Tewksbury Township Schools
|Unit Overview |
|Content Area: Math |
|Unit Title: Rational Numbers Unit: 2 |
|Target Course/Grade Level: Seventh Grade Timeline: 3 weeks |
|Unit Summary: Students develop an understanding of rational numbers and their different forms. They express fractions as decimals and decimals |
|as fractions. As with integers, students learn how to add, subtract, multiply, and divide fractions. Students solve real-world problems with |
|rational numbers. |
|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: B Gathering and Evaluating knowledge and information from a variety of sources, |
|including global perspective, fosters creativity and innovative thinking. |
|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, Creativity and Innovation |
|Mathematical Practices: |
|7.MP.1 Make sense of problems and persevere in solving them. |
|7.MP.2 Reason abstractly and quantitatively. |
|7.MP.3 Construct viable arguments and critique the reasoning of others. |
|7.MP.4 Model with mathematics. |
|7.MP.6 Attend to precision. |
|7.MP.7 Look for and make use of structure. |
|7.MP.8 Look for and express regularity in repeated reasoning. |
|Learning Targets |
|Domain: The Number System |
|Cluster: Apply and extend previous understandings of numbers to the system of rational numbers |
|Standard # | Standards |
|7.NS.1 |Apply and extend previous understandings of addition and subtraction |
| |to add and subtract rational numbers; represent addition and |
| |subtraction on a horizontal or vertical number line diagram. |
|7.NS.1b |Understand p + q as the number located a distance |q| from p, |
| |in the positive or negative direction depending on whether q is |
| |positive or negative. Show that a number and its opposite have |
| |a sum of 0 (are additive inverses). Interpret sums of rational |
| |numbers by describing real-world contexts. |
|7.NS.1c |Understand subtraction of rational numbers as adding the |
| |additive inverse, p – q = p + (–q). Show that the distance between |
| |two rational numbers on the number line is the absolute value of |
| |their difference, and apply this principle in real-world contexts. |
|7.NS.2 |Apply and extend previous understandings of multiplication and |
| |division and of fractions to multiply and divide rational numbers. |
|7.NS.2a |Understand that multiplication is extended from fractions to |
| |rational numbers by requiring that operations continue to |
| |satisfy the properties of operations, particularly the distributive |
| |property, leading to products such as (–1)(–1) = 1 and the rules |
| |for multiplying signed numbers. Interpret products of rational |
| |numbers by describing real-world contexts. |
|7.NS.2b |Understand that integers can be divided, provided that the divisor |
| |is not zero, and every quotient of integers (with non-zero divisor) |
| |is a rational number. If p and q are integers, then –(p/q) = (–p)/q = |
| |p/(–q). Interpret quotients of rational numbers by describing realworld |
| |contexts |
|7.NS.2c |Apply properties of operations as strategies to multiply and |
| |divide rational numbers. |
|7.NS.2d |Convert a rational number to a decimal using long division; know |
| |that the decimal form of a rational number terminates in 0s or |
| |eventually repeats. |
|7.NS.3 |Solve real-world and mathematical problems involving the four |
| |operations with rational numbers.1 |
|7.EE.3 |Solve multi-step real-life and mathematical problems posed with |
| |positive and negative rational numbers in any form (whole numbers, |
| |fractions, and decimals), using tools strategically. Apply properties of |
| |operations to calculate with numbers in any form; convert between |
| |forms as appropriate; and assess the reasonableness of answers using |
| |mental computation and estimation strategies. For example: If a woman |
| |making $25 an hour gets a 10% raise, she will make an additional 1/10 of |
| |her salary an hour, or $2.50, for a new salary of $27.50. If you want to place |
| |a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches |
| |wide, you will need to place the bar about 9 inches from each edge; this |
| |estimate can be used as a check on the exact computation. |
|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.B.2 |Assess data gathered to solve problems for which there are varying perspective (e.g., cross cultural, gender specific, |
| |generational, etc.) and determine how the data can best be used to design the multiple solutions. |
|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 |
|What are rational numbers? |A rational number is any number that can be written as a fraction a/b |
|Describe the relationship between rational numbers, integers, and |where b≠0 A repeating or terminating decimal that can be written as a |
|whole numbers. |fraction is a rational number. |
|How is adding unlike fractions similar to adding like fractions? How |Number that neither terminate or repeat are irrational numbers. |
|is it different? |When adding and subtracting fractions, one must get a common |
|How is multiplying fractions different from adding fractions? How is |denominator. An answer must always be in simplest form, which means the|
|it similar? |GCF of the numerator and denominator is 1. |
| |When dividing fractions, multiply by its reciprocal or multiplicative |
| |inverse. |
|Unit Learning Targets |
|Students will ... |
|Graph rational numbers and order and compare rational numbers |
|Change fractions to decimals and visa-versa |
|Add and subtract fractions with like and unlike denominators |
|Add and subtract with mixed numbers |
|Multiply and divide fractions and mixed numbers |
|Evidence of Learning |
|Summative Assessment |
|Express rational numbers as terminating and repeating decimals |
|Compare and order fractions, decimals and percents |
|Add, subtract, multiply and divide rational numbers |
|Equipment needed: grid paper, smartboard, elmo, whiteboards and markers |
|Teacher Instructional Resources: Textbook (To be determined) |
|Study Island |
|Khan Academy Videos |
|Formative Assessments |
|Skill sheets |Homework |
|Quizzes/Tests |Math games |
|Student workbook |Study Island |
| |
|Integration of Technology: |
|Smart Board to play online games, utilize online resources, generate models with Smart Software. |
|Kahn Academy Videos |
|Elmo – for demonstration |
|Study Island |
|Technology Resources: |
| |
| |
| – 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 7th grade online interactive activities for the students to complete |
| |
| - AAA math 7th grade – online interactive activities and problems for the student to complete. |
| |
| – Grade level material for practice, lessons, games, etc. |
| |
| |
|Opportunities for Differentiation: |
|Decelerate: use decimals out to the hundredths for calculating |
|Use simple common denominators |
|Have students write multiplication as repeated addition |
| |
|Accelerated: Have students create an expression involving multiplying or dividing polynomials with negative exponents. |
|Teacher Notes: |
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