Mathematics Grade 7 Accelerated Updated 2017-2018€¦ · · 2018-03-31Mathematics Grade 7...

West Iron County

Middle School Curriculum Map

Mathematics Grade 7 Accelerated Updated 2017-2018

Based on the

Common Core State Standards

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Preface

This curriculum map is aligned to the Common Core State Standards as defined in 2017 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 (through Topic 4) 9 weeks TERM 2 Unit I Rational Numbers and Exponents (from Topic 5) 4 weeks

Unit II Proportionality and Linear Relationships (through Topic 8) 5 weeks 1st Semester Exam, Project, Enrichments, etc.: Rational Numbers, Exponents, Proportionality

TERM 3 Unit II Proportionality and Linear Relationships (from Topic 9) 9 weeks TERM 4 Unit II Proportionality and Linear Relationships (from Topic 14) 2 weeks

Unit III Introduction to Sampling and Inference 7 weeks 2nd Semester Exam, Project, Enrichments, etc.: Linear Relationships, Inequalities, Statistics, Probability, Angles, Circles

NOTE: Supplemental exploratory instruction for geometry, when available in grade 7, includes Unit IV (Topics 19 through 22). In the absence of this instruction, Unit IV would be included as part of the Math 7 Accelerated curriculum. The map would be updated to reflect this. Daily instructional tools, materials, and methods:

v Pearson digits Interactive Middle School Math Program v Interactive notebook v SMART Board (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)

Periodic assessment and progress monitoring:

v Independent practice v Unit pretests v Unit posttests v Topic tests v AIMSweb Computation / Concepts & Applications progress monitoring assessments v Tier II – Strategic intervention (Pearson digits, Teacher Created Materials) v Tier III – Intensive intervention (Pearson digits, Teacher Created Materials, additional web-based material)

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.

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 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. 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)(x2 + x + 1), and (x – 1)(x3 + x2 + 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.

The Curriculum Map

UNIT I: RATIONAL NUMBERS AND EXPONENTS Unit I Pretest & Readiness Assessment TOPIC 1 – ADDING AND SUBTRACTING RATIONAL NUMBERS

Lesson from Pearson digits

Common Core State Standard(s)

Focus Question(s) Objective(s)/ “I Can” Statement(s)

Key Vocabulary

1-1: Rational Numbers, Opposites, and Absolute Value

7.NS.1.a When is it helpful to use a number’s opposite?

- 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.

- 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 digits - 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.

1-2: Adding Integers 7.NS.1.b What does it mean to add less than nothing to something?

- 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.

1-3: Adding Rational Numbers

7.NS.1.b.d How is adding rational numbers different than adding whole 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 apply properties of operations as strategies to add and subtract rational numbers.

1-4: Subtracting Integers 7.NS.1.c What does it mean to subtract less than nothing from something?

- 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).

1-5: Subtracting Rational Numbers

7.NS.1.b How is subtracting rational numbers different than subtracting whole numbers?

- 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.

1-6: Distance on a Number Line

7.NS.1.c In what situations does the order in which you subtract two numbers not matter?

- 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.

TOPIC 2 – MULTIPLYING AND DIVIDING RATIONAL NUMBERS




Key Vocabulary

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?

- 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.

- 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 digits - 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.

2-2: Multiplying Rational Numbers

7.NS.2.a How is multiplying rational numbers like multiplying fractions and multiplying decimals? How is it different?

- 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.

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?

- 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).

2-4: Dividing Rational Numbers

7.NS.2.b How does the relationship between multiplication and division help you divide rational numbers?

- I can apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers.

2-5: Operations with Rational Numbers

7.NS.2.c, 7.NS.3 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 solve real-world and mathematical problems involving the four operations with rational numbers.

TOPIC 3 – DECIMALS AND PERCENTS


Common Core State

Standard(s)


Key Vocabulary

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?

- 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.


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?

- 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.

3-3: Percents Greater Than 100 7.NS.3 What does it mean to have more than 100% of something?

- I can apply and extend previous understandings of fractions, decimals, and percents to use them interchangeably to solve real-world and mathematical problems.

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?

- 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.

3-6: Percent Error 7.RP.3 How are percents helpful to describe and understand variability in data?

- I can use proportional relationships to solve multistep ratio and percent problems involving percent error.

TOPIC 4 – RATIONAL AND IRRATIONAL NUMBERS




Key Vocabulary

4-1: Expressing Rational Numbers with Decimal Expansions

8.NS.1 What does being able to express numbers in equivalent forms allow you to do?

- I can express rational numbers using decimal expressions that terminate in 0s or eventually repeat.


4-2: Exploring Irrational Numbers

8.NS.1 What is the difference between an irrational number and a rational number? Can a number be both irrational and rational?

- I can describe irrational numbers.

4-3: Approximating Irrational Numbers

8.NS.2 How do you estimate an irrational number? Why might you need to be able to estimate an irrational number?

- I can estimate the value of irrational numbers.

4-4: Comparing and Ordering Rational and Irrational Numbers

8.NS.2 How can you compare rational and irrational numbers? Why might you want to?

