NF-Apply+&+extend+previous+understandings+of+multiplication+&+division+to+multiply+&+divide+fractions

5.NF.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?// 5.NF.4. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. a. 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.)// b. 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. 5.NF.5.Interpret multiplication as scaling (resizing), by: a. 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. b. 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. 5.NF.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. 5.NF.7. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.* a. 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.// b. 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.// c. 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?// //*//Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade. || ===‍‍‍‍‍‍‍‍‍‍**Anchor Standard**===
 * ===**Common Core Standard**===

**Mathematical Practice(s)**
1. Make sense of problems and persevere in solving them. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 6. Attend to precision. 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 4. Model with mathematics. 2. Reason abstractly and quantitatively. 4. Model with mathematics. 5. Use appropriate tools strategically. 7. Look for and make use of structure. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 7. Look for and express regularity in repeated reasoning. 1. Make sense of problems and persevere in solving them. <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">2. Reason abstractly and quantitatively. <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">3. Construct viable arguments and critique the reasoning of others. <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">4. Model with mathematics. <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">7. Look for and express regularity in repeated reasoning. <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">1. Make sense of problems and persevere in solving them. <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">3. Construct viable arguments and critique the reasoning of others. <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">4. Model with mathematics. <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">6. Attend to precision. <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">1. Make sense of problems and persevere in solving them. <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">4. Model with mathematics. <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Reason abstractly and quantitatively. <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Look for and make use of structure. <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">6. Attend to precision. <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">7. Look for and express regularity in repeated reasoning. || <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">5.TT.1 Use technology tools and skills to reinforce and extend classroom concepts and activities. || ===‍‍‍‍‍‍‍‍‍‍**Revised Bloom's Level of thinking**=== <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">5.NF.3 I can explain that a fraction is another way to represent division. <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">I can solve word problems involving division of whole numbers using fractional understanding.
 * 5.NF.3**
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">5.NF.4a **
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">5.NF.4b **
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">5.NF.5a **
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">5.NF5b **
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">5.NF.6 **
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">5.NF.7 **
 * ===‍‍‍‍‍‍‍‍‍‍**Information Technology Standard**===
 * 5.NF.3 Create**
 * 5.NF.4 Create**
 * 5.NF.5a Evaluate**
 * 5.NF.5b Create**
 * 5.NF.6 Create**
 * 5.NF.7 Create** ||


 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Understand that a fraction is another way to represent division.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Recognize any fraction as the numerator divided by the denominator.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Represent a division situation with a fraction.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Solve division problems with fractional remainders.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Generate context which involves division of whole numbers with fractional results.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Generate equations for a word problem.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Solve word problems involving division of whole numbers using fractional understanding.

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">5.NF.4a I can interpret the product of fractional multiplication using numbers and story context.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Use repeated addition to multiply a unit fraction by a whole number. (eg. 3/4 = ¼ + ¼ + ¼)
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Interpret the product of a fraction multiplied by a whole number. (eg. 2/3 + 2/3 + 2/3 + 2/3 is the same as 2/3 x 4 = 8/3)
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Create a visual model of multiplication of a fraction by a whole number.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Create a story context for multiplying a fraction by a whole number. ( eg. Kelly needs 2/3 of a yard of ribbon to make her bow. She wants to make 4 bows. How much ribbon does she need?)
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Interpret the product of a whole number multiplied by a fraction (eg. 4 x 2/3= 8/3)
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Create a visual model of multiplication of a whole number by a fraction.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Create a story context for multiplying a whole number by a fraction. (eg. Kris has 6 cookies. She only needs ½ of them. How many cookies does Kris need? 6 x ½ = 3)
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Interpret the product of a fraction multiplied by a fraction (eg. ½ x ½ = 1/4 )
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Create a visual model of multiplication of a fraction by a fraction.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Create a story context for multiplying a fraction by a fraction. (eg. Terri has ½ a pan of brownies. She gave ½ of that to her class. How much of the pan of brownies did she give to her class? ½ x ½ = 1/4)
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Interpret the product of fractional multiplication using numbers and story context.

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">5.NF.4b I can f <span style="color: black; font-family: 'times new roman','serif'; font-size: 16px;">ind the area of a rectangle with fractional side lengths.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Recall the area of a rectangle using multiplication of length and width in a visual model using square units.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Create an area model using fractional side lengths by tiling it with unit squares.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Use denominators of the fractions to partition the rectangle into equal sized pieces.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Use the numerators of the fractions to determine how many pieces there are.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Calculate the area of a rectangle with fractional side lengths.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Connect the visual model of the area of rectangles with the algorithm to fraction times a fraction multiplication (or mixed numbers).
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Find <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 13px;">the area of a rectangle with fractional side lengths

<span style="color: black; font-family: 'Times New Roman','serif'; font-size: 16px;">5.NF.5a I can estimate the product based on the size of the factors.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Explain the effect on the product if one of the factors is changed without performing the indicated multiplication.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Explain the effect on the product if one of the factors is doubled or halved.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Compare 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.

