Munching for Meaning

1
Munching for Meaning

• Prepared for
• Florida Council of Teachers of Mathematics
• October 12, 2007
• Pam Ferrante, ED.S., NBCT
• Donna Hunziker
• Project CENTRAL
• The University of Central Florida

2
Edible Activities

• The Magic Circle
• Concept- Students explore the area of a circle
  and the formula for it by decomposing the circle
  into a rectangle.

3
Procedures

• Concrete
• Cut eight diagonals across the pizza or tortilla,
  cutting the pieces into approximately equivalent
  sizes.
• Lay the pieces out horizontally alternating the
  pointed end up, then down, then up, etc. (forming
  a rectangular shape)
• Apply the formula for area of a rectangle to this
  figure.
• Examine the sides of the rectangle and discuss
  the relationship of these lengths to the original
  circles attributes

4
Procedures Cont.

• Representational
• Make a sketch of the original circle and the
  transformed rectangle
• Label the relationships of the measurements on
  each

radius
?
radius
?
5
More with the Magic Circle

• Abstract
• Write the formula for the area of a rectangle and
  use this formula to find a formula for the area
  of a circle based on the sketches and
  measurements taken on the transformed circle.
• Area of rectangle Length X width
• Area of a Circle ?

6
More Fun

• Fruity Cuts
• Concept-Students investigate the relationship of
  angles formed by parallel lines cut by a
  transversal.

7
Procedures

• Concrete
• Roll out and flatten a Fruit Roll-Up square
• Cut a pair of parallel lines across the Fruit
  Roll-Up square
• Cut a transversal across the parallel lines
  previously cut
• Explore the relationship between the various
  angles formed by the cuts
• Are any of the angles congruent? Which ones?
• Are any of the angles complementary? Which ones?
• Are any of the angles supplementary? Which ones?
• Why do these relationships exist?

8
Procedures Cont.

• Representational
• Sketch and label the angles formed by your
  parallel lines and transversal.

1
2
3
4
5
6
7
8
9
More with Fruity Cuts

• Abstract
• Write rules for the relationships that exist
  between the angles examined in the fruit square
• i.e. Measures of angles 1 and 7 are congruent
  and the measures of angles 2 and 8 are
  congruent which means that alternate exterior
  angles of two parallel lines cut by a
  transversal are congruent.

10
Crunchy Corners

• Concept- Students explore the relationship
  between the angles of a triangle and a straight
  angle having 180 degrees.

11
Procedures

• Concrete-
• Give each student several triangular chips to
  examine.
• Have students break off the corners of the chips
  and line up together along the edge of a ruler to
  form a straight line demonstrating that the sum
  of the angles of the triangle is 180 degrees.
• Have students repeat the process with different
  size chips.
• Does it make a difference what size triangle you
  use? Why or why not?
• Does it make a difference what size corner you
  break off? Why or why not?

12
Procedures Cont.

• Representational
• Make a sketch of the triangles transformation
  and realignment on the straight line

13
Abstract

• Write a rule about the relationship of the angles
  of a triangle.
• Does the rule apply to all triangles? (i.e.-
  right, scalene, equilateral, etc.)

14
Fraction Fun

• Concept-Students explore dividing fractions and
  mixed numbers by fractions.

15
Procedures

• Concrete-
• Designate a denominator to be associated with
  each color of licorice (i.e. red is fourths and
  black is thirds)
• Provide students with 5 ropes of each color
• Have students divide two ropes of each color into
  appropriate fractional pieces (i.e.- red into 4
  equal pieces, black into 3 equal pieces)
• Have students use ropes to explore problems like
  2 1/3 divided by ¼ and 4/3 divided by 2/3.
• Provide additional problems for students to
  explore or have them create their own using the
  given materials.
• Have students reflect upon what patterns they see
  with the problems and their answers
• When you divide by a fraction, what happens with
  your answer?
• Is it a larger or smaller number? Why?
• Will this always be true? Why or why not?

16
Procedures Cont.

• Representational
• Sketch ¾ divided by 2/3

One
and 1/8
2/3 in 3/4
17
Abstract

• Write a rule about dividing fractions by
  fractions
• What do you notice?