7-8 Grade Math
by Andrea Anderson
March 22, 2005
8.1.1 By the end of the eighth grade, students will recognize natural numbers, whole numbers, integers and rational numbers.
Define and understand the term rational number and demonstrate examples of rational numbers.
Define and understand the term integers and demonstrate examples of integers.
Compare and contrast rational numbers.
Properly utilize whole numbers, integers and rational numbers in real world situations.
Describe and compare relationships among all subsets of real numbers.
Demonstrate through graphing, rational numbers.
8.1.2 By the end of the eighth grade, students will determine equivalences among fractions, decimals and percents.
Represent decimals beyond the thousandths place.
Convert decimals to percents and vice versa.
Convert fractions to percents and vice versa.
Convert decimals to fractions and vice versa.
Find the equivalences between fractions, decimals, and percents.
Problem solve using fractions, decimals and percents.
8.1.3 By the end of eighth grade, students will write and use numbers in expanded exponential form and scientific notation.
Express numbers small and large in scientific notations.
Multiply numbers in scientific notation w and w/o calculators.
Divide numbers in scientific notation w and w/o calculators.
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.
Recognize the prime numbers 1 to 100.
Define the GCF.
Define the LCM.
Demonstrate an understanding of the associative, commutative, distributive, identity, inverse and distributive properties.
Solve problems using the order of operations to simplify numerical expressions involving a combination of grouping symbols.
Find the prime factorization of numbers using a factor tree and written with exponents.
Find the GCF and LCM for 2 or more numbers using a factor tree.
Determine the factors of a number using the divisibility tests of 2, 3, 5, 6,10 and 25.
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.
Add, subtract, divide and multiply proper and improper fractions with like and unlike denominators using technology and answers in lowest terms.
Add, subtract, divide and multiply mixed numbers with like and unlike denominators using technology and answers in lowest terms.
Add, subtract, multiply and divide decimals with 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.
Students will solve problems by identifying appropriate operations:
add, subtract, multiply and divide fractions.
add, subtract, multiply and divide decimals.
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.
Solve problems with whole numbers, fractions, decimals, percents w and w/o calculator.
Solve problems with integers and ratios w and w/o calculator.
Use proportions to solve scale model problems.
8.2.4 By the end of eighth grade, students will apply the order of operations to solve problems with and without the use of technology.
Solve problems by applying order of operations with exponents and nested parentheses w and w/o calculators.
8.2.5 By the end of eighth grade, students will apply strategies of estimation when solving problems with and without the use of technology.
Estimate all basic operations on problems with 4 digit numbers w/o calculators.
Use compatible numbers to perform mental math.
Estimate square roots of whole numbers up to 100 to the nearest whole number.
Use estimation fo check the reasonableness of an answer when using problem solving.
Properly round to an appropriate place value.
Perform estimation prior to calculations.
Determine the square root of a number between which to whole numbers
8.3.1 By the end of 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.
Choose appropriate tool and measure length to the nearest 1/16” and express in lowest terms.
Find perimeter by using appropriate tools of regular and irregular polygons in standard and metric units, by using a formula.
Use appropriate tools to measure area of regular and irregular polygons in standard and metric units.
Use appropriate tools to measure volume of a rectangular prism in metric and standard units.
Convert customary units of area. (square inches, square feet, square yard, square mile)
Use appropriate standard and metric measures to find circumference and area of circles.
Use appropriate tools to measure volume of cyclinders and cones in metric and standard units.
Measure angles using a protractor.
8.3.2 By the end of eighth grade, students will convert units within measurement systems using standard and metric, given conversion factors.
Convert customary capacity units. (cup, pint, quart, gallon. fl. ounce)
Convert customary units of length. (inch, feet, yard, mile)
Convert metric units of length, capacity and mass. (mm,cm,m,km,ml,l,kl,mg,g,kg)
Convert from customary system to metric system given the conversion formulas.
