West Iron County Middle School Curriculum Map

Transcription

1 West Iron County Middle School Curriculum Map Mathematics Grade 7 Accelerated Updated Based on the State Standards

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3 Preface This curriculum map is aligned to the State Standards as defined in 2018 for mathematics. The timeline presented for each unit is meant to aid in estimating and defining the relative pacing and sequencing of the course. It is not imperative that it be followed literally. The following is the breakdown, by term, of the units in Math 7 Accelerated: TERM 1 Unit I Rational Numbers and Exponents 9 weeks (It is advisable to split this unit up into two smaller units: Topics 1 to 3 & Topics 4 to 6.) TERM 2 Unit II Proportionality and Linear Relationships (It is advisable to split this unit up into two smaller units: Topics 7 to 9 & Topics 10 to 14. Topic 14 may be skipped if time doesn t allow for it to be completed during Term 2.) 8 weeks 1 st Semester Exam, Project, Enrichment, etc.: Rational Numbers, Exponents, Proportionality, Equations, Inequalities TERM 3 Unit IV Creating, Comparing, and Analyzing Geometric Figures 9 weeks (Topics 23 & 24 may be skipped if time doesn t allow for them to be completed during Term 3.) TERM 4 Unit III Introduction to Sampling and Inference 8 weeks 2 nd Semester Exam, Project, Enrichment, etc.: Linear Relationships, Inequalities, Statistics, Probability, Angles, Circles Daily instructional tools, materials, and methods: v Pearson Interactive Middle School Math Program v Interactive notebook v Smart Board or similar touch display (as available) v Chromebooks (as available) v Class discussion and practice v Small-group discussion and practice v Scientific calculators v Classroom website containing online resources, such as Khan Academy and Moby Max (as available) v Supplementary material provided by digital curriculums (in Google Drive) Periodic assessment and progress monitoring: v Independent practice v Unit pretests v Unit posttests v Topic tests v NWEA progress monitoring assessments v Tier II Strategic intervention (as available) v Tier III Intensive intervention (as available)

4 Standards for Mathematical Practice These mathematical practices should be integrated into daily lessons as applicable: CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, Does this make sense? They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. CCSS.Math.Practice.MP2 Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. CCSS.Math.Practice.MP3 Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and if there is a flaw in an argument explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. CCSS.Math.Practice.MP4 Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

5 CCSS.Math.Practice.MP5 Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. CCSS.Math.Practice.MP6 Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. CCSS.Math.Practice.MP7 Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 8 equals the well-remembered , in preparation for learning about the distributive property. In the expression x 2 + 9x + 14, older students can see the 14 as 2 7 and the 9 as They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 3(x y) 2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. CCSS.Math.Practice.MP8 Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y 2)/(x 1) = 3. Noticing the regularity in the way terms cancel when expanding (x 1)(x + 1), (x 1)(x 2 + x + 1), and (x 1)(x 3 + x 2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.

