ࡱ>   ` bjbj 7f%-vvvv8:֝$"(((ooo$hX׎oM"ooo׎vv((%ov8((orjTz( HT}QjMp{Ώ0p VVzVzooooooo׎׎yoooooood> >vvvvvv Sixth GradeSeventh GradeEighth Grade6.1Number, operation, and quantitative reasoning. The student represents and uses rational numbers in a variety of equivalent forms. The student is expected to:7.1Number, operation, and quantitative reasoning. The student represents and uses numbers in a variety of equivalent forms. The student is expected to:8.1Number, operation, and quantitative reasoning. The student understands that different forms of numbers are appropriate for different situations. The student is expected to:6.1ACompare and order non-negative rational numbers. Including numbers represented as: Fractions Mixed numbers (with like and unlike denominators) Decimals7.1ACompare and order integers and positive rational numbers. Using multiple forms of positive rational numbers, including numbers represented as fractions, percents, decimals, positive and negative integers within a single problem.8.1ACompare and order rational numbers in various forms including integers, percents, and positive and negative fractions and decimals. Using multiple forms of rational numbers, including numbers represented as fractions, percents, decimals, positive and negative integers within a single problem.6.1BGenerate equivalent forms of rational numbers including whole numbers, fractions, and decimals. Including: Proper and improper fractions Multiple forms within the problem7.1BConvert between fractions, decimals, whole numbers, and percents mentally, on paper, or with a calculator. Including mixed numbers8.1BSelect and use appropriate forms of rational numbers to solve real-life problems including those involving proportional relationships. Examples include: Using multiple forms of fractions, decimals, percents, positive and negative integers within a single problem.7.1CRepresent squares and square roots using geometric models.8.1CApproximate (mentally and with calculators) the value of irrational numbers as they arise from problem situations (such as , "2). Including using geometric problems using the square root of a number. 6.1CUse integers to represent real-life situations. Including positive and negative numbers.8.1DExpress numbers in scientific notation, including negative exponents, in appropriate problem situations. Including: Converting numbers back to standard form Scientific notation using positive or negative exponents6.1DWrite prime factorizations using exponents. Including using factor trees to find prime factorizations to be written with exponents.6.1EIdentify factors of a positive integer, common factors, and the greatest common factor of a set of positive integers. Include a set of at least 3 integers.6.1FIdentify multiples of a positive integer and common multiples and the least common multiple of a set of positive integers. Including: At least 3 integers in the set Correlation of the LCM to the LCD6.2Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve problems and justify solutions. The student is expected to:7.2Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, or divides to solve problems and justify solutions. The student is expected to:8.2Number, operation, and quantitative reasoning. The student selects and uses appropriate operations to solve problems and justify solutions.6.2AModel addition and subtraction situations involving fractions with objects, pictures, words, and numbers. Including: Mixed numbers Like and unlike denominators7.2ARepresent multiplication and division situations involving fractions and decimals with models, including concrete objects, pictures, words, and numbers. Including writing or selecting the correct expression6.2BUse addition and subtraction to solve problems involving fractions and decimals. Examples include: Problems with mixed numbers with like and unlike denominators Simplifying answers (converting improper fractions to whole or mixed numbers in lowest terms) Decimal problems with answer grids7.2BUse addition, subtraction, multiplication, and division to solve problems involving fractions and decimals. Examples include: Problems where your answer choices are models7.2CUse models, such as concrete objects, pictorial models, and number lines, to add, subtract, multiply, and divide integers and connect the actions to algorithms.6.2CUse multiplication and division of whole numbers to solve problems including situations involving equivalent ratios and rates. Examples include: Situations involving unit rate Fractions and decimals Problems involving ratios relating numbers to the words associated with given numbers Cross multiply and solve for x7.2DUse division to find unit rates and ratios in proportional relationships such as speed, density, price, recipes, and student-teacher ratio. Including: Fractions and decimals Cross multiply and solve for x8.2DUse multiplication by a constant factor (unit rate) to represent proportional relationships. Including: Using multiple forms of fractions, decimals, percents, positive and negative integers within a single problem. (Example: 1 gallon = 4 quarts (g = 4q)). Referring to the measurement side of the TAKS chart6.2DEstimate and round to approximate reasonable results and to solve problems where exact answers are not required. Including: Working with problems that have information expressed as ranges of numbers in the problem itself or ranges of numbers in its solution When rounding, use compatible numbers (those numbers that are easy to work with mentally; such as, the numbers 240 and 60 are compatible numbers for estimating 237 divided by 62 In a series of numbers round to the highest place of the smallest number (not single digits) Rounding money to the nearest cent6.2EUse