- I can use rational approximations of irrational numbers to compare the size of irrational numbers and locate them approximately on a number line diagram.

TOPIC 5 – INTEGER EXPONENTS




Key Vocabulary

5-1: Perfect Squares, Square Roots, and Equations of the form x2 = p

8.EE.2 How can you apply what you know about squares and square roots to write and solve equations of the form x2 = p? How can you use equations in that form?

- I can use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = 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.


5-2: Perfect Cubes, Cube Roots, and Equations of the form x3 = p

8.EE.2 How is solving an equation that includes cubes similar to solving an equation that includes squares? How is it different?

- I can use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = 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.

5-3: Exponents and Multiplication

8.EE.1 How can you apply what you know about multiplying numerical expressions to multiplying algebraic expressions containing exponents?

- I can know and apply the properties of integer exponents to generate equivalent numerical expressions.

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?

TOPIC 6 – SCIENTIFIC NOTATION




Key Vocabulary

6-1: Exploring Scientific Notation

8.EE.3, 8.EE.4 Why might you use powers of 10 to write 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. - 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.


6-2: Using Scientific Notation to Describe Very Large Quantities

8.EE.3 How can positive powers of 10 make large and small numbers easier to write and compare?

- 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.

6-3: Using Scientific Notation to Describe Very Small Quantities

8.EE.3 How can negative powers of 10 make small numbers easier to write and compare?

6-4: Operating with Numbers Expressed in Scientific Notation

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 perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used.

Unit 1 Posttest

UNIT II: PROPORTIONALITY AND LINEAR RELATIONSHIPS

Unit II Pretest & Readiness Assessment TOPIC 7 – RATIOS AND RATES




Key Vocabulary

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?

- I can apply and extend previous understandings of equivalent ratios.

- 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

7-2: Unit Rates 7.RP.1 How can you identify a rate? How can unit rates help you to solve problems?

- I can apply unit rates to solve a problem.

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?

- I can apply and extend previous understandings of equivalent ratios.

7-4: Unit Rates with Fractions

7.RP.1 How can you write a unit rate if at least one term is a fraction? How is this different from writing a unit rate where both terms are whole numbers?

- I can compute unit rates associated with ratios of fractions.

TOPIC 8 – PROPORTIONAL RELATIONSHIPS




Key Vocabulary

8-1: Proportional Relationships and Tables

7.RP.2.a 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?

- 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.


8-2: Proportional Relationships and Graphs

7.RP.2.a.d How can you tell if a graph shows a proportional relationship between two 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.

8-3: Constant of Proportionality

7.RP.2.b.d What is a constant of proportionality? What does the constant of proportionality tell you?

8-4: Proportional Relationships and Equations

7.RP.2.c 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?

- 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.

8-5: Maps and Scale Drawings

7.G.1 How can you use proportional relationships to solve problems that involve maps and scale drawings?

- I can solve problems involving scale drawings of geometric figures.

TOPIC 9 – PERCENTS




Key Vocabulary

9-1: The Percent Equation 7.RP.2.b.c How do percents and the percent equation help describe things in the real world?

- 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.


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?

- 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.

9-3: Simple Interest 7.RP.2, 7.RP.3 Why is simple interest called “simple”? When would you use simple interest?

- 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.

9-5: Percent Increase and Decrease

7.RP.2, 7.RP.3 How can you use a percent to represent change?

- 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.

9-6: Markups and Markdowns

7.RP.2, 7.RP.3 When are percent markups and percent markdowns used? How are they similar? How are they different?

- I can use proportional relationships to solve multi-step ratio and percent problems involving markups and markdowns.

TOPIC 10 – EQUIVALENT EXPRESSIONS




Key Vocabulary

10-1: Expanding Algebraic Expressions

7.EE.1, 7.EE.2 When would you want to expand an algebraic expression?

- 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.


10-2: Factoring Algebraic Expressions

7.EE.1, 7.EE.2 How does a common factor help you rewrite an algebraic expression?

10-3: Adding Algebraic Expressions

7.EE.1, 7.EE.2 When would you want to add algebraic expressions? How do properties of operations help you add expressions?

10-4: Subtracting Algebraic Expressions

7.EE.1, 7.EE.2 When would you want to subtract algebraic expressions? How do properties of operations help you subtract expressions?

TOPICS 11 & 12 – LINEAR EQUATIONS IN ONE VARIABLE




Key Vocabulary

11-2: Writing Two-Step Equations

7.EE.4.a What kinds of problems call for two operations?

- 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.


11-3: Solving Two-Step Equations

7.EE.3, 7.EE.4.a How is solving a two-step equation similar to solving a one-step equation?

- 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.

12-2: Solving Equations with Variables on Both Sides

8.EE.7.b Why do some equations have the same variable on both sides?

- 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.

12-3: Solving Equations Using the Distributive Property

8.EE.7.b How can you model a problem with an equation that uses the Distributive Property?

- 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.

12-4: Solutions – One, None, or Infinitely Many

8.EE.7.a What does it mean if an equation is simplified to 0 = 0? Do all problems have exactly one solution?

