Comparing Ordering Fractions Our Favorite Subject What Should
Comparing & Ordering Fractions Our Favorite Subject
What Should Students Understand about Fraction Concepts n Meaning of the denominator (number of equal-sized pieces into which the whole has been cut) n Meaning of the numerator (how many pieces are being considered) n The more pieces a whole is divided into, the smaller the size of the pieces 2
What is Equivalence, Anyway? n “Equivalence” means “equal value” n A fraction can have many different names n Understanding that 1/2 is equivalent to many other fractions helps you to use that benchmark n Simplify: when and why 3
Ordering Fractions with the same denominator can be compared by their numerators. 4
Ordering Fractions with the same numerator can be compared by their denominators. 5
Ordering Fractions close to a benchmark can be compared by finding their distance from the benchmark. 6
Ordering Fractions close to one can be compared by finding their distance from one. 7
Strategies for Ordering Fractions n Same denominator n Same numerator n Benchmarks: close to 0, 1, 1/2 n Same number of missing parts from the whole (”Residual strategy”) 8
“Clothesline” Fractions Activity , , 9
“Clothesline” Fractions Activity , 10
“Clothesline” Fractions Activity , , 11
“Clothesline” Fractions Activity , , 12
“Clothesline” Fractions Activity , , 13
“Clothesline” Fractions Activity X, , 14
“Clothesline” Fractions Activity , , (where x ≠ 0) 15
The Number Line Helps Develop n Fraction sense n Benchmarks n Relative magnitude (size) of fractions n Algebraic connections 16
What Should “Kids” Know? n Fractions aren’t just between zero and one; they live between all the numbers on the number line; n A fraction can have many different names; n There are more strategies than just “finding a common denominator” for comparing and ordering fractions; n Fractions can be ordered on a number line just like whole numbers. n The thinking involved when placing fractions on a number line can be symbolized algebraically. 17
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”) 18
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