order of operations to simplify whole number expressions (without exponents) in problem solving situations. Including: Problems with both addition or subtraction and multiplication or division with and without parentheses Simplifying order of operation problems including the use of exponents7.2ESimplify numerical expressions involving order of operations and exponents. Including negative values7.2FSelect and use appropriate operations to solve problems and justify the selections. Examples include: Problems with multiple operations Problems with answer grids8.2ASelect appropriate operations to solve problems involving rational numbers and justify the selections. Including formulating equations with appropriate order of operations. (Addition, subtraction, multiplication, division, square, and square root) with positive and negative integers, fractions, decimals, and percents.8.2BUse appropriate operations to solve problems involving rational numbers in problem situations. Including problems with multi-operations (addition, subtraction, multiplication, division, sqare, and square root) and mixed forms of rational numbers (positive and negative integers, fractions, decimals, and percents).7.2GDetermine the reasonableness of a solution to a problem. Including problems with the appropriate range8.2CEvaluate a solution for reasonableness. Including application problems for money, measurement, and percent. Examples include: Reasonableness that can be determined by estimating the solution and determining how big or small the answer should be. Then calculate your answer. The estimate and your calculation should be close to each other. Estimating by rounding all the numbers in a problem before doing any calculations. Then perform the operations with the rounded numbers. Think about how rounding the numbers, before calculating, causes your estimate to be greater or less than the answer.6.3Patterns, relationships, and algebraic thinking. The student solves problems involving direct proportional relationships. The student is expected to:7.3Patterns, relationships, and algebraic thinking. The student solves problems involving direct proportional relationships. The student is expected to:8.3Patterns, relationships, and algebraic thinking. The student identifies proportional or non-proportional linear relationships in problem situations and solves problems. The student is expected to:6.3AUse ratios to describe proportional situations. Including ratios that may or may not be in lowest terms represented in a table, equation, or verbal description.8.3ACompare and contrast proportional and non-proportional linear relationships. Including: Ratios that may not be in lowest terms represented in a table, graph, equation, verbal description and geometric representations Setting up a proportion problem from a verbal description Using data in a table Dilations (Enlargements and reductions) or geometric figures Measurements using standard and metric units Unit conversions6.3BRepresent ratios and percents with concrete models, fractions, and decimals. Including: Conversions of fractions, decimals, and percents Reinforcing percent over 100 Use of strategy of number goes on bottom when finding percent of a number Use of strategy is number goes on top IS = % (n) OF 100 7.3AEstimate and find solutions to application problems involving percent. Including: Percent increase Percent decrease8.3BEstimate and find solutions to application problems involving percents and other proportional relationships such as similarity and rates. Including: Ratios that may not be in lowest terms represented in a table, graph, equation, verbal description and geometric representations. Setting up a proportion problem from a verbal description Using data in a table Dilations (Enlargements and reductions) of geometric figures Measurements using standard and metric units Unit conversions6.3CUse ratios to make predictions in proportional situations. Including: Setting up a proportion problem from a verbal description Using data in a table Using conversions to express compatible time, measurement, and numbers7.3BEstimate and find solutions to application problems involving proportional relationships such as similarity, scaling, unit costs, and related measurement units. Including: Setting up a proportion problem from word problems Using data in a table Measurements using standard and metric units Unit conversions6.4Patterns, relationships, and algebraic thinking. The student uses letters as variables in mathematical expressions to describe how one quantity changes when a related quantity changes. The student is expected to:7.4Patterns, relationships, and algebraic thinking. The student represents a relationship in numerical, geometric, verbal, and symbolic form. The student is expected to:8.4Patterns, relationships, and algebraic thinking. The student makes connections among various representations of a numerical relationship. The student is expected to: 6.4AUse tables and symbols to represent and describe proportional and other relationships such as those involving conversions, arithmetic sequences (with a constant rate of change), perimeter, and area. Including Metric conversions for length Standard conversion for length Equations using variables (define) Graphs to include: Line Graph Bar Graph Multiple Bar Graph Pictograph Circle Graphs Line Plots Stem & Leaf 8.4AGenerate a different representation of data given another representation of data (such as a table, graph, equation, or verbal description). Including: Multiple representations of a table, graph, equation, sequence, or verbal description within a single context of a problem Present and future incremental predictions Vocabulary: (i.e. Interval, scale, nth