CCLS Mathematics Grade 7 Curriculum Guide

Transcription

1 MOUNT VERNON CITY SCHOOL DISTRICT CCLS Mathematics Grade 7 Curriculum Guide THIS HANDBOOK IS FOR THE IMPLEMENTATION OF THE GRADE 7 MATHEMATICS CURRICULUM IN MOUNT VERNON

2 Mount Vernon City School District Board of Education Adriane Saunders President Serigne Gningue Vice President Board Trustees Charmaine Fearon Rosemarie Jarosz Micah J.B. McOwen Omar McDowell Darcy Miller Wanda White Lesly Zamor Superintendent of Schools Dr. Kenneth Hamilton Deputy Superintendent Dr. Jeff Gorman Assistant Superintendent of Business Ken Silver Assistant Superintendent of Human Resources Denise Gagne-Kurpiewski Administrator of Mathematics and Science (K-12) Dr. Satish Jagnandan 2

3 TABLE OF CONTENTS I. COVER II. MVCSD BOARD OF EDUCATION III. TABLE OF CONTENTS IV. IMPORTANT DATES V. VISION STATEMENT VI. PHILOSOPHY OF MATHEMATICS CURRICULUM. 6 VII. NYS GRADE 7 COMMON CORE LEARNING STANDARDS..7 VII. MVCSD GRADE 7 MATHEMATICS PACING GUIDE VIII. WORD WALL IX. SETUP OF A MATHEMATICS CLASSROOM X. SECONDARY GRADING POLICY XI. SAMPLE NOTEBOOK RUBRIC XII. CLASSROOM AESTHETICS XIII. SYSTEMATIC DESIGN OF A MATHEMATICS LESSON

4 IMPORTANT DATES REPORT CARD 10 WEEK PERIOD MARKING PERIOD MARKING PERIOD BEGINS MP 1 September 8, 2015 MP 2 November 16, 2015 MP 3 February 1, 2016 MP 4 April 18, 2016 INTERIM PROGRESS REPORTS October 9, 2015 December 18, 2015 March 11, 2016 May 20, 2016 MARKING PERIOD ENDS November 13, 2015 January 29, 2016 April 15, 2016 June 23, 2016 DURATION REPORT CARD DISTRIBUTION 10 weeks Week of Nov. 23, weeks Week of February 8, weeks Week of April 25, weeks Last Day of School June 23, 2016 The Parent Notification Policy states Parent(s) / guardian(s) or adult students are to be notified, in writing, at any time during a grading period when it is apparent - that the student may fail or is performing unsatisfactorily in any course or grade level. Parent(s) / guardian(s) are also to be notified, in writing, at any time during the grading period when it becomes evident that the student's conduct or effort grades are unsatisfactory. 4

5 VISION STATEMENT True success comes from co-accountability and co-responsibility. In a coherent instructional system, everyone is responsible for student learning and student achievement. The question we need to constantly ask ourselves is, "How are our students doing?" The starting point for an accountability system is a set of standards and benchmarks for student achievement. Standards work best when they are well defined and clearly communicated to students, teachers, administrators, and parents. The focus of a standards-based education system is to provide common goals and a shared vision of what it means to be educated. The purposes of a periodic assessment system are to diagnose student learning needs, guide instruction and align professional development at all levels of the system. The primary purpose of this Instructional Guide is to provide teachers and administrators with a tool for determining what to teach and assess. More specifically, the Instructional Guide provides a "road map" and timeline for teaching and assessing the Common Core Learning Standards. I ask for your support in ensuring that this tool is utilized so students are able to benefit from a standards-based system where curriculum, instruction, and assessment are aligned. In this system, curriculum, instruction, and assessment are tightly interwoven to support student learning and ensure ALL students have equal access to a rigorous curriculum. We must all accept responsibility for closing the achievement gap and improving student achievement for all of our students. Dr. Satish Jagnandan Administrator for Mathematics and Science (K-12) 5

