Unit Overview
|Unit Overview |
|Content Area: Math |
|Unit Title: Multiplication/division of fractions Unit: 4 |
|Target Course/Grade Level: Fifth Grade Timeline: 3 weeks |
|Unit Summary: Students will demonstrate their understanding using concrete manipulatives, drawing models and explaining their thinking when |
|working with fractions in multiple contexts. They will multiply fractions including proper fractions, improper fractions and mixed numbers. |
|They will multiply fractions efficiently and accurately as well as solve problems in both contextual and non-contextual situations. They will |
|experience division problems with whole numbers divisors and unit fraction dividends or with unit fraction divisors and whole number dividends.|
|They will extend their understanding of the meaning of fractions, how many unit fractions are in a whole and their understanding of |
|multiplication and division as involving equal groups or shares and the number of objects in each group/share. |
|Primary interdisciplinary connections: Language Arts and Technology |
|9.1 21st-Centuries Life & Career Skills |
|Standard 9.1 All students will demonstrate the creative, critical thinking, collaboration, and problem-solving skills needed to function |
|successfully as both global citizens and workers in diverse ethnic and organizational cultures. |
|Strand: A. Critical Thinking and Problem Solving |
|C. Collaboration, Teamwork and Leadership |
|Content Statement: |
|9.1.8: A The ability to recognize a problem and apply critical thinking skills and problem |
|solving skills to solve the problem is a lifelong skill that develops over time. |
|9.1.8: C Collaboration and team work enable individuals or groups to achieve common goals |
|with greater efficiency. |
|Leadership abilities develop over time through participation in group and or teams that |
|that are engaged in challenging or competitive activities. |
|21st Century themes and skills: Critical Thinking and Problem Solving, Collaboration, Teamwork and |
|leadership |
|Mathematical Practices: |
|5.MP.1 Make sense of problems and persevere in solving them. |
|5.MP.2 Reason abstractly and quantitatively. |
|5.MP.3 Construct viable arguments and critique the reasoning of others. |
|5.MP.4 Model with mathematics. |
|5.MP.5 Use appropriate tools strategically. |
|5.MP.6 Attend to precision. |
|5.MP.7 Look for and make use of structure. |
|5.MP.8 Look for and express regularity in repeated reasoning. |
|Learning Targets |
|Domain: Number and Operations – Fractions |
|Cluster: Apply and extend previous understandings of multiplication and division to multiply and divide fractions. |
|Standard # | Standards |
|5.NF.3 |Interpret a fractions 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, eg. by using visual fraction models or |
| |equations to represent the problem. For example, interpret ¾ as the result of dividing 3 b 4, noting that ¾ multiplied by|
| |4 equals 3 and that when 3 wholes are shared equally among 4 people each person has a share of size ¾. 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.a |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) |
|5.NF.4.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.a |Interpret multiplication as scaling (resizing) by: 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. |
|5.NF.5.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 x a)/ (n x b) to the effect of multiplying a/b by 1. |
|5.NF.6 |Solve real world problems involving multiplication of fractions and mixed numbers, eg. by using visual fraction models or |
| |equations to represent the problem. |
|5.NF.7.a |Interpret division of a unit fraction by a non-zero whole number, (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 is not a requirement at this grade) 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. |
|5.NF.7.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 x (1/5) = 4. |
|5.NF.7.c |Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by |
| |unit fractions, eg. by using visual fraction models and equations to represent the problem. For example, how much |
| |chocolate will each person get if 3 people share ½ lb of chocolate equally? How many 1/3 cup servings are in 2 cups of |
| |raisins? |
|9.1.8.A.1 |Develop strategies to reinforce positive attitudes and productive behaviors that impact critical thinking and |
| |problem-solving skills. |
|9.1.8.A.2 |Implement problem-solving strategies to solve a problem in school or the community. |
|9.1.8.C.1 |Determine an individual’s responsibility for personal actions and contributions to group activities. |