6 Unit I Pretest & Readiness Assessment TOPIC 1 ADDING AND SUBTRACTING RATIONAL NUMBERS The Curriculum Map UNIT I: RATIONAL NUMBERS AND EXPONENTS 1-1: Rational Numbers, Opposites, and Absolute Value 7.NS.1.a When is it helpful to use a number s opposite? 1-2: Adding Integers 7.NS.1.b What does it mean to add less than nothing to something? 1-3: Adding Rational Numbers 7.NS.1.b.d How is adding rational numbers different than adding whole numbers? 1-4: Subtracting Integers 7.NS.1.c What does it mean to subtract less than nothing from something? 1-5: Subtracting Rational Numbers 1-6: Distance on a Number Line 7.NS.1.b 7.NS.1.c How is subtracting rational numbers different than subtracting whole numbers? In what situations does the order in which you subtract two numbers not matter? - I can apply and extend previous understandings of rational numbers, including opposites and absolute value as a distance from zero. - I can describe situations in which opposite quantities combine to make 0. - I can apply and extend previous understandings of addition and subtraction to add and subtract rational numbers. - I can use absolute value understanding to find 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. - I can recognize additive inverses as pairs of numbers that have a sum of 0. - I can use absolute value understanding to find 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. - I can apply properties of operations as strategies to add and subtract rational numbers. - I can use horizontal or vertical number line diagrams to represent addition and subtraction. - I can solve subtraction problems involving rational numbers by adding the additive inverse, p q = p + ( q). - I can apply and extend previous understandings of addition and subtraction to add and subtract rational numbers. - I can use horizontal or vertical number line diagrams to represent addition and subtraction. - I can find the distance between two rational numbers on the number line using the absolute value of their difference, and apply this principle in real-world contexts. - absolute value - Addition Property of Equality - additive inverse - algebraic expression - cube root - equation - evaluate an algebraic expression - exponent - exponential notation - integers - inverse operation - like terms - linear equation in one variable - long division - Multiplication Property of Equality - multiplicative inverses - natural numbers - negative numbers - opposite numbers -perfect square -positive numbers -radical - rational numbers - repeating decimal - scientific notation - significant - solution - solve - square root - terminating decimal - variable - zero pair Additional I Can statement for Topic 1: - I can interpret sums of rational numbers by describing real-world contexts.

7 TOPIC 2 MULTIPLYING AND DIVIDING RATIONAL NUMBERS 2-1: Multiplying Integers 7.NS.2.a.c How does knowing how to add positive and negative integers help you multiply positive and negative integers? How do properties of addition and multiplication help you multiply positive and negative integers? 2-2: Multiplying Rational Numbers 7.NS.2.a How is multiplying rational numbers like multiplying fractions and multiplying decimals? How is it different? 2-3: Dividing Integers 7.NS.2.b How does the relationship between multiplication and division help you divide integers? What does division of integers not have meaning and why? 2-4: Dividing Rational Numbers 2-5: Operations with Rational Numbers 7.NS.2.b 7.NS.2.c, 7.NS.3 How does the relationship between multiplication and division help you divide rational numbers? In a problem involving more than one operation with rational numbers, how do you decide the order in which to carry out the operations? - I can apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers. - I can 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 number. - I can apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers. - I can 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 number. - I can apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers. - I can 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. - I can understand that if p and q are integers, then (p/q) = ( p)/q = p/( q). - I can apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers. - I can apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers. - I can solve real-world and mathematical problems involving the four operations with rational numbers. - absolute value - Addition Property of Equality - additive inverse - algebraic expression - cube root - equation - evaluate an algebraic expression - exponent - exponential notation - integers - inverse operation - like terms - linear equation in one variable - long division - Multiplication Property of Equality - multiplicative inverses - natural numbers - negative numbers - opposite numbers -perfect square -positive numbers -radical - rational numbers - repeating decimal - scientific notation - significant - solution - solve - square root - terminating decimal - variable - zero pair Additional I Can statements for Topic 5: - I can interpret products and quotients of rational numbers by describing real-world contexts. - I can apply properties of operations as strategies to multiply and divide rational numbers.

