Classworks Common Core Transition Guide. Georgia 7th Grade Mathematics

Transcription

1 Classworks Common Core Transition Guide Georgia 7th Grade Mathematics OFFICIALLY ENDORSED

2 Classworks Common Core Transition Guide Teacher Support for Increasing Student Achievement With the increased rigor of the Common Core State Standards and the increased expectations of the College and Career Ready Practices, teachers are faced with meeting new challenges. The Classworks Common Core Transition Guide will assist you not only as you teach new skills and standards, but also as you add performance activities to the classroom and grade students on the ability to demonstrate college and career readiness. This guide provides two major resources: Performance-Based Projects with College and Career Readiness Rubrics Crosswalks aligning Classworks Units with the new standards Part One - Projects Classworks Projects provide the opportunity to tie real world applications to the skills you re teaching in the classroom. This guide includes up to ten projects that align to the Common Core State Standards and allows students to utilize collaboration, creativity, and problem solving to demonstrate mastery. These projects also include recommendations for using ipad and Android Tablet apps as research and creation tools, to help you integrate new technology into the classroom. Each project is easily graded using the College and Career Readiness Rubric, which are based on the College and Career Ready Practices. Rubrics are graded within Classworks, so you can track student performance throughout the school year. Part Two - Crosswalks This guide indicates key changes taking place in the transition from state standards to the Common Core. The Classworks Crosswalks will help you easily identify which grade level the standards were previously taught or if the standard is new. Each standard has Classworks units listed to help with concept introduction, practice, and review. Whether you need support for skills never before taught at your grade level, or need to add depth of knowledge and performance activities to an existing lesson plan, this Crosswalk will serve as the resource you need to create a College and Career Ready classroom. Send Us Feedback We appreciate all you are doing to help students prepare for a successful future and hope this guide provides the support needed to do so. Please send feedback to research@classworks.com. For additional information, please view the Common Core Resources user guide located in the Classworks Help Center. Curriculum Advantage 2013 As of March 2013

3 Applying Mathematical Practices with Classworks Projects

4 CC Standard Unit Code RP.7.2.a 1791 Linear Equations on the Coordinate Plane # Project Name Project Description Applying Mathematical Practices with Classworks Projects 7th Grade Students create a coordinate plane and use integers to graph linear equations on the coordinate plane. NS.7.2.c 1739 Rationalizations Students multiply and divide rational numbers. EE Numbers with Students evaluate the power of given Exponents numbers and chart the problem, base, exponent, and power. EE Concert Crowd Students write a review of a concert that includes variable expressions about the event and compares the written expressions to numerical ones. EE Finding the Least Common Multiple G Waterslides and More College and Career Ready Practices Students find a common denominator before adding or subtracting fractions. Students design water slides for a community park in their neighborhood. G Define the Angles Students demonstrate their understanding of acute, right, obtuse, and straight angles. G Wrap It Up Students create a presentation that gives tips for wrapping presents. SP Crossing the Students organize a table of raw data and Median calculate the mean, median, and mode. SP.7.8.b 1763 Earn Your Degree Ph.D. Curriculum Advantage 2012 Students convert percentage information into degrees and create circle graphs. Make sense of problems, persevere Reason abstractly & quant. Construct viable arguments Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Express regularity in repeated reasoning

