3.NS.3  The student will use mathematical reasoning and justification to represent and compare fractions (proper and improper) and mixed numbers with denominators of 2, 3, 4, 5, 6, 8, and 10), including those in context.

            Students will demonstrate the following Knowledge and Skills:

a)      Represent, name, and write a given fraction (proper or improper) or mixed number with denominators of 2, 3, 4, 5, 6, 8, and 10 using:

i)        region/area models (e.g., pie pieces, pattern blocks, geoboards);

ii)       length models (e.g., paper fraction strips, fraction bars, rods, number lines); and

iii)     set models (e.g., chips, counters, cubes).

b)      Identify a fraction represented by a model as the sum of unit fractions.

c)      Use a model of a fraction greater than one to count the fractional parts to name and write it as an improper fraction and as a mixed number (e.g., , , , ,  = 1 ).

d)      Compose and decompose fractions (proper and improper) with denominators of 2, 3, 4, 5, 6, 8, and 10 in multiple ways (e.g.,  =  +  or  =  +  =  + ) with models.

e)      Compare a fraction, less than or equal to one, to the benchmarks of 0, , and 1 using area/region models, length models, and without models.

f)        Compare two fractions (proper or improper) and/or mixed numbers with like numerators of 2, 3, 4, 5, 6, 8, and 10 (e.g.,  > ) using words (greater than, less than, equal to) and/or symbols (>, <, =), using area/region models, length models, and without models.

g)       Compare two fractions (proper or improper) and/or mixed numbers with like denominators of 2, 3, 4, 5, 6, 8, and 10 (e.g.,  <) using words (greater than, less than, equal to) and/or symbols (>, <, =), using area/region models, length models, and without models.

h)      Represent equivalent fractions with denominators of 2, 3, 4, 5, 6, 8, or 10, using region/area models and length models.