8 TOPIC 3 DECIMALS AND PERCENTS Common Core State Standard(s) 3-1: Repeating Decimals 7.NS.2.b When is it helpful to be able to write fractions as decimals? Why is it helpful to show that a decimal repeats? 3-2: Terminating Decimals 7.NS.2.b When is it helpful to be able to write fractions as decimals? How is a fraction written as a terminating decimal different from a fraction written as a repeating decimal? 3-3: Percents Greater Than NS.3 What does it mean to have more than 100% of something? 3-4: Percents Less Than 1 7.NS.3 What does it mean to have a fractional percent of something? 3-5: Fractions, Decimals, and Percents 7.NS.2.b, 7.NS.3 Why are there different representations of rational numbers? 3-6: Percent Error 7.RP.3 How are percents helpful to describe and understand variability in data? - I can 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. - I can convert a rational number to a decimal using long division. - I can recognize that the decimal form of a rational number terminates in 0s or eventually repeats. - I can convert a rational number to a decimal using long division. - I can recognize that the decimal form of a rational number terminates in 0s or eventually repeats. - I can apply and extend previous understandings of fractions, decimals, and percents to use them interchangeably to solve real-world and mathematical problems. - I can convert a rational number to a decimal using long division. - I can apply and extend previous understandings of fractions, decimals, and percents to use them interchangeably to solve real-world and mathematical problems. - I can use proportional relationships to solve multistep ratio and percent problems involving percent error. - absolute value - Addition Property of Equality - additive inverse - algebraic expression - cube root - equation - evaluate an algebraic expression - exponent - exponential notation - integers - inverse operation - like terms - linear equation in one variable - long division - Multiplication Property of Equality - multiplicative inverses - natural numbers - negative numbers - opposite numbers -perfect square -positive numbers -radical - rational numbers - repeating decimal - scientific notation - significant - solution - solve - square root - terminating decimal - variable - zero pair

9 TOPIC 4 RATIONAL AND IRRATIONAL NUMBERS 4-1: Expressing Rational Numbers with Decimal Expansions 4-2: Exploring Irrational Numbers 4-3: Approximating Irrational Numbers 4-4: Comparing and Ordering Rational and Irrational Numbers 8.NS.1 8.NS.1 8.NS.2 8.NS.2 What does being able to express numbers in equivalent forms allow you to do? What is the difference between an irrational number and a rational number? Can a number be both irrational and rational? How do you estimate an irrational number? Why might you need to be able to estimate an irrational number? How can you compare rational and irrational numbers? Why might you want to? - I can express rational numbers using decimal expressions that terminate in 0s or eventually repeat. - I can describe irrational numbers. - I can estimate the value of irrational numbers. - I can use rational approximations of irrational numbers to compare the size of irrational numbers and locate them approximately on a number line diagram. - absolute value - Addition Property of Equality - additive inverse - algebraic expression - cube root - equation - evaluate an algebraic expression - exponent - exponential notation - integers - inverse operation - like terms - linear equation in one variable - long division - Multiplication Property of Equality - multiplicative inverses - natural numbers - negative numbers - opposite numbers -perfect square -positive numbers -radical - rational numbers - repeating decimal - scientific notation - significant - solution - solve - square root - terminating decimal - variable - zero pair

10 TOPIC 5 INTEGER EXPONENTS 5-1: Perfect Squares, Square Roots, and Equations of the form x 2 = p 5-2: Perfect Cubes, Cube Roots, and Equations of the form x 3 = p 5-3: Exponents and Multiplication 8.EE.2 8.EE.2 8.EE.1 How can you apply what you know about squares and square roots to write and solve equations of the form x 2 = p? How can you use equations in that form? How is solving an equation that includes cubes similar to solving an equation that includes squares? How is it different? How can you apply what you know about multiplying numerical expressions to multiplying algebraic expressions containing exponents? 5-4: Exponents and Division 8.EE.1 How can you apply what you know about dividing numerical expressions to dividing algebraic expressions containing exponents? 5-5: Zero and Negative Exponents 8.EE.1 When do you need an exponent that is equal to zero? When do you need an exponent that is negative? What makes these exponents useful? - I can use square root and cube root symbols to represent solutions to equations of the form x 2 = p and x 3 = p, where p is a positive rational number. Know that the square root of 2 is irrational. - I can evaluate square roots of small perfect squares. - I can use square root and cube root symbols to represent solutions to equations of the form x 2 = p and x 3 = p, where p is a positive rational number. Know that the square root of 2 is irrational. - I can evaluate cube roots of small perfect cubes. - I can know and apply the properties of integer exponents to generate equivalent numerical expressions. - absolute value - Addition Property of Equality - additive inverse - algebraic expression - cube root - equation - evaluate an algebraic expression - exponent - exponential notation - integers - inverse operation - like terms - linear equation in one variable - long division - Multiplication Property of Equality - multiplicative inverses - natural numbers - negative numbers - opposite numbers -perfect square -positive numbers -radical - rational numbers - repeating decimal - scientific notation - significant - solution - solve - square root - terminating decimal - variable - zero pair

