Grade 8 Mathematics

8.1.1  By the end of the eighth grade, students will recognize natural numbers, whole numbers, integers, and rational numbers.

8.1.2  By the end of the eighth grade, students will determine equivalences among fractions, decimals, and percents. (Find the equivalencies among fractions, decimals, and percents; solve problems with appropriate equivalencies.)

8.1.3  By the end of the eighth grade, students will write and use numbers in expanded exponential form and scientific notation. (Write numbers in expanded form using exponential notation; express small and large numbers using scientific notation.)

8.1.4  By the end of the eighth grade, students will identify and display numbers including prime and composite, factors and multiples, divisibility, powers, and properties. (Properties of numbers may include but not be limited to order of operations, commutative, associative, distributive, identity, and inverse.)

8.2.1  By the end of the eighth grade, students will add, subtract, multiply, and divide decimals and proper, improper, and mixed fractions with uncommon and common denominators with and without the use of technology.

8.2.2  By the end of the eighth grade, students will identify the appropriate operation and do the correct calculations when solving word problems.

8.2.3  By the end of the eighth grade, students will solve problems involving whole numbers, integers, and rational numbers (fractions, decimals, ratios, proportions, and percents) with and without the use of technology. (Use proportions to solve scale-model problems with fractions and decimals; problems should be of increasing level of difficulty and involve real-life situations.)

8.2.4  By the end of the eighth grade, students will apply the order of operations to solve problems with and without the use of technology. (Evaluate all types of numerical expressions, including grouping symbols and exponents.)

8.2.5  By the end of the eighth grade, students will apply strategies of estimation when solving problems with and without the use of technology. (Properly round to an appropriate place value if context permits; perform estimation prior to calculation; without a calculator, estimate square roots of whole numbers up to one hundred to the nearest whole number; use compatible numbers to perform mental math; use estimation to check reasonableness of an answer.)

8.3.1  By the end of the eighth grade, students will select measurement tools and measure quantities for temperature, time, money, distance, angles, area, perimeter, volume, capacity, and weight/mass in standard and metric units at the designated level of precision.

8.3.2  By the end of the eighth grade, students will convert units within measurement systems using standard and metric, given conversion factors. (Convert between various units of area and various units of volume [square foot to square yards and cubic decimeters to liters, etc.]; check solutions to problems using unit analysis [feet/second to miles/hour].)

8.4.1  By the end of the eighth grade, students will identify, describe, compare, and classify two-and three- dimensional geometric figures (plane figures like polygons) and (circles and 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 the eighth grade, students will use geometric properties, the Pythagorean theorem, and the relationships of congruence, similarity, and symmetry.

8.4.3  By the end of the eighth grade, students will use 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 the eighth grade, students will solve problems given formulas for volume and surface area of rectangular prisms, cylinders, and cones.

8.4.5  By the end of the eighth grade, students will apply transformations to two- and three- dimensional geometric figures. (Draw geometric figures using translations or slides, rotations or turns, reflections or flips, and scale.)

8.4.6  By the end of the eighth grade, students will use geometric terms and representations to describe the physical world.

8.5.1  By the end of the eighth grade, students will collect, construct, and interpret data displays and compute mean, median, and mode. (Select appropriate representations of data when constructing data displays [graphs, tables, or charts].)

8.5.2  By the end of the eighth grade, students will read and interpret tables, charts, and graphs to make comparisons and predictions.

8.5.3  By the end of the eighth grade, students will conduct experiments or simulations to demonstrate theoretical probability and relative frequency. (Compare the results of a simulation [relating frequency] to the theoretical probability [a three color spinner or a coin].)

8.5.4  By the end of the eighth grade, students will identify statistical methods and probability for making decisions. (Identify the use of appropriate sampling techniques; identify the use of appropriate charts and graphs; identify the use of measures of central tendency [mean, median, mode] appropriately.)

8.6.1  By the end of the eighth grade, students will demonstrate knowledge and use of the one- and two dimensional coordinate systems. (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 the eighth grade, students will apply algebraic concepts and operations to solve linear equations and word problems. (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 the eighth grade, students will describe and represent relations, using tables, graphs, and rules. (Use variables to recognize and describe patterns.)

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