term, coordinate plane, position, sequence, trend, correlation, relationships, variables, positive, and negative) Graphs to include: Line Graph Bar Graph Multiple Bar Graph Histogram Scatter plot Pictograph Circle Graph Line Plots Stem and Leaf Venn Diagram8.5Patterns, relationships, and algebraic thinking. The student uses graphs, tables, and algebraic representations to make predictions and solve problems. The student is expected to:6.4BUse tables of data to generate formulas representing relationships involving perimeter, area, volume of a rectangular prism, etc. Including: Perimeter of regular polygons Circumference of a circle Vocabulary: (i.e. diameter, radius,  (3.14 and 22/7) Area of squares, rectangles, circles, and triangles Vocabulary: (i.e. height and base of triangle Volume of cubes, rectangular prisms and cylinders Find the nth term in a sequence Given area, find length or width7.4AGenerate formulas involving unit conversions, perimeter, area, circumference, volume, and scaling. Including: Perimeter of regular polygons Circumference Area of squares, rectangles, triangles, circles, trapezoids Volume of rectangular prism, cylinders, cubes Conversion from one standard unit to another as listed on the formula chart Conversion from one metric unit to another as listed on the formula chart8.5APredict, find, and justify solutions to application problems using appropriate tables, graphs, and algebraic equations. Including: Multiple representations of a table, graph, equation, sequence or verbal description within a single context of a problem Present and future incremental predictions Vocabulary: (i.e. Interval, scale, nth term, coordinate plane, position, sequence, trend, correlation, relationships, variables, positive, negative, algebraic equations, evaluate, rule prediction, between, pattern, exceed, arithmetic sequence, term) Positive, negative, and no correlation or trend. Answer choices in the form of an inclusive/exclusive relationship (Example: Between 5 and 12) (>, <, e", d") Graphs to include: Line Graph Bar Graph Multiple Bar Graph Histogram Scatter Plot Pictographs Circle Graph Line Plots Stem and Leaf7.4BGraph data to demonstrate relationships in familiar concepts such as conversions, perimeter, area, circumference, volume, and scaling. Including: Vocabulary (i.e. independent and dependent variable) Data that models a linear relationship. Example: Perimeter and conversions Data that models a quadratic (second degree) relationship. Example: Area Data that models a third degree relationship. Example: Volume7.4CUse words and symbols to describe the relationship between the terms in an arithmetic sequence (with a constant rate of change) and their positions in the sequence. Including: The nth term table Finding the nth term Using nth term to find a specific term8.5BFind and evaluate an algebraic expression to determine any term in an arithmetic sequence (with a constant rate of change). Including: Expressions in which the constant rate of change is expressed as a fraction or a decimal Nth term table Finding the nth term Using the nth term to find a specific term Numbers position in a sequence The formula for the arithmetic sequence (answers should be in distributive format) [The first term + common difference (n 1) ] Vocabulary: (i.e. substitute, algebraic expression, expression, rule, nth term, prediction, pattern, correlation, term, sequence)6.5Patterns, relationships, and algebraic thinking. The student uses letters to represent an unknown in and equation. The student is expected to:7.5Patterns, relationships, and algebraic thinking. The student uses equations to solve problems. The student is expected to:7.5AUse concrete and pictorial models to solve equations and use symbols to record the actions. Including equations with two variables6.5AFormulate equations from problem situations described by linear relationships. Including: Equations in the form of ab=c where a and c are numbers in the problem Using variables to represent an unknown in an equation Using more than one variable in an equation Using multiplication in various forms (parentheses, 3n, and ) Examples include: C = 5 (h + 25) X = 3n X = 30 8 Matching an equation with a real life situation7.5BFormulate problem situations when given a simple equation and formulate an equation when given a problem situation. Including prerequisites of: Translating word phrases to algebraic expressions Translating word phrases to algebraic equations. Including focusing on operational vocabulary (Examples: difference, total, product, and quotient)6.6Geometry and spatial reasoning. The student uses geometric vocabulary to describe angles, polygons, and circles. The student is expected to:7.6Geometry and spatial reasoning. The student compares and classifies two- and three-dimensional figures using geometric vocabulary and properties. The student is expected to:8.6Geometry and spatial reasoning. The student uses transformational geometry to develop spatial sense. The student is expected to:6.6AUse angle measurements to classify angles as acute, obtuse, or right. Including: A variety of objects with acute, obtuse, or right angles Reviewing geometric vocabulary including: Triangle vocabulary (i.e. acute, obtuse, right (define legs and hypotenuse), equiangular, isosceles, equilateral, and scalene Quadrilateral terms: (i.e. parallelogram, rectangle, square, trapezoid, and rhombus)7.6AUse angle measurements to classify pairs of angles as complementary or supplementary Including: Diagrams with multiple angles Prerequisite: name angles with three points6.6BIdentify relationships involving angles in triangles and quadrilaterals. Including: Understand sum of degrees in a triangle and a quadrilateral Understand