11 TOPIC 6 SCIENTIFIC NOTATION 6-1: Exploring Scientific Notation 6-2: Using Scientific Notation to Describe Very Large Quantities 6-3: Using Scientific Notation to Describe Very Small Quantities 6-4: Operating with Numbers Expressed in Scientific Notation 8.EE.3, 8.EE.4 Why might you use powers of 10 to write numbers? 8.EE.3 How can positive powers of 10 make large and small numbers easier to write and compare? 8.EE.3 How can negative powers of 10 make small numbers easier to write and compare? 8.EE.3, 8.EE.4 How can you apply what you know about multiplying and dividing expressions with exponents to operations with numbers in scientific notation? - I can use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities. - I can interpret scientific notation that has been generated by technology. - I can recognize numbers that are expressed in scientific notation and understand how multiplying by a power of 10 affects the values of numbers. - I can recognize numbers that are expressed in scientific notation and understand how multiplying by a power of 10 affects the values of numbers. - I can use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities and to express how many times as much one is than the other. - I can rewrite very large or very small numbers in scientific notation. - I can rewrite very large or very small numbers in standard form. - I can use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities. - I can perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. - absolute value - Addition Property of Equality - additive inverse - algebraic expression - cube root - equation - evaluate an algebraic expression - exponent - exponential notation - integers - inverse operation - like terms - linear equation in one variable - long division - Multiplication Property of Equality - multiplicative inverses - natural numbers - negative numbers - opposite numbers -perfect square -positive numbers -radical - rational numbers - repeating decimal - scientific notation - significant - solution - solve - square root - terminating decimal - variable - zero pair Unit 1 Posttest

12 Unit II Pretest & Readiness Assessment TOPIC 7 RATIOS AND RATES UNIT II: PROPORTIONALITY AND LINEAR RELATIONSHIPS 7-1: Equivalent Ratios 7.RP.1 What does it mean if two different ratios describe the same situation? How can being able to describe the situation in multiple ways help you to solve problems? 7-2: Unit Rates 7.RP.1 How can you identify a rate? How can unit rates help you to solve problems? 7-3: Ratios with Fractions 7.RP.1 How can you write a ratio if at least one term is a fraction? How is this different from writing a ratio where both the terms are whole numbers? 7-4: Unit Rates with 7.RP.1 How can you write a unit rate if Fractions at least one term is a fraction? How is this different from writing a unit rate where both terms are whole numbers? - I can apply and extend previous understandings of equivalent ratios. - I can apply unit rates to solve a problem. - I can apply and extend previous understandings of equivalent ratios. - I can compute unit rates associated with ratios of fractions. - constant of proportionality - equivalent fractions - fraction - intersecting lines - multiplicative inverse - origin - percent rate of change - proportion - proportional relationships - ratio - scale factor - similar figures - simultaneous equations - slope - system of linear equations - unit rate

