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VERTICAL ALIGNMENT MATH: GRADE 6 – GRADE 8 6.1 6.1A Sixth Grade Number, operation, and quantitative reasoning. The student represents and uses rational numbers in a variety of equivalent forms. The student is expected to: Compare and order non-negative rational numbers. 7.1 7.1A Including numbers represented as: Fractions Mixed numbers (with like and unlike denominators) Decimals 6.1B Generate equivalent forms of rational numbers including whole numbers, fractions, and decimals. Seventh Grade Number, operation, and quantitative reasoning. The student represents and uses numbers in a variety of equivalent forms. The student is expected to: Compare and order integers and positive rational numbers. 8.1 8.1A Using multiple forms of positive rational numbers, including numbers represented as fractions, percents, decimals, positive and negative integers within a single problem. 7.1B Including: Proper and improper fractions Multiple forms within the problem Convert between fractions, decimals, whole numbers, and percents mentally, on paper, or with a calculator. 8.1B Eighth Grade Number, operation, and quantitative reasoning. The student understands that different forms of numbers are appropriate for different situations. The student is expected to: Compare 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. Select and use appropriate forms of rational numbers to solve real-life problems including those involving proportional relationships. Including mixed numbers 7.1C Represent squares and square roots using geometric models. 8.1C Examples include: Using multiple forms of fractions, decimals, percents, positive and negative integers within a single problem. Approximate (mentally and with calculators) the value of irrational numbers as they arise from problem situations (such as Π, √2). Including using geometric problems using the square root of a number. 1 6.1C Use integers to represent real-life situations. 8.1D Including positive and negative numbers. 6.1D 6.1E 6.1F 6.2 Express numbers in scientific notation, including negative exponents, in appropriate problem situations. Including: Converting numbers back to standard form Scientific notation using positive or negative exponents Write prime factorizations using exponents. Including using factor trees to find prime factorizations to be written with exponents. Identify 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. Identify 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 LCD Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve problems and justify solutions. The student is expected to: 7.2 Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, or divides to solve problems and justify solutions. The student is expected to: 8.2 Number, operation, and quantitative reasoning. The student selects and uses appropriate operations to solve problems and justify solutions. 2 6.2A Model addition and subtraction situations involving fractions with objects, pictures, words, and numbers. 7.2A Including: Mixed numbers Like and unlike denominators 6.2B Use addition and subtraction to solve problems involving fractions and decimals. 7.2B 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 grids Use 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 Including writing or selecting the correct expression Use addition, subtraction, multiplication, and division to solve problems involving fractions and decimals. Examples include: Problems where your answer choices are models 7.2C 6.2C Represent multiplication and division situations involving fractions and decimals with models, including concrete objects, pictures, words, and numbers. 7.2D Use models, such as concrete objects, pictorial models, and number lines, to add, subtract, multiply, and divide integers and connect the actions to algorithms. Use 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 x 8.2D Use 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)). 3 with given numbers Cross multiply and solve for x Estimate and round to approximate reasonable results and to solve problems where exact answers are not required. 6.2D 6.2E 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 cent Use order of operations to simplify whole number expressions (without exponents) in problem solving situations. 7.2E Referring to the measurement side of the TAKS chart Simplify numerical expressions involving order of operations and exponents. Including negative values Including: Problems with both addition or subtraction and multiplication or division with and without parentheses Simplifying order of operation problems including the use of 4 exponents 7.2F Select and use appropriate operations to solve problems and justify the selections. 8.2A Examples include: Problems with multiple operations Problems with answer grids 8.2B 7.2G Determine the reasonableness of a solution to a problem. Including problems with the appropriate range 8.2C Select 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. Use appropriate operations to solve problems involving rational numbers in problem situations. Including problems with multioperations (addition, subtraction, multiplication, division, sqare, and square root) and mixed forms of rational numbers (positive and negative integers, fractions, decimals, and percents). Evaluate 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. 5 6.3 6.3A Patterns, relationships, and algebraic thinking. The student solves problems involving direct proportional relationships. The student is expected to: 7.3 Patterns, relationships, and algebraic thinking. The student solves problems involving direct proportional relationships. The student is expected to: Use ratios to describe proportional situations. 8.3 8.3A Including ratios that may or may not be in lowest terms represented in a table, equation, or verbal description. 6.3B Represent ratios and percents with concrete models, fractions, and decimals. 