2nd Six Weeks Newsletter - Region 13

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$Grade 8 Math STAAR and STAAR-M Fall 2012 by Objective$

2010—2011 Second Six Weeks PreviewMathematicsOne- and two-step equations were introduced in Grades 7 and 8. In Grade 7, concrete and pictorial models were used tosolve the equations, and symbols were used to record the actions. In Grade 8, equations were used to find solutions toapplication problems. In this lesson, one- and two-step equations will be reviewed using various representations. Theproperties of algebra will be used to simplify algebraic expressions and applied to multiple step equations. Equations aresolved using various representations such as concrete models, tables, graphs, and algebraic properties. Equations aredetermined for application problems, solved by a method of choice, and the solution justified in terms of the problemsituation. These skills are necessary not only in Algebra 1, but in subsequent courses in mathematics.Unit 3: Investigating Linear Functions. The student expectations bundled in this unit explore linear functions and theirconnections to linear equations. The unit begins by investigating the linear parent function and the effects of changingthe parameters on the graph of the parent function. The parameters of the parent function are connected to the slopeand y-intercept. Linear characteristics including slope, y-intercepts, and x-intercepts (zeros) are further developed usingmultiple representations such as tables, graphs, verbal descriptions and symbolic representations in a variety of ways tostudy relationships among quantities and connect algebraic and geometric representations of linear functions. Equationsand inequalities arise as a way of making predictions involving linear functions. Comparisons are made between the zerosof a linear function, the solutions of a linear equation, and the solutions of a linear inequality. The unit culminates indata collection activities and real- world problem solving that integrate all of the above concepts.In middle school mathematics, the initial understanding of the use of variables to represent quantities is introduced. Linearfunctions are investigated to develop the meaning of proportionality. Generating of equivalent expressions, solvingsimple linear equations, and application of formulas are part of the middle school curriculum. Future units will includefinding the equation of a line, solving linear equations and inequalities, and exploring linear systems of equations.GeometryUnit 5: Logical Reasoning. This unit bundles student expectations that address the process of logical reasoning. In thisunit, logical reasoning is used to determine the validity of statements, construct arguments to provide proof, and analyzesituations to find counterexamples. Both inductive and deductive reasoning is used to explore geometric situations, anddeductive reasoning is used to support arguments related to emerging theorems.Unit 6: Properties of Lines and Transversals. This unit bundles student expectations that address the relationshipbetween lines and their transversals, especially between parallel lines and their transversals. In this unit, students exploreparallel and perpendicular lines in the context of special angle pairs while connecting to algebraic representations.Students justify special angle pairs formed by parallel lines within an axiomatic system and justify parallel and perpendicularlines both geometrically and algebraically.Logical reasoning explored in the previous unit is applied to justify conjectures about properties of parallel lines andtransversals in this unit. Properties of parallel lines and transversals are used with concepts from Algebra 1 to connectgeometry with algebra. Properties of parallel lines and transversals will continue to be used to justify conjecturesthroughout the geometry curriculum.Unit 7: Triangles and Their Properties. This unit bundles student expectations that address connections between trianglesand their properties. In this unit, students explore properties and classifications of triangles in a variety of ways includingcoordinate, concrete, axiomatic and algebraic. Slope and equations of lines will be used to investigate and comparespecial segments of triangles.As addressed in previous units, students should enter high school understanding most of the properties of triangles. Inhigh school geometry, this knowledge is extended and applied using deductive reasoning to establish or refute conjecturesabout triangles and their properties. Triangles and their properties play a key role in developing other geometricconcepts including congruent triangles, area and volume, similar figures, and the study of other polygons. These understandingscan be applied when exploring spatial and geometric concepts throughout the geometry curriculum.Unit 8: Congruent Triangles. This unit bundles student expectations that address triangle congruence relationships andapplication of logical reasoning to justify congruence. In this unit, the concept of congruence is extended to the simplestof polygons, triangles. Congruent triangles are explored both from the standpoint of congruent transformations and anaxiomatic structure. Triangle congruence is justified using congruent transformations and proofs with postulates andtheorems. Concepts of congruent triangles are extended to prove further characteristics of triangles using CorrespondingParts of Congruent Triangles.16
