#### 8.1: Students know the properties of rational and irrational numbers expressed in a variety of forms. They understand and use exponents, powers, and roots.

8.1.1: Read, write, compare, and solve problems using decimals in scientific notation.

8.1.2: Know that every rational number is either a terminating or repeating decimal and that every irrational number is a non-repeating decimal.

8.1.3: Understand that computations with an irrational number and a rational number (other than zero) produce an irrational number.

8.1.4: Understand and evaluate negative integer exponents.

8.1.5: Use the laws of exponents for integer exponents.

8.1.6: Use the inverse relationship between squaring and finding the square root of a perfect square integer.

8.1.7: Calculate and find approximations of square roots.

#### 8.2: Students compute with rational numbers expressed in a variety of forms. They solve problems involving ratios, proportions, and percentages.

8.2.1: Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) in multi-step problems.

8.2.2: Solve problems by computing simple and compound interest.

8.2.4: Use mental arithmetic to compute with common fractions, decimals, powers, and percents.

#### 8.3: Students solve simple linear equations and inequalities. They interpret and evaluate expressions involving integer powers. They graph and interpret functions. They understand the concepts of slope and rate.

8.3.2: Solve systems of two linear equations using the substitution method and identify approximate solutions graphically.

8.3.4: Use the correct order of operations to find the values of algebraic expressions involving powers.

8.3.5: Identify and graph linear functions and identify lines with positive and negative slope.

8.3.6: Find the slope of a linear function given the equation and write the equation of a line given the slope and any point on the line.

8.3.8: Demonstrate an understanding of the relationships among tables, equations, verbal expressions, and graphs of linear functions.

8.3.10: Graph functions of the form y = nx² and y = nx³ and describe the similarities and differences in the graphs.

#### 8.4: Students deepen their understanding of plane and solid geometric shapes and properties by constructing shapes that meet given conditions, by identifying attributes of shapes, and by applying geometric concepts to solve problems.

8.4.1: Identify and describe basic properties of geometric shapes: altitudes, diagonals, angle and perpendicular bisectors, central angles, radii, diameters, and chords.

8.4.2: Perform simple constructions, such as bisectors of segments and angles, copies of segments and angles, and perpendicular segments. Describe and justify the constructions.

8.4.4: Draw the translation (slide), rotation (turn), reflection (flip), and dilation (stretches and shrinks) of shapes.

8.4.5: Use the Pythagorean Theorem and its converse to solve problems in two and three dimensions.

#### 8.5: Students convert between units of measure and use rates and scale factors to solve problems. They compute the perimeter, area, and volume of geometric objects. They investigate how perimeter, area, and volume are affected by changes of scale.

8.5.1: Convert common measurements for length, area, volume, weight, capacity, and time to equivalent measurements within the same system.

8.5.2: Solve simple problems involving rates and derived measurements for attributes such as velocity and density.

8.5.3: Solve problems involving scale factors, area, and volume using ratio and proportion.

8.5.4: Use formulas for finding the perimeter and area of basic two-dimensional shapes and the surface area and volume of basic three-dimensional shapes, including rectangles, parallelograms, trapezoids, triangles, circles, prisms, cylinders, spheres, cones, and pyramids.

8.5.5: Estimate and compute the area and volume of irregular two- and three-dimensional shapes by breaking the shapes down into more basic geometric objects.

#### 8.6: Students collect, organize, represent, and interpret relationships in data sets that have one or more variables. They determine probabilities and use them to make predictions about events.

8.6.1: Identify claims based on statistical data and, in simple cases, evaluate the reasonableness of the claims. Design a study to investigate the claim.

8.6.2: Identify different methods of selecting samples, analyzing the strengths and weaknesses of each method, and the possible bias in a sample or display.

8.6.3: Understand the meaning of, and be able to identify or compute the minimum value, the lower quartile, the median, the upper quartile, the interquartile range, and the maximum value of a data set.

8.6.4: Analyze, interpret, and display single- and two-variable data in appropriate bar, line, and circle graphs; stem-and-leaf plots; and box-and-whisker plots and explain which types of display are appropriate for various data sets.

8.6.5: Represent two-variable data with a scatterplot on the coordinate plane and describe how the data points are distributed. If the pattern appears to be linear, draw a line that appears to best fit the data and write the equation of that line.

8.6.6: Understand and recognize equally likely events.

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.