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# 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

### 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

## Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

### 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

### 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

### 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

## 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

### 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

### 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