Mathematics Curriculum Grade 8 - District 146

Eighth Grade Benchmark Math FrameworkWithin a well-balanced mathematics curriculum, the primary focal points at Grade 8 areusing basic principles of algebra to analyze and represent proportional and nonproportionalrelationships and using probability to describe data and make predictions.The course also covers the basics of the system of real numbers and the geometry of 3-dimensions. The big ideas in the course are:Focal Point 8.1: Real Numbers and IntegersStudents merge the integer, rational, and decimal number systems, along with theirrationals, to form the real numbers. The various representations for numbersare studied and the role of exponents in expressing such numbers is highlighted,especially with scientific notation. Students develop great fluency in operating withreal numbers and solving grade appropriate problems. These understandings arecharacterized by students developed abilities to:Enabling Objective 8.1.1: Eighth graders recognize and apply scientific notationwith or without a calculator.Performance Expectations:A. Read and write numbers using scientific notation.B. Interpret and display scientific notation on a calculator.C. Solve problems using scientific notationEnabling Objective 8.1.2: Eighth graders demonstrate an understanding ofintegers and integer operations.Performance Expectations:A. Evaluate expressions involving integers.B. Evaluate expressions containing positive and negative exponents.Enabling Objective 8.1.3: Eighth graders demonstrate an understanding of realnumbers.Performance Expectations:A. Estimate a reasonable answer prior to calculation by using appropriate toolsand procedures.B. Represent fractions, decimals, mixed numbers, percents and roots inmultiple forms.Property of Community Consolidated Schools District 146Tinley Park, ILNo quoting or citations without expressed permission of the DistrictJune, 2010

2Enabling Objective 8.3.1: Eighth graders apply measurement concepts, skills, tools,and formulas in solving problems involving all forms of linear, capacity, mass, angular,or time measurement.Performance Expectations:A. Convert linear measurements, area measurements, weights/masses, andcapacity measures within metric and customary systems to other measureunits within the same system.B. Estimate measurements of length, area, volume, weight/mass, angles, andtime.C. Work fluently with rulers, protractors, and other measurement devices inperforming direct or similarity (scaled) measurements.Enabling Objective 8.3.2: Eighth graders discern when to and how to apply thePythagorean Theorem.Performance Expectations:A. Know and apply the Pythagorean Theorem in finding unknown measures inright triangles and in verifying that a given triangle is a right triangle.B. Solve application problems using the Pythagorean Theorem.Enabling Objective 8.3.3: Eighth graders understand 2-D figures, 3-D figures,similarity, congruence and transformations.Performance Expectations:A. Apply concepts and formulas related to two- and three-dimensional figuresto find indicated lengths, perimeters/ circumferences, areas, volumes, andsurface areas.B. Know and apply concepts and properties of congruent and similar figures.C. Describe and draw the images of transformed figures on a coordinate gridindicating the translations, reflections, rotations, and scales involved.D. Apply rotational and reflectional symmetry and angle measurement toinvestigate properties of regular polygons.Focal Point 8.4: Data and ProbabilityStudents develop methods of deriving and describing chance in compound settings.Students use trees, tables, and graphical methods of describing the nature ofchance in two-stage experiments and related settings. They also expand theirProperty of Community Consolidated Schools District 146Tinley Park, ILNo quoting or citations without expressed permission of the DistrictJune 2010

3study of data to begin the study of variability in distributions of data. Theseunderstandings are characterized by students developed abilities to:Enabling Objective 8.4.1: Eighth graders understand simple probability.Performance Expectations:A. Determine and explain whether events are fair or outcomes are equallylikely to occur.B. Compute the probabilities for simple compound events, using such methodsas organized lists, tree diagrams, and area models.Enabling Objective 8.4.2: Eighth graders analyze and graph data.Performance Expectations:A. Explain how measures of variation (range, IQR, Q 1, Q 3 , outliers, clusters)describe the set of data.B. Formulate questions, design experiments and surveys, collect data, andconsider potential sources of bias in design and data collection (simulations)C. Select and produce a graphical representation of data (line graphs, bargraphs, stem-and-leaf plots, histograms, scatter plots, circle graphs, andbox-and whisker plots).D. Analyze and apply measures of central tendency.Focal Point 8.5: Expressions and EquationsStudents develop a robust understanding of linear equations by writing, reexpressing,and solving linear equations with integer coefficients and solutions.Equations in two variables are graphed on the coordinate plane and the nature oftheir graphs related to rate of change and location of solutions. Finally, studentssolve applied problems related to other topics in mathematics and topics in otherdisciplines using equations and formula. These understandings are characterized bystudents developed abilities to:Property of Community Consolidated Schools District 146Tinley Park, ILNo quoting or citations without expressed permission of the DistrictJune 2010

4Enabling Objective 8.5.1: Eighth graders simplify/solve algebraic expressions,linear equations and linear inequalities.Performance Expectations:A. Translate verbal and written words into algebraic expressions, equations,and inequalities.B. Recognize and generate equivalent forms for simple algebraic expressions.C. Analyze patterns to extend the pattern and to write an algebraicexpression for a given term in the pattern.D. Solve and graph one variable linear equations and linear inequalities thatmay have variables on both sides, negative coefficients, and fractionalcoefficients.Enabling Objective 8.5.2: Eighth graders graph linear equations.Performance Expectations:A. Use multiple representations to produce and represent functions in tables,graphs and symbolic form.B. Find and interpret the slope of a line from a table, graph, or problemcontext.C. Explore relationships between symbolic expressions and graphs of lines,paying particular attention to the meaning of intercept and slope.D. Understand, explain, and apply slope as a constant rate of change.E. Use tables and slope-intercept to graph linear equations.F. Graph and identify vertical and horizontal lines from equations and tables.G. Use graphs to analyze the nature of changes in quantities in linearrelationships.H. Interpret the coordinates of the vertical or horizontal intercepts in aproblem situation.Enabling Objective 8.5.3: Eighth graders use formulas to solve problems.Performance Expectations:A. Recognize and use distance = (rate) x (time) to handle distance and timeproblems.B. Apply geometric measurement formulas to solve problems.C. Be able to explain applications of algebra to real life situations and solveproblems with rate of change (using algebraic representations).Property of Community Consolidated Schools District 146Tinley Park, ILNo quoting or citations without expressed permission of the DistrictJune 2010

Property of Community Consolidated Schools District 146Tinley Park, ILNo quoting or citations without expressed permission of the DistrictJune 20105