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# Teaching of Mathematics ELED 3150

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This 13 page Class Notes was uploaded by Haleigh Larson Sr. on Wednesday October 21, 2015. The Class Notes belongs to ELED 3150 at Tennessee Tech University taught by Staff in Fall. Since its upload, it has received 17 views. For similar materials see /class/225740/eled-3150-tennessee-tech-university in Education at Tennessee Tech University.

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Date Created: 10/21/15

Eighth Grade Number and Operation Content Standard 10 The student will develop number and operation sense needed to represent numbers and number relationships verbally symbolically and graphically and to compute uently and make reasonable estimates in problem solving Learning Expectations 11 Understand numbers ways of representing numbers relationships among numbers and number systems 12 Understand operations and how they relate to one another 13 Solve problems compute uently and make reasonable estimates Accomplishments 811 Understand numbers ways ofrepresenting numbers relationships among numbers and number systems recognize the place value ofa given digit use exponents to express a monomial written in expanded form determine the square root of perfect squares use a variety of models to demonstrate the relationships within the real number system eg Venn diagrams webs work exibly with fractions decimals and percents to solve problems compare and order fractions decimals and percents connect whole numbers fractions decimals percents and integers to locations on the number line develop meaning for percents greaterthan 100 and less than one use appropriate mathematical language and symbols to express numerical relationships eg lt gt 12 understand and use ratios and proportions to represent quantitative relationships recognize and use exponential scienti c and calculator notation to represent large numbers in realworld situations demonstrate understanding of opposites reciprocals and integers identify the opposite ofa rational number use concrete pictorial and symbolic representations of integers apply numbertheory concepts to solve problems eg divisibility factors multiples composite numbers prime factorization relatively prime 73927 LOTquot39D 10039 22 0253 812 Understand operations and how they relate to one another m C39 000 understand the meaning and effects ofarithmetic operations with fractions decimals and integers apply the associative and commutative properties of addition and multiplication to simplify computations with integers fractions and decimals use the distributive property to simplify computations with integers fractions and decimals apply order ofoperations in computing with rational numbers understand and use the inverse relationships of addition and subtraction multiplication and division and squaring and nding square roots to simplify computations and solve problems 813 Solve problems compute uently and make reasonable estimates a 0039 DO LOTquot 339 select and use appropriate methods and tools for computing with whole numbers fractions decimals percents and integers in problemsolving situations eg mental computation estimation calculators computers paper and pencil develop and analyze procedures for computing with fractions decimals and integers develop and use strategies to estimate the results of rational number computations in real world situations judge the reasonableness of the results of rational number estimates and computations solve onestep realworld problems involving whole numbers fractions decimals and percents raise rational numbers to whole number powers solve multistep realworld problems involving whole numbers fractions decimals and percents develop analyze and explain methods for solving problems involving proportions eg scaling finding equivalent ratios calculate rates involving cost per unit to determine the best buy Eighth Grade Benchmarks Performance Indicators State As documented through state assessment at Level 1 the student is able to 81spi1 identify the opposite and the reciprocal ofa rational number 81spi2 compare rational numbers using the appropriate symbol lt gt at Level 2 the student is able to 81spi3 use ratios and proportions to represent realworld situations ie scale drawings probability 81 spi4 determine the approximate locations of rational numbers on a number line 81spi5 determine the square roots of perfect squares lt 169 81spi6 work flexibly with fractions decimals and percents to solve one and two step word problems 81spi7 compute efficiently and accurately with whole numbers fractions decimals and percents 81spi8 use estimation strategies to select a reasonable solution to a realworld problem involving computing with rational numbers 81spi9 calculate rates involving cost per unit to determine the best buy at Level 3 the student is able to 81spi10 use exponential scientific and calculator notation to represent large numbers in realworld situations 81spi11 apply order ofoperations in computing with rational numbers using no more than two parentheses and exponents 1 and 2 Performance Indicators Teacher As documented through teacher observation at Level 1 the student is able to 81tpi1 explain the inverse relationships of addition and subtraction multiplication and division and squares and square roots 81tpi2 