Plainfield Public Schools Mathematics Rigorous Curriculum Design Unit Planning Organizer

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1 1 Plainfield Public Schools Mathematics Rigorous Curriculum Design Unit Planning Organizer Subject(s) Mathematics Grade/Course 7th Unit of Study Unit 1 Number System Pacing 7 weeks 2 weeks for re-teaching/enrichment MATHEMATICAL PRACTICES Practices in bold are to be emphasized in the unit. 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

2 2 UNIT STANDARDS COMMON CORE N.J. PRIORITY 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. a. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. b. 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 realworld contexts. c. 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. d. Apply properties of operations as strategies to add and subtract rational numbers. 7.NS.2. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. a. 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. b. 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 real-world contexts. c. Apply properties of operations as strategies to multiply and divide rational numbers. d. 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. COMMON CORE SUPPORTING STANDARDS 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)

3 3 Unwrapped Skills (students need to be able to do) Unwrapped Concepts (students need to know) DOK Levels FOCUS STANDARD: 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. e. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. f. 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 realworld contexts. g. 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. h. Apply properties of operations as strategies to add and subtract rational numbers Apply and extend Understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Opposite Quantities 3 DESRIBE situations in which opposite quantities combine to make 0 2 UNDERSTAND UNDERSTAND (the number located a distance q from p, in the positive or negative direction depending on whether q is positive or negative )Absolute Value subtraction of rational numbers as adding the additive inverse Properties of Operations 2 2 APPLY FOCUS STANDARD: properties of operations as strategies to add and subtract rational number 4 7. NS.2. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. e. 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.

4 4 f. 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 real-world contexts. g. Apply properties of operations as strategies to multiply and divide rational numbers. h. 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. Apply and extend Understand Understand Apply Convert Previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations integers can be divided, provided that the divisor is not zero, and every quotient of integers Properties of operations as strategies to multiply and divide rational numbers. a rational number to a decimal using long division SUPPORTING STANDARD: 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.) Solve real-world and mathematical problems involving the four operations with rational numbers 3 Essential Questions Corresponding Big Ideas

5 5 How is the number system used to fit different situations? How can we compare and contrast numbers? When are negative numbers used and why are they important? Why is it useful for me to know the absolute value of a number? Why do we need to agree on a specific order of operations? How does changing the order of operations affect the outcome when simplifying an expression? How is the order of operations like a recipe for chocolate cookies? Numbers can represent quantities, relationships, location, and position. Rational numbers have multiple interpretations, and making sense of them depends on identifying the unit. The concept of unit is fundamental to the interpretation of rational numbers. The concept of unit is fundamental to the interpretation of rational numbers. One interpretation of a rational number is as a part-whole relationship. One interpretation of a rational number is as a measure. One interpretation of a rational number is as a quotient. One interpretation of a rational number is as a ratio. One interpretation of a rational number is as an operator. Negative numbers are used to represent quantities that are less than zero such as temperature, scores in games or sports, and loss of income in business. Absolute value is useful in ordering and graphing positive and negative numbers. Recognize how addition, subtraction multiplication, division, powers, parentheses and roots of numbers effect the magnitude of the result Unit Vocabulary Terms Unwrapped Priority Standards Concepts Supporting Standards Concepts and Other Unit-Specific Terms Evaluate Exponent Order of Operations Rational numbers Term Constant Coefficient Order of Operations Expressions Equations Reciprocal Variable Inequality Solution Distributive property Associative property Absolute value

6 6 Performance Task # 1 Task 1 Full Description: Goal: Arrange integers in order. Role: You are a analyzing a Julie Brown Anderson s dive. Audience: Reader of article. Situation: You are interviewing for a job at a sports magazine. You have been asked to comment on the scuba diving techniques of certain divers. Product: Brief article describing the dive of Julie Brown Anderson on 5/9/12. Which standard(s) (priority/supporting) will the task address? 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. i. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. j. 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. What essential Question(s) and corresponding Big Idea(s) will this task target? Why is it useful for me to know the absolute value of a number? Why do we need to agree on a specific order of operations? How does changing the order of operations affect the outcome when simplifying an expression? Absolute value is useful in ordering and graphing positive and negative numbers. Recognize how addition, subtraction multiplication, division, powers, parentheses and roots of numbers effect the magnitude of the result Which unwrapped specific concepts and skills will this task target? Describe Understand Show Interpret Apply Positive and negative numbers Opposite Quantities Addition and Subtraction Equivalent forms of rational numbers Absolute Value Properties of Operations How will the students apply the concepts and skills? What will they do and/or produce? Construct a number line of the order of the integers. What resources, instruction, and information will students need in order to complete the task? Teacher model.

7 7 What evidence of learning will I look for to show that I know all of my students have conceptually learned the concepts and skills the standard(s)? Students will be able to collect data and write a paragraph to compare and contrast. Students have shown proficient on the rubric. How can I differentiate the application and/or evidence to meet the varying needs of my students? To differentiate the application, small groups of students with learning needs will be given a number line to work with and the ELL students will pair with an English/Spanish speaking student to complete task. Give a personal cue to begin work Give work in smaller units Provide immediate reinforces and feedback Make sure the appropriate books and materials are available Introduce the assignment in sequential steps Check for student understanding of instructions Check on progress often in the first few minutes of work Provide time suggestions for each task Provide a checklist for long detailed tasks Use technological resources