<span style="color: black; font-family: 'Times New Roman','serif'; font-size: 16px;">5.NF.5b I can explain why multiplying a given number by any fraction greater than 1 will result in a product greater than the given number and multiplying any given number by any fraction less than one will result in a product less than the given number.
 * Explore the effect of multiplying by a fraction greater than 1.
 * Create visual models to explain the effect of multiplying by a fraction greater than 1.
 * Generalize a rule about what happens when you multiply by a fraction greater than 1.
 * Explore the multiplying by a fraction less than 1.
 * Create visual models to explain the effect of multiplying by a fraction less than 1.
 * Generalize a rule about what happens when you multiply by a fraction less than 1.
 * Explain why multiplying a fraction by n/n creates an equivalent fraction. (eg. 2/3 x 6/6= 12/18 which is the same as 2/3)
 * Explain the effect on a product when factors are greater than, less than or equal to 1.

<span style="color: black; font-family: 'Times New Roman','serif'; font-size: 16px;">5.NF.6 I can s <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">olve real world problems involving multiplication of fractions.


 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Create visual models to represent real word problems involving multiplication of fractions and mixed numbers.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Create equations for word problems involving multiplication of fractions and mixed numbers.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Generate real world problems involving multiplication of fractions and mixed numbers.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Solve real world problems involving multiplication of fractions and mixed numbers.

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">5.NF.7a I can <span style="color: black; font-family: 'times new roman','serif'; font-size: 16px;">interpret and compute division of a unit fraction by a non zero whole number.


 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Explain dividing a unit fraction by a whole number results in equal parts that are smaller than the original fraction.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Create models and use equipartitioning to demonstrate dividing a unit fraction by a whole number.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Connect fact families to dividing a unit fraction by a whole number.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Explain the relationship between multiplication, division, and reciprocals.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Generalize a rule for dividing unit fractions by a whole number.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Apply knowledge of inverse operations to solve division of unit fractions by a whole number.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Solve word problems involving division of unit fractions by a whole number.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Create word problems involving division of unit fractions by a whole number.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Write equations to justify solution strategies.
 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 13px;">Interpret division of a unit fraction by a whole number.

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">5.NF.7b I can <span style="color: black; font-family: 'times new roman','serif'; font-size: 16px;">interpret and compute division of a whole number by a unit fraction.


 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Explain why dividing a whole number by a unit fraction results a quotient that is larger than the whole number.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Create models and use equipartitioning to demonstrate dividing a whole number by a unit fraction.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Connect fact families to dividing a whole number by a unit fraction.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Explain the relationship between multiplication, division, and reciprocals.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Generalize a rule for dividing a whole number by a unit fraction.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Apply knowledge of inverse operations to solve division of a whole number by a unit fraction.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Solve word problems involving division of a whole number by a unit fraction.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Create word problems involving division of a whole number by a unit fraction.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Write equations to justify solution strategies.
 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 13px;">Interpret division of <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">a whole number by a unit fraction.

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">5.NF.7c I can s <span style="color: black; font-family: 'times new roman','serif'; font-size: 16px;">olve real world problems involving division of fractions.


 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Create visual models for word problems involving division of fractions.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Create a division word problem using a unit fraction and whole number.


 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Solve real world problems involving division of fractions.

‍‍‍‍‍‍‍‍‍‍**Essential Vocabulary**
<span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Fraction <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Numerator <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Denominator <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Division <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Divisor <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Dividend <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Whole Number <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Mixed Number <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Remainder <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Fractional Remainder <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Equation || 5.NF.4a <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Unit fraction <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Numerator <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Denominator <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Partition <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Equal <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Product <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Multiply <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Simplify <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Mixed number <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Improper <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">fraction <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Fraction <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Numerator <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Denominator <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Area <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Area model <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Tiling <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Algorithm <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Side lengths <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Square units || 5.NF.5a. <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Compare <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Product <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Factor <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Doubled <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Halved <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Resizing <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Scaling <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Fraction <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Equal <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Compare <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Generalize <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Effect <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Greater than <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Less than <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Equal to <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Mixed number <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Unit fraction <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Simplify || 5.NF.6 <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Visual model <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Multiplication <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Equation <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Real world problem || 5.NF.7 <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Equipartition <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Fraction <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Numerator <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Denominator <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Unit fraction <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Inverse operation <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Whole number <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Division <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Fact family <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Reciprocal <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Dividend <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Divisor <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Quotient ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">5.NF.3
 * 5.NF.4b**
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">5.NF.5b **

‍‍‍‍‍‍‍‍‍‍**Differentiation**
===‍‍‍‍‍‍‍‍‍‍**Intervention:[|Fraction Review Interactive Site]**===

[|Lesson Resources/Differentiation]
See Van de Walle Pages 167-172 //Teaching Student Centered Mathematics//

[|www.mathisfun.com] []

[|Fraction Unit from NCDPI] www.softschools.com/math/games/fractions_practice.jsp www.ixl.com www.math-play.com/5th-grade-math-games.html www.adaptedmind.com/p.php?tagId=717#

===‍‍‍‍‍‍‍‍‍‍**Notes and Additional Information**===