Know that there are numbers that are not rational, and approximate them by rational numbers. NS.A.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. NS.A.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 (e.g., π^2). For example, by truncating the decimal expansion of Math A U01-L01-A02 Write rational numbers in equivalent forms by simplifying fractions. and and and and U01-L01-A03 U01-L01-A05 U01-L01-A04 U01-L01-A05 U04-L16-A02 U04-L16-A03 U04-L16-A04 U04-L16-A05 U04-L1-A02 U04-L19-A05 U04-L1-A03 U04-L1-A04 U04-L1-A05 U04-L19-A02 U04-L19-A04 U04-L19-A03 U04-L19-A04 Write rational numbers in equivalent forms by rewriting fractions as decimals. Write rational numbers in equivalent forms by rewriting decimals as fractions. Classify numbers by defining rational, integer, whole, or counting numbers. Identify irrational numbers by applying the definitions of rational and irrational numbers. Locate irrational numbers on a number line by estimating their values. Approximate irrational square roots by applying estimation processes. Estimate the values of irrational expressions by performing simple mental calculations. 1
2 (square root of 2), show that 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. Work with radicals and integer exponents. EE.A.1 EE.A.2 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 3^( 5) = 3^( 3) = 1/(3^3) = 1/27. 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 U03-L12-A02 Evaluate expressions by applying U03-L12-A03 definitions of integer exponents. and U03-L12-A04 U03-L12-A05 U03-L12-A09 U03-L13-A02 Evaluate expressions by applying U03-L13-A03 properties of integer exponents. and U03-L13-A04 U03-L13-A05 U03-L13-A09 U03-L13-A02 Rewrite expressions by applying U03-L13-A03 operations and properties of and U03-L13-A04 integer exponents. U03-L13-A05 U03-L13-A09 U04-L17-A02 Evaluate the values of square roots by recognizing the square roots of perfect squares. U04-L17-A03 Solve equations of the form 2
rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that 2 is irrational. EE.A.3 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. For example, estimate the population of the United States as 3 10^ and the population of the world as 7 10^9, and determine that the world population is more than 20 times larger. and U04-L17-A04 x^2=p by evaluating square roots. U04-L17-A05 U04-L1-A02 Identify irrational square roots by recognizing non-perfect squares. and U03-L14-A02 U03-L14-A09 U03-L14-A03 U03-L14-A05 U03-L14-A09 Rewrite large or small numbers by using scientific or standard notation. Compare large or small numbers by interpreting scientific notation. EE.A.4 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 and and U03-L15-A02 U03-L15-A04 U03-L15-A05 U03-L15-A09 U03-L15-A03 U03-L15-A04 U03-L15-A05 U03-L15-A09 Multiply and divide numbers that include scientific notation by applying properties of exponents. Add and subtract numbers that include scientific notation by applying algebraic properties. 3
y g y quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. U03-L14-A04 Express large and small values by choosing appropriate units. U03-L14-A04 Interpret output generated by technology by rewriting the value in scientific notation. Analyze and solve linear equations and pairs of simultaneous linear equations. EE.C.7.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). and Word Problem Investigation U02-L06-A03 U02-L06-A04 U02-L06-A05 Solve two-step linear equations by applying inverse operations. EE.C..C Solve real-world and mathematical problems leading to two linear Word Problem Investigation U02-L06-A02 U02-L06-A05 Write single-variable linear equations by interpreting real-life situations. 4
Define, evaluate, and compare functions. equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. F.A.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. (Function notation is not required for Grade.) F.A.2 Compare properties of two functions each represented in a different way and and and U02-L10-A02 U02-L10-A03 U02-L10-A04 U02-L10-A05 U02-L10-A04 U03-L11-A02 U03-L11-A05 U03-L11-A03 U03-L11-A04 Identify relations as functions by applying the definition of functions. Evaluate linear functions by finding output values that correspond to given input values. Identify values of functions by naming points from graphs of functions. Graph a linear function by using a table or equation. Compare properties of linear functions by interpreting graphs and tables. 5
(algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. Use functions to model relationships between quantities. F.B.4 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. and U03-L11-A03 U03-L11-A05 U03-L11-A04 U03-L11-A05 Determine the rates of change for linear functions by interpreting graphs and tables. Determine the initial values for linear functions by interpreting graphs and tables. F.B.5 Describe qualitatively the U02-L0-A02 Analyze graphs by determining 6
Understand congruence and similarity using physical models, transparencies, or geometry software. G.A.1 functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. 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. and Enrichment and Enrichment and Enrichment Word Problem Investigation and Word Problem Investigation and Exploration Exploration U02-L0-A04 U02-L0-A05 U02-L0-A03 U02-L0-A04 U02-L0-A05 U02-L0-A02 U02-L0-A03 U02-L0-A04 U02-L0-A05 U02-L09-A03 U02-L09-A04 U02-L09-A05 U02-L09-A02 U02-L09-A05 U05-L21-A02 U05-L21-A03 U05-L21-A05 U05-L24-A09 U05-L25-A09 U05-L22-A02 U05-L22-A03 U05-L22-A05 U05-L25-A09 U05-L23-A02 where they are increasing and decreasing. Analyze graphs by determining whether they are linear or nonlinear. Describe the relationship between two quantities by analyzing graphs. Create graphs by analyzing situations. Verify properties of translations by experimenting using technology. Verify properties of reflections by experimenting using technology. Verify properties of rotations by 7
and Exploration U05-L23-A03 U05-L23-A05 U05-L23-A09 U05-L21-A02 U05-L21-A09 U05-L22-A09 U05-L22-A02 experimenting using technology. U05-L24-A02 Transform angles by applying U05-L24-A03 translations, reflections, and U05-L24-A04 rotations. Exploration U05-L24-A05 U05-L24-A09 U05-L25-A09 U05-L25-A02 Transform parallel lines by U05-L25-A03 translations, reflections, and U05-L25-A04 rotations. Exploration U05-L25-A05 U05-L25-A09 G.A.2 Understand that a twodimensional U06-L26-A02 Determine whether two figures figure is and U06-L26-A04 are congruent by applying congruent to another if the transformations. second can be obtained U06-L26-A03 Demonstrate congruence by from the first by a U06-L26-A05 describing a sequence of sequence of rotations, transformations. reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. G.A.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures Identify mapping statements by analyzing translations. Identify mapping statements by
G.A.5 using coordinates. 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 angleangle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. and and and and U05-L23-A04 U05-L21-A09 U05-L22-A09 U05-L23-A09 U06-L27-A02 U06-L27-A05 U06-L27-A02 U06-L27-A05 U06-L27-A03 U06-L27-A04 U06-L27-A05 U06-L2-A02 U06-L2-A05 U06-L2-A03 U06-L2-A05 U06-L2-A04 U06-L2-A05 U05-L22-A09 analyzing reflections. U05-L23-A09 U05-L23-A03 Identify mapping statements by analyzing rotations. U05-L21-A04 Identify the coordinates of a U05-L22-A04 transformation's image by applying mapping statements. Explain when angles are congruent by describing angle pair relationships. Explain when angles are supplementary by describing angle pair relationships. Solve problems by using angle pair relationships. Explain the relationship between the three interior angles of a triangle by examining their measures. Explain the relationship between exterior angles of a triangle by comparing their relationships to interior angles. Solve problems by using the relationships of angles in a triangle. 9
Understand and apply the Pythagorean Theorem. G.B.6 Explain a proof of the Pythagorean Theorem and its converse. G.B.7 G.B. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. and U06-L29-A02 Explain the Pythagorean Theorem by justifying why it works. U06-L29-A03 Explain the converse of the Pythagorean Theorem by justifying why it works. U04-L20-A02 U04-L20-A03 and U04-L20-A04 Word Problem U04-L20-A05 Investigation U06-L29-A03 Determine whether a triangle is a right triangle by using the converse of the Pythagorean Theorem. U06-L29-A04 U06-L29-A05 Determine lengths of missing sides of right triangles by applying the Pythagorean Theorem. Solve real-world problems with right triangles by applying the Pythagorean Theorem. Determine the distance between two points on a graph by applying the Pythagorean Theorem. 10