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

MA.8.1.1 2000

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

MA.8.1.2 2000

Know that every rational number is either a terminating or repeating decimal and that every irrational number is a nonrepeating decimal.

MA.8.1.3 2000

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

MA.8.1.4 2000

Understand and evaluate negative integer exponents.

MA.8.1.5 2000

Use the laws of exponents for integer exponents.

MA.8.1.6 2000

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

MA.8.1.7 2000

Calculate and find approximations of square roots.

MA.8.2 2000 - Computation

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

MA.8.2.1 2000

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

MA.8.2.2 2000

Solve problems by computing simple and compound interest.

MA.8.2.3 2000

Use estimation techniques to decide whether answers to computations on a calculator are reasonable.

MA.8.2.4 2000

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

MA.8.3 2000 - Algebra and Functions

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.

MA.8.3.1 2000

Write and solve linear equations and inequalities in one variable, interpret the solution or solutions in their context, and verify the reasonableness of the results.

MA.8.3.2 2000

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

MA.8.3.3 2000

Interpret positive integer powers as repeated multiplication and negative integer powers as repeated division or multiplication by the multiplicative inverse.

MA.8.3.4 2000

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

MA.8.3.5 2000

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

MA.8.3.6 2000

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

MA.8.3.7 2000

Demonstrate an understanding of rate as a measure of one quantity with respect to another quantity.

MA.8.3.8 2000

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

MA.8.3.9 2000

Represent simple quadratic functions using verbal descriptions, tables, graphs and formulas, and translate among these representations.

MA.8.3.10 2000

Graph functions of the form y=nx^{2} and y=nx^{3} and describe the similarities and differences in the graphs.

MA.8.4 2000 - Geometry

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.

MA.8.4.1 2000

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

MA.8.4.2 2000

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

MA.8.4.3 2000

Identify properties of three-dimensional geometric objects (e.g., diagonals of rectangular solids) and describe how two or more figures intersect in a plane or in space.

MA.8.4.4 2000

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

MA.8.4.5 2000

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

MA.8.5 2000 - Measurement

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.

MA.8.5.1 2000

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

MA.8.5.2 2000

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

MA.8.5.3 2000

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

MA.8.5.4 2000

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.

MA.8.5.5 2000

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

MA.8.6 2000 - Data Analysis and Probability

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.

MA.8.6.1 2000

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

MA.8.6.2 2000

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

MA.8.6.3 2000

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.

MA.8.6.4 2000

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.

MA.8.6.5 2000

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.

MA.8.6.6 2000

Understand and recognize equally likely events.

MA.8.6.7 2000

Find the number of possible arrangements of several objects by using the Basic Counting Principle.

MA.8.7 2000 - Problem Solving

Students make decisions about how to approach problems and communicate their ideas.

MA.8.7.1 2000

Analyze problems by identifying relationships, telling relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.

MA.8.7.2 2000

Make and justify mathematical conjectures based on a general description of a mathematical question or problem.

MA.8.7.3 2000

Decide when and how to break a problem into simpler parts.

MA.8.7.4 2000

Apply strategies and results from simpler problems to solve more complex problems.

MA.8.7.5 2000

Make and test conjectures by using inductive reasoning.

MA.8.7.6 2000

Express solutions clearly and logically by using the appropriate mathematical terms and notation. Support solutions with evidence in both verbal and symbolic work.

MA.8.7.7 2000

Recognize the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.

MA.8.7.8 2000

Select and apply appropriate methods for estimating results of rational-number computations.

MA.8.7.9 2000

Use graphing to estimate solutions and check the estimates with analytic approaches.

MA.8.7.10 2000

Make precise calculations and check the validity of the results in the context of theproblem.

MA.8.7.11 2000

Decide whether a solution is reasonable in the context of the original situation.

MA.8.7.12 2000

Note the method of finding the solution and show a conceptual understanding of the method by solving similar problems.