CLUSTER: Represent and interpret data. 2.MD.9. Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. EE.2.MD.9-10. Create picture graphs from collected measurement data. 2.MD.10. Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. Second Grade Mathematics Domain: Geometry CCSS Grade-Level Standards DLM Essential Elements CLUSTER: Reason with shapes and their attributes. 2.G.1. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. EE.2.G.1. Identify common two-dimensional shapes: square, circle, triangle, and rectangle. 2.G.2. Partition a rectangle into rows and columns of same-size squares, and count to find the total number of them. Not applicable. 2.G.3. Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. Not applicable. See EE.4.G.3 and EE.4.NF.1–2.
6.EE.9.Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Not applicable. Sixth Grade Mathematics Domain: Geometry CCSS Grade-Level Standards DLM Essential Elements CLUSTER: Solve real-world and mathematical problems involving area, surface area, and volume. 6.G.1. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. EE.6.G.1. Solve real-world and mathematical problems about area using unit squares. 6.G.2. Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. EE.6.G.2. Solve real-world and mathematical problems about volume using unit cubes. 6.G.3. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Not applicable. 6.G.4. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. Not applicable. Sixth Grade Mathematics Domain: Statistics and Probability CCSS Grade-Level Standards DLM Essential Elements
F-LE.2. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). F-LE.3. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. F-LE.4. For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. Not applicable. CLUSTER: Interpret expressions for functions in terms of the situation they model. F-LE.5. Interpret the parameters in a linear or exponential function in terms of a context. Not applicable. See EE.F-IF.1–3. High School Mathematics Domain: Functions—Trigonometric Functions CCSS Grade-Level Standards DLM Essential Elements CLUSTER: Extend the domain of trigonometric functions using the unit circle. F-TF.1. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. Not applicable. F-TF.2. Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. Not applicable. F-TF.3. (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4, and π/6, and use the unit circle to express the values of since, cosine, and tangent for π – x, π + x, and 2π – x in terms of their values for x, where x is any real number. Not applicable. F-TF.4. (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. Not applicable. CLUSTER: Model periodic phenomena with trigonometric functions. F-TF.5. Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. Not applicable.
High School Mathematics Domain: Geometry—Similarity, Right Triangles, and Trigonometry CCSS Grade-Level Standards DLM Essential Elements CLUSTER: Understand similarity in terms of similarity transformations. G-SRT.1. Verify experimentally the properties of dilations given by a center and a scale factor: Not applicable. See EE.G-CO.6–8. G-SRT.1.a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. G-SRT.1.b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. G-SRT.2. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. Not applicable. See EE.G-CO.6–8. G-SRT.3. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. Not applicable. See EE.G-CO.6–8. CLUSTER: Prove theorems involving similarity. G-SRT.4. Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. Not applicable. G-SRT.5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Not applicable. See EE.G-CO.6–8. CLUSTER: Define trigonometric ratios, and solve problems involving right triangles. G-SRT.6. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. Not applicable. G-SRT.7. Explain and use the relationship between the sine and cosine of complementary angles. Not applicable. G-SRT.8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. Not applicable. CLUSTER: Apply trigonometry to general triangles.
G-GMD.3. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. Not applicable. See EE.8.G.9 and EE.G-GPE.7. CLUSTER: Visualize relationships between two-dimensional and three-dimensional objects. G-GMD.4. Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. EE.G-GMD.4. Identify the shapes of cross-sections of three-dimensional objects. High School Mathematics Domain: Geometry—Modeling with Geometry CLUSTER: Apply geometric concepts in modeling situations. G-MG.1. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). EE.G-MG.1–3. Use properties of geometric shapes to describe real-life objects. G-MG.2. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). G-MG.3. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). High School Mathematics Domain: Statistics and Probability—Interpreting Categorical and Quantitative Data CCSS Grade-Level Standards DLM Essential Elements CLUSTER: Summarize, represent, and interpret data on a single count or measurement variable. S-ID.1. Represent data with plots on the real number line (dot plots, histograms, and box plots). EE.S-ID.1–2. Given data, construct a simple graph (line, pie, bar, or picture) or table, and interpret the data. S-ID.2. Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.