13 TOPIC 8 PROPORTIONAL RELATIONSHIPS 8-1: Proportional Relationships and Tables 8-2: Proportional Relationships and Graphs 8-3: Constant of Proportionality 8-4: Proportional Relationships and Equations 8-5: Maps and Scale Drawings 7.RP.2.a 7.RP.2.a.d 7.RP.2.b.d 7.RP.2.c 7.G.1 What does it mean for two quantities to have a proportional relationship? How can you tell if a table shows a proportional relationship between two quantities? How can you tell if a graph shows a proportional relationship between two quantities? What is a constant of proportionality? What does the constant of proportionality tell you? How can you tell if an equation shows a proportional relationship between two quantities? How can you identify the constant of proportionality in an equation that represents a proportional relationship? How can you use proportional relationships to solve problems that involve maps and scale drawings? - I can decide whether two quantities are in a proportional relationship by testing for equivalent ratios in a table. - I can recognize and represent proportional relationships between quantities. - I can decide whether two quantities are in a proportional relationship by graphing on a coordinate plane and observing whether the graph is a straight line through the origin. - I can 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. - I can identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams and verbal descriptions of proportional relationships. - I can identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams and verbal descriptions of proportional relationships. - I can represent proportional relationships by equations. - I can solve problems involving scale drawings of geometric figures. - constant of proportionality - equivalent fractions - fraction - intersecting lines - multiplicative inverse - origin - percent rate of change - proportion - proportional relationships - ratio - scale factor - similar figures - simultaneous equations - slope - system of linear equations - unit rate

14 TOPIC 9 PERCENTS 9-1: The Percent Equation 7.RP.2.b.c How do percents and the percent equation help describe things in the real world? 9-2: Using the Percent Equation 7.RP.2, 7.RP.3 In what situations are fixed numbers better than percents of an amount? In what situations are percents better than fixed numbers? 9-3: Simple Interest 7.RP.2, 7.RP.3 Why is simple interest called simple? When would you use simple interest? 9-5: Percent Increase and Decrease 9-6: Markups and Markdowns 7.RP.2, 7.RP.3 7.RP.2, 7.RP.3 How can you use a percent to represent change? When are percent markups and percent markdowns used? How are they similar? How are they different? - I can identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams and verbal descriptions of proportional relationships. - I can represent proportional relationships by equations. - I can recognize and represent proportional relationships between quantities. - I can use proportional relationships to solve multi-step ratio and percent problems involving taxes and gratuities. - I can use proportional relationships to solve multi-step ratio and percent problems involving commissions & fees. - I can recognize and represent proportional relationships between quantities. - I can use proportional relationships to solve multi-step ratio and percent problems involving taxes and gratuities. - I can use proportional relationships to solve multi-step ratio and percent problems involving commissions and fees. - I can recognize and represent proportional relationships between quantities. - I can use proportional relationships to solve multi-step ratio and percent problem involving simple interest. - I can recognize and represent proportional relationships between quantities. - I can use proportional relationships to solve multi-step ratio and percent problems involving percent increase and decrease. - I can use proportional relationships to solve multi-step ratio and percent problems involving markups and markdowns. - constant of proportionality - equivalent fractions - fraction - intersecting lines - multiplicative inverse - origin - percent rate of change - proportion - proportional relationships - ratio - scale factor - similar figures - simultaneous equations - slope - system of linear equations - unit rate

15 TOPIC 10 EQUIVALENT EXPRESSIONS 10-1: Expanding Algebraic Expressions 10-2: Factoring Algebraic Expressions 10-3: Adding Algebraic Expressions 10-4: Subtracting Algebraic Expressions 7.EE.1, 7.EE.2 7.EE.1, 7.EE.2 7.EE.1, 7.EE.2 7.EE.1, 7.EE.2 When would you want to expand an algebraic expression? How does a common factor help you rewrite an algebraic expression? When would you want to add algebraic expressions? How do properties of operations help you add expressions? When would you want to subtract algebraic expressions? How do properties of operations help you subtract expressions? - I can apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. - I can 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. - constant of proportionality - equivalent fractions - fraction - intersecting lines - multiplicative inverse - origin - percent rate of change - proportion - proportional relationships - ratio - scale factor - similar figures - simultaneous equations - slope - system of linear equations - unit rate