use of hash marks to describe congruent sides Define isosceles, scalene, and equilateral triangles.7.6BUse properties to classify triangles and quadrilaterals Including: Triangle vocabulary: (i.e. acute, obtuse, right (define legs and hypotenuse), equiangular, isosceles, equilateral, and scalene) Quadrilateral terms: (i.e. parallelogram, rectangle, square, trapezoid, and rhombus)7.6CUse properties to classify three-dimensional figures, including pyramids, cones, prisms, and cylinders. Including vocabulary (i.e. faces, edges, vertices, bases, and lateral face)7.6DUse critical attributes to define similarity. Include: All polygons Corresponding sides are proportional Corresponding angles are congruent Using proportions to find missing sides Identifying pictorially similar figures Students needing to identify corresponding angles and sides by a similarity statement. Example: "ABC similar ~ "DEF8.6AGenerate similar figures using dilations including enlargements and reductions. Including: Figures graphed on a coordinate grid Figures with dimensions labeled in the diagram Vocabulary: (i.e. similar, dilation, enlargement, reduction, coordinate, plane, vertex, dimension, proportional, corresponding side, scale factor) Multiply to solve for dilations by using the scale factor Enlargements scale factor greater than 1 Reductions scale factor less than 16.6CDescribe the relationship between radius, diameter, and circumference of a circle. Including: Identifying a method for finding the radius, diameter, or circumference of a circle. d= C/ Vocabulary (i.e. chord and segment) Using C = d & 2r6.7Geometry and spatial reasoning. The student uses coordinate geometry to identify location in two dimensions. The student is expected to:7.7Geometry and spatial reasoning. The student uses coordinate geometry to describe location on a plane. The student is expected to:8.7Geometry and spatial reasoning. The student uses geometry to model and describe the physical world. The student is expected to:6.7ALocate and name points on a coordinate plane using ordered pairs of non-negative rational numbers. Include: Only quadrant one Using a variety of grids (using different incremental units) Locating points using fraction and decimal coordinates (x,y) Use strategy you have to crawl on the x before you can stand up and walk on the y or you have to go over to the elevator before you can go up or down when plotting points. Vocabulary: x-axis, x-coordinate, y-coordinate, quadrants, y-axis, origin)7.7ALocate and name points on a coordinate plane using ordered pairs of integers. Include: All four quadrants Vocabulary: (i.e. x-axis, x-coordinate, y-coordinate, quadrants, origin)8.7DLocate and name points on a coordinate plane using ordered pairs of rational numbers Including: Using all four quadrants Vocabulary (i.e. x-axis, y-axis, x-coordinate, y-coordinate, quadrants, origin)7.7BGraph reflections across the horizontal or vertical axis and graph translations on a coordinate plane. Include all four quadrants Reflection across x-axis (x,y) ! (x,-y) Reflection across y-axis (x,y) ! (-x,y)8.6BGraph dilations, reflections, and translations on a coordinate plane. Including: All four quadrants Reflections across the x or y axes Dilations include enlargements or reductions Vocabulary: (i.e. similar, dilation, enlargement, reduction, coordinate, plane, vertex, dimension, proportional, corresponding side, scale factor, translation, and reflection)7.8Geometry and spatial reasoning. The student uses geometry to model and describe the physical world. The student is expected to:8.7Geometry and spatial reasoning. The student uses geometry to model and describe the physical world. The student is expected to:7.8ASketch three-dimensional figures when given the top, side, and front views8.7ADraw three-dimensional figures from different perspectives. Include: Drawing three dimensional figures when given a specified view Drawing two dimensional views when a three dimensional figure is given7.8BMake a net (two-dimensional model) of the surface area of a three-dimensional figure. Include figures such as: Cylinders Cones Prisms Pyramids Cube7.8CUse geometric concepts and properties to solve problems in fields such as art and architecture. Include all two- and three-dimensional figures listed on the formula chart and combinations of figures such as a half circle and rectangle pieced together.8.7BUse geometric concepts and properties to solve problems in fields such as art and architecture. Include: Using the given data to solve for perimeter, circumference, area, volume, or dimension Various representations of limits of measures8.7CUse pictures or models to demonstrate the Pythagorean Theorem. Including: When inscribed in a circle or polygon and/or real life pictorial examples Vocabulary: (i.e. hypotenuse, leg, radius, diameter)6.8Measurement. The student solves application problems involving estimation and measurement of length, area, time, temperature, volume, weight, and angles. The student is expected to:7.9Measurement. The student solves application problems involving estimation and measurement. The student is expected to:8.8Measurement. The student uses procedures to determine measures of three-dimensional figures. The student is expected to:6.8AEstimate measurements (including circumference) and evaluate reasonableness of results. Including: Length, perimeter, and circumference in metric and standard units Area in metric and standard units Understanding and utilizing the conversions and formulas on the mathematics chart to solve problems Recognizing abbreviations of measurement units Recognizing symbol (H") means approximately equal to Recalling rounding fractions and decimals when estimating to nearest 0, , or 