|9.1.8.C.2 |Demonstrate the use of compromise, consensus and community building strategies for carrying out different task, |
| |assignments and projects. |
|9.1.8.C.3 |Model leadership skills during classroom and extracurricular activities. |
|Unit Essential Questions |Unit Enduring Understandings |
|How do operations affect numbers? |Computational fluency includes understanding not only the meaning, but |
|What makes a computational strategy both effective and efficient? |also the appropriate use of numerical operations. |
|How can we decide when to use an exact answer and when to use an |The magnitude of numbers affects the outcome of operations on them. |
|estimate? |In many cases, there are multiple algorithms for finding mathematical |
| |solution, and those algorithms are frequently associated with different |
| |cultures. |
| |Context is critical when using estimation. |
|Unit Learning Targets |
|Students will ... |
|Multiply fractions or whole numbers by a fraction. |
|Divide a unit fraction by a whole number and a whole number by a fraction. |
|Calculate area of a rectangle with fractional sides. |
|Estimate a product by understanding when multiplying less than a whole number, the product will be less than the other factor. If it is |
|greater than one, the product will be more than the other factor. (Scaling or resizing) |
|Understand a fraction is a division problem, as numerator (dividend) over denominator (divisor). |
|Solve real world problems with modeling. |
|Find the reciprocal of a number. |
|Develop strategies to divide fractions by using the relationship between multiplication and division. |
|Evidence of Learning |
|Summative Assessment |
|Solve a multiplication equation of fraction by fraction, fraction by whole numbers, and mixed numbers. |
|Solve division equation of unit fractions by whole numbers and whole numbers by unit fractions, using reciprocals. |
|Given the fractional dimensions of a rectangle, find the area. (Unit fractions and mixed numbers) |
|When given an appropriate array, create a multiplication model using shading or tiling to demonstrate the product. (Students must have LCM/LCD|
|and multiplication array of whole numbers, and estimation to the nearest whole number) |
|When given a simple multiplication word problem where one factor is a fraction (unit or mixed), students will predict the product will be |
|larger or smaller than the given whole number. |
|When given a visual fraction model (completed array) of a non-zero whole less then ten and a unit fraction, students will rewrite the division |
|problem as a multiplication problem. |
|. |
|Equipment needed: Smart Board, white boards, computers, number lines, fraction cubes, calculators |
|Teacher Instructional Resources: Scott Foresman and Addison Wesley |
|Study Island |
|Khan Academy Videos |
|Formative Assessments |
|Skill sheets |Quizzes/Tests |
|Student workbook |Drawing model |
|Homework |Study Island |
| |
|Integration of Technology: |
|Smart Board to play online games and utilize online resources. |
|Kahn Academy Videos |
|Elmo – for demonstration |
|Scott Foresman – Pearson Success Net - |
|Study Island |
|Technology Resources: |
|Click the links below to access additional resources used to design this unit: |
| - game for practice of multiplication of |
|fractions |
| |
| - game for practice of division |
|of fractions |
| |
| – Interactive 2.0 instructional and practice site. Students can view instructional videos and complete practice |
|modules for additional practice/remediation. |
| |
| - Web-based instruction, practice, assessment and reporting built from NJ standards. |
| |
| - IXL 5th grade online interactive activities for the students to complete |
| |
| - AAA math 5th grade – online interactive activities and problems for the student to complete. |
| |
| -5th grade math worksheets and lessons on operations with fractions |
| |
| |
|Opportunities for Differentiation: |
|Decelerate: Student will only multiply and divide fractions by fractions, whole numbers by fractions and fractions by whole numbers. |
| |
|Accelerated: Students will multiply and divide all types of fractions and mixed numbers. They will also be required to use cross reduction |
|prior to completing the operation. |
|Teacher Notes: |
|Will need to know area of a figure (whole numbers) |
|Will need to be able to calculate the area of several types of quadrilaterals prior to introducing finding the area of quadrilaterals with |
|fractional parts. Use modeling and manipulates prior to math computation. |
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