5 Student: Teacher: Grade 7 Math CCR PRACTICES Score Makes sense of problems and perseveres in solving them Reasons abstractly and quantitatively Constructs viable arguments and critiques the reasoning of others Models with mathematics Uses appropriate tools strategically Attends to precision Looks for and makes use of structure Looks for and expresses regularity in repeated reasoning Unable to grasp the meaning of problems and does not know how to go about solving them. Unable to move beyond the concrete into more abstract relationships. Unable to build a logical argument or follow the arguments of others. Unable to use models to solve everyday problems. Not acquainted with tools or does not know how to use them appropriately. Is careless while working and is unable to communicate with clarity. Does not perceive patterns in nature or numbers. Is unable to mentally combine steps to find shortcuts in calculations. Masters skills Masters 25% of the skills from the activity but cannot apply them to other situations. May attempt to solve problems before thinking them through; does not persevere until finding a solution. Does not understand the relationships of the quantities in a problem and needs assistance to represent them symbolically. Needs assistance to follow a logical argument or construct reasoning; does not recognize faulty logic. Needs assistance to choose useful models and understand how they relate to the problem. Requires assistance to choose the most appropriate tools and use them properly. Has difficulty expressing reasoning and may provide only partial answers. Can recognize patterns when clearly pointed out; needs assistance to extend patterns. Does not notice repeated calculations but can learn shortcuts; may not be aware if results are unreasonable. Masters 50% of the skills from the activity but struggles to apply them to other situations. Has a general idea of how to solve a problem and with assistance can work through to find a solution. Sometimes uses the correct symbols and operations to represent a problem; may need assistance to manipulate the symbols. Can follow the steps in an argument but needs assistance constructing arguments. Understands how models represent situations in everyday life; may not interpret results in the context of the situation. Can select and use some tools, such as measurement tools, but needs help choosing and utilizing other tools. May arrive at correct answers but fails to provide sufficient explanation and/or appropriate degree of precision. Is aware of patterns in numbers and operations but does not recognize the implications of those patterns. May notice that calculations are repeated but does not independently discover shortcuts; sometimes fails to notice that results are unreasonable. Masters 75% of the skills from the activity and can apply them to other situations 50% of the time. Develops a plan for solving a problem and usually is able to evaluate the validity of solutions. Usually understands the meaning of the quantities in a problem and can represent and manipulate them symbolically. Usually analyzes situations accurately and constructs reasonable arguments; recognizes flaws in an argument but may not be able to correct them completely. Understands the relationship of the quantities in a problem and usually represents and solves them accurately with models. Usually knows the best tool to use in a given situation and how to use it; employs strategies like estimation to detect errors. Is able to define terms, express reasoning, and give appropriate answers but sometimes may lack sufficient detail. Recognizes structure and patterns in nature and numbers and is able to make some connections to more general principles. Recognizes repeated calculations and uses shortcuts to solve problems; usually checks the reasonableness of results. Masters 100% of the skills from the activity and can apply them to other situations 75% of the time. Uses a variety of strategies to gain insight into a problem; perseveres until finding a solution, continually ensuring that conclusions make sense. Comprehends the relationships in problem situations; can think abstractly to work with the symbols and is aware of what the symbols stand for. Builds rational arguments from given conditions and definitions; justifies conclusions and accurately evaluates the arguments of others. Perceives how to simplify a complicated situation using models; identifies the important quantities in a problem and analyzes their relationships, improving the model as necessary. Is acquainted with a wide variety of tools and makes sound decisions about which ones are most helpful in any situation; recognizes limitations of the tools and uses strategies to detect errors. Communicates reasoning process and provides complete answers with thorough explanations, correct units, and sufficient precision. Discerns structure and patterns and can apply them to solve problems and to draw conclusions about general principles. Discovers shortcuts and formulas for solving problems with repeated calculations; consistently checks work to make sure results are reasonable. Masters 100% of the skills from the activity and can demonstrate them 100% of the time in other situations. Copyright 2011 Classworks by Curriculum Advantage, Inc.

6 Common Core Crosswalks

7 Concept Intro Ratios and Proportional Relationships Analyze proportional relationships and use them to solve real world and mathematical problems. 1782: Finding Unit Rates 1 1 RP.7 RP.7.A RP.7.1 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 Ω/º miles per hour, equivalently 2 miles per hour. Practice Review RP.7.2 RP.7.2.a RP.7.2.b RP.7.2.c RP.7.2.d Recognize and represent proportional relationships between quantities. 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. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. 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. 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. 1781: Understanding Proportion : Finding Unit Rates : Understanding Proportion Curriculum Advantage

8 RP.7.3 Use proportional relationships to solve multistep ratio 1781: Understanding Proportion and percent problems. Examples: simple interest, tax, 1783: Skill Builder Determining markups and markdowns, gratuities and commissions, Percentages fees, percent increase and decrease, percent error. 1787: Using Percents 1784: Proportion and Percent NS.7 NS.7.A NS.7.1 Concept Practice Review Intro The Number System Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. 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. NS.7.1.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. 1749: Understanding Inverse Operations NS.7.1.b NS.7.1.c Understand p + q as the number located a distance q 1738: Adding and Subtracting Rational from p, in the positive or negative direction depending on Numbers whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). 1700: Skill Builder Determining Number Sequence Interpret sums of rational numbers by describing realworld contexts. Understand subtraction of rational numbers as adding the 1749: Understanding Inverse Operations 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. NS.7.1.d Apply properties of operations as strategies to add and subtract rational numbers. 1737: Skill Builder Properties of Rational Numbers 2 Curriculum Advantage

9 NS.7.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. NS.7.2.a Understand that multiplication is extended from fractions 1739: Multiplying and Dividing Rational to rational numbers by requiring that operations continue Numbers 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 realworld contexts. Concept Intro Practice Review NS.7.2.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. 1734: Multiplying and Dividing Integers NS.7.2.c NS.7.2.d NS.7.3 EE.7 EE.7.A EE.7.1 Apply properties of operations as strategies to multiply 1739: Multiplying and Dividing Rational and divide rational numbers. Numbers Convert a rational number to a decimal using long 1740: Skill Builder Converting Rational division; know that the decimal form of a rational number Numbers terminates in 0s or eventually repeats. Solve real world and mathematical problems involving the four operations with rational numbers. 1613: Skill Builder Using Operations to Solve Real world Problems 1746: Understanding Order of Operations Expressions and Equations Use properties of operations to generate equivalent expressions. Apply properties of operations as strategies to add, 1738: Adding and Subtracting Rational subtract, factor, and expand linear expressions with Numbers rational coefficients. 1746: Understanding Order of Operations Curriculum Advantage