6 PHILOSOPHY OF MATHEMATICS CURRICULUM The Mount Vernon City School District recognizes that the understanding of mathematics is necessary for students to compete in today s technological society. A developmentally appropriate mathematics curriculum will incorporate a strong conceptual knowledge of mathematics through the use of concrete experiences. To assist students in the understanding and application of mathematical concepts, the mathematics curriculum will provide learning experiences which promote communication, reasoning, and problem solving skills. Students will be better able to develop an understanding for the power of mathematics in our world today. Students will only become successful in mathematics if they see mathematics as a whole, not as isolated skills and facts. As we develop mathematics curriculum based upon the standards, attention must be given to both content and process strands. Likewise, as teachers develop their instructional plans and their assessment techniques, they also must give attention to the integration of process and content. To do otherwise would produce students who have temporary knowledge and who are unable to apply mathematics in realistic settings. Curriculum, instruction, and assessment are intricately related and must be designed with this in mind. All three domains must address conceptual understanding, procedural fluency, and problem solving. If this is accomplished, school districts will produce students who will 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. 6

7 New York State P-12 Common Core Learning Standards for Mathematics Mathematics - Grade 7: Introduction In Grade 7, instructional time should focus on four critical areas: (1) developing understanding of and applying proportional relationships; (2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples. 1. Students extend their understanding of ratios and develop understanding of proportionality to solve single- and multi-step problems. Students use their understanding of ratios and proportionality to solve a wide variety of percent problems, including those involving discounts, interest, taxes, tips, and percent increase or decrease. Students solve problems about scale drawings by relating corresponding lengths between the objects or by using the fact that relationships of lengths within an object are preserved in similar objects. Students graph proportional relationships and understand the unit rate informally as a measure of the steepness of the related line, called the slope. They distinguish proportional relationships from other relationships. 2. Students develop a unified understanding of number, recognizing fractions, decimals (that have a finite or a repeating decimal representation), and percents as different representations of rational numbers. Students extend addition, subtraction, multiplication, and division to all rational numbers, maintaining the properties of operations and the relationships between addition and subtraction, and multiplication and division. By applying these properties, and by viewing negative numbers in terms of everyday contexts (e.g., amounts owed or temperatures below zero), students explain and interpret the rules for adding, subtracting, multiplying, and dividing with negative numbers. They use the arithmetic of rational numbers as they formulate expressions and equations in one variable and use these equations to solve problems. 3. Students continue their work with area from Grade 6, solving problems involving the area and circumference of a circle and surface area of three-dimensional objects. In preparation for work on congruence and similarity in Grade 8 they reason about relationships among two-dimensional figures using scale drawings and informal geometric constructions, and they gain familiarity with the relationships between angles formed by intersecting lines. Students work with three-dimensional figures, relating them to two-dimensional figures by examining cross-sections. They solve real-world and mathematical problems involving area, surface area, and volume of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes and right prisms. 4. Students build on their previous work with single data distributions to compare two data distributions and address questions about differences between populations. They begin informal work with random sampling to generate data sets and learn about the importance of representative samples for drawing inferences. Mathematical Practices 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. 7

8 Grade 7 Overview Ratios and Proportional Relationships Analyze proportional relationships and use them to solve real-world and mathematical problems. The Number System Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Expressions and Equations Use properties of operations to generate equivalent expressions. Solve real-life and mathematical problems using numerical and algebraic expressions and equations. Ratios & Proportional Relationships Geometry Draw, construct and describe geometrical figures and describe the relationships between them. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. Statistics and Probability Use random sampling to draw inferences about a population. Draw informal comparative inferences about two populations. Investigate chance processes and develop, use, and evaluate probability models. 7.RP Analyze proportional relationships and use them to solve real-world and mathematical problems. 1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2 / 1/4 miles per hour, equivalently 2 miles per hour. 2. Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. 3. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. The Number System 7.NS Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. 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 real-world 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. 8

9 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. 3. Solve real-world and mathematical problems involving the four operations with rational numbers. 1 1 Computations with rational numbers extend the rules for manipulating fractions to complex fractions. Expressions & Equations 7.EE Use properties of operations to generate equivalent expressions. 1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 2. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a a = 1.05a means that increase by 5% is the same as multiply by Solve real-life and mathematical problems using numerical and algebraic expressions and equations. 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 $ 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. 4. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Geometry 7.G Draw construct, and describe geometrical figures and describe the relationships between them. 1. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. 2. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. 9