16 TOPICS 11 & 12 LINEAR EQUATIONS IN ONE VARIABLE 11-2: Writing Two-Step Equations 11-3: Solving Two-Step Equations 12-2: Solving Equations with Variables on Both Sides 12-3: Solving Equations Using the Distributive Property 12-4: Solutions One, None, or Infinitely Many 7.EE.4.a 7.EE.3, 7.EE.4.a 8.EE.7.b 8.EE.7.b 8.EE.7.a What kinds of problems call for two operations? How is solving a two-step equation similar to solving a onestep equation? Why do some equations have the same variable on both sides? How can you model a problem with an equation that uses the Distributive Property? What does it mean if an equation is simplified to 0 = 0? Do all problems have exactly one solution? - I can use variables to represent quantities in a real-world or mathematical problem, and construct simple equations to solve problems by reasoning about the quantities. - I can 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. - I can solve word problems leading to equations of the form px + q = r, where p, q, and r are specific rational numbers. Solve equations of this form fluently. - I can solve linear equations in one variable. - I can solve linear equations with rational number coefficients, including equations whose solutions require collecting like terms. - I can solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. - I can solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property. - I can transform linear equations in one variable into simpler forms until an equivalent equation with one solution (x = a), infinitely many solutions (a = a), or no solution (a = b) results. - constant of proportionality - equivalent fractions - fraction - intersecting lines - multiplicative inverse - origin - percent rate of change - proportion - proportional relationships - ratio - scale factor - similar figures - simultaneous equations - slope - system of linear equations - unit rate

17 TOPIC 13 INEQUALITIES 13-1: Solving Inequalities Using Addition or Subtraction 13-2: Solving Inequalities Using Multiplication or Division 13-3: Solving Two-Step Inequalities 13-4: Solving Multi-Step Inequalities 7.EE.4.b 7.EE.4.b 7.EE.4.b 7.EE.4.b How is the solution to an inequality different from the solution to an equation? What role does the concept of balance play when you solve inequalities? What kinds of problems call for two operations? How is it possible for two different inequalities to describe the same situation? What does it mean for two inequalities to be equivalent? - I can use variables to represent quantities in a real-world or mathematical problem, and construct simple inequalities to solve problems by reasoning about the quantities. - I can graph the solution set of the inequality and interpret it in the context of the problem. - I can use variables to represent quantities in a real-world or mathematical problem, and construct simple inequalities to solve problems by reasoning about the quantities. - I can use variables to represent quantities in a real-world or mathematical problem, and construct simple inequalities to solve problems by reasoning about the quantities. - I can 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, and graph the solution set of the inequality and interpret it in the context of the problem. - I can 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. - constant of proportionality - equivalent fractions - fraction - intersecting lines - multiplicative inverse - origin - percent rate of change - proportion - proportional relationships - ratio - scale factor - similar figures - simultaneous equations - slope - system of linear equations - unit rate

18 TOPIC 14 PROPORTIONAL RELATIONSHIPS, LINES, AND LINEAR EQUATIONS 14-1: Graphing Proportional Relationships 14-2: Linear Equations: y = mx 8.EE.5 8.EE.5, 8.EE.6 What does the graph of a proportional relationship look like? When and how can a graph of a proportional relationship be helpful? What does it mean for an equation to be linear? What kind of relationship can be modeled by equations in the form y = mx? 14-3: The Slope of a Line 8.EE.5 What does the slope of a line tell you about the line? 14-4: Unit Rate and Slope 8.EE.5 How are unit rates and slope related? 14-5: The y-intercept of a Line 8.EE.6 What is the y-intercept of a graph? What does the y- intercept tell you about the equation being graphed? - I can graph proportional relationships, interpreting the unit rate as the slope of the graph. - I can define the equation y = mx for a line through the origin. - I can compare two different proportional relationships represented in different ways. - I can graph proportional relationships, interpreting the unit rate as the slope of the graph. - I can graph proportional relationships, interpreting the unit rate as the slope of the graph. - I can compare two different proportional relationships represented in different ways. - I can define the equation y = mx + b for a line intercepting the vertical axis at b. - constant of proportionality - equivalent fractions - fraction - intersecting lines - multiplicative inverse - origin - percent rate of change - proportion - proportional relationships - ratio - scale factor - similar figures - simultaneous equations - slope - system of linear equations - unit rate 14-6: Linear Equations: y = mx + b 8.EE.6 How are equations in the form y = mx similar to equations in the form y = mx + b? How do you know when to use each? Unit II Posttest