7.3A Estimate and find solutions to application problems involving percent. 8.3B 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. Patterns, relationships, and algebraic thinking. The student identifies proportional or non-proportional linear relationships in problem situations and solves problems. The student is expected to: Compare 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 conversions Estimate and find solutions to application problems involving percents and other proportional relationships such as similarity and 6 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 Including: Percent increase Percent decrease 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 conversions IS = % (n) OF 100 6.3C Use ratios to make predictions in proportional situations. 7.3B Including: Setting up a proportion problem from a verbal description Using data in a table Using conversions to express compatible time, measurement, and numbers 6.4 Patterns, 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: 7.4 Estimate 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 conversions Patterns, relationships, and algebraic thinking. The student represents a relationship in numerical, geometric, verbal, and symbolic form. The student is expected to: 8.4 Patterns, relationships, and algebraic thinking. The student makes connections among various representations of a numerical relationship. The student is expected to: 7 6.4A Use 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. 8.4A Generate 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) 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 8.5 Graphs to include: Line Graph Bar Graph Multiple Bar Graph Histogram Scatter plot Pictograph Circle Graph Line Plots Stem and Leaf Venn Diagram Patterns, relationships, and algebraic thinking. The student uses graphs, tables, and algebraic representations to make predictions and solve problems. The student is expected to: 8 6.4B Use 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, Π (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 width 7.4A Generate 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 chart 8.5A Predict, 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) (>, <, ≥, ≤) Graphs to include: Line Graph Bar Graph Multiple Bar Graph Histogram Scatter Plot Pictographs Circle Graph Line Plots 9 7.4B 7.4C Stem and Leaf Graph 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: Volume Use 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 term 8.5B Find 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 Number’s position in a sequence The formula for the arithmetic sequence (answers should be in distributive format) [The first term + common difference (n – 1) ] 10 6.5 Patterns, relationships, and algebraic thinking. The student uses letters to represent an unknown in and equation. The student is expected to: 7.5 7.5A 6.5A Formulate equations from problem situations described by linear relationships. 7.5B 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 •) 6.6 Examples include: C = 5 (h + 25) X = 3n X = 30 • 8 Matching an equation with a real life situation Geometry and spatial reasoning. The Vocabulary: (i.e. substitute, algebraic expression, expression, rule, nth term, prediction, pattern, correlation, term, sequence) Patterns, relationships, and algebraic thinking. The student uses equations to solve problems. The student is expected to: Use concrete and pictorial models to solve equations and use symbols to record the actions. Including equations with two variables Formulate 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) 7.6 Geometry and spatial reasoning. The 8.6 Geometry and spatial reasoning. The 11 student uses geometric vocabulary to describe angles, polygons, and circles. The student is expected to: 6.6A 6.6B Use 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: o Triangle vocabulary (i.e. acute, obtuse, right (define legs and hypotenuse), equiangular, isosceles, equilateral, and scalene o Quadrilateral terms: (i.e. parallelogram, rectangle, square, trapezoid, and rhombus) Identify relationships involving angles in triangles and quadrilaterals. 7.6A student compares and classifies twoand three-dimensional figures using geometric vocabulary and properties. The student is expected to: Use angle measurements to classify pairs of angles as complementary or supplementary student uses transformational geometry to develop spatial sense. The student is expected to: Including: Diagrams with multiple angles Prerequisite: name angles with three points 7.6B 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. 7.6C Use 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) Use properties to classify threedimensional figures, including 12 pyramids, cones, prisms, and cylinders. 7.6D Including vocabulary (i.e. faces, edges, vertices, bases, and lateral face) Use critical attributes to define similarity. 8.6A 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 ~ ∆DEF 6.6C 6.7 Generate 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 1 Describe 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/Π Vocabulary (i.e. chord and segment) Using C = Πd & 2Πr Geometry and spatial reasoning. The 7.7 Geometry and spatial reasoning. The 8.7 Geometry and spatial reasoning. The 13 6.7A student uses coordinate geometry to identify location in two dimensions. The student is expected to: Locate and name points on a coordinate plane using ordered pairs of non-negative rational numbers. 7.7A 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) student uses coordinate geometry to describe location on a plane. The student is expected to: Locate and name points on a coordinate plane using ordered pairs of integers. 