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 circle’s 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 radiusradius ? ?

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. 12 3 4 56 78

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 triangle’s 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 Oneand 1/8 2/3 in 3/4

17. Abstract Write a rule about dividing fractions by fractions What do you notice?