Unit Overview
|Unit Overview |
|Content Area: Math |
|Unit Title: Adding/Subtracting Fractions Unit: 3 |
|Target Course/Grade Level: Fifth Grade Timeline: 3 weeks |
|Unit Summary: Students will apply their understanding of equivalent fractions and their ability to rewrite fractions in an equivalent form to |
|find common denominators. They will understand that multiplying the denominator will always give a common denominator but may not result in |
|the smallest denominator. They will solve word problems involving addition/subtraction of fractions, including problems that have fractions |
|with denominators. |
|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 |
|B. Creativity and Innovation |
|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. |
|9.1.8:B Gathering and Evaluating knowledge and information from a variety of sources, |
|including global perspective, fosters creativity and innovative thinking. |
|21st Century themes and skills: Critical Thinking and Problem Solving, Collaboration, Teamwork and |
|Leadership, Creativity and Innovation |
|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 5.NF |
|Cluster: Use equivalent fractions as a strategy to add and subtract fractions |
|Standard # | Standards |
|5.NF.1 |Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent|
| |fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, |
| |2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd). |
|5.NF.2 |Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike|
| |denominators, eg. by using visual fraction models or equations to represent the problem. Use benchmark fractions and |
| |number sense of fractions to estimate mentally and assess the reasonableness of answers. For example |
|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 ... |
|Determine Greatest Common Factor (GCF) and Least Common Multiple (LCM). |
|Add and subtract fractions with unlike denominators. |
|Convert between mixed numbers and improper fractions. |
|Determine equivalent fractions. |
|Use fraction models of equations to represent word problems. |
|Estimate and assess solutions to real-world problems involving fractions. |
|Evidence of Learning |
|Summative Assessment |
|Show equivalent forms of a given fraction, including proper and mixed number forms of fractions. |
|Show equivalent forms of a given fraction when adding unit fractions and mixed numbers when presented horizontally and vertically. |
|Show equivalent forms of a given fraction when subtracting unit fractions and mixed numbers when regrouping is required when presented |
|horizontally and vertically. |
|Convert a mixed number to improper fraction and vv. |
|Make a list to find GCF or LCM with up to three numbers up to hundreds. |
|through prime factorization |
|through listing factors and/or multiplies |
|Round to the nearest bench mark fraction and estimate answers to given equations. |
|Show all fractions in simplest form. |
|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 |Homework |
|Quizzes/Tests |Math games |
|Student workbook |Study Island |
|Drawing Models | |
| |
|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: |
| - On line board game that allows students to practice adding and |
|subtracting fractions with like and unlike denominators. |
| |
| – 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. |
| |
| – Demonstration and practice online program illustrating adding and subtracting|
|fractions and mixed numbers. |
| |
| - 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: When adding and subtracting fractions use fractions that when the denominators are multiplied together the resulting products are |
|in fact the LCD (LCM). When students have to determine LCM and GCF use numbers that are smaller and they can mentally determine the LCM and |
|GCF. Subtractions of fractions limit those fractions that do not require regrouping. |
| |
|Accelerated: When adding and subtracting fractions use denominators in the fractions that when combined through multiplication does not result |
|in the LCD. Students need to determine the LCD prior to making the equivalent fractions that then can be added or subtracted. Students will |
|be able to add and subtract fractions that require regrouping. |
|Teacher Notes: Instructor should begin with reviewing addition and subtraction of fractions with common denominators. Review equivalent |
|fractions prior to applying to adding and subtraction of fractions with unlike denominators. |
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