10 3. Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. 4. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. 5. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. 6. Solve real-world and mathematical problems involving area, volume and surface area of two- and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Statistics & Probability 7.SP Use random sampling to draw inferences about a population. 1. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. 2. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. Draw informal comparative inferences about two populations. 3. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. 4. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book. Investigate chance processes and develop, use, and evaluate probability models. 5. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. 6. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. 7. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? 8. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. 10

11 b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes ), identify the outcomes in the sample space which compose the event. c. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood? 11

12 Grade 7 Common Core Mathematics Test Cluster Emphases Cluster Emphases for Instruction on the 2013 Grade 7 Common Core Mathematics Test Cluster Emphasis Recommended Instructional Time Approximate Number of Test Points Major 65 75% 70 80% Supporting 15 25% 10 20% Additional 5 15% 5 10% CCLS Standard Content Emphasis Ratios and Proportional Relationships 7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. Major 7.RP.2 Recognize and represent proportional relationships between quantities Major 7.RP.3 Use proportional relationships to solve multistep ratio and percent problems Major The Number System 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.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers Expressions and Equations 7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. 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. 7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. Geometry 7.G.1 Solve problems involving scale drawings of geometric figures, such as computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Major Major Major Major Major Major Major Additional 12

13 7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. 7.G.3 Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. 7.G.4 Know the formulas for the area and circumference of a circle and solve problems; give an informal derivation of the relationship between the circumference and area of a circle. 7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and use them to solve simple equations for an unknown angle in a figure 7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms Statistics and Probability 6.SP.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. 6.SP.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape 6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number 6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots 6.SP.5 Summarize numerical data sets in relation to their context, such as by: a. Reporting the number of observations b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. 7.SP.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. 7.SP.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions 7.SP.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. 7.SP.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. 7.SP.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. Additional Post Additional Post Additional Additional Post Additional Post Additional Additional Additional Additional Additional Supporting Supporting Additional Additional Supporting 13

14 7.SP.6 7.SP.7 7.SP.8 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Supporting Supporting Supporting = Standards recommended for greater emphasis Post = Standards recommended for instruction in May-June 14

15 MATHEMATICS 7 PACING GUIDE This guide using NYS Grade 7 Mathematics CCLS Modules was created to provide teachers with a time frame to complete the Grade 7 New York State Mathematics Curriculum. Module Unit Title Standards Days Month i-ready Lessons 1 Ratios and Proportional Relationships 7.RP.1, 7.RP.2, 7.RP.3, 7.EE.4, 7.G.1 26 Sept. 8 Oct. 19 Topic A 10; Topic B 11; Topic C 9, 12, 13; Topic D 22 2 Rational Numbers 7.NS.1, 7.NS.2, 7.NS.3, 7.EE.2, 7.EE.4 26 Oct. 20 Nov. 25 Topic A 1, 2, 3, 7; Topic B 4, 5, 6; Topic C Expressions and Equations 7.EE.1, 7.EE.2, 7.EE.3, 7.EE.4, 7.G.4, 7.G.5, 7.G.6 31 Nov. 30 Jan. 21 Topic A 14, 15; Topic B 16, 17, 18; Topic C 20, 21, 23, 24 4 Percent and Proportional Relationships 5 Statistics and Probability 7.RP.1, 7.RP.2, 7.RP.3, 7.EE.3, 7.G.1 23 Jan. 22 Mar. 1 7.SP.1, 7.SP.2, 7.SP.3, 7.SP.4, 7.SP.5, 7.SP.6, 7.SP.7, 7.SP.8 24 Mar. 2 Apr. 12 Topic A 12; Topic B 13; Topic C 22; Topic D 12, 13 Topic A 30, 31, 33; Topic B 32; Topic C 26, 27; Topic D 28, 29 NYSED GRADE 7 MATHEMATICS TEST: WEDNESDAY, APRIL 13 FRIDAY, APRIL 15, Geometry 7.G.2, 7.G.3, 7.G.5, 7.G.6 43 Apr. 18 June 17 Topic A 18; Topic B 19; Topic C 25; Topic D 20, 21, 24; Topic E 23 Red End of Module Assessment Period Green Priority Standards account for approximately 70-80% of number of test points. Note that the curriculum assumes that each school day includes minutes of math: minutes on the day s Session, and 5-10 minutes on Fluency activities. Designed to fit within the calendar of a typical school year, grade 7 includes a total of 139 lessons. This provides some leeway for going further with particular ideas and/or accommodating local circumstances. Although pacing will vary somewhat in response to variations in school calendars, needs of students, your school's years of experience with the curriculum, and other local factors, following the suggested pacing and sequence will ensure that students benefit from the way mathematical ideas are introduced, developed, and revisited across the year. 15

