G.3 - Number and Operations-Fractions

This text resource illustrates the Standards Map for the Grade 3 Number and Operations-Fractions domain in the Common Core State Standards.

Standards

Common Core Mathematics: G.3

In Grade 3, instructional time should focus on four critical areas: (1) developing understanding of multiplication and division and strategies for multiplication and division within 100; (2) developing understanding of fractions, especially unit fractions (fractions with numerator 1); (3) developing understanding of the structure of rectangular arrays and of area; and (4) describing and analyzing two-dimensional shapes.
Common Core Mathematics: G.3 > NF

Number and Operations—Fractions (NF)
Common Core Mathematics: G.3 > NF > C.1

Develop understanding of fractions as numbers.

Common Core Mathematics: G.3 > NF > C.1 > S.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.

Content	Skills	Learning Targets	Big Ideas	Essential Questions
Fractions 1/b is quantity formed by one part when partitioned into b equal parts a/b is quantity formed by a parts of size 1/b	2 - Understand (a fraction 1/b is the quantity formed by one part when partitioned into b equal parts) 2 - Understand (a fraction a/b is the quantity formed by a parts of size 1/b)	2 - I can understand a fraction 1/b is the quantity formed by one part when partitioned into b equal parts. 2 - I can understand a fraction a/b is the quantity formed by a parts of size 1/b.	A. Fractions are quantities that are parts of a whole.	A.1 What is the relationship between a fraction and a whole number?

Common Core Mathematics: G.3 > NF > C.1 > S.2

Understand a fraction as a number on the number line; represent fractions on a number line diagram.

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.
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.

Content	Skills	Learning Targets	Big Ideas	Essential Questions
Fractions As numbers on a number line As number line diagrams Fractions [a] On number line Interval from 0 to 1 Partitioning into b parts Part equals 1/b Fractions [b] On number line Marking a 1/b lengths from 0 Endpoint is a/b	2 - Understand (Fraction as a number on a number line) 3 - Represent (Fractions on a number line diagram) 3 - Represent (1/b on number line [a]) 2 - Define (Interval from 0 to 1 as whole [a]) 2 - Partition (Whole into b parts [a]) 2 - Recognize (Each part is 1/b [a]) 1 - Locate (1/b on number line by using endpoint of partition from 0 [a]) 3 - Represent (a/b on number line [b]) 2 - Mark (Lengths 1/b from 0 [b]) 2 - Recognize (Resulting interval equals a/b [b]) 1 - Locate (a/b as endpoint [b])	2 - I can understand a fraction as a number on a number line. 3 - I can represent fractions on a number line diagram. 3 - I can represent 1/b on number line. [a] 2 - I can define the interval from 0 to 1 as a whole. [a] 2 - I can partition whole into b parts. [a] 2 - I can recognize each part is 1/b. [a] 1 - I can locate 1/b on number line by using the endpoint of partition from 0. [a] 3 - I can represent a/b on number line. [b] 2 - I can mark a lengths 1/b from 0. [b] 2 - I can recognize that the resulting interval equals a/b. [b] 1 - I can locate a/b as the endpoint. [b]	A. Fractions have locations on a number line just as whole numbers do. B. Fractions are numbers that represent part of a whole. C. The numerator of a fraction represents the number of equal parts in the fraction and the denominator represents the number of equal partitions in a whole.	A.1 How do I know where to put a fraction on a number line? B.1 How can I graph a fraction on an number line? C.1 What is the difference between 1/b and a/b?

Common Core Mathematics: G.3 > NF > C.1 > S.3

Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
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.
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.
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.

Content	Skills	Learning Targets	Big Ideas	Essential Questions
Fractions Equivalence Special cases Comparison By size Fractions [a] Equivalent By size By point on number line Fractions [b] Equivalent Explain equivalence Visual model Fractions [c] Equivalent to whole numbers Fractions [d] Comparing Same numerator Same denominator Referring to same whole Use symbols >, +, < Visual model	2 - Explain (Equivalence of fractions in special cases [a]) 2 - Compare (Fractions by reasoning about their size [a]) 2 - Understand (2 fractions as equivalent if same size [a]) 1 - Understand (2 fractions equivalent if same point on number line [a]) 2 - Recognize (Simple equivalent fractions [b]) 2 - Generate (Simple equivalent fractions [b]) 2 - Explain (Why fractions are equivalent [b]) 3 - Use (Visual model [b]) 2 - Express (Whole numbers as fractions [c]) 2 - Recognize (Fractions equivalent to whole numbers [c]) 2 - Compare (2 fractions with same numerator by reasoning [c]) 2 - Compare (2 fractions with the same denominator by reasoning [c]) 2 - Recognize (Comparisons are valid only when referring to same whole [d]) 1 - Record (Results [d]) 3 - Use (>, =, < [d]) 5 - Justify (Conclusions [d]) 3 - Use (Visual fraction model [d])	2 - I can explain equivalence of fractions in special cases. 2 - I can compare fractions by reasoning about their size. 2 - I can understand 2 fractions as equivalent if same size. [a] 2 - I can understand 2 fractions equivalent if same point on number line. [a] 2 - I can recognize simple equivalent fractions. [b] 2 - I can generate simple equivalent fractions. [b] 2 - I can explain why fractions are equivalent. [b] 3 - I can use a visual fraction model. [b] 2 - I can express whole numbers as fractions. [c] 2 - I can recognize fractions equivalent to whole numbers. [c] 2 - I can compare 2 fractions with same numerator by reasoning. [d] 2 - I can compare 2 fractions with the same denominator by reasoning. [d] 2 - I can recognize comparisons are valid only when referring to same whole. [d] 1 - Record results. [d] 3 - I can use >, =, <. [d] 5 - I can justify conclusions. [d] 3 - I can use visual fraction model. [d]	A. Fractions can be equal to each other. B. Fractions can be compared by their size. C. Equivalent fractions are just 2 different names for the same number. D. Being able to create equivalent fractions is important when doing math problems that involve fractions. E. Whole numbers may need to be written as fractions when computing with fractions. F. Comparing whole numbers or fractions is an important skill in mathematics.	A.1 Can fractions ever be equal to each other? B.1 How can I compare fractions? C.1 What are equivalent fractions? D.1 Why do I need to know how to make equivalent fractions? E.1 When will I need to change a whole number to a fractions? F.1 Why is comparing fractions important?

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