Unit 3: Fraction Equivalents

1. MGSE4.OA.1 Understand that a multiplicative comparison is a situation in which one quantity is multiplied by a specified number to get another quantity. a. Interpret a multiplication equation as a comparison e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. b. Represent verbal statements of multiplicative comparisons as multiplication equations

2. MGSE4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by using visual fraction models, 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

2.1. Fractions can be compared by reasoning about the relative size of the fractions. Relational reasoning is important in teaching understanding of fractions.

2.2. Measurement involves comparing an attribute of an item or situation with a unit that has the same attribute. Lengths are compared to units of length.

3. MGSE4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number e.g., by using a visual such as a number line or area model. 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). 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?

4. MGSE4.NF.3 Understand a fraction 𝑎 𝑏 with a numerator >1 as a sum of unit 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. 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. 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.

5. MGSE4.MD.1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. a. Understand the relationship between gallons, cups, quarts, and pints. b. Express larger units in terms of smaller units within the same measurement system. c. Record measurement equivalents in a two column table.

6. MGSE4.NF.1 Explain why two or more fractions are equivalent 𝑎𝑏 = 𝑛 × 𝑎 𝑛 × 𝑏 ex: 14 = 3 × 1 3 × 4 by using visual fraction models. Focus attention on how the number and size of the parts differ even though the fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

6.1. Measurement involves comparing an attribute of an item or situation with a unit that has the same attribute. Lengths are compared to units of length.

6.2. Units can be partitioned to create fractional units.

6.3. Equivalent fractions are ways of describing the same amount by using different-sized fractional parts.

6.4. Measurement involves comparing an attribute of an item or situation with a unit that has the same attribute. Lengths are compared to units of length.

6.5. Units can be partitioned to create fractional units.

7. MGSE4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

7.1. The meanings of each operation with fractions are the same as the meanings for the operations with whole numbers. Operations with fractions should begin by applying the same meaning to fractional parts.

7.2. For addition and subtraction, the numerator tells the number of parts and the denominator of the unit. The parts are added and subtracted.

7.3. Repeated addition support development of concepts and algorithms for multiplication of fractions.

7.4. Fractions can and should be represented across different interpretations (part-whole, number, division (operators)) and different models; area, length, and set.

7.5. The total length measure and the size of the unit are inversely related. (Smaller units result in a larger length measure, larger units result in a smaller length measure).

7.6. The total length measure and the size of the unit are inversely related. (Smaller units result in a larger length measure, larger units result in a smaller length measure).

8. MGSE4.MD.4 Make a line plot to display a data set of measurements in fractions of a unit (1 2 , 1 4 , 1 8 ). Solve problems involving addition and subtraction of fractions with common denominators by using information presented in line plots. For example, from a line plot, find and interpret the difference in length between the longest and shortest specimens in an insect collection.