19 Unit III Pretest & Readiness Assessment TOPIC 15 SAMPLING UNIT III: INTRODUCTION TO SAMPLING AND INFERENCE 15-1: Populations and Samples 15-2: Estimating a Population 15-3: Convenience Sampling 7.SP.1 7.SP.1, 7.SP.2 7.SP.1 When is it reasonable to use a small group to represent a larger group? When is it not reasonable? When can you use a small group to estimate things about a larger group? How do you sample in a way that is convenient? What are the advantages and disadvantages of convenience sampling? 15-4: Systematic Sampling 7.SP.1 How do you sample systematically? What are the advantages and disadvantages of systematic sampling? 15-5: Simple Random Sampling 15-6: Comparing Sampling Methods 7.SP.1, 7.SP.2 7.SP.1 How do you sample randomly? What are the advantages and disadvantages of simple random sampling? For what situations is each type of sampling most effective? - I can understand that statistics can be used to gain information about a population by examining a sample of the population. - I can understand that generalizations about a population from a sample are valid only if the sample is representative of that population. - I can use data from a random sample to draw inferences about a population with an unknown characteristic of interest. - I can generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. - I can understand that statistics can be used to gain information about a population by examining a sample of the population. - I can understand that generalizations about a population from a sample are valid only if the sample is representative of that population. - I can use data from a random sample to draw inferences about a population with an unknown characteristic of interest. - I can understand that statistics can be used to gain information about a population by examining a sample of the population. - I can understand that generalizations about a population from a sample are valid only if the sample is representative of that population. - population - sample of a population - bias - inference - mean - median - range - quartiles - interquartile range - box plot - frequency - grouped frequency table - histogram - maximum value - mean absolute deviation - measures of center - measure of spread - minimum value - mutually exclusive - sampling

20 TOPIC 16 COMPARING TWO POPULATIONS 16-1: Statistical Measures 7.SP.1, 7.SP.4 What can you do to make data more useful? How does what you are looking for determine how data are best used and represented? 16-2: Multiple Populations and Inferences 16-3: Using Measures of Center 16-4: Using Measures of Variability 16-5: Exploring Overlap in Data Sets 7.SP.1, 7.SP.3, 7.SP.4 7.SP.4 7.SP.4 7.SP.3, 7.SP.4 When does a group represent one population? When does it represent more than one population? How can you tell? How can you compare two groups using a single number from each group? How else can you compare two groups using a single number from each group? How do measures of center and variability help you determine how much two groups have in common? - I can understand that statistics can be used to gain information about a population by examining a sample of the population. - I can use measures of center and measures of variability for numerical data from random samples. - I can understand that statistics can be used to gain information about a population by examining a sample of the population. - I can use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. - I can differentiate between single and multiple populations. - I can use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. - I can 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. - I can use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. - population - sample of a population - bias - inference - mean - median - range - quartiles - interquartile range - box plot - frequency - grouped frequency table - histogram - maximum value - mean absolute deviation - measures of center - measure of spread - minimum value - mutually exclusive - sampling