16 Module Unit Title Standards Days Month i-ready Lessons 1 Ratios and Proportional Relationships 7.RP.1, 7.RP.2, 7.RP.3, 7.EE.4, 7.G.1 26 Sept. 8 Oct. 19 Topic A 10; Topic B 11; Topic C 9, 12, 13; Topic D 22 In Module 1, students build on their Grade 6 experiences with ratios, unit rates, and fraction division to analyze proportional relationships. They decide whether two quantities are in a proportional relationship, identify constants of proportionality, and represent the relationship by equations. These skills are then applied to real-world problems including scale drawings. Standards Topics Days 7.RP.2a A Proportional Relationships Lesson 1: An Experience in Relationships as Measuring Rate Lesson 2: Proportional Relationships Lessons 3 4: Identifying Proportional and Non-Proportional Relationships in Tables Lessons 5 6: Identifying Proportional and Non-Proportional Relationships in Graphs 6 7.RP.2b 7.RP.2c 7.RP.2d 7.EE.4a B Unit Rate and the Constant of Proportionality Lesson 7: Unit Rate as the Constant of Proportionality Lessons 8 9: Representing Proportional Relationships with Equations Lesson 10: Interpreting Graphs of Proportional Relationships 4 Mid-Module Assessment: Topics A through B (assessment 1 day, remediation or further applications 1 day) 2 7.RP.1 7.RP.3 7.EE.4a C Ratios and Rates Involving Fractions Lessons 11 12: Ratios of Fractions and Their Unit Rates Lesson 13: Finding Equivalent Ratios Given the Total Quantity Lesson 14: Multistep Ratio Problems Lesson 15: Equations of Graphs of Proportional Relationships Involving Fractions 5 7.RP.2b 7.G.1 D Ratios of Scale Drawings Lesson 16: Relating Scale Drawings to Ratios and Rates 7 16

17 Lesson 17: The Unit Rate as the Scale Factor Lesson 18: Computing Actual Lengths from a Scale Drawing Lesson 19: Computing Actual Areas from a Scale Drawing Lesson 20: An Exercise in Creating a Scale Drawing Lessons 21 22: An Exercise in Changing Scales End-of-Module Assessment: Topics A through D (assessment 1 day, remediation or further applications 1 day) 2 Total Number of Instructional Days 26 17

