4.NF. Grade 4 - Number and Operations---Fractions

4.NF.A. Extend understanding of fraction equivalence and ordering.

• Money in the piggy bank
• Running Laps

4.NF.A.1. Explain why a fraction $a/b$ is equivalent to a fraction $(n \times a)/(n \times b)$ 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.

• Explaining Fraction Equivalence with Pictures
• Fractions and Rectangles

4.NF.A.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.

• Comparing Fractions Using Benchmarks Game
• Doubling Numerators and Denominators
• Listing fractions in increasing size
• Using Benchmarks to Compare Fractions

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

• Comparing two different pizzas

4.NF.B.3. Understand a fraction $a/b$ with $a > 1$ as a sum of fractions $1/b$.

• Writing a Mixed Number as an Equivalent Fraction

4.NF.B.3.a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

• Comparing Sums of Unit Fractions

4.NF.B.3.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: $\frac38 = \frac18 + \frac18 + \frac18$; $\frac38 = \frac18 + \frac28$; $2 \frac18 = 1 + 1 + \frac18 = \frac88 + \frac88 + \frac18.$

• Making 22 Seventeenths in Different Ways

4.NF.B.3.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.

• Cynthia's Perfect Punch
• Peaches
• Plastic Building Blocks
• Writing a Mixed Number as an Equivalent Fraction

4.NF.B.3.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.

• No tasks yet illustrate this standard.

4.NF.B.4. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

• Extending Multiplication From Whole Numbers to Fractions

4.NF.B.4.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 $5 \times (1/4)$, recording the conclusion by the equation $5/4 = 5 \times (1/4).$

• No tasks yet illustrate this standard.

4.NF.B.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 $3 \times (2/5)$ as $6 \times (1/5)$, recognizing this product as $6/5$. (In general, $n \times (a/b) = (n \times a)/b.$)

• No tasks yet illustrate this standard.

4.NF.B.4.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?

• Sugar in six cans of soda

4.NF.C. Understand decimal notation for fractions, and compare decimal fractions.

4.NF.C.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.Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. For example, express $3/10$ as $30/100$, and add $3/10 + 4/100 = 34/100$.

• Adding Tenths and Hundredths
• Dimes and Pennies
• Expanded Fractions and Decimals
• Fraction Equivalence
• How Many Tenths and Hundredths?

4.NF.C.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.

• Dimes and Pennies
• Expanded Fractions and Decimals
• How Many Tenths and Hundredths?

4.NF.C.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.

• Using Place Value