NF 3.0:   Number and Operations Fractions

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Number and Operations Fractions 3.0

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

 

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

b.  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.

c.  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.

d.  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.

money

 

3.1   Know and understand that fractions and decimals are two different representations of the same concept (e.g., 50 cents is ½ of a dollar, 75 cents is ¾ of a dollar).

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3.  Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

a.  Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

 

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Cookies for Grampy

 

b.  Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples:
3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

 

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Solve My Math

 

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c.  Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

 

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Action Fraction

d.Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

 

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Thinking Blocks

 

 

 

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

3.  Interpret a fraction as division of the numerator by the denominator (a/b = a รท b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

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