8 8 Performance Task # 1 Scoring Guide Advanced or Exemplary All Goal criteria plus: Correctly identified the intervals, 0-3: Decreasing, going down into water, 3-31: basically level with some increasing, 31-39: increasing, coming our of the dive, going out of the water Proficient Goal criteria: Write four different scenarios for divers Diagrams correctly depict the addition equations Created number line and ordered integers Filled in table of information correctly (estimations accurate) Progressing Meets _3 of the Goal criteria More work is needed Beginning Meets fewer than _3_ of the Goal criteria Task to be repeated after re-teaching Comments: Interdisciplinary Connections and Related Priority Standards Specific to Task #1 CCSS.ELA-Literacy.W.7.2b Develop the topic with relevant facts, definitions, concrete details, quotations, or other information and examples. CCSS.ELA-Literacy.W.7.7 Conduct short research projects to answer a question, drawing on several sources and generating additional related, focused questions for further research and investigation. Science F2 Explain the mechanisms that cause varying daily temperature ranges in a coastal community and in a community located in the interior of the country Performance Task # 1 Scoring Guide 21 st Century Learning Skills Specific to Task #1 those that apply for task: Teamwork and Collaboration Initiative and Leadership Curiosity and Imagination Innovation and Creativity Critical thinking and Problem Solving Flexibility and Adaptability Effective Oral and Written Communication Accessing and Analyzing Information Other

9 9 Performance Task # 2 Task 2 Full Description: You have given the scuba divers a course in how deep they can go below sea level before the pressure becomes dangerous to their lives, they have asked you to help them figure out how fast they can ascend to the surface. Role: You are a scuba diving instructor. Audience: Students in your class. Situation: You are a scuba diving instructor and your class needs instruction on how fast they can return to the surface. Product : Construct mathematical equations to model scenario Which standard(s) (priority/supporting) will the task address? 7. NS.2. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. a. 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. b. 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 real-world contexts. c. Apply properties of operations as strategies to multiply and divide rational numbers. What essential Question(s) and corresponding Big Idea(s) will this task target? How is the number system used to fit different situations? Why do we need to agree on a specific order of operations? How does changing the order of operations affect the outcome when simplifying an expression? How is the order of operations like a recipe for chocolate cookies? Numbers can represent quantities, relationships, location, and position. Rational numbers have multiple interpretations, and making sense of them depends on identifying the unit. The concept of unit is fundamental to the interpretation of rational numbers. The concept of unit is fundamental to the interpretation of rational numbers. One interpretation of a rational number is as a part-whole relationship. One interpretation of a rational number is as a quotient. Recognize how addition, subtraction multiplication, division, powers, parentheses and roots of numbers effect the magnitude of the result

10 10 Which unwrapped specific concepts and skills will this task target? Skill : Concepts: Add and Subtract Describe Understand show Absolute Value Properties of Operations Positive and negative numbers Equivalent forms of rational Opposite Quantities interpret Apply How will the students apply the concepts and skills? What will they do and/or produce? Students will write four addition equations and draw a diagram of the zones to depict the equations. What resources, instruction, and information will students need in order to complete the task? Students will need to know the dangerous pressure point to dive and the zones below sea level. What evidence of learning will I look for to show that I know all of my students have conceptually learned the concepts and skills the standard(s)? The evidence will be the equations with correct solutions and the diagram. How can I differentiate the application and/or evidence to meet the varying needs of my students? Give a personal cue to begin work Give work in smaller units Provide immediate reinforces and feedback Make sure the appropriate books and materials are available Introduce the assignment in sequential steps Check for student understanding of instructions Check on progress often in the first few minutes of work Provide time suggestions for each task Provide a checklist for long detailed tasks Use technological resources

11 11 Performance Task # 2 Scoring Guide Advanced or Exemplary All Goal criteria plus: has ALL of parts 2 and 3 correct WITH correct labeling of units. Proficient Goal criteria: Write four equations for the scenarios for dives (First) Has 3 of the correct answers for the 4 scenarios (Second) Has 2 of the correct answers for the Third part Has correctly labeled 5 of the 7 questions Progressing Meets _2 of the Goal criteria More work is needed Beginning Meets fewer than _2_ of the Goal criteria Task to be repeated after re-teaching Comments: Interdisciplinary Connections and Related Priority Standards Specific to Task #2 CCSS.ELA-Literacy.W.7.2b Develop the topic with relevant facts, definitions, concrete details, quotations, or other information and examples. CCSS.ELA-Literacy.W.7.7 Conduct short research projects to answer a question, drawing on several sources and generating additional related, focused questions for further research and investigation. Science F2 Explain the mechanisms that cause varying daily temperature ranges in a coastal community and in a community located in the interior of the country 21 st Century Learning Skills Specific to Task #2 Check all those that apply for each task: Teamwork and Collaboration Initiative and Leadership Curiosity and Imagination Innovation and Creativity Critical thinking and Problem Solving Flexibility and Adaptability Effective Oral and Written Communication Accessing and Analyzing Information Other

12 12 Research-Based Effective Teaching Strategies Task /Activities that solidifies mathematical concepts Use questioning techniques to facilitate learning Reinforcing Effort, Providing Recognition Practice, reinforce and connect to other ideas within mathematics Promotes linguistic and nonlinguistic representations Cooperative Learning Setting Objectives, Providing Feedback Varied opportunities for students to communicate mathematically Use technological and /or physical tools 21 st Century Learning Skills those that apply to the unit: Teamwork and Collaboration Initiative and Leadership Curiosity and Imagination Innovation and Creativity Critical thinking and Problem Solving Flexibility and Adaptability Effective Oral and Written Communication Accessing and Analyzing Information Other

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