1. Understanding elapsed time7.9AEstimate measurements and solve application problems involving length (including perimeter and circumference) and area of polygons and other shapes. Include: All polygons on the formula chart Using rulers on formula chart Problems with answer grids8.8AFind lateral and total surface area of prisms, pyramids, and cylinders using concrete models and nets (two-dimensional models). No spheres, no cones Including: Unit conversions in two and three dimensions Using formula chart rulers and formulas Various representations of limits of measures of edges Vocabulary (i.e. surface area, prism, rectangular prism, triangular prism, cylinder, pyramid, lateral surface area, edge, face, vertex, height, base, total surface area, net) Recognizing symbol (H") means approximately equal to7.9BConnect models for volume of prisms (triangular and rectangular) and cylinders to formulas of prisms (triangular and rectangular) and cylinders. Including matching nets and models to appropriate formulas to problem solve.8.8BConnect models of prisms, cylinders, pyramids, spheres, and cones to formulas for volume of these objects. Including: Matching nets and models to appropriate formulas to problem solve Real-life models (i.e. sphere-basketball)6.8BSelect and use appropriate units, tools, or formulas to measure and to solve problems involving length (including perimeter), area, time, temperature, volume, and weight. Including: Measure with the ruler on the mathematics chart Utilize the conversions and formulas on the mathematics chart to solve problems Recognize abbreviations of measurement units Use of answer grid Recall degree scale of a thermometer Use the given dimensions of a figure to solve problems Find perimeter of regular and irregular polygons Find area of the following geometric shapes: squares, parallelograms, rectangles, triangles, trapezoids, and circles7.9CEstimate measurements and solve application problems involving volume of prisms (rectangular and triangular) and cylinders.8.8CEstimate measurements and use formulas to solve application problems involving lateral and total surface area and volume. Including: Measurements in metric and standard units for cubes, cylinders, cone, spheres, and prisms Rounding all dimensions to whole numbers Using 3 for (pi symbol) The capital B on the formula chart is the area of the base Vocabulary: (i.e. surface area, prism, rectangular prism, triangular prism, cylinder, pyramid, lateral surface area, edge, face, vertex, height, base, total surface area, net, volume) Real-life models (i.e. rectangular prism = a present or a shoe box)6.8CMeasure Angles Including: Use a pictorial representation of a protractor and use an actual protractor to measure and construct angles Measure angles in a given geometric figure Understand angle symbols Using the actual protractor to measure angles to the nearest degree Measure angles where the rays do not lie on zero degree Recall geometry vocabulary Find measure of adjacent angles6.8DConvert measures within the same measurement system (customary and metric) based on relationships between units. Include: All measures on the formula chart Utilizing the King Henry acronym for converting metrics Using the given dimensions of a figure to solve problems Recognizing abbreviations of measurement units8.9Measurement. The student uses indirect measurement to solve problems. The student is expected to:8.9AUse the Pythagorean Theorem to solve real-life problems. Including: When inscribed in a circle or polygon and/or real life pictorial examples Vocabulary: (i.e. hypotenuse, leg, radius, diameter)8.9BUse proportional relationships in similar two-dimensional figures or similar three-dimensional figures to find missing measurements. Including: Setting up proportions or using a scale factor Identifying the corresponding sides of similar figures when the figure is rotated and/or not rotated Vocabulary: (i.e. similar, corresponding, scale factor, dimensions, rotation, proportional and two- and three-dimensional figures)8.10Measurement. The student describes how changes in dimensions affect linear, area, and volume measurements. The student is expected to:8.10ADescribe the resulting effects on perimeter and area when dimensions of a shape are changed proportionally. Including: Using a scale factor and/or dilations with whole numbers or fractions Finding missing dimensions or area or perimeter Using the same scale factor proportionately in a figure the effects Vocabulary: (i.e. perimeter, area, scale factors, dilation/dilated, enlargement, reduction, similar, dimension, proportional) Generalizing the effects on perimeter, area and volume if the length, width, and height are changed by the same scale factor8.10BDescribe the resulting effect on volume when dimensions of a solid are changed proportionally.6.9Probability and statistics. The student uses experimental and theoretical probability to make predictions. The student is expected to:7.10Probability and statistics. The student recognizes that a physical or mathematical model can be used to describe the experimental and theoretical probability of real-life events. The student is expected to:8.11Probability and statistics. The student applies concepts of theoretical and experimental probability to make predictions. The student is expected to:6.9AConstruct sample spaces using lists and tree diagrams. Including: Vocabulary: (i.e. sample space, tree diagram) Matching a situation with a situation with sample space that lists all possible combinations or select the missing portion of a given sample space7.10AConstruct sample spaces for simple or composite experiments. Including with and without replacement. Construct tree diagrams6.9BFind the probabilities