apply the associative commutative and distributive properties to simplify computations with integers fractions and decimals at Level 2 the student is able to 81tpi3 develop meaning for integers 81tpi4 use concrete pictorial and symbolic representations of integers 81tpi5 represent quantitative relationships using ratios and proportions 81tpi6 understand the meaning and effects ofarithmetic operations with fractions decimals and integers 81 tpi7 select and use appropriate methods and tools for computing with whole numbers fractions decimals percents and integers in problemsolving situations ie mental computation estimation calculators computers paper and pencil 81tpi8 develop and analyze procedures for computing with whole numbers fractions decimals percents and integers in realworld situations 81tpi9 use a variety of models to demonstrate the relationship within the real number system ie Venn diagram web at Level 3 the student is able to Algebra 81tpi10 apply number theory concepts to solve problems ie divisibility relatively prime composite prime factorization factors multiples 81tpi11 express a monomial written in expanded form using exponents 81tpi12 develop analyze and explain methods for solving problems involving proportions ie scaling finding equivalent ratios Content Standard 20 The student will understand and generalize patterns as they represent and analyze quantitative relationships and change in a variety ofcontexts and problems using graphs tables and equations Learning Expectations Accomplishments 21 Understand patterns relations and functions 22 Represent and analyze mathematical situations and structures using algebraic symbols 23 Use mathematical models to represent and understand quantitative relationships 24 Analyze change in various contexts 821 Understand patterns relations and functions a C39 00 represent analyze and generalize a variety of patterns with tables graphs words and when possible symbolic rules develop understanding for arithmetic and geometric sequences relate and compare different forms of representation for a relationship identify functions as linear or nonlinear e compare and contrast properties of functions from tables graphs or equations 822 Represent and analyze mathematical situations and structures using algebraic symbols a formulate multistep equations that represent relationships and realworld situations b develop meaning for intercept and slope c use symbolic algebra to represent situations and solve problems d use a variety of forms to represent linear relationships e recognize and generate equivalent forms for simple algebraic expressions f evaluate a rstdegree algebraic expression given values for two or more variables g solve one and twostep linear equations involving integers h use a variety of methods to solve realworld problems involving multistep linear equations eg manipulatives technology pencil and paper apply given formulas to solve realworld problems solve onestep linear inequalities identify the graph of a linear equation identify the graphical representation ofthe solution to a onevariable linear inequality develop understanding for particular values of patterns relationships and functions eg x and y intercepts slope maximum and minimum values 3 39 823 Use mathematical models to represent and understand quantitative relationships a use a variety of representations to solve realworld problems eg graphs tables equations 824 Analyze change in various contexts a compare linear relationships to nonlinear relationships b develop meaning for rate of change in realworld situations Eighth Grade Benchmarks Performance Indicators State As documented through state assessment at Level 1 the student is able to 82spi1 generalize a variety of patterns with symbolic rules 82spi2 evaluate a firstdegree algebraic expression given values for two or more variables at Level 2 the student is able to 82spi3 represent situations and solve realworld problems using symbolic algebra 82spi4 connect symbolic expressions and graphs of lines 82spi5 generate equivalent forms for simple algebraic expressions 82spi6 solve one and twostep linear equations involving integers 82spi7 apply given formulas to solve realworld problems 82spi8 interpret graphs which represent rates of change at Level 3 the student is able to 82spi9 formulate multistep equations that represent relationships and realworld situations 82spi10 solve onestep linear inequalities 82spi11 connect the appropriate graph to a linear equation Performance Indicators Teacher As documented through teacher observation at Level 1 the student is able to 82tpi1 use a variety of forms to represent linear relationships 82tpi2 represent and analyze a variety of patterns with tables graphs and words at Level 2 the student is able to 82tpi3 use a variety of methods to solve realworld problems involving multistep linear equations ie manipulatives technology pencil and paper 82tpi4 compare and contrast different forms of representation for a relationship 82tpi5 compare and contrast properties of functions from tables graphs or equations 82tpi6 use a variety of representations to solve realworld problems ie graphs tables equations 82tpi7 compare linear relationships to nonlinear relationships at Level 3 the student is able to Geometry 82tpi8 develop meaning ofintercept slope and rate of change in realworld problems 82tpi9 develop understanding