18 Module Unit Title Standards Days Month i-ready Lessons 2 Rational Numbers 7.NS.1, 7.NS.2, 7.NS.3, 7.EE.2, 7.EE.4 26 Oct. 20 Nov. 25 Topic A 1, 2, 3, 7; Topic B 4, 5, 6; Topic C - 8 In Grade 6, students formed a conceptual understanding of integers through the use of the number line, absolute value, and opposites and extended their understanding to include the ordering and comparing of rational numbers (6.NS.C.5, 6.NS.C.6, 6.NS.C.7). This module uses the Integer Game: a card game that creates a conceptual understanding of integer operations and serves as a powerful mental model students can rely on during the module. Students build on their understanding of rational numbers to add, subtract, multiply, and divide signed numbers. Previous work in computing the sums, differences, products, and quotients of fractions serves as a significant foundation as well. Standards Topics Days 7.NS.A.1 A Addition and Subtraction of Integers and Rational Numbers Lesson 1: Opposite Quantities Combine to Make Zero Lesson 2: Using the Number Line to Model the Addition of Integers Lesson 3: Understanding Addition of Integers Lesson 4: Efficiently Adding Integers and Other Rational Numbers Lesson 5: Understanding Subtraction of Integers and Other Rational Numbers Lesson 6: The Distance Between Two Rational Numbers Lesson 7: Addition and Subtraction of Rational Numbers Lessons 8 9: Applying the Properties of Operations to Add and Subtract Rational Numbers 7.NS.A.2 B Multiplication and Division of Integers and Rational Numbers Lesson 10: Understanding Multiplication of Integers Lesson 11: Develop Rules for Multiplying Signed Numbers Lesson 12: Division of Integers Lesson 13: Converting Between Fractions and Decimals Using Equivalent Fractions Lesson 14: Converting Rational Numbers to Decimals Using Long Division Lesson 15: Multiplication and Division of Rational Numbers Lesson 16: Applying the Properties of Operations to Multiply and Divide Rational Numbers

19 Mid-Module Assessment: Topics A through B (assessment 1 day, remediation or further applications 1 day) 2 7.NS.A.3 7.EE.A.2 7.EE.B.4a C Applying Operations with Rational Numbers to Expressions and Equations Lesson 17: Comparing Tape Diagram Solutions to Algebraic Solutions Lessons 18 19: Writing, Evaluating, and Finding Equivalent Expressions with Rational Numbers Lesson 20: Investments Performing Operations with Rational Numbers Lesson 21: If-Then Moves with Integer Number Cards Lessons 22 23: Solving Equations Using Algebra 5 End-of-Module Assessment: Topics A through C (assessment 1 day, remediation or further applications 2 days) 3 Total Number of Instructional Days 26 19

20 Module Unit Title Standards Days Month i-ready Lessons 3 Expressions and Equations 7.EE.1, 7.EE.2, 7.EE.3, 7.EE.4, 7.G.4, 7.G.5, 7.G.6 31 Nov. 30 Jan. 21 Topic A 14, 15; Topic B 16, 17, 18; Topic C 20, 21, 23, 24 In Grade 6, students formed a conceptual understanding of integers through the use of the number line, absolute value, and opposites and extended their understanding to include the ordering and comparing of rational numbers (6.NS.C.5, 6.NS.C.6, 6.NS.C.7). This module uses the Integer Game: a card game that creates a conceptual understanding of integer operations and serves as a powerful mental model students can rely on during the module. Students build on their understanding of rational numbers to add, subtract, multiply, and divide signed numbers. Previous work in computing the sums, differences, products, and quotients of fractions serves as a significant foundation as well. Standards Topics Days 7.EE.A.1 7.EE.A.2 A Use Properties of Operations to Generate Equivalent Expressions Lessons 1 2: Generating Equivalent Expressions Lessons 3 4: Writing Products as Sums and Sums as Products Lesson 5: Using the Identity and Inverse to Write Equivalent Expressions Lesson 6: Collecting Rational Number Like Terms 6 7.EE.B.3 7.EE.B.4 7.G.B.5 B Solve Problems Using Expressions, Equations, and Inequalities Lesson 7: Understanding Equations Lessons 8 9: Using the If-Then Moves in Solving Equations Lessons 10 11: Angle Problems and Solving Equations Lesson 12: Properties of Inequalities Lesson 13: Inequalities Lesson 14: Solving Inequalities Lesson 15: Graphing Solutions to Inequalities 9 Mid-Module Assessment: Topics A through B (assessment 1 day, remediation or further applications 1 day) 2 7.G.B.4 C Use Equations and Inequalities to Solve Geometry Problems 11 20

21 7.G.B.6 Lesson 16: The Most Famous Ratio of All Lesson 17: The Area of a Circle Lesson 18: More Problems on Area and Circumference Lesson 19: Unknown Area Problems on the Coordinate Plane Lesson 20: Composite Area Problems Lessons 21 22: Surface Area Lessons 23 24: The Volume of a Right Prism Lessons 25 26: Volume and Surface Area End-of-Module Assessment: Topics A through C (assessment 1 day, remediation or further applications 2 days) 3 Total Number of Instructional Days 31 21

