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1 FLORIDA STANDARDS TO BOOK CORRELATION FOR GRADE 7 ADVANCED After a standard is introduced, it is revisited many times in subsequent activities, lessons, and exercises. Domain: The Number System 8.NS.1.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. Section 7.4 Approximating Square Roots Extension 7.4 Repeating Decimals 8.NS.1.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions. Section 7.4 Approximating Square Roots Domain: Expressions and Equations 7.EE.2.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. Section 11.1 Writing and Graphing Inequalities Section 11.2 Solving Inequalities Using Addition or Subtraction Section 11.3 Solving Inequalities Using Multiplication or Division Section 11.4 Solving Two-Step Inequalities 8.EE.1.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. Section 10.1 Exponents Section 10.2 Product of Powers Property Section 10.3 Quotient of Powers Property Section 10.4 Zero and Negative Exponents xviii

2 8.EE EE EE EE EE EE.3.7 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. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that 2 is irrational. Section 7.1 Finding Square Roots Section 7.2 Finding Cube Roots Section 7.3 The Pythagorean Theorem Section 7.4 Approximating Square Roots Section 7.5 Using the Pythagorean Theorem 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. Section 10.5 Reading Scientific Notation Section 10.6 Writing Scientific Notation Section 10.7 Operations in Scientific Notation Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology. Section 10.5 Reading Scientific Notation Section 10.6 Writing Scientific Notation Section 10.7 Operations in Scientific Notation Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. Section 4.1 Graphing Linear Equations Section 4.3 Graphing Proportional Relationships Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Section 4.2 Slope of a Line Extension 4.2 Slopes of Parallel and Perpendicular Lines Section 4.3 Graphing Proportional Relationships Section 4.4 Graphing Linear Equations in Slope-Intercept Form Section 4.5 Graphing Linear Equations in Standard Form Solve linear equations in one variable. a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). Section 1.1 Solving Simple Equations Section 1.2 Solving Multi-Step Equations Section 1.3 Solving Equations with Variables on Both Sides Section 1.4 Rewriting Equations and Formulas xix

3 8.EE.3.8 b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Section 1.1 Solving Simple Equations Section 1.2 Solving Multi-Step Equations Section 1.3 Solving Equations with Variables on Both Sides Section 1.4 Rewriting Equations and Formulas Analyze and solve pairs of simultaneous linear equations. a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. Section 5.1 Solving Systems of Linear Equations by Graphing Section 5.4 Solving Special Systems of Linear Equations b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. Section 5.1 Solving Systems of Linear Equations by Graphing Section 5.2 Solving Systems of Linear Equations by Substitution Section 5.3 Solving Systems of Linear Equations by Elimination Section 5.4 Solving Special Systems of Linear Equations c. Solve real-world and mathematical problems leading to two linear equations in two variables. Section 5.1 Solving Systems of Linear Equations by Graphing Section 5.2 Solving Systems of Linear Equations by Substitution Section 5.3 Solving Systems of Linear Equations by Elimination Section 5.4 Solving Special Systems of Linear Equations Domain: Functions 8.F.1.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. Section 6.1 Relations and Functions Section 6.2 Representations of Functions 8.F F.1.3 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Section 6.3 Linear Functions Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. Section 6.3 Linear Functions Section 6.4 Comparing Linear and Nonlinear Functions xx

4 8.F F.2.5 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. Section 4.6 Writing Equations in Slope-Intercept Form Section 4.7 Writing Equations in Point-Slope Form Section 6.3 Linear Functions Describe qualitatively the functional relationship between two quantities by analyzing a graph. Sketch a graph that exhibits the qualitative features of a function that has been described verbally. Section 6.5 Analyzing and Sketching Graphs Domain: Geometry 7.G.1.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Section 12.5 Scale Drawings 7.G G G G.2.5 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Section 12.3 Triangles Section 12.4 Quadrilaterals Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangle pyramids. Extension 14.5 Cross Sections of Three-Dimensional Figures Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Section 13.1 Circles and Circumference Section 13.2 Perimeters of Composite Figures Section 13.3 Areas of Circles Section 14.3 Surface Areas of Cylinders Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. Section 12.1 Adjacent and Vertical Angles Section 12.2 Complementary and Supplementary Angles Extension 12.3 Angle Measures of Triangles xxi

5 7.G G G G G.1.4 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Section 13.4 Areas of Composite Figures Section 14.1 Surface Areas of Prisms Section 14.2 Surface Areas of Pyramids Section 14.4 Volumes of Prisms Section 14.5 Volumes of Pyramids Verify experimentally the properties of rotations, reflections, and translations: a. Lines are taken to lines and line segments to line segments of the same length. b. Angles are taken to angles of the same measure. c. Parallel lines are taken to parallel lines. Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. Section 2.1 Congruent Figures Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Section 2.7 Dilations Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. Section 2.5 Similar Figures Section 2.6 Perimeters and Areas of Similar Figures Section 2.7 Dilations xxii

6 8.G G G G G.3.9 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. Section 3.1 Parallel Lines and Transversals Section 3.2 Angles of Triangles Section 3.3 Angles of Polygons Section 3.4 Using Similar Triangles Explain a proof of the Pythagorean Theorem and its converse. Section 7.3 The Pythagorean Theorem Section 7.5 Using the Pythagorean Theorem Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. Section 7.3 The Pythagorean Theorem Section 7.5 Using the Pythagorean Theorem Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Section 7.3 The Pythagorean Theorem Section 7.5 Using the Pythagorean Theorem Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. Section 8.1 Volumes of Cylinders Section 8.2 Volumes of Cones Section 8.3 Volumes of Spheres Section 8.4 Surface Areas and Volumes of Similar Solids Domain: Statistics and Probability 7.SP.1.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. Section 15.6 Samples and Populations 7.SP SP.2.3 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. Section 15.6 Samples and Populations Extension 15.6 Generating Multiple Samples 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. Section 15.7 Comparing Populations xxiii

7 7.SP SP SP SP SP SP.1.1 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. Section 15.7 Comparing Populations Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. Section 15.1 Outcomes and Events Section 15.2 Probability Section 15.3 Experimental and Theoretical Probability 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. Section 15.3 Experimental and Theoretical Probability Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. Section 15.2 Probability Section 15.3 Experimental and Theoretical Probability b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. Section 15.3 Experimental and Theoretical Probability Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. Section 15.4 Compound Events Section 15.5 Independent and Dependent Events b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language, identify the outcomes in the sample space which compose the event. Section 15.4 Compound Events Section 15.5 Independent and Dependent Events c. Design and use a simulation to generate frequencies for compound events. Extension 15.5 Simulations Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. Section 9.1 Scatter Plots Section 9.2 Lines of Fit Section 9.4 Choosing a Data Display xxiv

8 8.SP SP SP.1.4 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. Section 9.2 Lines of Fit Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. Section 9.2 Lines of Fit Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. Section 9.3 Two-Way Tables xxv

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