Eighth Grade Geometry – For High School Credit
Recommended Prerequisite: Algebra I
Grades Offered: 8
Credit: 1
SDE Course Code: 3108
MNPS Course Code: MTH4038Y
Course Description
Geometry develops the concepts of plane, solid, and coordinate geometry through the use of proofs, both deductive and inductive, while simultaneously developing logical thought and reasoning processes.
Course of Study
Number Sense and Number Theory
· The student will recognize, order, represent, and graph rational and irrational numbers
○ Demonstrate an understanding of the relative size of rational and irrational numbers by …
§ Matching a given irrational number to the appropriate point on a number line
§ Ordering a set of rational and irrational numbers
Estimation, Measurement, and Computation
· The student will apply appropriate units of measurement; develop effective estimation and computation strategies for solving real-world problems involving length, area, and volume; and choose appropriate techniques and tools to measure quantities in order to meet specifications for precision, accuracy, and tolerance
○ Use concepts of length, area, and volume to estimate and solve real-world problems by …
§ Determining the perimeter or area of a triangle or rectangle when the dimensions are given as binomials in one variable
§ Determining the perimeter or area of a triangle or rectangle in a real-world situation given the dimensions expressed as linear algebraic expressions in one variable
§ Determining the volume or surface area of a rectangular solid in a real-world situation
○ Apply measurement concepts and relationships in algebraic and geometric problem-solving situations where appropriate to determine the length, perimeter, area, surface area, and volume for two- and three-dimensional figures in real world situations
○ Choose appropriate techniques and tools to measure quantities in order to meet specifications for precision, accuracy, and tolerance
Patterns, Functions, and Algebraic Thinking
· The student will recognize, extend, and create, and analyze a variety of geometric, spatial, and numerical patterns; solve real-world problems related to algebra and geometry; and use properties of various geometric figures to analyze and solve problems
○ Recognize, extend, and create geometric, spatial, and numerical patterns to:
§ Extend a geometric pattern
○ Analyze mathematical patterns related to algebra and geometry in real-world problem solving to:
§ Solve multi-step linear equations applied to geometric figures
§ Solve systems of two linear equations with integral coefficients to find length, width, perimeter, and area of geometric figures
§ Solve systems of two linear equations with integral coefficients to determine if the lines are parallel, intersecting, or coinciding
§ Choose the equations of parallel or perpendicular lines given either the coordinates or the graphs
§ Apply the concept of rate of change from a pattern of data
○ Solve problems in number theory, geometry, probability and statistics, and measurement and estimation using algebraic thinking and symbolism by …
§ Applying ratio and proportion to problems involving polygons
§ Applying the triangle inequality property to determine if a triangle exits and to order by size both its angles and sides
§ Identifying by graphical representation the inequality that represents the possible lengths of the third side of a triangle when given the other two sides
§ Determining the perimeter, area, surface area, or volume given the ratio of two similar geometric figures
§ Applying the Triangle Sum or Exterior Angle Theorems to determine the measures of the angles of a triangle when the angle measures are expressed algebraically
§ Applying the properties of angles, arcs, chords, tangents and/or secants to solve problems
§ Determining the equation of a circle given the graph of the circle or the coordinates of important points (e.g., center, endpoints of diameter)
○ Apply coordinate geometry to analyze and solve problems by …
§ Determining the slope given the graph of a linear equation
§ Determining the distance, midpoint, or slope when given the coordinates of two points
Statistics and Probability
· The student will investigate, explore, and apply geometric representations to calculate theoretical probability
○ Apply geometric representations to calculate theoretical probability by …
§ Making a prediction from a geometric representation of a real-world data set
§ Determining the probability of an even using a spinner and a circle graph
§ Determining the probability of an event represented as a subset of the area of a two-dimensional geometric figure
Spatial Sense and Geometric Concepts
· The student will investigate, model, and apply geometric properties and relationships and use indirect reasoning to make conjectures; deductive reasoning to draw conclusions; and both inductive and deductive reasoning to establish the truth of statements
○ Analyze relationships among corresponding parts of similar and congruent figures by …
§ Comparing congruence or similarity between triangles or quadrilaterals given a diagram
§ Solving problems involving complementary, supplementary, congruent, vertical, or adjacent angles given angle measures expressed algebraically
§ Solving problems involving the angles formed when parallel lines are cut by transversals
○ Apply geometric properties of solids, polygons, and circles to real-world problems
§ Applying the reflexive, transitive, or symmetric properties of equality
§ Applying properties of quadrilaterals to solve real-world problems given a diagram
§ Solving real-world problems using measures of interior and exterior angles of regular polygons
§ Determining which three-dimensional solid is represented by a given net
§ Determining the area of shaded regions involving circles and polygons
§ Solving problems using the properties of angles, arcs, chords, tangents, and secants
§ Finding the area of a sector or segment of a circle given a diagram
○ Justify conclusions using deductive reasoning to
§ Determine whether triangles in a diagram are congruent because the ASA, SSS, AAS, SAS, or hypotenuse-leg theorems apply to the given situation
§ Determine if a triangle is acute, obtuse, or right given the lengths of the sides of a triangle
○ Use inductive reasoning to make conjectures
○ Communicate position using spatial sense of two- and three-dimensional coordinate systems
○ Demonstrate an understanding of transformations of geometric figures by …
§ Determining whether a figure has been translated, dilated, reflected, or rotated given a diagram
§ Choosing the three-dimensional geometric object that has been rotated or reflected given a diagram
○ Apply right triangle relationships including the Pythagorean Theorem, the distance formula, and trigonometric ratios by …
§ Determining the length of the missing side of a right triangle
§ Determining the trigonometric ratio of a right triangle needed to solve a real-world problem given a diagram
§ Solving real-world problems using 30-60-90 and 45-45-90 degree triangles
○ Demonstrate understanding of geometric properties of congruence, similarity, perpendicularity, and parallelism
○ Recognize and articulate relationships among families of geometric figures (e.g. quadrilaterals, prisms)
○ Use indirect and deductive reasoning to establish the truth of a statement
Eighth Grade TCAP indicators should be reviewed to prepare students for success on spring testing.
