Home
Grade 4 Common Core State Standards
for Fraction and Decimals 
Extend understanding of fraction equivalence and ordering.
4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × 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 equivalent fractions.
 Lesson: Equality of Fractions
 Worksheet #1
 Worksheet #2
Note: A visual demonstration of why the numerator and denominator can be multiplied by the same whole number to obtain equal fractions can be seen in Equality Step 1 TeachingFractionBarsVideos
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.
 Lesson: Inequality of Fractions
 Worksheet #1
 Worksheet #2
 Lesson: Decreasing and Increasing Fractions
 Worksheet #5
 Worksheet #6
 Lesson: Number Lines and Mixed Numbers
 Worksheet #7
 Worksheet #8
Note: Visual illustrations of inequality of fractions, comparing fractions to ½, and decreasing and increasing fractions can be seen in Inequality Step 1 and Inequality Step 2 TeachingFractionBarsVideos
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.
 Lesson: Adding Fraction  Same Denominators
 Worksheet #3
 Worksheet #4
 Worksheet #5
 Lesson: Subtracting Fraction  Same Denominators
 Worksheet #6
 Worksheet #7
 Worksheet #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.
 Lesson: Adding Mixed Numbers  Same Denominators
 Worksheet #9
 Worksheet #10
 Worksheet #11
 Lesson: Subtracting Mixed Numbers  Same Denominators
 Worksheet #12
 Worksheet #13
 Worksheet #14
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.
 Lesson: Solving Word Problems  Fractions and Mixed Numbers
 Worksheet #15
 Worksheet #16
4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
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 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).
 Lesson: Whole Numbers Times Unit Fractions
 Worksheet #1
 Worksheet #2
 Worksheet #3
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 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × 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?
 Lesson: Solving Word Problems  Whole Numbers Times Fractions
 Worksheet #6
 Worksheet #7
Note: Visual models for solving word problems involving products of whole numbers and fractions also can be seen in Multiplication Step 1 TeachingFractionBarsVideos
Understand decimal notation for fractions, and compare decimal fractions.
4.NF.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
 Lesson: Adding Fractions with Denominators of 10 and 100
 Worksheet #1
 Worksheet #2
Note: The lesson and worksheet for 4.NF.5 both use the Decimal Squares model for illustrating fractions with denominators of 1 and 100.
4.NF.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
 Lesson: Forming Decimal Number Lines for Tenths
 Worksheet #5
 Worksheet #6
 Lesson: Decimal Number Lines for Hundredths
 Worksheet #7
 Worksheet #8
Note: In the above lessons, the Decimal Squares region model is connected to the number line linear model for tenths and hundredths. There are examples for students to measure objects to become familiar with the tenths and hundredths number lines and applications. These number lines are then used in two of the preceding four worksheets to provide further practice with measuring. The remaining two worksheets provide practice for locating and naming decimals on the tenths and hundredths number lines.
4.NF.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.
 Lesson: Equality of Decimals
 Worksheet #1
 Worksheet #2
 Worksheet #3
 Lesson: Inequality of Decimals
 Worksheet #4
 Worksheet #5
 Worksheet #6
Note: The two preceding lessons involve activities for equality and inequality of tenths and hundredths. The activities for thousandths are noted as optional in these lessons and on the activity sheets. As requested by the 4.NF.7 requirement, the content of each of these lessons is illustrated by a visual model. For these lessons, place value tables are introduced and related to the visual model for decimals. Worksheet #6 involves examples using the same whole when comparing decimal amounts.


Please direct questions and comments about this page to abbj@.unh.edu
© Copyright 20012012, Albert Bradley Bennett, Jr.