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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