geometric shapes tangram activities the university of texas at dallas

Geometric ShapesGeometric ShapesTangram ActivitiesTangram Activities

The University of Texas at Dallas

Can You Give The Names of These Can You Give The Names of These Shapes?Shapes?

SQUARE

RETANGLE

PARALLELOGRAM

TRAPEZOID

RIGHTTRIANGLE


COMPARING SHAPESCOMPARING SHAPES


HOW ARE THEY DIFFERENT?HOW ARE THEY DIFFERENT?

• Squares and rectangles both have right angles

HOW ARE THE SQUARE AND RECTANGLE ALIKE?HOW ARE THE SQUARE AND RECTANGLE ALIKE?

• All the sides of the square are equal.

• Rectangles have equal lengths and widths. 4cm 4cm

7cm

7cm

5cm

5cm

5cm

5cm


HOW ARE THE RECTANGLE AND PARALLELOGRAM HOW ARE THE RECTANGLE AND PARALLELOGRAM ALIKE?ALIKE?

• Both have opposite sides parallel and equal in length.

HOW ARE THEY DIFFERENT?HOW ARE THEY DIFFERENT?

• Rectangles have right angles. Parallelograms do not have right angles. If a parallelogram has right angles, it becomes a rectangle. Rectangles are really special parallelograms.


3cm

3cm

4cm

4cm

4cm 4cm

7cm

7cm


HOW DOES A TRAPEZOID COMPARE TO A HOW DOES A TRAPEZOID COMPARE TO A PARALLELOGRAM?PARALLELOGRAM?

• Trapezoids have exactly 1 pair of parallel sides.

• Parallelograms have 2 pairs of parallel sides.

3cm

3cm

4cm

4cm


TANGRAM ACTIVIESTANGRAM ACTIVIES

LOOK AT THE 7 TANGRAM PIECES.LOOK AT THE 7 TANGRAM PIECES.


CAN YOU GIVE THE NAME OF EACH PIECE?CAN YOU GIVE THE NAME OF EACH PIECE?

A BF C

G

DE

• A, B, C, D, E are right triangles. Notice that A and B are larger than the others and are the same size. • How does C compare with A and B?• What about D and E?• F is a square. • G is a parallelogram.

TANGRAM ACTIVITIESTANGRAM ACTIVITIES

Look at the grid of figures. You will use the Look at the grid of figures. You will use the tangram pieces to form the shapes at the top:tangram pieces to form the shapes at the top:

triangle, square, rectangle, parallelogram, or triangle, square, rectangle, parallelogram, or trapezoid using 1, 2, 3, 4, 5, 6 or 7 tangram trapezoid using 1, 2, 3, 4, 5, 6 or 7 tangram pieces.pieces.

As we make the shapes, draw them in the As we make the shapes, draw them in the space on the table and label the pieces used space on the table and label the pieces used (i.e. A, B, C …)(i.e. A, B, C …)



Going across the table, complete the table Going across the table, complete the table for 1 piece.for 1 piece.

Why is there an ‘X’ under rectangle and Why is there an ‘X’ under rectangle and trapezoid on the table? trapezoid on the table?


Answer


Because we cannot make those shapes Because we cannot make those shapes with any of the tangrams provided using with any of the tangrams provided using only 1 piece.only 1 piece.



Using a small triangle (E or D) and the Using a small triangle (E or D) and the parallelogram, complete the table for 2 pieces.parallelogram, complete the table for 2 pieces.

Do not forget to draw and label your answers.Do not forget to draw and label your answers.


Note for tutor. Click Me ! Click Me!!!

TANGRAM ACTIVITESTANGRAM ACTIVITES

Let students move triangles around and Let students move triangles around and discover shapes they can make in any discover shapes they can make in any order. order.

Ask them how they know a figure is a Ask them how they know a figure is a parallelogram, trapezoid, etc. as they find parallelogram, trapezoid, etc. as they find them.them.


TANGRAM ACTIVITIESTANGRAM ACTIVITIES Here is one solution. Solutions with different orientations of the Here is one solution. Solutions with different orientations of the

shapes are the same. shapes are the same.

Not Not possiblepossible

D E


E

DE

G

E

D

Thuy

2 pieces: 2 small triangles and 1 parallelogram



Now use 3 tangram pieces to complete Now use 3 tangram pieces to complete the table.the table.

DO YOU KNOW WHICH PIECES TO DO YOU KNOW WHICH PIECES TO USE?USE?



