Comparing & Ordering Fractions Our Favorite Subject.

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Presentation transcript:

Comparing & Ordering Fractions Our Favorite Subject

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

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

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

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

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 “Clothesline” Fractions Activity,,

10 “Clothesline” Fractions Activity,

11 “Clothesline” Fractions Activity,,

12 “Clothesline” Fractions Activity,,

13 “Clothesline” Fractions Activity,,

14 “Clothesline” Fractions Activity X,,

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

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

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 Contact Us : Slides and Fraction Tents Master are available at: (click on “PDC Presentations”)