Math problem solving

Strategy

Strategy: Combining Venn Diagrams &Tangrams
Appropriate Grade Level: Middle School
Procedures/Steps:The teacher should have available: homemade tangrams in four different colors, homemade attribute-label cards (made by listing positive and negative attributes values on the back of the tangrams on card stock. Examples of attribute cards are: “triangle”, “not triangle,” “blue,” and “not blue” and largeVenn diagrams, drawn on paper.
The teacher reviews with students briefly about “set theory” concepts, including naming and drawing geometric shapes, drawing circles on the board to illustrate the intersection of two sets, having students categorize geometric shapes in the circles, showing how to classify shapes (or sets) by using three different attributes to label the circles, and introducing the new idea—“the negative, not, or compliment of” statement.
First, students are divided into groups of four. Each group receives one set of playing cards, Venn Diagrams, and four sets of tangrams, including one set of blue, green, yellow, and red.
Each player uses seven tangram pieces of same color as his or her tangram pieces
Label cards are placed face down on the playing surface, and the Venn diagram is three overlapping circles, making seven spaces inside the circle.
Give each group a packet of various geometric shapes, of various colors and sizes.
students to work together to identify and classify the shapes.
When most groups are finished the teacher should ask what strategies were used to do this?
Teacher writes on the board: deal cards into three hoops, classify your tangrams, and use mathematical arguments to capture misplaced cards.
Play begins with first player turning over three label cards and placing one in each of the 3 circles. Each player follows by putting their tangrams in the appropriate circle, and classifying them
Students use mathematical reasoning to argue against any pieces that are incorrectly placed and where they are to be placed. If identified correctly, the student takes the piece. If not, the piece stays. It is then the next players turn. Play continues this way, until all pieces have been picked up.
For the second round, place 3 new cards face down and repeat steps 9-10.
Closure—Talk in your groups about the experience.
Comments and/or tips:When done in the proper order, and thoroughly, students learn to collaboratively develop skills in reasoning and proof.
Source:
Moyer, P.S. (2003). Classify & capture: Using venn diagrams and tangrams
to develop abilities in mathematical reasoning and proof. Mathematics
Teaching in the Middle School, 8, 325-330.