8.4.1 By the end of eighth grade, students will identify, describe, compare and classify 2 and 3 dimensional geometric figures(plane and 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.
Classify different types of triangles and quadrilaterals.
Compare and contrast different 3-D solid figures.
Describe the properties of lines, line segments, rays, angles, parallel and perpendicular.
Describe and define all types of plane figures.
Describe and define all types of angles using a protractor.
8.4.2 By the end of eighth grade, students will use geometric properties, the Pythagorean theorem and the relationships of congruence, similarity and symmetry.
Apply the properties of similar polygons to solve problems.
Apply the Pythagorean Theorem to solve problems.
Apply the properties of symmetry.
Demonstrate an understanding of numerical squares and square roots.
Apply properties of angles formed by parallel and perpendicular lines.
8.4.3 By the end of eighth grade, students will use formulas to solve problems involving perimeter and area of square, rectangle, parallelogram, trapezoid and triangle and area and circumference of circles.
Calculate using formulas:
perimeter of rectangles
perimeter of squares
perimeter of triangles
perimeter of parallelograms
perimeter of trapezoids
perimeter of triangles
circumference of circles
Calculate using formulas:
area of rectangles
area of squares
area of parallelograms
area of trapezoids
area of triangle
area of circles
8.4.4 By the end of eighth grade, students will solve problems given formulas for volume and surface area of rectangular prisms, cylinders and cones.
Solve problems involving surface area of rectangular prisms, using formulas.
Solve problems involving volume of rectangular prisms, using formulas.
Solve problems involving surface area of cylinders and cones, using formulas.
Solve problems involving volume of cylinders and cones, using formulas.
8.4.5 By the end of eighth grade, students will apply transformations to 2 and 3 dimensional geometric figures.
Draw transformations of geometric figures such as slides, flips and turns.
Use scale factor on a given polygon in order to draw a similar polygon.
8.4.6 By the end of eighth grade, students will use geometric terms and representations to describe the physical world.
Identify and draw geometric figures to solve real-world problems involving area and perimeter of:
parallelograms
trapezoids
triangles
Identify and draw plane figures and solids to solve real-world problems involving:
area
perimeter/circumference
surface area
volume
8.5.1 By the end of eighth grade, students will collect, construct, and interpret data displays and compute mean, median and mode.
Collect, analyze, interpret and display data from a variety of representations. (charts, tables, graphs)
Display data in a line graph, scatter graph and pie graph.
Calculate mean, median and mode given a set of data.
8.5.2 By the end of eighth grade, students will read and interpret tables, charts and graphs to make comparisons and predictions.
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 theoretical probability and relative frequency.
Conduct a probability experiment and explain the results.
Compare the results of relative frequency to the theoretical probability.
8.5.4 By the end of eighth grade, students will identify statistical methods and probability for making decisions.
Recognize and use measures of central tendency appropriately.
Identify the use of appropriate sampling techniques.
Identify the use of appropriate charts and graphs.
8.6.1 By the end of eighth grade, students will demonstrate knowledge and use of the one and two dimensional coordinate systems.
Locate and graph ordered pairs on the coordinate plane.
Generate a table of ordered pairs to graph an equation in two variables.
Identify parts of a coordinate plane.
Graph and locate numbers on a number line.
Graph inequalities on a number line.
8.6.2 By the end of eighth grade, students will apply algebraic concepts and operations to solve linear equations and word problems.
Solve mult-step equations with one variable.
Use properties to simplify expressions with one or more variables.
Solve 3 step equations with one variable and real numbers.
Use the 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 fo zero.
Write and solve algebraic equations given a story problem.
8.6.3 By the end of eighth grade, students will describe and represent relations, using tables, graphs and rules.
Create an x,y table for one step equations.
State the one step equations for an x,y table.
Graph a given table of data.
Complete a table involving two variables
Construct a table of values for a given graph.
Use variables to recognize and describe patterns.
