Learning About the World

Mathematics


Number Relationships and Operations -- Numbers and Operations in Base Ten - Fractions

Goal 2d: Children understand fractions as numbers, and use that knowledge to compare fractions and explain the equivalence of fractions.

By the end of each age group or grade level, most children will have met prior age group or grade level standards in this domain.

Infants Through Older Toddlers

Infants

(0-12 Months)

  1. No standards in this age group for this Element.

Young Toddlers

(9-18 Months)

  1. No standards in this age group for this Element.

Older Toddlers

(18-36 Months)

  1. No standards in this age group for this Element.
Younger Preschoolers Through Kindergartners

Younger Preschoolers

(36-48 months)

  1. No standards in this age group for this Element.

Older Preschoolers

(48-60 months)

  1. No standards in this age group for this Element.

Kindergartners

  1. No standards in this age group for this Element.
First Graders Through Third Graders

First Graders

  1. No Standards in this Element. CCSS Geometry Standard 1.G.A.3 builds towards Numbers & Operations in Base Ten-Fractions

Second Graders

  1. No Standards in this Element. CCSS Geometry Standard 2.G.A.3 builds towards Numbers & Operations in Base Ten-Fractions

Third Graders

Develop understanding of fractions as numbers.

  1. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b
  2. Understand a fraction as a number on the number line; represent fractions on a number line diagram.
    1. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.
    2. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.
  3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
    1. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
    2. Recognize and generate simple equivalent fractions (e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent (e.g., by using a visual fraction model).
    3. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.
    4. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions (e.g., by using a visual fraction model).

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Secretary Daniel M. French
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Barre, VT 05641

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