1. Read the article: use the The van Hiele Tangram- find it in the article called: Developing geometric thinking through activities that Begin With Play , by P van Hiele 1.2 Make one A4 Chart Definition page:describe what is a tangram 1.3 Make One taskcard on A4 -Describe an activity. Look at the article but make your own taskcards see Figure 6 p 313 in the article 1.4 Make one demo van Hiele tangram: An examples of the van Hiele tangram (38,8 cm x 22,4,2cm) Make 1van Hiele tangram from thick high quality card board or wood (38,8 cm x 22,4,2cm) for teaching aid, that you can show on the board to the children.

09:46 think and talk about shapes hildren may have joined two pe make another piece, for example, using pieces 5 and 6 to make piece 3. We can ask them to find all the pieces that can be made from two oth top of the piece that they next to the piece for easy record their solutions, children a piece and then draw how they made it with the other pieces of show their method with colored 312 NG CHILDREN HEMATICS f Van-Hiele learni... markers on a triangle grid. They also notice that some pieces fit with either This activity leads children to notice that joining side up but that other pieces do not, Pieces 2 and 3 two pieces sometimes makes a shape that is not the fit either side up: piece 7 does not, since flipping it same as one of the seven original pieces, They can changes its orientation and how it looks. Is piece 1 investigate how many different shapes can be made a flipable piece? Are pieces 4, 5, or 6? with a pair of pieces, joining them by sides that match. With pieces 5 and 6, six shapes are possible, Puzzle Cards and the only one of which is the same as an original piece. Try these combinations, and then try the same Mosaic Puzzle activity with pieces 1 and 2. Next I present more complex puzzles. Directions New shapes are introduced by puzzles that can be given orally or by task cards, like those in require two or more pieces. The shape in figure 5 figure 6. Read and try them. They illustrate how can be made two ways. One uses pieces 2 and 4 puzzles that are created with two pieces can have number side up; the other uses pieces 2 and 4 solutions that use other pieces. Think about what flipped over with the number side down. Make the geometry they involve and the conversations that shape both ways. Can it be made with pieces 1 and 7? With pieces 1 and 7 flipped over? What other Task cards two pieces make this shape, and do they also work if they are flipped over? House Puzzle Making the shape in different ways with two 1. On a piece of paper, make a house like this one with two pieces pieces may inspire children to ask, Can we make it 2. Trace around the house you made to form a shape. with three pieces, too? Try pieces 1, 2, and 5, and 3. Make the shape with two other pieces. then make it in a different way with these three 4. Make the shape with three pieces. Can you find two ways to do it? pieces. Also, try pieces 1, 2, and 5 flipped over. 5. Can it be made with four pieces? In solving puzzles like these, children work visually with angles that fit and sides that match A house FIGURE 4 Tall-House Puzzle 1. On a piece of paper, make a tall house with piece 2 as the roof and one other piece. 2. Trace around the tall house you made. 3. Make the shape with pieces 5 and 7. 4. Can it be made with three pieces? Make a Puzzle 1. Use any two, three, or four pieces. Make a shape. Trace around it on a large index card. Color it. 2. Can you make this shape with other pieces? 3. Write your name and a title for your shape on the index card. This shape can be made several different ways. FIGURE 5 FEBRUARY 1999 313 children might have while doing them. rectangles, too, and asked to make them. Have chil- Some students use strategies to solve these puz- dren make the "tall" rectangle with pieces 1, 5, 6, zles. For example, in part 4 of both house puzzles, and 7 and the rectangle in a "crooked" position with children who know that rectangle piece 3 can be pieces 1 and 7 and the flip sides of pieces 5 and 6. made from pieces 5 and 6 may use this relationship Can other rectangles be made? Of course, the to figure out a solution by putting piece 1 or 2 on largest is the large rectangle in figure 1. It is a chal top and pieces 5 and 6 in the rectangular space on lenge for students to reconstruct it without seeing the bottom. It is important for children to share the completed design. Children can arrange the their approaches with classmates, perhaps by using pieces in several ways, and they enjoy finding new an overhead projector to "show and tell." Teachers ways. By making various rectangles, children should also encourage problem posing. Children will after some time-discover that all rectangles enjoy creating puzzles for others to solve. Puzzles are not enlargements of one another, as