22 Module Unit Title Standards Days Month i-ready Lessons 4 Percent and Proportional Relationships 7.RP.1, 7.RP.2, 7.RP.3, 7.EE.3, 7.G.1 23 Jan. 22 Mar. 1 Topic A 12; Topic B 13; Topic C 22; Topic D 12, 13 In Module 4, students deepen their understanding of ratios and proportional relationships from Module 1 (7.RP.A.1, 7.RP.A.2, 7.RP.A.3, 7.EE.B.4, 7.G.A.1) by solving a variety of percent problems. They convert between fractions, decimals, and percents to further develop a conceptual understanding of percent (introduced in Grade 6 Module 1) and use algebraic expressions and equations to solve multi-step percent problems (7.EE.B.3). An initial focus on relating to the whole serves as a foundation for students. Students begin the module by solving problems without using a calculator to develop an understanding of the reasoning underlying the calculations. Material in early lessons is designed to reinforce students understanding by having them use mental math and basic computational skills. To develop a conceptual understanding, students will use visual models and equations, building on their earlier work with these. As the lessons and topics progress and students solve multi-step percent problems algebraically with numbers that are not as compatible, teachers may let students use calculators so that their computational work does not become a distraction. This will also be noted in the teacher s lesson materials. Standards Topics Days 7.RP.A.1, 7.RP.A.2c, 7.RP.A.3 A Finding the Whole Lesson 1: Percent Lesson 2: Part of a Whole as a Percent Lesson 3: Comparing Quantities with Percent Lesson 4: Percent Increase and Decrease Lesson 5: Finding One-Hundred Percent Given Another Percent Lesson 6: Fluency with Percents 6 7.RP.A.1 7.RP.A.2 7.RP.A.3 7.EE.B.3 B Percent Problems Including More than One Whole Lesson 7: Markup and Markdown Problems Lesson 8: Percent Error Problems Lesson 9: Problem-Solving when the Percent Changes Lesson 10: Simple Interest Lesson 11: Tax, Commissions, Fees, and Other Real-World Percent Problems 5 22

23 Mid-Module Assessment: Topics A through B (assessment 1 day, remediation or further applications 1 day) 2 7.RP.A.2b 7.G.A.1 C Scale Drawings Lesson 12: The Scale Factor as a Percent for a Scale Drawing Lesson 13: Changing Scales Lesson 14: Computing Actual Lengths from a Scale Drawing Lesson 15: Solving Area Problems Using Scale Drawings 4 7.RP.A.2c 7.RP.A.3 7.EE.B.3 D Population, Mixture, and Counting Problems Involving Percents Lesson 16: Population Problems Lesson 17: Mixture Problems Lesson 18: Counting Problems 3 End-of-Module Assessment: Topics A through D (assessment 1 day, remediation or further applications 2 days) 3 Total Number of Instructional Days 22 23

