tongue and thank them for extending my thinking because they are correct.
As I send my students back to their seats to create their own tangrams I assign them to tell each other the names of the shapes derived from the seven tangram shapes in the story. I circulate, and then bring them back to share their discussion. As you can see, throughout this lesson I'm checking in frequently on student understanding as well as participation. Also, this is an informal, anecdotal assessment.
Creation of Tangram Pieces
While students are listing the names of the tangram shapes, I listen and notice I do not hear trapezoid, rhombus or parallelogram - which are elements of the lesson we are about to do. I do hear names of polygons classified by the number of sides from a previous days lesson called The Greedy Triangle. Students build on each other's thinking, such as saying "A pentagon has five sides and a hexagon has seven." "Remember an octagon has eight sides like an octopus has eight legs. We learned that each of the shapes has a prefix that tells how many sides the shape has."
Now I know, informally, many of the students have learned that the terms for geometrical shapes have a root word and a prefix! And they are identifying, comparing and analyzing the attributes of two dimensional shapes to develop their mathematical vocabulary (MP6) to describe the geometric shape attributes and have classified two-dimensional figures in a hierarchy based on properties (number of sides). (5.G.4)
And if they didn't, they have just had a review.
For this next part of my lesson, students will be using the scissors I was placing on desks while I listening to their discussions. I also pass out 7" x 7" squares cut from construction paper the day before. I always make sure to have extra because there will be a couple of students who have difficulty following directions or with cutting the shapes unevenly. You could have some preprinted tangram pieces ready for the students who will need them. The purpose of this part of the lesson is developing the precise vocabulary to use when naming the attributes of shapes and to classify two-dimensional figures. The procedure I use practices, and assesses, close listening skills.
I have the students "turn their voices off." As they listen/watch, I go slower than I normally do, telling students we will go "step by step". This signals my students that they must finish each step and then wait for the next instruction. The expectation also is that they will be patient and wait for other to finish.
As I show (without speaking) my students what to do, I uncover the vocabulary. I have to admit this is another lesson my wonderful teammate Cathy Mooney shared with our schools' staff over 7 years ago. I love silent instruction because the students really have to listen and watch and make the metacognitive tie to the vocabulary. By using an interactive whiteboard, I am able to reveal the words (creates excitement). If you don't have an interactive whiteboard, another way to do this is to create "signs" which you would "reveal" by bringing them up with your other hand to hold side-by-side with what you are showing.
Throughout this part of the lesson I am imagining myself as Vanna White on Wheel of Fortune, revealing (on the interactive whiteboard) the shapes to the class. I even try to imitate her hand movements to keep it entertaining. As you will see, before teaching this lesson you'll need to practice this sequence.
Here we go! As I reveal...
Square - I fold the square in half and cut to reveal,
Triangle - I hold one up (keeping the other handy, as I will need it later). I reveal...
Right Angle - I point to the right angle and continue to do so as students arrive at this same point, with the expectation that they copy the movement.
Congruent - I hold up both triangles and demonstrate they are the same size placing one over the other.
I then fold one triangle in half and reveal Line of Symmetry, holding and pointing until the line as students arrive at the same point with the expectation that they copy the movement.
Next, I cut on the fold and demonstrate Similar with the bigger triangle. After students have arrived at this point, I put these aside and take the other large triangle, fold it in half and then fold the tip down and cut to reveal...
Triangle to Trapezoid - Cut the trapezoid in half, fold into a square, then into a triangle and cut. With the other half, fold the right angle up and cut to reveal a parallelogram.
Throughout this part of the lesson I have been walking around, helping where needed, directing another student to help or nodding thank you to the ones who have jumped in to help another student.
There will always be one or two students who do not have the pieces cut correctly or evenly. This time, I had a student who was so focused on getting the shapes cut perfectly they had perfect squares and triangles but all too small. I have copied extras of the tangram pattern to give to these students. The multi step process is not intended to defeat, discourage, or embarrass any student and I want to emphasize that the process isn't the point. So, I ask them if they have learned a new vocabulary term during this lesson. They answer ,"Yes trapezoid!" I say "Great, you have learned what I wanted you to from this and here is a tangram pattern for you to cut out. Thank you for using patience and perseverance!" To keep the rest of the class on task while those who need to are cutting out the shapes, I ask them to try to put the tangram pieces back into the shape of a square. I observe their visual, spacial, and reasoning skills while listening again for correct vocabulary terms - especially parallelogram and trapezoid.
I have my students glue envelops into their math journals and put the tangram pieces into it for save storage. If you need to break this lesson up into different days this is a great place to do it.
Wow we have done a lot but now it is time to really put the correct vocabulary on the tangram shapes. I place each shape under my document camera and students identify, and then label their own shapes.
Vocabulary needs to be used in many contexts for it to become part of students’ mathematical language. How we create those contexts is critical, because mathematical language is precise (MP6). Through showing, identifying, and noting the names of our shapes (MP4 - Model with Mathematics), students refine their mathematical communication skills.
Once students have correctly labeled their tangram pieces, I passed out the Tangram Challenges. This can be used as a separate lesson or an extension. I choose to use it as a challenge for all of my students. The reason I choose to use this activity is because it brings in Howard Gardner's Multiple Intelligences. Specifically the visual spatial.
In the first weeks of school, I give my students a Multiple Intelligences test and this year there is a highly level of musical students and fewer in visual spatial. When I see this I try to incorporate lessons that not only use the students strengths but also helps build the weaker areas. This activity is going to be difficult but rewarding in the end because it will strengthen their visual spatial skills.
The class worked on the challenge for about 20 minutes before frustration started to show - students not on task and being disruptive. This is a sign to me to adjust my delivery of the assignment. I asked if anyone needed help and the majority raised their hands. By working under the document camera I was able to showing them how to make a square with 3 small triangles. Students started to ask if they could bring their pieces up to make the shapes so I passed the teaching over to them. I was then able to walk around the room helping individuals. We work through each of the shapes going down the column first, building the square with the 3 small triangles, 5 small pieces and all seven pieces. At this point many of the students could "see" what they needed to do so the few who still needed my support I asked to move to the carpet and we worked in a small group to complete most of the challenge.
Student self-reflection helps students learn by thinking about their own thinking process or metacognition. It balances the quantitative information with qualitative information. There are many sources out there promoting student self-reflection. This one is from Linda Suskie’s Assessing Student Learning: A Common Sense GuideIn the last 10 years we have really focused on quantitative information and have missed out on the qualitative. The Common Core Standards really are bringing us back to the depth (qualitative) and not the quantity of worksheets produced (quantitative).
For today's reflection I asked my students to write in their journals. I love exit slips and sticky note reflections but when the reflection is written into the journals students can go back a reread and reflect again:)
Reflection 1, 2, 3
1. What were the new shapes you learned about today? Name and description please!
2. How did the silence help you work to make the tangram shapes?
3. What did you learn about your own thinking when you worked on the tangram shapes?