of a simple event and its complement and describe the relationship between the two. Including: Vocabulary: (i.e. theoretical probability, experimental probability, complement, simple event, outcome, likely, and random) Flipping a coin Drawing an object from a box without looking7.10BFind the probability of independent events. Including: Flipping a coin Drawing an object from a box without looking Compound events: Drawing an object from a box without looking, replacing the object, and drawing another object (and/or situations)8.11AFind the probabilities of dependent and independent events. Including: Displaying the results as a fraction or a decimal or percent Working the problem from a verbal description Analyzing data from a table or graph Using experimental results and comparing those results with the theoretical results.8.11BUse theoretical probabilities and experimental results to make predictions and decisions. Including: Displaying the results as a fraction or a decimal or percent Working the problem from a verbal description Analyzing data from a table or graph Using experimental results and comparing those results with the theoretical results.8.11CSelect and use different models to simulate an event. Including: Displaying the results as a fraction or a decimal or percent Using experimental results from independent and dependent events and comparing those results with the theoretical results (such as using spinners, dice, and/or marbles in a sack in a probability event)6.10Probability and statistics. The student uses statistical representations to analyze data. The student is expected to:7.11Probability and statistics. The student understands that the way a set of data is displayed influences its interpretation. The student is expected to:8.12Probability and statistics. The student uses statistical procedures to describe data. The student is expected to:6.10ASelect and use an appropriate representation for presenting and displaying different graphical representations of the same data including line plot, line graph, bar graph, and stem and leaf plot. Including: Vocabulary: (i.e. scale and interval)7.11ASelect and use an appropriate representation for presenting and displaying relationships among collected data, including line plot, line graph, bar graph, stem and leaf plot, circle graph, and Venn diagrams, and justify the selection. Including: Frequency tables Vocabulary (i.e. intervals, scale)8.12CSelect and use an appropriate representation for presenting and displaying relationships among collected data, including line plots, line graphs, stem and leaf plots, circle graphs, bar graphs, box and whisker plots, histograms, and Venn diagrams, with and without the use of technology. Including: Frequencly tables Vocabulary (i.e. intervals, scale)7.11BMake inferences and convincing arguments based on an analysis of given or collected data. Including using the data to make predictions.8.12BDraw conclusions and make predictions by analyzing trends in scatter plots. Including: Scatter plots that show no real trend Positive, negative, and no correlations or trends Describe the scatter plot in words (increasing and decreasing)7.12Probability and statistics. The student uses measures of central tendency and range to describe a set of data. The student is expected to:8.12Probability and statistics. The student uses statistical procedures to describe data. The student is expected to:6.10BIdentify mean (using concrete objects and pictorial models), median, mode, and range of a set of data. Including: matching the mean, median, mode, and/or range with a given set of data which may be listed in the text of the item or presented in a graphical representation. Introduce: Identifying the missing piece of data that will produce a target mean, mode, median, and/or range for a data set.7.12ADescribe a set of data using mean, median, mode, and range.7.12B Choose among mean, median, mode, or range to describe a set of data and justify the choice for a particular situation. Including problems such as: Given a set of data the student selects the best measure of central tendency to describe that data8.12ASelect the appropriate measure of central tendency or range to describe a set of data and justify the choice for a particular situation. Including: Finding mean, median, mode and range to justify an answer The effects of changing data on mean, median, mode, and range6.10CSketch circle graphs to display data. Including knowledge of relationship between percent and fractions.6.10DSolve problems by collecting, organizing, displaying, and interpreting data.8.13Probability and statistics. The student evaluates predictions and conclusions based on statistical data. The student is expected to:8.13AEvaluate methods of sampling to determine validity of an inference made from a set of data. Including biased sampling due to methods of collecting the data.8.13BRecognize misuses of graphical or numerical information and evaluate predictions and conclusions based on data analysis. Including analyzing all parts of a bar graph (title, vertical and horizontal scale) and table of values for possible misleading information.6.11Underlying processes and mathematical tools. The student applies Grade 6 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to:7.13Underlying processes and mathematical tools. The student applies Grade 7 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to:8.14Underlying processes and mathematical tools. The student applies Grade 8 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to:6.11AIdentify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics. This student expectation can be tested in every strand including one or more than one TEKS at a