24 Module Unit Title Standards Days Month i-ready Lessons 5 Statistics and Probability 7.SP.1, 7.SP.2, 7.SP.3, 7.SP.4, 7.SP.5, 7.SP.6, 7.SP.7, 7.SP.8 24 Mar. 2 Apr. 12 Topic A 30, 31, 33; Topic B 32; Topic C 26, 27; Topic D 28, 29 NYSED GRADE 7 MATHEMATICS TEST: WEDNESDAY, APRIL 13 FRIDAY, APRIL 15, 2016 In this module, students begin their study of probability, learning how to interpret probabilities and how to compute probabilities in simple settings. They also learn how to estimate probabilities empirically. Probability provides a foundation for the inferential reasoning developed in the second half of this module. Additionally, students build on their knowledge of data distributions that they studied in Grade 6, compare data distributions of two or more populations, and are introduced to the idea of drawing informal inferences based on data from random samples. Standards Topics Days 7.SP.C.5 7.SP.C.6 7.SP.C.7 7.SP.C.8a 7.SP.C.8b 7.SP.C.6 7.SP.C.7 7.SP.C.8c A B Calculating and Interpreting Probabilities Lesson 1: Chance Experiments Lesson 2: Estimating Probabilities by Collecting Data Lesson 3: Chance Experiments with Equally Likely Outcomes Lesson 4: Calculating Probabilities for Chance Experiments with Equally Likely Outcomes Lesson 5: Chance Experiments with Outcomes that Are Not Equally Likely Lesson 6: Using Tree Diagrams to Represent a Sample Space and to Calculate Probabilities Lesson 7: Calculating Probabilities of Compound Events Estimating Probabilities Lesson 8: The Difference Between Theoretical Probabilities and Estimated Probabilities Lesson 9: Comparing Estimated Probabilities to Probabilities Predicted by a Model Lessons 10 11: Using Simulation to Estimate a Probability Lesson 12: Using Probability to Make Decisions Mid-Module Assessment: Topics A through B SP.A.1 C Random Sampling and Estimated Population Characteristics 8 24

25 7.SP.A.2 Lesson 13: Populations, Samples, and Generalizing from a Sample to a Population Lesson 14: Selecting a Sample Lesson 15: Random Sampling Lesson 16: Methods for Selecting a Random Sample Lesson 17: Sampling Variability Lesson 18: Estimating a Population Mean Lesson 19: Understanding Variability when Estimating a Population Proportion Lesson 20: Estimating a Population Proportion 7.SP.B.3 7.SP.B.4 D Topic D: Comparing Populations Lesson 21: Why Worry About Sampling Variability? Lessons 22 23: Using Sample Data to Decide if Two Population Means Are Different 2 End-of-Module Assessment: Topics A through D (assessment 1 day, remediation or further applications 1 day) 2 Total Number of Instructional Days 24 25

26 Module Unit Title Standards Days Month i-ready Lessons 6 Geometry 7.G.2, 7.G.3, 7.G.5, 7.G.6 43 Apr. 18 June 17 Topic A 18; Topic B 19; Topic C 25; Topic D 20, 21, 24; Topic E 23 In Module 6, students delve further into several geometry topics they have been developing over the years. Grade 7 presents some of these topics (e.g., angles, area, surface area, and volume) in the most challenging form students have experienced yet. Module 6 assumes students understand the basics; the goal is to build a fluency in these difficult problems. The remaining topics (i.e., working on constructing triangles and taking slices (or cross sections) of three-dimensional figures) are new to students. Standards Topics Days 7.G.B.5 A Unknown Angles Lesson 1: Complementary and Supplementary Angles Lessons 2 4: Solve for Unknown Angles using Equations 7.G.A.2 B Constructing Triangles Lesson 5: Unique Triangles Lesson 6: Drawing Geometric Shapes Lesson 7: Drawing Parallelograms Lesson 8: Drawing Triangles Lesson 9: Conditions for a Unique Triangle Three Sides and Two Sides and the Included Angle Lesson 10: Conditions for a Unique Triangle Two Angles and a Given Side Lesson 11: Conditions on Measurements that Determine a Triangle Lesson 12: Unique Triangles Two Sides and a Non-Included Angle Lessons 13 14: Checking for Identical Triangles Lesson 15: Using Unique Triangles to Solve Real-World and Mathematical Problems Mid-Module Assessment: Topics A through B (assessment 1 day, remediation or further applications 1 day) G.A.3 C Slicing Solids 6 26

27 Lessons 16: Slicing a Right Rectangular Prism with a Plane Lesson 17: Slicing a Right Rectangular Pyramid with a Plane Lesson 18: Slicing on an Angle Lesson 19: Understanding Three-Dimensional Figures 7.G.B.6 D Problems Involving Area and Surface Area Lesson 20: Real-World Area Problems Lesson 21: Mathematical Area Problems Lesson 22: Area Problems with Circular Regions Lessons 23 24: Surface Area 7.G.B.6 E Problems Involving Volume Lesson 25: Volume of Right Prisms Lesson 26: Volume of Composite Three-Dimensional Objects Lesson 27: Real-World Volume Problems End-of-Module Assessment: Topics C through E (assessment 1 day, remediation or further applications 2 days) Total Number of Instructional Days 43 27

