## Numbers and Operations - Fractions

**Extend understanding of fraction equivalence and ordering.**

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.

See tncore.org for the following tasks: 12 Cookies, Papa's Pizza, Star Bar.

Learn Zillion - Detailed Common Core lessons with video slideshow. Extended resources are listed on right side of screen.

Study Jams -Introduction to fractions video.

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.

See tncore.org for the following tasks: 12 Cookies, Getting to School, Papa's Pizza, Star Bar.

Study Jams -Equivalent fractions

Learn Zillion - Detailed Common Core lessons with video slideshow. Extended resources are listed on right side of screen.

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

Learn Zillion - Detailed Common Core lessons with video slideshow. Extended resources are listed on right side of screen.

**Fraction Boot Camp (lesson plan)**from lessonplanspage.com has activities that cover NF.3, 3a, 3b, & 3d (Lesson, fraction word problem cards, fraction game board, zombie fraction cards)

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

See tncore.org for the following tasks: 12 Cookies, Closer to 1, Papa's Pizza, Salty Pretzels

Learn Zillion - Detailed Common Core lessons with video slideshow. Extended resources are listed on right side of screen.

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.

See tncore.org for the following tasks: Chocolate Chips, Closer to 1

Learn Zillion - Detailed Common Core lessons with video slideshow. Extended resources are listed on right side of screen.

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.

See tncore.org for the following task: Salty Pretzels

Learn Zillion - Detailed Common Core lessons with video slideshow. Extended resources are listed on right side of screen.

Study Jams -Mixed Numbers (adding and subtracting)

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.

Learn Zillion - Detailed Common Core lessons with video slideshow. Extended resources are listed on right side of screen.

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).

See tncore.org for the following task(s): 12 Cookies

Learn Zillion - Detailed Common Core lessons with video slideshow. Extended resources are listed on right side of screen.

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.)

Study Jams -Least common multiples

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?

See tncore.org for the following task(s): Celebrate

Learn Zillion - Detailed Common Core lessons with video slideshow. Extended resources are listed on right side of screen.

**Understand decimal notation for fractions, and compare decimal fractions.**

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 100.4 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

Learn Zillion - Detailed Common Core lessons with video slideshow. Extended resources are listed on right side of screen.

Study Jams - Place Value of Decimals

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.

Learn Zillion - Detailed Common Core lessons with video slideshow. Extended resources are listed on right side of screen.

Study Jams - Place a Decimal on a Number Line

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.