### 1: Calculations and Estimations

#### 1.1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems

1.1.1: Compare real numbers

1.1.4: Locate real numbers on a number line (including approximations of irrational numbers)

#### 1.2: Compute fluently and make reasonable estimates

1.2.3: Mentally multiply and divide by powers of 10 to estimate results of computations involving numbers expressed in scientific notation

1.2.4: Develop and use strategies to estimate the results of real number computations, determine the amount of error, and judge the reasonableness of results

### 2: Statistics and Probability

#### 2.1: Select and use appropriate statistical methods to analyze data

2.1.2: Analyze bivariate data and identify the type of function (linear, quadratic, exponential) that could be used to model the data

#### 2.2: Understand and apply basic concepts of probability

2.2.1: Compute the probability of a compound event (e.g., toss a coin three times to find the probability of two heads)

2.2.2: Determine probabilities of dependent and independent events (e.g., use colored marbles with and without replacement)

2.2.4: Determine all possible outcomes of a particular event or all possible arrangements of objects in a given set by applying counting strategies, combinations, and permutations

#### 2.3: Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

2.3.1: Determine appropriate designs for simulations (surveys, observational studies, and experiments) and modeling to study a problem and construct empirical probability distributions to represent results

2.3.2: Use matrices, histograms, scatter plots, stem-and-leaf plots, and box-and whisker-plots to interpret data

#### 2.4: Develop and evaluate inferences and predictions that are based on data

2.4.1: Make inferences and predictions from data in histograms, scatter plots, and parallel box plots

### 3: Algebraic Relationships

#### 3.1: Understand patterns, relations, and functions

3.1.1: Represent and generalize sequences resulting from linear, quadratic, and exponential relationships using recursive or explicit formulas tables of values and graphs

3.1.3: Evaluate and make a table for two-variable formulas and match a graph or table of values to its formula

3.1.4: Identify independent and dependent variables and determine the domain and range of a function in a problem situation

#### 3.2: Represent and analyze mathematical situations and structures using algebraic symbols

3.2.1: Algebraically represent situations and solve problems involving quadratic and exponential equations, including exponential growth and decay

3.2.2: Use graphs to solve non-linear equations, including quadratics

3.2.3: Represent and solve system of linear equations with 2 variables using simultaneous equations and by graphing

3.2.6: Translate between and interpret quadratic and exponential relationships represented by words, symbols, tables, and graphs

3.2.7: Determine and interpret maxima or minima and zeros of quadratic functions, and linear functions where y = constant

3.2.8: Graph linear inequalities in two variables

3.2.9: Graph quadratic and exponential equations

3.2.10: Analyze how changing a parameter (i.e., k, b) in a quadratic or exponential function of the form y=k^x+b, y=kx^2+b, or y=k(x+b)^2 affects its graph

#### 3.3: Use mathematical models to represent and understand quantitative relationships

3.3.1: Model situations, make predictions and inferences, and solve problems using linear, quadratic, and exponential functions

3.3.2: Determine when data represented in a table or graph represents a linear, quadratic, or exponential relationship

#### 3.4: Analyze change in various contexts

3.4.1: Approximate and interpret rates of change in graphical and numeric data

3.4.2: Analyze the nature of change of each variable in a non-linear relationship as suggested by a table of values, a graph or a formula

### 4: Measurement

#### 4.1: Understand measurable attributes of objects and the units, systems and processes of measurement

4.1.1: Determine the appropriate units, scales, and tools for problem situations involving measurement

4.1.3: Determine the precision of a given measuring tool (e.g., 1 degree for a standard protractor)

#### 4.2: Apply appropriate techniques, tools, and formulas to determine measurements

4.2.1: Develop and use strategies and formulas for calculating surface area and volume of cones and spheres

4.2.2: Use formulas to solve problems involving finding missing dimensions given perimeter, area, surface area and volume of polygons, circles, prisms, pyramids, cones, cylinders, and spheres

4.2.4: Determine perimeter and area of shapes of circles and polygons (annulus, etc.) in context

4.2.5: Determine the surface area and volume of a complex figure composed of a combination of two or more geometric figures or a figure derived from a regular solid (e.g., hemisphere, frustum of a cone)

4.2.6: Compare and contrast the formulas for surface area and volume of cylinders and cones

4.2.7: Determine a shape that has minimum or maximum perimeter, area, surface area, or volume under specified conditions

### 5: Geometry

#### 5.1: Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

5.1.1: Determine defining properties that characterize classes of three-dimensional figures and their component parts

5.1.2: Recognize and represent three-dimensional figures and their component parts

5.1.3: Justify and use theorems involving the angles formed by parallel lines cut by a transversal

5.1.4: Develop, understand, and apply properties of circles and of inscribed and circumscribed polygons

5.1.5: Use measures of sides and of interior and exterior angles of polygons to classify figures and solve problems

5.1.6: Prove congruence of two triangles or their corresponding component parts

5.1.7: Determine the measures of corresponding angles, sides, and corresponding parts of congruent and similar figures

5.1.8: Use angle, side length and triangle inequality relationships to solve problems

5.1.9: Use trigonometric functions, and angle and side relationships of special right triangles (30- 60-right triangles and isosceles right triangles) to solve for an unknown length and determine distances and solve problems

5.1.10: Investigate relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles

5.1.12: Justify and use theorems involving the properties of triangles, quadrilaterals, circles, and their component parts to verify congruence and similarity

#### 5.2: Use visualization, spatial reasoning, and geometric modeling to solve problems

5.2.1: Model, sketch, label and where appropriate construct cones and spheres, and basic elements of geometric figures (e.g., altitudes, midpoints, medians, angle bisectors, and perpendicular bisectors) using compass and straightedge or technology

5.2.2: Describe how two or more objects are related in space (e.g., skew lines, the possible ways three planes might intersect)

5.2.3: Make a model of a three-dimensional figure from a two-dimensional drawing and make a two-dimensional representation of a three-dimensional object through scale drawings, perspective drawings, blueprints or computer simulations

#### 5.3: Specify locations and describe spatial relationships using coordinate geometry and other representational systems

5.3.2: Calculate slope, distance and midpoint between points with an emphasis on practical applications (use coordinate formulas)

#### 5.4: Apply transformations and use symmetry to analyze mathematical situations

5.4.1: Use coordinate geometry to determine whether a figure is symmetrical with respect to a line or a point

5.4.2: Determine whether a given pair of figures on a coordinate plane represent a translation, reflection, rotation and/or dilation

5.4.3: Determine the image of a figure on a coordinate graph under translations, reflections, and rotations

5.4.4: Given a figure and its image on a coordinate graph, determine the translation vector or locate the axis of reflection

5.4.5: Determine the coordinates of and draw the dilation of a figure on a coordinate graph

5.4.6: Analyze the congruence, similarity, and line or rotational symmetry of figures using transformations

Correlation last revised: 1/20/2017

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.