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Mathematics Standards
Grade 8
8.1 Numeration/Number Sense
8.1.1 By the end of eighth grade, students will
recognize and utilize real numbers such as whole numbers, integers, and rational
numbers.
8.1.2 By the end of eighth grade, students will apply relationships between
fractions, decimals, and percents in a variety of situations.
Student demonstrations:
· Find the equivalencies between fractions, decimals, and percents.
· Solve problems with appropriate equivalencies.
8.1.3 By the end of eighth grade, students will
represent and use numbers in a variety of different forms.
Student demonstrations:
· Write numbers in expanded form using exponential notation.
· Express small and large numbers using scientific notation.
8.1.4 By the end of eighth grade, students will apply
appropriate use of number theory such as prime and composite, factors and
multiples, divisibility, powers, properties, and identities.
8.2 Computation/Estimation
8.2.1 By the end of eighth grade, students will add, subtract, multiply, and
divide decimals and proper, improper, and mixed
fractions with uncommon and common denominators both with and without the use of
technology.
8.2.2 By the end of eighth grade, students will identify the appropriate
operation and do the correct calculations to solve word problems.
8.2.3 By the end of eighth grade, students will solve problems involving whole
numbers, integers, and rational numbers (fractions, decimals, ratios,
proportions, and percents) both with and without the use of technology. Problems
will be of varying complexities and can involve real-life data.
Student demonstrations:
· Use proportions to solve scale-model problems with fractions and decimals.
8.2.4 By the end of eighth grade, students will apply
the order of operations to solve problems both with and without the use of
technology.
Student demonstrations:
· Evaluate all types of numerical expressions, including grouping symbols and exponents.
8.2. By the end of eighth grade, students will apply
strategies of estimation to a variety of problems both with and without the use
of technology.
Student demonstrations:
· Properly round to an appropriate place value if context permits.
· Perform estimation prior to calculation.
· Without a calculator, estimate square roots of whole numbers of zero to one hundred to the nearest whole number.
· Use compatible numbers to perform mental math.
8.3
Measurement
8.3.1 By the end of eighth grade, students will select appropriate tools and
properly measure quantities for temperature, time, money, length and width, area
and perimeter, volume and capacity, weight and mass in both standard and metric
units at the level of precision required.
8.3.2 By the end of eighth grade, students will convert units within
measurement systems using proper conversion factors (standard and metric).
Student demonstrations:
· Convert between various units of area and various units of volume, such as square foot to square yards and cubic decimeters to liters, etc.
· Check solutions to problems using unit analysis such as feet/second to miles/hour.
8.4 Geometry/Spatial Concepts
8.4.1 By the end of eighth grade, students will identify, describe, compare, and
classify geometric figures such as plane figures like polygons and circles;
solid figures like prisms, pyramids, cones, spheres, and cylinders; and lines,
line segments, rays, angles, parallel and perpendicular lines.
8.4.2 By the end of eighth grade, students will understand and apply geometric
properties and relationships of congruence, similarity, symmetry, and
Pythagorean theorem.
8.4.3 By the end of eighth grade, students will understand and apply the
formulas to solve problems involving perimeter and area of a square, rectangle,
parallelogram, trapezoid and triangle and area and circumference of circles.
8.4.4 By the end of eighth grade, students will solve
problems using the formulas for volume and surface area of rectangular prisms,
cylinders, and cones.
8.4.5 By the end of eighth grade, students will apply transformations to
geometric figures such as translations or slides, rotations or turns,
reflections or flips, and scale or dilate.
8.4.6 By the end of eighth grade, students will use geometric representations to
solve problems and describe the physical world.
8.5 Data Analysis, Probability, and Statistical Concepts
8.5.1 By the end of eighth grade, students will collect, analyze, interpret, and
display data.
Student demonstrations:
· Determine and calculate the appropriate measure of central tendency to describe the data set.
· Use appropriate representations of data such as graphs, tables, and charts.
· 8.5.2 By the end of eighth grade, students will read and interpret tables, charts, and graphs to make comparisons, predictions, and inferences.
· 8.5.3 By the end of eighth grade, students will conduct experiments or simulations to demonstrate an understanding of theoretical probability and relative frequency.
· 8.5.4 By the end of eighth grade, students will recognize appropriate use of statistical methods and appropriate use of probability as a means for decision making.
Student demonstrations:
· Recognize and use appropriate sampling techniques.
· Recognize and use appropriate charts and graphs.
· Recognize and use measures of central tendency appropriately.
8.6 Algebraic Concepts
8.6.1 By the end of eighth grade, students will demonstrate knowledge and use of
the one- and two-dimensional coordinate systems.
Student demonstrations:
· Order numbers on a number line.
· Graph ordered pairs on a coordinate plane.
· Generate a table of ordered pairs to graph an equation in two variables.
8.6.2 By the end of eighth grade, students will apply
algebraic concepts and algebraic operations to solving problems.
Student demonstrations:
· Solve multi-step equations with one variable.
· Use order of operations to evaluate algebraic expressions for given replacement values of the variables.
· Recognize and apply commutative, associative, distributive, inverse, and identity properties, and the properties of zero.
8.6.3 By the end of eighth grade, students will
describe and represent relations, using tables, graphs, and rules.
Student demonstrations:
· Use variables to recognize and describe patterns.
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