2010—2011 Second Six Weeks PreviewMathematicsAs addressed in previous units, students should enter high school with an understanding of congruent figures. In highschool geometry, this knowledge is extended and applied using deductive reasoning to establish or refute conjecturesabout congruent triangles. These understandings can be applied and extended when exploring other congruent figuresand similar figures.Mathematical Models with ApplicationsUnit 3: Statistics: Bivariate Data. The student expectations bundled in this unit involve collection and analysis of bivariatedata. In this unit, students incorporate the use of graphical and numerical analysis of the patterns in bivariate (twovariables) data for interpretation, validation, and making inferences in real-world problem situations.In middle school, students laid the foundations for bivariate statistics including graphing scatterplots. In Algebra 1, scatterplotswere graphed and analyzed for correlation. In Math Models with Applications, this is extended to include findingregression equations that best model data represented in scatterplots. Analysis of bivariate data continues in Algebra 2and Precalculus as students analyze real-world situations and select functions that best fit the data.Unit 4: Statistics Project. The student expectations bundled in this unit involve formulating a hypothesis, collectingdata, analyzing data, and presenting the findings. In this unit, students will combine the student expectations from previousunits to design a problem situation of their own that can be tested by data collection and analysis. They will incorporatethe use of graphical and numerical analysis of the patterns in data for interpretation, validation, and making inferencesin their problem situation. Students will then create displays and present their findings.Concepts developed in the first three units of study in Math Models with Applications will be applied in this unit to developand complete the statistics project. The ability to formulate a hypothesis, collect and analyze data to test the hypothesis,and present the findings are skills that can be applied in other mathematics and science courses, as well as inthe real world.Algebra IIUnit 4: Linear Functions, Equations, and Inequalities. The student expectations bundled in this unit investigate andexplore the characteristics and applications of linear functions, equations, and inequalities. In this unit the linear parentfunction is introduced and effects of parameter changes on the graph of the parent function are explored. Linear functionsare modeled using various representations and characteristics such as slope and intercepts are determined andanalyzed. Equations and inequalities are formulated, modeled, and solved by various methods to make predictions interms of problem situations.In middle school mathematics, the initial understanding of the use of variables to represent quantities is introduced. Linearfunctions are investigated to develop the meaning of proportionality. The generating of equivalent expressions, solvingsimple linear equations and formulas are experienced. In high school mathematics according to the TEKS, symbolicreasoning plays a critical role in algebra and provides powerful ways to represent mathematical situations and expressgeneralizations. Linear functions are further developed using multiple representations such as tables, graphs, verbal representations,and symbolic representations in a variety of ways to study relationships among quantities and connect algebraicand geometric representations of functions. Equations and inequalities arise as a way of asking and answeringquestions involving functional relationships.Unit 5: Linear Systems and ProgrammingThe student expectations bundled in this unit involve the application of systems of equations and inequalities to solveproblem situations. While previous units typically explored one relationship at a time, this unit on systems of equationsrequires students to work with two or more relationships simultaneously. Systems of equations and inequalities are exploredthrough tabular, graphical, and algebraic methods. In addition, special attention is given to interpreting situationsin verbal form. Students are provided with concrete strategies for taking “word problems” and translating them into algebraicmodels to be solved and analyzed.In Algebra 1, students formulated and solved 2x2 systems of equations. In Algebra 2, students extend their investigationsto include linear programming and 3x3 systems of equations. In later units, students will also apply these skills tosolve systems involving non-linear systems. Solving systems of equations and inequalities develops the algebraic skillsnecessary in many real-world situations.17
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2nd Six Weeks Newsletter - Region 13

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