I had the opportunity recently to attend a David McKillop workshop. The Development of Geometric Thinking really opened my eyes to the huge impact the Shape and Space strand of the math curriculum has on mathematical reasoning. I've come to the conclusion that, were I back in the classroom, this is the unit I would teach first. Too often this unit is considered one of the "fluffy" ones at the K-3 level, and left as the last unit, or something to teach in December, when the students aren't really paying that much attention anyway. Geometric thinking, however, teaches and strengthens so many important aspects:
- Hand-Eye Coordination
- Visual Discrimination
- Figure-Ground Perception (Google "Gestalt Psychology")
- Position in Space Perception
- Visual Memory
- Perceptual Consistency
- Perception of Spatial Relationships
Tangrams are an excellent resource at any age group to teach many of the outcomes of the Shape and Space unit. Originating in China during the Tang Dynasty, it has been around for over 200 years. It is a dissection puzzle. There are 7 pieces of the puzzle, called tans, and these are rearranged to form shapes. Usually all 7 pieces must be used, and the shapes must not overlap each other in any way.
The puzzle includes 5 triangles, one square and one parallelogram. If you don't happen to own commercial plastic tangrams, they are easy to print onto card stock, laminate and use over and over. If your children are adept with scissors, you could also have them cut out the shapes themselves, and then they have their own copy.
Here are some great activities to do with tangrams:
1. Sort the tans into groups. How are the pieces in each group alike? How are they different?
2. Recreate the square that they came in.
3. Show a picture of a shape made with tangrams on the projector. Have the puzzle show the lines between the shapes. Ask the students to recreate using their own shapes.
4. Now show a puzzle that does not have the lines between the pieces. This ups the ante a bit. Start with small 2- or 3- piece puzzles and build up to all 7 pieces.
5. Show a puzzle that has 2-4 puzzle pieces for 6-8 seconds. Remove the image and have students recreate the shape from memory.
6. One student creates a design with 3-5 puzzle pieces and hides it from his/her partner. Using words only, the student describes the design to the partner and the partner must recreate it. This activity uses a great amount of mathematical language!
There are lots of tangram puzzle shapes available online if you Google "tangram puzzle." There are also lots of books that use tangrams. Some of my favourite ones are Grandfather Tang's Story, Then and Now on Old MacDonald's Farm and Three Pigs, One Wolf and Seven Magic Shapes. I highly recommend using actual tangram pieces that students can manipulate, but there are also some good iPad apps out there that use tangrams. They are:
Hands-On Math Tangrams, $2.99
TanZen Lite, free