Math Department

Middle School Resources

Elementary Math Performance Standards

Eighth Grade

Each ASD mathematics course reflects the program statement and incorporates the general program goals. In addition, each course consists of a specific set of standards that determine the course content and a set of performance standards that delineate what a student should be able to do after successfully completing the course. After satisfactorily completing the ASD Eighth Grade mathematics curriculum, a student will be proficient in the fourteen strands of mathematics which comprise the mathematics curriculum. As evidence of proficiency, the student will be able to:

8:1 Estimation

.1 Estimate solutions to problems to check reasonableness of results.
.2 Estimate probability of an event from random samples or experimental data.
.3 Use estimation to compare metric and standard units.
.4 Explain when an estimate is appropriate and when an exact answer is needed.
.5 Use estimation to check calculator or computer accuracy.
.6 Estimate the square root of a number by finding the two square numbers between which it lies.

8:2 Number Sense

.1 Solve problems using ratio, proportion, and percent.
.2 Describe and model the relationship between equivalent fractions, decimals, percents, or ratios when solving problems.
.3 Use manipulatives, diagrams, or symbols to explain how to solve different types of percent problems.
.4 Use mental math to calculate discounts, taxes, interest, commissions and gratuities.
.5 Compare and order real numbers using >, <, and =.
.6 Write and solve problems that use primes, factors, and multiples .
.7 Explain the relationship between the subsets of the real number system.
.8 Model counting in a different base system.
.9. Explain order of operations

8:3 Concepts of Number Operations

.1 Use manipulatives or diagrams to explain how to approximate a square root.
.2 Write and solve problems involving multiple operations.
.3 Use manipulatives, diagrams, symbols, and words to describe addition, subtraction, multiplication and division of integers.
.4 Use manipulatives or a diagram to explain absolute value.
.5 Use the commutative, associative, and distributive properties to solve problems with variables and rational numbers.
.6 Use inverse operations and the properties of zero and 1 to solve problems with variables and rational numbers.
.7 Use and explain prime factorization.

8:4. Computation

.1 Use paper and pencil, mental math, or a calculator to efficiently and accurately solve problems with real numbers.
.2 Apply order of operations to real numbers.
.3 Use percent to create circle graphs.
.4 Add, subtract, multiply and divide fractions, decimals and integers with and without a calculator.
.5 Solve problems using percent of increase or decrease.
.6 Write and solve practical problems that use real numbers.
.7 Convert numbers between standard form and scientific notation using both positive and negative exponents.

8:5 Geometry

.1 Identify, classify, and compare polygons and polyhedra.
.2 Identify and use the vocabulary related to regular and irregular polygons, circles, polyhedra, and their components.
.3 Use the relationships of angles formed by parallel, perpendicular and intersecting lines to solve problems.
.4 Describe the relationship of angles in different types of polygons.
.5 Construct or draw geometric figures in three dimensions.
.6 Identify corresponding parts in similar and congruent geometric figures using a scale factor.
.7 Use similarity and congruence to find missing angles or sides of figures.
.8 Graph translations, rotations, reflections and dilations of plane figures and describe the transformation in words and symbols.
.9 Describe the use of translations, reflections and rotations in a tessellation (e.g., Escher drawing).
.10 Draw a polygon that will not tessellate and explain why.
.11 Model and apply the Pythagorean Theorem.

8:6 Measurement

.1 Use, compare, and convert between units in the metric system for length, mass, area, and volume.
.2 Use, compare, and convert between units in the standard system for length, time, weight, area and volume.
.3 Use multiple strategies, including formulas, to find rates and to find volume and surface area; use correct units.
.4 Explain what precision can be expected when measuring.
.5 Use indirect measurement to solve problems.
.6 Explain what happens to ratios when changes are made to one or more dimensions of a figure.
.7 Use manipulatives or diagrams to explain the Pythagorean Theorem.
.8 Solve practical problems involving proportions, the Pythagorean Theorem, and ¹

8:7 Statistics

.1 Present data as a scatter plot, stem & leaf, circle graph, line graph, histogram, box & whiskers, and bar graph; make an argument for which graph best represents the data.
.2 Find a line of best fit or trend line for a given set of data and use it to predict future outcomes.
.3 Analyze data using patterns or trends and make decisions or defend a conclusion.
.4 Explain or demonstrate how statistics are used to influence decisions.
.5 Conduct an experiment or simulation that leads to a generalization or formula.
.6 Identify rules and formulas, based on multiple experiments and observed outcomes.

8:8 Probability

.1 Express the theoretical and experimental probabilities of dependent, independent and multiple (compound) events as a ratio or percent.
.2 Predict the probability of a dependent event occurring, design an experiment to test the probability, compute the outcome, and compare it to the original prediction.
.3 Use a variety of strategies to determine the number of possible outcomes.

8:9 Patterns

.1 Identify and explain a classic pattern (e.g. Pascal's Triangle, Fibonacci Numbers, Pythagorean Triples, etc.).
.2 Translate an arithmetic or geometric pattern into a rule.
.3 Find a rule from a sequential pattern and translate it into symbolic form to determine the nth term.
.4 Use patterns from tables or graphs to predict an outcome.
.5 Use patterns as a strategy for solving problems.
.6 Find a missing item in an arithmetic and geometric sequence, with and without a calculator, and predict the graph of each function.
.7 Use tables of ordered pairs, graphs on coordinate planes, and linear equations as tools to represent and analyze patterns.

8:10 Algebra

.1 Translate word problems into numerical expression, inequalities, or equations.
.2 Write word problems from symbolic statements.
.3 Solve and graph two-step equations and inequalities.
.4 Graph the equation of a line that is in slope/intercept form.
.5 Identify slopes as positive, negative, zero, or undefined.
.6 Combine like terms to simplify expressions.
.7 Use order of operations including grouping symbols and exponents to solve problems.
.8 Use the commutative, associative, and distributive and properties of 0 and 1 to solve two-step equations and check the solutions.
.9 Represent a linear function as a table and a graph.

8:11 Problem Solving

.1 Evaluate, interpret, and justify solutions to problems.

8:12 Communication

.1 Explain and use a variety of problem solving strategies.
.2 Represent a problem numerically, graphically, symbolically, and translate between these alternative representations.
.3 Use math vocabulary, symbols, and notations to explain, justify, and defend mathematical ideas.

8:13 Reasoning

.1 Recognize and apply deductive and inductive reasoning in both concrete and abstract contexts.

8:14 Connections

.1 Use mathematical ideas from one area of mathematics to explain an idea from another area of mathematics (e.g., algebra to geometry).
.2 Translate between various representations of equivalent representations.