was the can be presented as cutout shapes or can be drawn case for equilateral triangles. Also, in contrast with on cards and set out in a math center. Students can equilateral triangles, the rectangle is a common label puzzles with their names for example, Big everyday shape, and children should be asked to 09:46 think and talk about shapes hildren may have joined two pe make another piece, for example, using pieces 5 and 6 to make piece 3. We can ask them to find all the pieces that can be made from two oth top of the piece that they next to the piece for easy record their solutions, children a piece and then draw how they made it with the other pieces of show their method with colored 312 NG CHILDREN HEMATICS f Van-Hiele learni... markers on a triangle grid. They also notice that some pieces fit with either This activity leads children to notice that joining side up but that other pieces do not, Pieces 2 and 3 two pieces sometimes makes a shape that is not the fit either side up: piece 7 does not, since flipping it same as one of the seven original pieces, They can changes its orientation and how it looks. Is piece 1 investigate how many different shapes can be made a flipable piece? Are pieces 4, 5, or 6? with a pair of pieces, joining them by sides that match. With pieces 5 and 6, six shapes are possible, Puzzle Cards and the only one of which is the same as an original piece. Try these combinations, and then try the same Mosaic Puzzle activity with pieces 1 and 2. Next I present more complex puzzles. Directions New shapes are introduced by puzzles that can be given orally or by task cards, like those in require two or more pieces. The shape in figure 5 figure 6. Read and try them. They illustrate how can be made two ways. One uses pieces 2 and 4 puzzles that are created with two pieces can have number side up; the other uses pieces 2 and 4 solutions that use other pieces. Think about what flipped over with the number side down. Make the geometry they involve and the conversations that shape both ways. Can it be made with pieces 1 and 7? With pieces 1 and 7 flipped over? What other Task cards two pieces make this shape, and do they also work if they are flipped over? House Puzzle Making the shape in different ways with two 1. On a piece of paper, make a house like this one with two pieces pieces may inspire children to ask, Can we make it 2. Trace around the house you made to form a shape. with three pieces, too? Try pieces 1, 2, and 5, and 3. Make the shape with two other pieces. then make it in a different way with these three 4. Make the shape with three pieces. Can you find two ways to do it? pieces. Also, try pieces 1, 2, and 5 flipped over. 5. Can it be made with four pieces? In solving puzzles like these, children work visually with angles that fit and sides that match A house FIGURE 4 Tall-House Puzzle 1. On a piece of paper, make a tall house with piece 2 as the roof and one other piece. 2. Trace around the tall house you made. 3. Make the shape with pieces 5 and 7. 4. Can it be made with three pieces? Make a Puzzle 1. Use any two, three, or four pieces. Make a shape. Trace around it on a large index card. Color it. 2. Can you make this shape with other pieces? 3. Write your name and a title for your shape on the index card. This shape can be made several different ways. FIGURE 5 FEBRUARY 1999 313 children might have while doing them. rectangles, too, and asked to make them. Have chil- Some students use strategies to solve these puz- dren make the "tall" rectangle with pieces 1, 5, 6, zles. For example, in part 4 of both house puzzles, and 7 and the rectangle in a "crooked" position with children who know that rectangle piece 3 can be pieces 1 and 7 and the flip sides of pieces 5 and 6. made from pieces 5 and 6 may use this relationship Can other rectangles be made? Of course, the to figure out a solution by putting piece 1 or 2 on largest is the large rectangle in figure 1. It is a chal top and pieces 5 and 6 in the rectangular space on lenge for students to reconstruct it without seeing the bottom. It is important for children to share the completed design. Children can arrange the their approaches with classmates, perhaps by using pieces in several ways, and they enjoy finding new an overhead projector to "show and tell." Teachers ways. By making various rectangles, children should also encourage problem posing. Children will after some time-discover that all rectangles enjoy creating puzzles for others to solve. Puzzles are not enlargements of one another, as was the can be presented as cutout shapes or can be drawn case for equilateral triangles. Also, in contrast with on cards and set out in a math center. Students can equilateral triangles, the rectangle is a common label puzzles with their names for example, Big everyday shape, and children should be asked to