Number and Operations
· Determine the square root of perfect squares
· Work flexibly with fractions, decimals, and percents in word problems
· Understand and use ratios and proportions to represent quantitative relationships
· Recognize and use exponential, scientific, and calculator notation to write large numbers
in real-world situations
· Identify the opposites and reciprocal for an integer
· Identify the opposite of a rational number
· Use the distributive property to simplify computations with integers, fractions, and
decimals
· Apply order of operations in computing with rational numbers
· Estimate the results of rational number computations in real-world situations
· Judge the reasonableness of the results of rational number estimates and computations
· Develop, analyze, explain, and use methods for solving problems involving proportions
· (e.g., scaling, finding equivalent ratios)
· Calculate rates involving cost per unit to determine the best buy
Algebra
· Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and when possible symbolic rules
· Formulate multi-step equations that represent relationships and real-world situations
· Use symbolic algebra to represent situations and solve problems.
· Recognize and generate equivalent forms for simple algebraic expressions
· Evaluate a first-degree algebraic expression given values for two or more variables
· Solve one- and two-step linear equations involving integers
· Apply given formulas to solve real-world problems
· Solve one-step linear inequalities
· Identify the graph of a linear equation and vice versa
· Interpret graphs that represent rates of change in real-world situations
Geometry
· Describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties
Measurement
· Understand relationships among units and convert from one unit to another within the same system
· Understand, select, and use units of appropriate size and type to measure angles, perimeter, areas, surface area, and volume
· Use a variety of strategies to estimate length, perimeter, circumference, area, and volume
· Select and apply techniques and tools to accurately measure length, perimeter, area, volume, and angles to appropriate levels of precision
· Apply formulas and/or other strategies to solve problems involving perimeter, circumference of circles, and the area of triangles, parallelograms, trapezoids, and circles
· Find area of complex and irregular shapes
· Solve problems involving rate/time/distance (i.e., d = rt )
· Solve problems involving scale factors using ratio and proportion
· Construct tables and graphs to represent rates of change
Data Analysis and Probability
· Select, create, interpret, and use appropriate graphical representations of real-world data (e.g., histograms, box plots, scatterplots)
· Determine and interpret measures of center and spread (e.g., mean, median, interquartile range)
· Discuss and understand the relationship between data sets and their graphical representations (e.g., bar graphs, line graphs, circle graphs, histograms, stem-and-leaf plots, box plots, scatterplots)
· Recognize misleading presentations of data
· Determine an appropriate sample and sample size to test a hypothesis
· Connect the symbolic representation of a probability to an experiment
Standards:
MNPS Standards:
http://www.mnps.org/PageFactory.aspx?PageID=3403
State Standards:
http://www.state.tn.us/education/ci/cistandards2001/math/cimath.htm
Textbook:
Basal: Larson, et al, McDougal Littell Geometry, 2nd Edition, 2004, McDougal Littell
Online Textbook:
http://www.classzone.com/books/geometry/index.cfm
Recommended and/or required resources:
· TI 83+ Graphing Calculator or TI 92 or computer
· TCAP Item Sampler - http://www.state.tn.us/education/tsachsamp.htm
· Geometer’s Sketchpad or Cabri Geometry software
· A variety of manipulatives: graph paper, rulers, protractors, two-color counters, fraction bars, centimeter cubes or snap cubes, geoboards, miras, pattern blocks, compass, straight edge, tangrams, Cuisenaire rods, base ten blocks, color tiles, three-dimensional solids (e.g., sphere, cylinder, prism, cone, pyramid), meter sticks, etc.