MULTIPLYING AND DIVIDING FRACTIONS AND MIXED NUMBERS
Lesson 1: Multiplying Fractions and Whole Numbers
Lesson 2: Multiplication and Scaling Lesson 3: Estimating Products Lesson 4: Multiplying Two Fractions Lesson 5: Area Models Lesson 6: Multiplying Mixed Numbers Lesson 7: Problem Solving: Multiple Step Lesson 8: Fractions and Division Lesson 9: Fractions, Mixed Numbers, Decimals, and Quotients Lesson 10: Dividing Whole Numbers by Unit Fractions Lesson 11: Diving Unit Fractions by Non Zero Whole Numbers Lesson 12: Problem Solving: Draw a Picture and Write an Equation 
Vocabulary

Lesson 1: Multiplying Fractions and Whole Numbers
Main Idea: Students multiply a fraction by a whole number. They learn that the product of a whole number and a fraction can be interpreted in different ways, one interpretation being repeated addition. They also learn that multiplying a whole number by a fraction involves division as well as multiplication and the product is a fraction of the whole number.
Standard(s): 5.NF.B.4a Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd.)
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Main Idea: Students multiply a fraction by a whole number. They learn that the product of a whole number and a fraction can be interpreted in different ways, one interpretation being repeated addition. They also learn that multiplying a whole number by a fraction involves division as well as multiplication and the product is a fraction of the whole number.
Standard(s): 5.NF.B.4a Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd.)
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Math Arcade
Cool Math
Learn Zillion LZ126
Lesson 2: Multiplication as Scaling
Main Idea: Students compare the size of the product to the size of one factor without multiplying, in order to consider multiplication as scaling. They learn that the relative size of the factors can be used to determine the relative size of the product.
Standard(s): 5.NF.B.5b 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 x a) /(n x b) to the effect of multiplying a/b by 1.
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Main Idea: Students compare the size of the product to the size of one factor without multiplying, in order to consider multiplication as scaling. They learn that the relative size of the factors can be used to determine the relative size of the product.
Standard(s): 5.NF.B.5b 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 x a) /(n x b) to the effect of multiplying a/b by 1.
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Lesson 3: Estimating Products
Main Idea: Students use compatible numbers and rounding to estimate with fractions. They learn how rounding and compatible numbers can be used to estimate the product of fractions or mixed numbers.
Standard(s): 5.NF.B.5a 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.
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Main Idea: Students use compatible numbers and rounding to estimate with fractions. They learn how rounding and compatible numbers can be used to estimate the product of fractions or mixed numbers.
Standard(s): 5.NF.B.5a 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.
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Lesson 4: Multiplying Two Fractions
Main Idea: Students give the product of two fractions. They learn that a unit square can be used to show the area meaning of fraction multiplication. They also learn that when you multiply two fractions that are both less than one, the product is smaller than either fraction and to multiply fractions , write the product of the numerators over the product of the denominators.
Standard(s): 5.NF.B.4a Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd.)
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Main Idea: Students give the product of two fractions. They learn that a unit square can be used to show the area meaning of fraction multiplication. They also learn that when you multiply two fractions that are both less than one, the product is smaller than either fraction and to multiply fractions , write the product of the numerators over the product of the denominators.
Standard(s): 5.NF.B.4a Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd.)
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Lesson 5: Area Models
Main Idea: Students find areas of rectangles. They learn that products of fractions can be represented as areas of rectangles.
Standard (s): 5.NF.B.4b Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. 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.
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Main Idea: Students find areas of rectangles. They learn that products of fractions can be represented as areas of rectangles.
Standard (s): 5.NF.B.4b Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. 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.
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Video on School Tube
Amoeba Multiplication
Lesson 6: Multiplying Mixed Numbers
Main Idea: Students multiply mixed numbers. They learn that one way to find the product of mixed numbers is to change the calculation to an equivalent one involving improper fractions.
Standard (s): 5.NF.B.4a Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd.)
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Main Idea: Students multiply mixed numbers. They learn that one way to find the product of mixed numbers is to change the calculation to an equivalent one involving improper fractions.
Standard (s): 5.NF.B.4a Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd.)
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Lesson 7: Problem Solving Multiple Step
Main Idea: Students solve multiplestep problems. They learn how some problems can be solved by first finding and solving a subproblem, and then using that answer to solve the original problem.
Standard (s):
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Main Idea: Students solve multiplestep problems. They learn how some problems can be solved by first finding and solving a subproblem, and then using that answer to solve the original problem.
Standard (s):
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Lesson 8: Fractions and Division
Main Idea: Students use fractions and visual models to represent division and compare fractional parts of whole objects and sets. They learn that a fraction describes the division of a whole into equal parts, and it can be interpreted in more than one way depending on the whole being divided.
Standard (s): 5.NF.B.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.
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Main Idea: Students use fractions and visual models to represent division and compare fractional parts of whole objects and sets. They learn that a fraction describes the division of a whole into equal parts, and it can be interpreted in more than one way depending on the whole being divided.
Standard (s): 5.NF.B.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.
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Lesson 9: Fractions, Mixed Number, Decimals, and Quotients
Main Idea: Students divide whole numbers and express the quotient in different ways. They learn that a fraction, mixed number, or decimal can be used to represent the quotient of two whole numbers.
Standard (s): 5.NF.B.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 50pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?
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Main Idea: Students divide whole numbers and express the quotient in different ways. They learn that a fraction, mixed number, or decimal can be used to represent the quotient of two whole numbers.
Standard (s): 5.NF.B.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 50pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?
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Lesson 10: Dividing Whole Numbers by Unit Fractions
Main Idea: Students divide whole numbers by fractions. They learn that one way to find the quotient of mixed numbers is to change the calculation to an equivalent one involving multiplication of improper fractions.
Standard (s): 5.NF.B.7b 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 x (1/5) = 4.
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Main Idea: Students divide whole numbers by fractions. They learn that one way to find the quotient of mixed numbers is to change the calculation to an equivalent one involving multiplication of improper fractions.
Standard (s): 5.NF.B.7b 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 x (1/5) = 4.
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Lesson 11: Dividing Unit Fractions by NonZero Whole Numbers
Main Idea: Students discover the inverse relationship between multiplication and division that will help divide unit fractions by whole numbers. They learn how the inverse relationship between multiplication and division can help you understand how to divide with fractions.
Standard (s): 5.NF.B.7a Interpret division of a unit fraction by a nonzero 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) x 4 = 1/3.
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Main Idea: Students discover the inverse relationship between multiplication and division that will help divide unit fractions by whole numbers. They learn how the inverse relationship between multiplication and division can help you understand how to divide with fractions.
Standard (s): 5.NF.B.7a Interpret division of a unit fraction by a nonzero 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) x 4 = 1/3.
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Lesson 12: Problem Solving: Draw a Picture and Write an Equation
Main Idea: Students use diagrams and write equations to solve problems. They learn how information in a problem can often be shown with a diagram and used to solve the problem. They also learn that some problems can be solved by writing and completing a number sentence or equation.
Standard (s): 5.NF.B.7a Interpret division of a unit fraction by a nonzero 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) x 4 = 1/3.
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Main Idea: Students use diagrams and write equations to solve problems. They learn how information in a problem can often be shown with a diagram and used to solve the problem. They also learn that some problems can be solved by writing and completing a number sentence or equation.
Standard (s): 5.NF.B.7a Interpret division of a unit fraction by a nonzero 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) x 4 = 1/3.
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