- 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.

TOPIC 13 – INEQUALITIES




Key Vocabulary

13-1: Solving Inequalities Using Addition or Subtraction

7.EE.4.b How is the solution to an inequality different from the solution to an equation?

- 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.


13-2: Solving Inequalities Using Multiplication or Division

7.EE.4.b What role does the concept of balance play when you solve inequalities?

- 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.

13-3: Solving Two-Step Inequalities

7.EE.4.b What kinds of problems call for two operations?

- 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.

13-4: Solving Multi-Step Inequalities

7.EE.4.b How is it possible for two different inequalities to describe the same situation? What does it mean for two inequalities to be equivalent?

TOPIC 14 – PROPORTIONAL RELATIONSHIPS, LINES, AND LINEAR EQUATIONS




Key Vocabulary

14-1: Graphing Proportional Relationships

8.EE.5 What does the graph of a proportional relationship look like? When and how can a graph of a proportional relationship be helpful?

- I can graph proportional relationships, interpreting the unit rate as the slope of the graph.


14-2: Linear Equations: y = mx

8.EE.5, 8.EE.6 What does it mean for an equation to be linear? What kind of relationship can be modeled by equations in the form y = mx?

- I can define the equation y = mx for a line through the origin. - I can compare two different proportional relationships represented in different ways.

14-3: The Slope of a Line 8.EE.5 What does the slope of a line tell you about the line?

- I can graph proportional relationships, interpreting the unit rate as the slope of the graph.

14-4: Unit Rate and Slope 8.EE.5 How are unit rates and slope related?

- 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.

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 define the equation y = mx + b for a line intercepting the vertical axis at b.

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

UNIT III: INTRODUCTION TO SAMPLING AND INFERENCE

Unit III Pretest & Readiness Assessment TOPIC 15 – SAMPLING




Key Vocabulary

15-1: Populations and Samples

7.SP.1 When is it reasonable to use a small group to represent a larger group? When is it not reasonable?

- 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

15-2: Estimating a Population

7.SP.1, 7.SP.2 When can you use a small group to estimate things about a larger group?

- 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.

15-3: Convenience Sampling

7.SP.1 How do you sample in a way that is convenient? What are the advantages and disadvantages of convenience sampling?

- 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.

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

7.SP.1, 7.SP.2 How do you sample randomly? What are the advantages and disadvantages of simple random sampling?

- 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.

15-6: Comparing Sampling Methods

7.SP.1 For what situations is each type of sampling most effective?

TOPIC 16 – COMPARING TWO POPULATIONS




Key Vocabulary

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?

- 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.

- 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

16-2: Multiple Populations and Inferences

7.SP.1, 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?

- 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.

16-3: Using Measures of Center

7.SP.4 How can you compare two groups using a single number from each group?

- I can use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.

16-4: Using Measures of Variability

7.SP.4 How else can you compare two groups using a single number from each group?

16-5: Exploring Overlap in Data Sets

7.SP.3, 7.SP.4 How do measures of center and variability help you determine how much two groups have in common?

- 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.

TOPIC 17 – PROBABILITY CONCEPTS




Key Vocabulary

17-1: Likelihood and Probability

7.SP.5, 7.SP.6 What are effective ways to describe the likelihood of an event?

- 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.

- 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

17-2: Sample Spaces 7.SP.7 What is the difference between an action and an event?

- I can develop a probability model and use it to find probabilities of events.

17-3: Relative Frequency and Experimental Probability

7.SP.6 In what situations is conducting an experiment a good way to determine the probability of an event? How can you evaluate the reasonableness of an experimental probability?

- 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.

17-4: Theoretical Probability

7.SP.7.a How do you tell the difference between a theoretical and an experimental 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.

17-5: Probability Models 7.SP.7.a How do you choose the best type of probability model for a situation?

- 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.

TOPIC 18 – COMPOUND EVENTS




Key Vocabulary

18-1: Compound Events 7.SP.8.b What makes an event a compound event? What are the different types of compound events?

- I can represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams.

- 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

18-2: Sample Spaces of Compound Events

7.SP.8.b How do you know a sample space is complete? How do you know when you have accounted for all possibilities?

- I can represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams.

18-3: Finding Compound Probabilities Using Organized Lists

7.SP.8.a.b How is the number of outcomes of a multi-step process related to the number of outcomes for each step?

- 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.

18-4: Finding Compound Probabilities Using Tables

7.SP.6, 7.SP.8.a In what situation should you use an organized list, a table, or a tree diagram to find the probability of a compound event?

- 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.

18-5: Finding Compound Probabilities Using Tree Diagrams

7.SP.8.c How can you use random numbers to simulate real-world situations?

- I can design and use a simulation to generate frequencies for compound events.

18-6: Finding Probabilities Using Simulation

7.EE.3, 7.SP.8 In what situations should you use a simulation to find the probability of a compound event?

- I can find probabilities of compound events using simulation.

Unit III Posttest

Mathematics Grade 7 Accelerated Updated 2017-2018€¦ · · 2018-03-31Mathematics Grade 7...

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