time.7.13AIdentify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics. This student expectation can be tested in every strand including one or more than one TEKS at a time.8.14AIdentify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics. This student expectation can be tested in every strand including one or more than one TEKS at a time.6.11BUse a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness. This student expectation can be tested in every strand including one or more than one TEKS at a time.7.13BUse a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness. This student expectation can be tested in every strand including one or more than one TEKS at a time.8.14BUse a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness. This student expectation can be tested in every strand including one or more than one TEKS at a time.6.11CSelect or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem. This student expectation can be tested in every strand including one or more than one TEKS at a time.7.13CSelect or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem. This student expectation can be tested in every strand including one or more than one TEKS at a time.8.14CSelect or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem. This student expectation can be tested in every strand including one or more than one TEKS at a time.6.11DSelect tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems.7.13DSelect tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems.8.14DSelect tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems.6.12Underlying processes and mathematical tools. The student communicates about Grade 6 mathematics through informal and mathematical language, representations, and models. The student is expected to:7.14Underlying processes and mathematical tools. The student communicates about Grade 7 mathematics through informal and mathematical language, representations, and models. The student is expected to:8.15Underlying processes and mathematical tools. The student communicates about Grade 8 mathematics through informal and mathematical language, representations, and models. The student is expected to:6.12ACommunicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models. This student expectation can be tested in every strand including one or more than one TEKS at a time.7.14A,j k n o   V w 0 1 2 ; `dė̵̵̵̵̞̞̹̞h5yhk!hk!B*phhk!B*phhk!h3ch3cB*phh3cB*phh3ch'B*phh'h'B*phh' hk!56 h3c56hg-h'56hg-h'5jhlx<5UmHnHu5+,0k o   $ U V x & F$Ifgd' $Ifgd'Ff$IfFfO $$Ifa$gd' $$Ifa$gdk!n 1 2 $$Ifa$gdk!$If : ; :.(($If $$Ifa$gdk!kd$$Iflֈ%4)8``` t0`944 la; F d  $$Ifa$gdk! & F$Ifgd'$If  %:.(.$If $$Ifa$gdk!kdp$$Iflֈ%4)8``` t0`944 la%`e $$Ifa$gdk!$If`bfnp !"GGJK,-12Ž஦{h5yB*ph hGW56 h5y56hg-hg-56hg-hg-B*phhg-B*phhg-hGWhGWB*phhGWB*phhGWhk!h'h'B*phh'B*phh'hGh5yhk!hk!B*phhk!B*ph-:8,&$If $$Ifa$gdk!kd$$$Iflֈ%4)8``` t0`944 labdfp!"-V & F*$IfgdGW $$Ifa$gdk!$If :.(($If $$Ifa$gdk!kd$$Iflֈ%4)8``` t0`944 la $$Ifa$gdk!$If$:.(($If $$Ifa$gdk!kd $$Iflֈ%4)8``` t0`944 la $$Ifa$gdk!$IfFG:.(($If $$Ifa$gdk!kd@ $$Iflֈ%4)8``` t0`944 laGRq $$Ifa$gdk! & F$Ifgdg-$IfGK:.(.$If $$Ifa$gdk!kd $$Iflֈ%4)8``` t0`944 laK-2 & F$Ifgdg-Ff $$Ifa$gdk!$If\ ,-12_`amT  J!K!O!P!!ৣ𣛐yyhThTB*phhTB*phhThGWhGWB*phhGWB*phhGWhNzsh GB*phhNzsB*phhNzshg-h GB*phh5yB*phh5yhg-hg-B*phh GB*phhg-B*phhg-h5yh5yB*ph/ [\:.(($If $$Ifa$gdk!kd $$Iflֈ%4)8``` t0`944 la\n -2 $$Ifa$gdk! & F$Ifgdg-$If :.(.$If $$Ifa$gdk!kd$$Iflֈ%4)8``` t0`944 la(kdu$$Iflֈ%4)8``` t0`944 la $$Ifa$gdk!$If$CZ`al & F+$IfgdGW & FA$Ifgd G & F$Ifgdg-$If $$Ifa$gdk!ST:.(($If $$Ifa$gdk!kd)$$Iflֈ%4)8``` t0`944 laT_     $$Ifa$gdk! & F$IfgdT$If   ! :.(($If $$Ifa$gdk!kd$$Iflֈ%4)8``` t0`944 la !K!P!!!!!! $$Ifa$gdk! & F$IfgdT$If !!!!!!!!!"d"e"i"j""""######$$$$$$$4%a%b%f%g%%%%'''](`(a((((())))޼ޟhTh 956 h 956 hNzs56hThT56hyhyB*phhyB*phhy hNzshyhGWhGWB*phhGWB*phhGW hNzshNzshNzshNzsB*phhNzsB*phhNzshT3!!!!!:.(.$If $$Ifa$gdk!kd$$Iflֈ%4)8``` t0`944 la!""("J"e"j"""# $$Ifa$gdk! & F$IfgdNzs$If ##kdS$$Iflֈ%4)8``` t0`944 lap<######$$$$If $$Ifa$gdk!$$kdF$$Iflֈ%4)8``` t0`944 lap<$$$$3%4%b%g%%%%%%&&'$If $$Ifa$gdk!''kd9$$Iflֈ%4)8``` t0`944 lap<''](a((()))))l*m*n*s****M++++,, & F,$Ifgd 9Ffm$If $$Ifa$gdk!)k*l*n*r*s****,,l,9-A-C-I-O-c-d-h-i--------l.m.n.//00000O1P1Q1111222m3n3q3r34ɼɼɱ譥譥萉 hO56 hNzs56hThT56hNzshNzsB*phhNzsB*phhNzshTh GB*phh Gh G>*B*phh GB*phh 9h 9B*phh 9B*phh 9hThThTB*phhTB*ph3,,,k,l,:.(($If $$Ifa$gdk!kd$$Iflֈ%4)8``` t0`944 lal,w,,,-9-;-O-b-c-d-i-------m.n.y..5/ & F-$Ifgd 9 & F$IfgdNzs $$Ifa$gdk! $Ifgd G & F $IfgdT$If5/K/////-kd7$$Iflֈ%4)8``` t0`944 la & F-$Ifgd 9//000M0c000P1Q1\1111111 & F$IfgdNzs & F $IfgdT$If $$Ifa$gdk!11122:.(.$If $$Ifa$gdk!kd$$Iflֈ%4)8``` t0`944 la2n3r3444"4444515T5g5r5|55555555 $Ifgd G & F $Ifgd G & F $IfgdRFf $$Ifa$gdk!$If444!4"4441525S555555R6S6T6.8/8088w9;;;;;P<Q<R<====>>>~@@AAAAAAbBļȣ㣔ĜļӼ~~hC hChChNzshNzsB*phhNzsB*ph hEBhRhNzshB~hO56hOhOB*phhOB*phhOhRh GB*phh GB*phhRB*phhR hEBhEBhEBhGhThT56.555S6T6_667777777777 88"8/8 & F/$Ifgd G & F/$IfgdO $IfgdO & F.$IfgdO $$Ifa$gdk!$If/808182838:.(.$If $$Ifa$gdk!kd$$Iflֈ%4)8``` t0`944 la384888888v9w9999(:::P;;;;Q<R<]<{<< & F$IfgdNzs & F $IfgdR $IfgdRFf! $$Ifa$gdk!$If<<<?===>>>>>??@@@@@A&A@AXArA & F1$IfgdO $IfgdO & F0$IfgdO$If $$Ifa$gdk! & F$IfgdNzsrAAAA-kd+#$$Iflֈ%4)8``` t0`944 la & F1$IfgdOAAAAaBbBmBBB8CwCxCyC & F$IfgdC$If $$Ifa$gdk! bBvCwC|CCC'DDDDDDEEEEEFFFFoGpGsGtGGGGGXH~HHHH.J/J3J4JJѾ崪ynjcj hEBh_ hrh_ h_ B*phh_ B*phh_ h@+h@+B*phh@+B*ph hEBh@+h@+ hC56h_ h_ 56h_ hR56hwChwCB*phh GB*phhwCB*phhwChY vhC hChChChCB*phhCB*ph&yCzCkd#$$Iflֈ%4)8``` t0`944 lap<zC{C|CC&D'D2DEDZDDDEEEgEvEEEEXFF & F2$IfgdwC & F$Ifgd G & F$IfgdC$If $$Ifa$gdk!FFkd$$$Iflֈ%4)8``` t0`944 lap<FFpGtGGGGGGGGWHXHHHHFf"'$If $$Ifa$gdk!HHHHH:.