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5.NF.7 2011 Domain: Number and Operations in Base Ten Cluster: Apply and extend previous understandings of multiplication and division to multiply and divide fractions Standards 7. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. 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. 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. 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? Essential Questions How can you use models to show division of fractions? How can drawing a picture and writing an equation help to solve a problem? How can you model dividing a fraction by a whole number? Content Statements Enduring Understandings Information in a problem can be represented by a model or diagram and used to solve the problem. Dividing a whole number by a fraction results in a quotient greater than the original whole number. The inverse relationships between division and multiplication can be Activities, Investigation, and Student Experiences 1. Fold a square sheet of paper vertically in half. Fold the paper vertically in half again. Ask students the fraction represented by each section of the sheet of paper. Fold the paper in half horizontally. Ask students the fraction represented by each section of the sheet of paper. Shade ¾ of the vertical sections red and ½ of the horizontal sections blue. The part that is shaded both red and blue shows ½ x ¾. Ask students to solve ½ x ¾. 5.NF.7 Students will use models or mental math to divide fractions. used to divide the fractions. Students can use diagrams and equations to solve problems. Assessments 5.NF.7 Four students sitting at a table were given 1/3 of a pan of brownies to share. How much of a pan will each student get if they share the pan of brownies equally? o The diagram shows the 1/3 pan divided into 4 equal shares with each share equaling 1/12 of the pan. You have 1/8 of a bag of pens and you need to share them among 3 people. How much of the bag does each person get? How many 1/3 –cup servings are in 2 cups of 2011 2. Fractions on a ruler: Use the ruler to model for students how to find how many ½ inch segments are in 2 inches. How many ½ inch segments are in 3 inches? How many ¼ inch segments are in 2 inches? 3 inches? Have pairs take turns posing similar questions to one another. Encourage them to use different fractional segments and whole inch measurements. 5.NF.7 raisins? o Student Answer – I know that there are three 1/3 cup servings in 1 cup of raisins. Therefore, there are 6 servings in 2 cups of raisins. I can also show this since 2 divided by 1/3 = 2x3 = 6 servings of raisins. Knowing how many in each group/share and finding how many groups/shares Angelo has 4 lbs of peanuts. He wants to give each of his friends 1/5 lb. How many friends can receive 1/5 lb of peanuts? A diagram for 4 ÷ 1/5 is shown below. Students explain that since there are five fifths in one whole, there must be 20 fifths in 4 lbs. 1 lb. of peanuts How much rice will each person get if 3 people share 1/2 lb of rice equally? 2011 5.NF.7 2011 o A student may think or draw ½ and cut it into 3 equal groups then determine that each of those part is 1/6. o A student may think of ½ as equivalent to 3/6. 3/6 divided by 3 is 1/6. Equipment Needed: Teacher Resources: Student whiteboards http://www.math-drills.com/fractions.shtml Calculators http://illuminations.nctm.org/ActivityDetail.aspx?ID= 64 http://www.ixl.com/math/grade-5/divide-fractions-bywhole-numbers http://mathstory.com/algebrah/Algebrahindex.html http://illuminations.nctm.org/ActivityDetail.aspx?ID= 80 http://illuminations.nctm.org/ActivityDetail.aspx?ID= 64 http://www.superteacherworksheets.com/fractions/fr action-word-problems-easy.pdf http://www.thirteen.org/edonline/adulted/lessons/stuf f/lp46_fracword.pdf\ Internet Smartboard Manipulatives Overhead 5.NF.7 2011 http://coedpages.uncc.edu/abpolly/math/core/unpacki ng/unpacked-5th.pdf