10 EE.7.2 Understand that rewriting an expression in different 1748: Skill Builder Equivalent Numeric forms in a problem context can shed light on the problem Expressions 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 1.05." EE.7.B EE.7.3 Solve real life and mathematical problems using numerical and algebraic expressions and equations. Solve multi step real life and mathematical problems 1739: Multiplying and Dividing Rational posed with positive and negative rational numbers in any Numbers form (whole numbers, fractions, and decimals), using 1697: More Multi step Multiplication and tools strategically. Apply properties of operations to Division Problems 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. Concept Intro Practice 3 Review Curriculum Advantage

11 EE.7.4 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. EE.7.4.a Solve word problems leading to equations of the form px 1785: Writing an Equation + q = r and p(x + q) = r, where p, q, and r are specific 1751: Solving Equations Using rational numbers. Solve equations of these forms fluently. Multiplication and Division Compare an algebraic solution to an arithmetic solution, 1750: Skill Builder Solving Equations identifying the sequence of the operations used in each 1746: Understanding Order of Operations approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Concept Intro Practice Review EE.7.4.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. 1755: Graphing Inequalities on a Number Line 1 G.7 G.7.A G.7.1 Geometry Draw, construct, and describe geometrical figures and describe the relationships between them. 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. 1633: Introducing Scale Drawings Curriculum Advantage

12 G.7.2 Draw (freehand, with ruler and protractor, and with 1773: Skill Builder Angle Measurement technology) geometric shapes with given conditions. of Triangles Focus on constructing triangles from three measures of 1772: Measuring Angles angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Concept Practice Review Intro G.7.3 G.7.B G.7.4 G.7.5 Describe the two dimensional figures that result from slicing three dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. 1761: Introducing Nets 1769: Skill Builder Attributes of Threedimensional Figures 1762: Finding Surface Area Solve real life and mathematical problems involving angle measure, area, surface area, and volume. Know the formulas for the area and circumference of a 1777: Applying the Formula for the Area circle and use them to solve problems; give an informal of a Circle derivation of the relationship between the circumference 1774: More Finding Circumferences and area of a circle. 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 : Measuring Angles G.7.6 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. 1679: Applying the Formula for Volume 1762: Finding Surface Area 1776: Skill Builder Area of Triangles and Quadrilaterals 1778: Applying the Formula for the Area of Other Polygons 1779: Applying the Formula for the Volume of Cylinders Curriculum Advantage

13 SP.7 Statistics and Probability SP.7.A Use random sampling to draw inferences about a population. SP.7.1 Understand that statistics can be used to gain information 1719: Introducing Sampling and about a population by examining a sample of the Predicting population; generalizations about a population from a 1720: Introducing Surveys 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. Concept Intro Practice Review SP.7.2 SP.7.B SP.7.3 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. 1719: Introducing Sampling and Predicting 1720: Introducing Surveys Draw informal comparative inferences about two populations. Informally assess the degree of visual overlap of two 1725: Introducing Mean, Median, and numerical data distributions with similar variabilities, Mode 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 Curriculum Advantage

14 SP.7.4 Use measures of center and measures of variability for 1725: Introducing Mean, Median, and numerical data from random samples to draw informal Mode 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. Concept Practice Review Intro SP.7.C SP.7.5 SP.7.6 Investigate chance processes and develop, use, and evaluate probability models. Understand that the probability of a chance event is a 1797: Skill Builder Determining number between 0 and 1 that expresses the likelihood of Probability Results the event occurring. Larger numbers indicate greater 1796: Certain, Possible, and Impossible likelihood. A probability near 0 indicates an unlikely Events event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. Approximate the probability of a chance event by 1800: Introducing Fair and Unfair Games collecting data on the chance process that produces it and 1796: Certain, Possible, and Impossible observing its long run relative frequency, and predict the Events 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 Curriculum Advantage

15 SP.7.7 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. Concept Intro Practice Review SP.7.7.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. 1797: Skill Builder Determining Probability Results 3 SP.7.7.b SP.7.8 Develop a probability model (which may not be uniform) 1796: Certain, Possible, and Impossible by observing frequencies in data generated from a chance Events 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? Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation SP.7.8.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. 1797: Skill Builder Determining Probability Results 3 Curriculum Advantage

16 SP.7.8.b Represent sample spaces for compound events using 1693: Skill Builder Outcomes from Tree methods such as organized lists, tables and tree diagrams. Diagrams For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event. Concept Intro Practice 2 Review SP.7.8.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? 1724: Introducing Frequency Distributions 1 1 Curriculum Advantage