1. Comparing & Ordering Fractions Our Favorite Subject

2. 2 What Should Students Understand about Fraction Concepts Meaning of the denominator (number of equal-sized pieces into which the whole has been cut) Meaning of the numerator (how many pieces are being considered) The more pieces a whole is divided into, the smaller the size of the pieces

3. 3 What is Equivalence, Anyway? “Equivalence” means “equal value” A fraction can have many different names Understanding that 1/2 is equivalent to many other fractions helps you to use that benchmark Simplify: when and why

4. 4 Ordering Fractions Fractions with the same denominator can be compared by their numerators.

5. 5 Ordering Fractions Fractions with the same numerator can be compared by their denominators.

6. 6 Ordering Fractions Fractions close to a benchmark can be compared by finding their distance from the benchmark.

7. 7 Ordering Fractions Fractions close to one can be compared by finding their distance from one.

8. 8 Strategies for Ordering Fractions Same denominator Same numerator Benchmarks: close to 0, 1, 1/2 Same number of missing parts from the whole (”Residual strategy”)

9. 9 “Clothesline” Fractions Activity,,

10. 10 “Clothesline” Fractions Activity,

11. 11 “Clothesline” Fractions Activity,,

12. 12 “Clothesline” Fractions Activity,,

13. 13 “Clothesline” Fractions Activity,,

14. 14 “Clothesline” Fractions Activity X,,

15. 15 “Clothesline” Fractions Activity, (where x ≠0),

16. 16 The Number Line Helps Develop Fraction sense Benchmarks Relative magnitude (size) of fractions Algebraic connections

17. 17 Fractions aren’t just between zero and one; they live between all the numbers on the number line; A fraction can have many different names; There are more strategies than just “finding a common denominator” for comparing and ordering fractions; Fractions can be ordered on a number line just like whole numbers. The thinking involved when placing fractions on a number line can be symbolized algebraically. What Should “Kids” Know?

18. 18 Contact Us : nbezuk@mail.sdsu.edu sklass@projects.sdsu.edu Slides and Fraction Tents Master are available at: http://pdc.sdsu.edu (click on “PDC Presentations”)