28 WORD WALLS ARE DESIGNED to promote group learning support the teaching of important general principles about words and how they work Foster reading and writing in content area Provide reference support for children during their reading and writing Promote independence on the part of young students as they work with words Provide a visual map to help children remember connections between words and the characteristics that will help them form categories Develop a growing core of words that become part of their vocabulary Important Notice A Mathematics Word Wall must be present in every mathematics classroom. Math Word Wall Create a math word wall Place math words on your current word wall but highlight them in some way.

29 SETUP OF THE MATHEMATICS CLASSROOM I. Prerequisites for a Mathematics Classroom Teacher Schedule Class List Seating Chart Code of Conduct / Discipline Grade Level Common Core Learning Standards (CCLS) Updated Mathematics Student Work Mathematics Grading Policy Mathematics Diagrams, Charts, Posters, etc. Grade Level Number Line Grade Level Mathematics Word Wall Mathematics Portfolios Mathematics Center with Manipulatives (Grades K - 12) II. III. Updated Student Work A section of the classroom must display recent student work. This can be of any type of assessment, graphic organizer, and writing activity. Teacher feedback must be included on student s work. Board Set-Up Every day, teachers must display the Lesson # and Title, Objective(s), Common Core Learning Standard(s), Opening Exercise and Homework. At the start of the class, students are to copy this information and immediately begin on the Fluency Activity or Opening Exercise. Student s Name: Teacher s Name: School: Date: Lesson # and Title: Objective(s) CCLS: Opening Exercise: IV. Spiraling Homework Homework is used to reinforce daily learning objectives. The secondary purpose of homework is to reinforce objectives learned earlier in the year. The assessments are cumulative, spiraling homework requires students to review coursework throughout the year. 29

30 SECONDARY MATHEMATICS GRADING POLICY This course of study includes different components, each of which are assigned the following percentages to comprise a final grade. I want you--the student--to understand that your grades are not something that I give you, but rather, a reflection of the work that you give to me. COMPONENTS 1. Common Assessments 35% 2. Quizzes 20% 3. Homework 20% 4. Notebook and/or Journal 10% 5. Classwork / Class Participation 15% o Class participation will play a significant part in the determination of your grade. Class participation will include the following: attendance, punctuality to class, contributions to the instructional process, effort, contributions during small group activities and attentiveness in class. Important Notice As per MVCSD Board Resolution 06-71, the Parent Notification Policy states Parent(s) / guardian(s) or adult students are to be notified, in writing, at any time during a grading period when it is apparent - that the student may fail or is performing unsatisfactorily in any course or grade level. Parent(s) / guardian(s) are also to be notified, in writing, at any time during the grading period when it becomes evident that the student's conduct or effort grades are unsatisfactory. 30

31 SAMPLE NOTEBOOK SCORING RUBRIC Student Name: Teacher Name: Criteria Points Completion of Required Sections All required sections are complete. One required section is missing. Two or three required sections are missing. More than three required sections are missing. Missing Sections No sections of the notebook are missing. One sections of the notebook is missing. Two sections of the notebook are missing. Three or more sections of the notebook are missing. Headers / Footers No required header(s) and/or footer(s) are missing within notebook. One or two required header(s) and/or footer(s) are missing within notebook. Three or four required header(s) and/or footer(s) are missing within notebook. More than four required header(s) and/or footer(s) are missing within notebook. Organization All assignment and/or notes are kept in a logical or numerical sequence. One or two assignments and/or notes are not in a logical or numerical sequence. Three or Four assignments and/or notes are not in a logical or numerical sequence. More than four assignments and/or notes are not in a logical or numerical sequence. Neatness Overall notebook is kept very neat. Overall notebook is kept in a satisfactory condition. Overall notebook is kept in a below satisfactory condition. Overall notebook is unkept and very disorganized. Total Teacher s Comments: 31