Let students move the pieces on their own Let students move the pieces on their own before you give the hint. Some students may before you give the hint. Some students may not need the hint at all. Others may need it after not need the hint at all. Others may need it after just a few tries. just a few tries.

As students find solutions, continue to ask how As students find solutions, continue to ask how they know the figure is correct. For example: they know the figure is correct. For example: “How do you know that’s a parallelogram?”“How do you know that’s a parallelogram?”


More

TANGRAM ACTIVITIESTANGRAM ACTIVITIES Ask students to demonstrate how the hint is true. Ask students to demonstrate how the hint is true.

This idea will help them with more complicated This idea will help them with more complicated figures.figures.

Let students explore how the pieces can fit Let students explore how the pieces can fit together. together.

For example:For example:

D FD

F

Perfect Fit Not Fit


HINT


Use the 2 small triangles (E, D) and the Use the 2 small triangles (E, D) and the medium triangle C to form the shapes.medium triangle C to form the shapes.

All 5 shapes can be made my moving only All 5 shapes can be made my moving only 1 piece.1 piece.




E

DB

ED CED

CED

C

E

DC

Solution:

Thuy

3 pieces: 2 small and 1 big triangle


Use 4 pieces to complete the table for 4 Use 4 pieces to complete the table for 4 pieces.pieces.

You decide which pieces are needed to You decide which pieces are needed to make the shapes.make the shapes.

HINT



Students may choose any 4 pieces to make the shapes.Students may choose any 4 pieces to make the shapes. The 2 small triangles, the square, and the parallelogram can be The 2 small triangles, the square, and the parallelogram can be

used to make a parallelogram, rectangle and trapezoid.used to make a parallelogram, rectangle and trapezoid. The square, parallelogram, a small triangle, and a large triangle will The square, parallelogram, a small triangle, and a large triangle will

make a triangle. make a triangle. Two small triangles, the medium triangle and a large triangle can be Two small triangles, the medium triangle and a large triangle can be

used to make all of the shapes.used to make all of the shapes. The next slide will show a solution using only triangles. However The next slide will show a solution using only triangles. However

there are other solutions as well using other pieces.there are other solutions as well using other pieces. Ask students to begin with triangle and show how the other shapes Ask students to begin with triangle and show how the other shapes

can be made by moving only 1 piece.can be made by moving only 1 piece. Is there a shape that requires moving more than 1 piece?Is there a shape that requires moving more than 1 piece?




E D

C

B

EDC

B

ED

C

B EDC

B

ED

C

BCompare your solution.


Use 3 smaller triangles, the square and the Use 3 smaller triangles, the square and the parallelogram to complete the table for 5 pieces.parallelogram to complete the table for 5 pieces.

Use all the hints mentioned.Use all the hints mentioned.



The University of Texas at DallasE

DCF

G

ED

C

F G

E

DC

F

G

E

D

C

F

G

E

DC

F

G

Solution:


Use 6 pieces to create a rectangle, Use 6 pieces to create a rectangle, parallelogram, and trapezoid (others parallelogram, and trapezoid (others shapes cannot be made).shapes cannot be made).

Decide which pieces you want to use.Decide which pieces you want to use.


HINT


Use all pieces except 1 large triangleUse all pieces except 1 large triangle




Ask students to begin with the Ask students to begin with the parallelogram and show how to create the parallelogram and show how to create the other shapes by moving only 1 piece.other shapes by moving only 1 piece.


SOLUTION



Not Not PossiblePossible

Not Not PossiblePossible

E DC

A

FGE D

C

A

F

G

E DCA

FG

Solution:


Use all 7 pieces to complete the table.Use all 7 pieces to complete the table.

DO YOU KNOW WHERE TO START?DO YOU KNOW WHERE TO START?

HINT



First make the triangle using 5 pieces. First make the triangle using 5 pieces.

Then the 2 large triangles can be moved Then the 2 large triangles can be moved around the make the rest of the shapes.around the make the rest of the shapes.




Continue to ask how they know a Continue to ask how they know a parallelogram is a parallelogram, etc.parallelogram is a parallelogram, etc.

If students didn’t need the hint and found If students didn’t need the hint and found other solutions, have them make the other solutions, have them make the triangle and show how it can be triangle and show how it can be transformed to the other shapes.transformed to the other shapes.




E

D

C

AB

F

G

ED

C AB

F G

ED

C ABF G

ED

C A B

F G

ED

C A

BF GSolution:

geometric shapes tangram activities the university of texas at dallas

Documents