4.OA.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of
the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and
the starting number 1, generate terms in the resulting sequence and observe that the terms
appear to alternate between odd and even numbers. Explain informally why the numbers will
continue to alternate in this way.
4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n Å~ a)/(n Å~ b) by using visual fraction
models, with attention to how the number and size of the parts differ even though the two
fractions themselves are the same size. Use this principle to recognize and generate
4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by
creating common denominators or numerators, or by comparing to a benchmark fraction
such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the
same whole. Record the results of comparisons with symbols >, =, or <, and justify the
conclusions, e.g., by using a visual fraction model.
Build fractions from unit fractions by applying and extending previous understandings of
operations on whole numbers.
4.NF.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.
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.
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.
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.
4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole
a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model
to represent 5/4 as the product 5 Å~ (1/4), recording the conclusion by the equation
5/4 = 5 Å~ (1/4).
b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply
a fraction by a whole number. For example, use a visual fraction model to express 3 Å~
(2/5) as 6 Å~ (1/5), recognizing this product as 6/5. (In general, n Å~ (a/b) = (n Å~ a)/b.)
c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by
using visual fraction models and equations to represent the problem. For example, if
each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at
the party, how many pounds of roast beef will be needed? Between what two whole
numbers does your answer lie?
4.MD.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8).
Solve problems involving addition and subtraction of fractions by using information presented
in line plots. For example, from a line plot find and interpret the difference in length between
the longest and shortest specimens in an insect collection.