Middle Grades

1

• Middle Grades
• Mathematics Methods

2
Angles of a Triangle 180 degrees theorem

• Students mark the three angles of their triangle
  A, B, and C.
• Cut or tear off the three angles shown.
• Place the triangles so that their sides are
  adjacent and they meet at a common point.
• Ask if a student can suggest a theorem about the
  sum of the measures of the angles of the triangle.

3
How many squares?

• Materials
• Geoboards, Rubber bands, Dot Paper, Pencils
• Procedure
• Make different squares on a geoboard
• Sketch each of the squares you make on dot paper.
• How many squares did you find? How do you know
  you have found all the squares possible?
• ExtensionHow many different rectangles can you
  make on a geoboard?

4
Area of a Circle

• Divide a circle into a series of pie-shaped
  wedges that resemble triangles.
• Discuss the formula for the circumference of the
  circle
• Cut the circle into triangles and rearrange them
  in alternating directions
• Figure is a parallelogram. The base of the
  parallelogram is about one-half the
  circumference. The height is the same as the
  radius of the original circle, r.
• Discuss formulas.

5
Pizzas Small, Medium, or Large?

• Pizzas are often sold in small, medium, and large
  sizesusually measured by the diameter of the
  circular pizza. Of course, the prices are
  different for the three sizes. Do you think a
  large pizza is usually the best buy?
• Double Daves sells small, medium, and large
  pizzas. The small pizza is 9 inches in diameter,
  the medium pizza is 12 inches in diameter, and
  the large pizza is 15 inches in diameter. For a
  plain cheese small pizza, Double Daves charges
  6.00 for a medium pizza, the charge is 9.00
  for a large pizza, the charge is 12.00. Are
  these fair prices?
• ____________________________
• Which measures should be most closely related to
  the prices chargedcircumference, area, radius,
  or diameter? Why?
• Use your results to write a report on the
  fairness of the pizza prices.

6
TangramsUse a seven piece tangram set to
construct as many of the following as you can.
Click here for tangram puzzles on the web
NCTM Tangram Applets
7
Polyominoes
Click here for links to pentomino puzzles

• A polyomino is a polygon made up of squares
  joined edge-to-edge. There is only one type of
  domino (2 squares) and two types of trominoes (3
  squares).
• Using snap cubes find the five tetrominoes (4
  squares)
• Using snap cubes find the 12 pentominoes (5
  squares)
• Create a pentomino one-difference looparrange
  the pieces into a loop so that only one square
  needs to be moved to change a shape into the next
  one
• Find combinations of pentominoes that can be put
  together to make rectangles and squares

8
van Hiele Levels of Geometric Thought

• Five-level hierarchy of ways for
  understanding spatial ideas
• Level 0 Visualization
• Level 1 Analysis
• Level 2 Informal Deduction
• Level 3 Deduction
• Level 4 Rigor

9
Group Assignment

• Your group will identify activities for the van
  Hiele levels 0-3 of geometric thought
  ____________________________________
• Describe an activity discussed in your textbook
  that would be appropriate for students at each
  van Hiele level 0-3
• Explain what makes this activity appropriate for
  a specific van Hiele level
• Present the activities and your explanations to
  your classmates