for arithmetic and geometric sequences 82tpi10 identify the graphical representation of the solution to a onevariable linear inequality Content Standard 30 The student will develop an understanding of geometric concepts and relationships as the basis for geometric modeling and reasoning to solve problems involving one two and threedimensional gures Learning Expectations 31 Analyze characteristics and properties of two and threedimensional geometric gures 32 Specify locations and describe spatial relationships using coordinate geometry and other representational systems 33 Apply transformations and use symmetry to analyze mathematical situations 34 Use visualization spatial reasoning and geometric modeling to solve problems Accomplishments 831 Analyze characteristics and properties of two and threedimensional geometric gures a Q 0 Cquot quot39D describe classify and understand relationships among types of two and threedimensional objects using their de ning properties understand relationships among the angles eg complementary supplementary interior exterior vertical corresponding solve problems using angle relationships eg complementary supplementary interior exterior vertical corresponding determine the measure of an angle ofa triangle given the measures of the other two angles understand relationships among the angles and side lengths of similar geometric gures determine congruence of line segments angles and polygons by direct comparison of given attributes develop understanding of the Pythagorean theorem 832 Specify locations and describe spatial relationships using coordinate geometry and other representational systems a graph points in the coordinate system 833 Apply transformations and use symmetry to analyze mathematical situations a describe sizes positions and orientations of shapes undertransformations eg rotations translations re ections dilations b relate symmetry and congruence to reflections about a line 834 Use visualization spatial reasoning and geometric modeling to solve problems a use appropriate tools and methods to draw geometric objects with speci ed properties eg side lengths angle measure b use twodimensional representations of threedimensional objects to visualize c use visualization and spatial reasoning to solve realworld problems d recognize and apply geometric ideas and relationships such as tessellations in areas outside the mathematics classroom eg art science everyday life Eighth Grade Benchmarks Performance Indicators State As documented through state assessment at Level 1 the student is able to 83spi1 classify types oftwo and threedimensional geometric gures using their de ning properties 83spi2 use ordered pairs to describe given points in a coordinate system at Level 2 the student is able to 83spi3 identify relationships among angles ie complementary supplementary interior exterior vertical corresponding 83spi4 recognize similar geometric gures 83spi5 determine the measure ofan angle of a triangle given the measures of the other two angles 83spi6 apply relationships among angles and side lengths of similar geometric gures 83spi7 apply spatial reasoning and visualization to solve realworld problems at Level 3 the student is able to 83spi8 apply geometric ideas and relationships in areas outside the mathematics classroom ie art science everyday life 83spi9 solve problems using angle relationships ie complementary supplementary interior exterior vertical corresponding Performance Indicators Teacher As documented through teacher observation at Level 1 the student is able to 83tpi1 describe relationships among types of two and threedimensional objects using their de ning properties 83tpi2 compare given attributes of line segments angles and polygons to determine congruence 83tpi3 build a threedimensional object from a twodimensional representation net of that object and vice versa at Level 2 the student is able to 83tpi4 describe sizes positions and orientations of shapes under transformations ie rotations translations re ections dilations 83tpi5 use appropriate tools and methods to draw geometric objects with speci ed properties ie side lengths angle measure 83tpi6 use twodimensional representations ofthreedimensional objects to visualize at Level 3 the student is able to 83tpi7 develop understanding of the Pythagorean theorem 83tpi8 relate symmetry and congruence to reflections about a line 83tpi9 compare and contrast the volumes of a variety of geometric solids Measurement Content Standard 40 The student will become familiar with the units and processes of measurement in order to use a variety oftools techniques and formulas to determine and to estimate measurements in mathematical and realworld problems Learning Expectations 41 Understand measurable attributes of objects and the units systems and processes of measurement 42 Apply appropriate techniques tools and formulas to determine measurements Accomplishments 841 Understand measurable attributes of objects and the units systems and processes of measurement understand both metric and customary systems of 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 039s 0 842 Apply appropriate techniques tools and formulas to determine measurements 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 0 apply formulas andor other strategies to solve problems involving perimeter circumference of circles and the area oftriangles parallelograms