(($If $$Ifa$gdk!kd8)$$Iflֈ%4)8``` t0`944 laHH)I`IIIIIIII/J4JJJJJ(K)KKK $Ifgdr & F$Ifgdr $$Ifa$gdk! & F$Ifgd_ $Ifgd_ & F $Ifgd_ $IfJJJUKKKK"L%L&LLLLL\M^MM NNNNNEOFOGOOOOOPPPPPPPQQQQQ7RRRRRRRTTTTjUlUnU̺̾̾ݠݠݎ݊hY v hEBhrh:h:B*ph hEBh:h:h GB*phh:B*phh: hY v56 hr56h:h:56 hEBh_ hrhrB*phh GB*phhrB*phhrh_ 6KKKK"L4( $$Ifa$gdk!kd)$$Iflֈ%4)8``` t0`944 la$If"L&LLL]M^McMMMMMNNNNFOGOROpOOO & F $Ifgdr & F$Ifgd G & F$Ifgd G & F$Ifgd:Ff+$If $$Ifa$gdk!OOOOO4( $$Ifa$gdk!kd.$$Iflֈ%4)8``` t0`944 la$IfOOO5PpPPPPPPoQQQQ & F!$Ifgdr $$Ifa$gdk! & F$Ifgd:$If QQQQQ:.(.$If $$Ifa$gdk!kd.$$Iflֈ%4)8``` t0`944 laQ6R7RRRR $$Ifa$gdk!$IfRRRRR:.(.$If $$Ifa$gdk!kd{/$$Iflֈ%4)8``` t0`944 laRRRRRRSBSjSTTlUnUUUVVVW4W & F$$IfgdY v $$Ifa$gdk! & F"$Ifgdr$IfnUV3W4W5WWXXXXYYYvZwZzZ{ZZZg[P\\\\\\\J]K]L]]]]] ^ ^ ^^^ƿّ~zzvnch,h,B*phh,B*phh,hY vhhB*phhB*phhh:hB*ph hY v56 h56 hZ2 56hh:56 hEBh:h:h:B*phh:B*phh: hEBhrhY vhB*phhB*phhY vB*ph&4W5W:WWW:.(($If $$Ifa$gdk!kd=0$$Iflֈ%4)8``` t0`944 laWWHXXXXXXX $$Ifa$gdk! & F$Ifgd:$IfXXXYY:.(.$If $$Ifa$gdk!kd0$$Iflֈ%4)8``` t0`944 laYwZ{ZZZ[f[g[p[[[[\\\K]L]U]h]]] ^ ^^ & F#$Ifgd & F$Ifgd:Ff3 $$Ifa$gdk!$If^0^^^-kd5$$Iflֈ%4)8``` t0`944 la & F4$Ifgd,^^^^^````8a:a$IfgdJF~ $$Ifa$gdk!$If )*kdS$$Iflֈ%4)8``` t0`944 lap<*+,-.4jkv} & F?$IfgdJF~$If $$Ifa$gdk! }~kdT$$Iflֈ%4)8``` t0`944 lap<~ݍލ @Ffgr & FD$Ifgdu8 & F($IfgdeFf$W$If $$Ifa$gdk!ލ?@EFefg 89>?-./ÒǒȒ;=VaҔźͶ벪ԘźԶ{t{t{ hp56hehe56hphu8B*phhpB*ph hEBhehu8hu8B*phhu8B*phhu8hpheheB*phheB*ph hEBh[i&heh[i&h[i&B*phh[i&B*phh[i&h,h.56 hJF~56-:.(.$If $$Ifa$gdk!kd:Y$$Iflֈ%4)8``` t0`944 la 9?. & F@$Ifgdp $$Ifa$gdk!$If ./016:.(.$If $$Ifa$gdk!kdY$$Iflֈ%4)8``` t0`944 la6ÒȒ<=CUVӔٔFf[ $$Ifa$gdk!$IfҔӔؔٔ ! ,-.[349>?EFGBFG<=ø⴬颛˔ø˔ø| hSm56 he56hxhjv56 hphp hp56hxhp56h[i&B*phh[i&hphpB*phhpB*phhpheheB*phheB*ph hEBhe hEBh[i&heh[i&h[i&B*ph0 :.(.$If $$Ifa$gdk!kd^$$Iflֈ%4)8``` t0`944 la ! - & F)$Ifgdp & F)$Ifgde$If $$Ifa$gdk! -.4Z[:.(($If $$Ifa$gdk!kd^$$Iflֈ%4)8``` t0`944 la[ $$Ifa$gdk!$If:.(.$If $$Ifa$gdk!kdo_$$Iflֈ%4)8``` t0`944 la(kd#`$$Iflֈ%4)8``` t0`944 la $$Ifa$gdk!$If4Ff4b$If $$Ifa$gdk!45kdJd$$Iflֈ%4)8``` t0`944 lap<56789?F$If $$Ifa$gdk!FGkd=e$$Iflֈ%4)8``` t0`944 lap<GLBG=B89?۝ܝBHKQT $IfgdFfqg$If $$Ifa$gdk!=AB79ܝABGHJKPQSTU`fglmrsxzSTYZɪͪžͺ벫ͺԠԠ hSm56hxhx56 hEBhxhx hEBhhB*phh hEBhSmhSmB*ph hEBhjvhSmhjvhjvB*phhjvB*phhjvhxhjv56 h568TU[:.(($If $$Ifa$gdk!kdi$$Iflֈ%4)8``` t0`944 laagmsy $IfgdG $$Ifa$gdk!$If yz:.(($If $$Ifa$gdk!kd;j$$Iflֈ%4)8``` t0`944 la $IfgdG $$Ifa$gdk!$If  :.(.$If $$Ifa$gdk!kdj$$Iflֈ%4)8``` t0`944 laTZ(kdk$$Iflֈ%4)8``` t0`944 la $$Ifa$gdk!$IfɪΪabhhn $IfgdFfm$If $$Ifa$gdk!ͪΪ`bghmn[`aEFJK2BCKLMN#$ij9ѼѼѼܩؼؼǴǞѼhhSmB*phhxhxB*phhB*phh hEBhSmhSmB*phU hEBhxhSmhxB*phhx h56 hSm56hxhx56=Communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models. This student expectation can be tested in every strand including one or more than one TEKS at a time.8.15ACommunicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models. This student expectation can be tested in every strand including one or more than one TEKS at a time.6.12BEvaluate the effectiveness of different representations to communicate ideas.7.14BEvaluate the effectiveness of different representations to communicate ideas. 8.15BEvaluate the effectiveness of different representations to communicate ideas. 6.13Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to:7.15Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to:8.16Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to:6.13AMake conjectures from patterns or sets of examples and non-examples. Including: Defining a concept introduced at a higher grade Showing a pattern, examples, and/or non-examples Expecting students to choose a correct response by analyzing the pattern, examples, or non-examples7.15AMake conjectures from patterns or sets of examples and non-examples. Including: Defining a concept introduced at a higher grade Showing a pattern, examples, and/or non-examples Expecting students to choose a correct response by analyzing the pattern, examples, or non-examples8.16AMake conjectures from patterns or sets of examples and non-examples. Including: Defining a concept introduced at a higher grade Showing a pattern, examples, and/or non-examples Expecting students to choose a correct response by analyzing the pattern, examples, or non-examples6.13BValidate his/her conclusions using mathematical properties and relationships. This student expectation can be tested in every strand including one or more than one TEKS at a time.7.15BValidate his/her conclusions using mathematical properties and relationships. This student expectation can be tested in every strand including one or more than one TEKS at a time.8.16BValidate his/her conclusions using mathematical properties and relationships. This student expectation can be tested in every strand including one or more than one TEKS at a time.     PAGE  PAGE 1 VERTICAL ALIGNMENT MATH: GRADE 6 GRADE 8  [a:.(.$If $$Ifa$gdk!kdo$$Iflֈ%4)8``` t0`944 laa(kdpp$$Iflֈ%4)8``` t0`944 la $$Ifa$gdk!$If FK12=mMNY & F$Ifgd & F$IfgdSm $IfgdSm & F$IfgdxFfsr$If $$Ifa$gdk!$iju: & F$Ifgd$If $Ifgd $$Ifa$gdk!9:;IJKkmnoqrtuwxz{ûhlx<hlx<5 hlx<5h4(0JmHnHuh\hlx< hlx<0Jjhlx<0JUhRPjhRPUh9QhB*phh hEBhSmhSmB*phhSmhxB*phhx hEBhx hEBh.:;A:.(($If $$Ifa$gdk!kdt$$Iflֈ%4)8``` t0`944 laJKl $Ifgd $$Ifa$gdk!$If lmnpqst:88888kd=u$$Iflֈ%4)8``` t0`944 latvwyzh]hgdlx< &`#$gd\51h0:p'= /!`"`#$% M$$If!vh5`55`55`5#v`#v#v`#v#v`#v:Vl  t<`95`55`55`5/ p<kd$$Iflֈ%4)8```  t<0`944 lap<?$$If!vh5`55`55`5#v`#v#v`#v#v`#v:Vl  t<`95`55`55`5p<kde$$Iflֈ%4)8```  t<0`944 lap<$$If!vh5`55`55`5#v`#v#v`#v#v`#v:Vl t`95`55`55`5$$If!vh5`55`55`5#v`#v#v`#v#v`#v:Vl t`95`55`55`5$$If!vh5`55`55`5#v`#v#v`#v#v`#v:Vl t`95`55`55`5$$If!vh5`55`55`5#v`#v#v`#v#v`#v:Vl t`95`55`55`5$$If!vh5`55`55`5#v`#v#v`#v#v`#v:Vl t`95`55`55`5$$If!vh5`55`55`5#v`#v#v`#v#v`#v:Vl t`95`55`55`5$$If!vh5`55`55`5#v`#v#v`#v#v`#v:Vl 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