21 TOPIC 17 PROBABILITY CONCEPTS 17-1: Likelihood and Probability 7.SP.5, 7.SP.6 What are effective ways to describe the likelihood of an event? 17-2: Sample Spaces 7.SP.7 What is the difference between an action and an event? 17-3: Relative Frequency 7.SP.6 In what situations is conducting and Experimental an experiment a good way to Probability determine the probability of an event? How can you evaluate the reasonableness of an 17-4: Theoretical Probability 7.SP.7.a experimental probability? How do you tell the difference between a theoretical and an experimental probability? 17-5: Probability Models 7.SP.7.a How do you choose the best type of probability model for a situation? - I can identify the probability of a chance event using a number between 0 and 1 to express the likelihood of the event occurring. - I can 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. - I can develop a probability model and use it to find probabilities of events. - I can 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. - I can develop a probability model and use it to find probabilities of events. - I can compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. - I can develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. - I can develop a probability model and use it to find probabilities of events. - I can develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. - I can develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. - probability of an event - action - outcome - sample space - event - trial - relative frequency - experimental probability - theoretical probability - simulation - probability model - uniform probability model - compound event - independent events - dependent events - The Counting Principle

22 TOPIC 18 COMPOUND EVENTS 18-1: Compound Events 7.SP.8.b What makes an event a compound event? What are the different types of compound events? 18-2: Sample Spaces of 7.SP.8.b How do you know a sample space Compound Events is complete? How do you know when you have accounted for all 18-3: Finding Compound Probabilities Using Organized Lists 18-4: Finding Compound Probabilities Using Tables 18-5: Finding Compound Probabilities Using Tree Diagrams 18-6: Finding Probabilities Using Simulation Unit III Posttest 7.SP.8.a.b 7.SP.6, 7.SP.8.a 7.SP.8.c 7.EE.3, 7.SP.8 possibilities? How is the number of outcomes of a multi-step process related to the number of outcomes for each step? In what situation should you use an organized list, a table, or a tree diagram to find the probability of a compound event? How can you use random numbers to simulate real-world situations? In what situations should you use a simulation to find the probability of a compound event? - I can represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. - I can represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. - I can 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. - I can identify the outcomes in a sample space that compose a compound event described in everyday language. - I can 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. - I can find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. - I can 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. - I can design and use a simulation to generate frequencies for compound events. - I can find probabilities of compound events using simulation. - probability of an event - action - outcome - sample space - event - trial - relative frequency - experimental probability - theoretical probability - simulation - probability model - uniform probability model - compound event - independent events - dependent events - The Counting Principle

23 UNIT IV: CREATING, COMPARING, AND ANAYLYZING GEOMETRIC FIGURES Unit IV Pretest & Readiness Assessment TOPIC 19 ANGLES 19-1: Measuring Angles 7.EE.4.a, 7.G.2 All angles are formed by two rays. What makes angles different from each other? 19-2: Adjacent Angles 7.EE.4.a, 7.G.2, 7.G.5 A whole is the sum of its parts. How can you apply this idea to angles? 19-3: Complementary Angles 19-4: Supplementary Angles 7.EE.4.a, 7.G.2, 7.G.5 7.EE.4.a, 7.G.2, 7.G.5 What do you know about the measures of two angles that form a right angle? What do you know about the measures of two angles that form a straight angle? 19-5: Vertical Angles 7.EE.4.a, 7.G.2, 7.G.5 Two intersecting lines form angles. How can you describe the relationship between the angles that are opposite each other? - I can name parts of a geometric figure using appropriate letters and symbols. - I can measure parts of geometric figures using the appropriate tools and units of measure. - I can use variables to represent quantities in a real-world or mathematical problem and construct simple equations to solve problems by reasoning about the quantities. - I can name parts of a geometric figure using appropriate letters and symbols. - I can use facts about adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. - I can use facts about complementary angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. - I can draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. - I can use facts about supplementary angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. - I can draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. - I can name parts of a geometric figure using appropriate letters and symbols - I can use facts about vertical angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. - angle - vertex of an angle - right angle - obtuse angle - acute angle - straight angle - adjacent angles - complementary angles - supplementary angles - vertical angles