trapezoids and circles d nd area of complex and irregular shapes e apply given formulas to nd volume of selected prisms and cylinders f compare and contrast the volumes of a variety of geometric solids g solve problems involving ratetimedistance ie d rt h I J o m solve problems involving scale factors using ratio and proportion solve realworld problems using the Pythagorean Theorem construct tables and graphs to represent rates of change k nd measures using proportional relationships and properties of similar gures I determine the measure ofangles by applying angle relationships eg complementary supplementary interior exterior vertical corresponding Eighth Grade Benchmarks Performance Indicators State As documented through state assessment at Level 1 the student is able to 84spi1 select units of appropriate size and type to measure angles perimeter area surface area and volume 84spi2 convert from one unit to another within the same system at Level 2 the student is able to 84spi3 estimate length perimeter circumference area and volume using a variety of strategies 84spi4 apply formulas to nd the area oftriangles parallelograms and trapezoids 84spi5 solve realworld problems involving ratetimedistance ie d rt 84spi6 apply formulas to nd the circumference and area of circles 84spi7 estimate or nd the area of irregular and complex shapes at Level 3 the student is able to 84spi8 solve problems involving scale factors using ratios and proportions 84spi9 solve realworld problems using the Pythagorean Theorem no radicals Performance Indicators Teacher As documented through teacher observation at Level 1 the student is able to 84tpi1 construct tables and graphs to represent rates of chang 84tpi2 explain the Pythagorean Theorem at Level 2 the student is able to 84tpi3 use units of appropriate size and type to measure angles perimeter area surface area and volume 84tpi4 solve realworld problems involving scale factors using ratio and proportion 84tpi5 nd measures using proportional relationships and properties of similar gures 84tpi6 determine the measure of angles by applying angle relationships ie complementary supplementary interior exterior vertical corresponding 84tpi7 use techniques and tools to accurately measure length area volume and angles to appropriate levels of precision at Level 3 the student is able to 84tpi8 apply given formulas and other strategies to compare and contrast the volumes of selected geometric solids 84tpi9 solve realworld problems using the Pythagorean Theorem Data Analysis amp Probability Content Standard 50 The student will understand and apply basic statistical and probability concepts in order to organize and analyze data and to make predictions and conjectures Learning Expectations 51 Formulate questions that can be addressed with data and collect organize and display relevant data to answer questions 52 Select and use appropriate statistical methods to analyze data 53 Develop and evaluate inferences and predictions that are based on data 54 Understand and apply basic concepts of probability Accomplishments 851 Formulate questions that can be addressed with data and collect organize and display relevant data to answer questions a formulate questions design studies and collect realworld data for investigations using a variety of collection methods eg random sampling simulations b select create and use appropriate graphical representations ofrealworld data eg histograms box plots scatterplots 852 Select and use appropriate statistical methods to analyze data a nd use and interpret measures of center and spread eg mean interquartile range b develop meaning for frequency distribution and outliers c discuss and understand the relationship between data sets and their graphical representations eg bar graphs line graphs circle graphs histograms stemandleaf plots box plots scatterplots 853 Develop and evaluate inferences and predictions that are based on data a make conjectures and predictions based on data b recognize misleading presentations of data c d e develop meaning for lines of best t determine an appropriate sample to test a hypothesis make conjectures to formulate new questions for future studies 854 Understand and apply basic concepts of probability 00quot d e develop meaning of mutually exclusive events connect the symbolic representation of a probability to an experiment use a variety of methods to compute probabilities for compound events eg multiplication organized lists tree diagrams area models distinguish between theoretical and experimental probability nd the probability of dependent and independent events Eighth Grade Benchmarks Performance Indicators State As documented through state assessment at Level 1 the student is able to 85spi1 identify an appropriate sample to test a given hypothesis at Level 2 the student is able to 85spi2 interpret appropriate graphical representations of data ie histograms box plots scatterplots 85spi3 determine the mean ofa given set of realworld data 85spi4 connect data sets and their graphical representations ie histograms stemandleaf plots box plots scatterplots 85spi5 make conjectures and predictions based on data 85spi6 connect the symbolic representation of a probability to an experiment at Level 3 the student is able to 85spi7 determine the median ofa given set of realworld data even number of

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