3-5 Number and Operations—Fractions Domain

This text resource has associated with it the Number and Operations—Fractions (NF) Domain of the Common Core Mathematics Standards.

This resource was used to facilitate the unwrapping of the linked standards. To view the unwrapping results in this resource click the "Info" button above.

1. Common Core Mathematics: G.4
   

   In Grade 4, instructional time should focus on three critical areas: (1) developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; (2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; (3) understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.

   Content	Skills	Learning Targets	Big Ideas	Essential Questions
   Multi-Digit Operations Multiplication Division with multi-digit dividends Fractions Fraction equivalence Addition and subtraction with like denominators Multiplication by whole numbers Geometric Figures Property classification Parallel sides Perpendicular sides Particular angle measures Symmetry	3 - Understand (multi-digit multiplication) 3 - Understand (division with multi-digit dividends) 2 - Understand (fraction equivalence) 2 - Understand (addition and subtraction of fractions with like denominators) 2 - Understand (multiplication of fractions by whole numbers) 3 - Understand (geometric figure analysis and classification) 2 - Classify (geometric figures by their properties, parallel sides, perpendicular sides, particular angle measures, symmetry) 4 - Analyze (geometric figures by their properties, parallel sides, perpendicular sides, particular angle measures, symmetry)	2 - I can understand and apply (develop fluency) multi-digit multiplication. 3 - I can understand and apply (develop fluency) dividing to find quotients involving multi-digit dividends. 2 - I can understand fraction equivalence. 2 - I can understand addition and subtraction of fractions with like denominators. 2 - I can understand multiplication of fractions by whole numbers. 2 - I can understand geometric figures can be analyzed and classified based on their properties. 2 - I can classify geometric figures based on their properties, such as parallel sides, perpendicular sides, particular angle measures and symmetry. 4 - I can Analyze geometric figures based on their properties, such as parallel sides, perpendicular sides, particular angle measures and symmetry.	A. A number of objects can be multiplied and divided using multi-digit numbers. B. Fractions may look different but still be equal. C. Math operations can be done on fractions to solve problems. D. Geometric figures can be classified and analyzed by their properties.	A.1 What is multiplication? A.2 How do you use multiplication with multi-digit numbers? A.3 What is division? A.3 How do you use division with multi-digit numbers? B.1 Can two fractions look different but still be equal? C.1 How can fractions be added? C.2 How can fractions be subtracted? C.3 How can fractions be multiplied with whole numbers? D.1 What are the different properties of geometric figures? D.2 How can they be used to classify or analyze them?

2. Common Core Mathematics: G.4 > NF
   

   Number and Operations — Fractions (NF)

3. Common Core Mathematics: G.4 > NF > C.1
   

   Extend understanding of fraction equivalence and ordering.

4. Common Core Mathematics: G.4 > NF > C.1 > S.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.

5. Common Core Mathematics: G.4 > NF > C.1 > S.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.

6. Common Core Mathematics: G.4 > NF > C.2
   

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

7. Common Core Mathematics: G.4 > NF > C.2 > S.3
   

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

   1. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
   2. 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.
   3. 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.
   4. 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.
8. Common Core Mathematics: G.4 > NF > C.2 > S.4
   

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

   1. 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).
   2. 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.)
   3. 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?
9. Common Core Mathematics: G.4 > NF > C.3
   

   Understand decimal notation for fractions, and compare decimal fractions.

10. Common Core Mathematics: G.4 > NF > C.3 > S.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.

    Content	Skills	Learning Targets	Big Ideas	Essential Questions
    Junk Junk 1	None Available	None Available	None Available	None Available

11. Common Core Mathematics: G.4 > NF > C.3 > S.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.

12. Common Core Mathematics: G.4 > NF > C.3 > S.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.

13. Common Core Mathematics: G.5
    

    In Grade 5, instructional time should focus on three critical areas: (1) developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions); (2) extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations; and (3) developing understanding of volume.

14. Common Core Mathematics: G.5 > NF
    

    Number and Operations—Fractions NF)

15. Common Core Mathematics: G.5 > NF > C.1
    

    Use equivalent fractions as a strategy to add and subtract fractions.

16. Common Core Mathematics: G.5 > NF > C.1 > S.1
    

    Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.

    For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

17. Common Core Mathematics: G.5 > NF > C.1 > S.2
    

    Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.

    For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

18. Common Core Mathematics: G.5 > NF > C.2
    

    Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

19. Common Core Mathematics: G.5 > NF > C.2 > S.3
    

    Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

    For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

20. Common Core Mathematics: G.5 > NF > C.2 > S.4
    

    Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

    1. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b.
       For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)
        
    2. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
21. Common Core Mathematics: G.5 > NF > C.2 > S.5
    

    Interpret multiplication as scaling (resizing), by:

    1. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
        
    2. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
22. Common Core Mathematics: G.5 > NF > C.2 > S.6
    

    Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

23. Common Core Mathematics: G.5 > NF > C.2 > S.7
    

    Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

    1. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.
       For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.
        
    2. Interpret division of a whole number by a unit fraction, and compute such quotients.
       For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.
        
    3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.
       For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?