8.7D Include: All four quadrants Vocabulary: (i.e. x-axis, xcoordinate, y-coordinate, quadrants, origin) 7.7B Graph 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) student uses geometry to model and describe the physical world. The student is expected to: Locate 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, xcoordinate, y-coordinate, quadrants, origin) 8.6B Graph 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 14 7.8 7.8A Geometry and spatial reasoning. The student uses geometry to model and describe the physical world. The student is expected to: Sketch three-dimensional figures when given the top, side, and front views 8.7 8.7A reflection) Geometry and spatial reasoning. The student uses geometry to model and describe the physical world. The student is expected to: Draw 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 given 7.8B 7.8C Make a net (two-dimensional model) of the surface area of a threedimensional figure. Include figures such as: Cylinders Cones Prisms Pyramids Cube Use geometric concepts and properties to solve problems in fields such as art and architecture. 8.7B 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. 8.7C Use 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 measures Use pictures or models to demonstrate 15 the Pythagorean Theorem. 6.8 6.8A Measurement. The student solves application problems involving estimation and measurement of length, area, time, temperature, volume, weight, and angles. The student is expected to: Estimate 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 (≈) means approximately equal to Recalling rounding fractions and decimals when estimating to nearest 0, ½ , or 1. Understanding elapsed time 7.9 7.9A Measurement. The student solves application problems involving estimation and measurement. The student is expected to: Estimate measurements and solve application problems involving length (including perimeter and circumference) and area of polygons and other shapes. 8.8 8.8A Including: When inscribed in a circle or polygon and/or real life pictorial examples Vocabulary: (i.e. hypotenuse, leg, radius, diameter) Measurement. The student uses procedures to determine measures of three-dimensional figures. The student is expected to: Find lateral and total surface area of prisms, pyramids, and cylinders using concrete models and nets (twodimensional models). No spheres, no cones Include: All polygons on the formula chart Using rulers on formula chart Problems with answer grids 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 (≈) means approximately equal to 16 7.9B Connect models for volume of prisms (triangular and rectangular) and cylinders to formulas of prisms (triangular and rectangular) and cylinders. 8.8B Including matching nets and models to appropriate formulas to problem solve. 6.8B Select 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 circles 7.9C Estimate measurements and solve application problems involving volume of prisms (rectangular and triangular) and cylinders. 8.8C Connect 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. spherebasketball) Estimate 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) 17 6.8C 6.8D Measure 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 angles Convert 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 units 8.9 8.9A Measurement. The student uses indirect measurement to solve problems. The student is expected to: Use the Pythagorean Theorem to solve real-life problems. 18 8.9B 8.10 8.10A Including: When inscribed in a circle or polygon and/or real life pictorial examples Vocabulary: (i.e. hypotenuse, leg, radius, diameter) Use 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) Measurement. The student describes how changes in dimensions affect linear, area, and volume measurements. The student is expected to: Describe 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 19 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 factor Describe the resulting effect on volume when dimensions of a solid are changed proportionally. Probability and statistics. The student applies concepts of theoretical and experimental probability to make predictions. The student is expected to: 8.10B 6.9 Probability and statistics. The student uses experimental and theoretical probability to make predictions. The student is expected to: 7.10 6.9A Construct sample spaces using lists and tree diagrams. 7.10A 6.9B 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 space Find the probabilities of a simple event Probability 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: Construct sample spaces for simple or composite experiments. 8.11 Including with and without replacement. Construct tree diagrams 7.10B Find the probability of independent 8.11A Find the probabilities of dependent and 20 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 looking events. 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) 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. Use theoretical probabilities and experimental results to make predictions and decisions. 8.11B 8.11C 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. Select 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 21 6.10 6.10A Probability and statistics. The student uses statistical representations to analyze data. The student is expected to: Select 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. 7.11 7.11A Including: Vocabulary: (i.e. scale and interval) Probability and statistics. The student understands that the way a set of data is displayed influences its interpretation. The student is expected to: Select 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. 8.12 8.12C Including: Frequency tables Vocabulary (i.e. intervals, scale) 7.11B Make inferences and convincing arguments based on an analysis of given or collected data. 8.12B Including using the data to make predictions. 7.12 6.10B Identify mean (using concrete objects 7.12A Probability and statistics. The student uses measures of central tendency and range to describe a set of data. The student is expected to: Describe a set of data using mean, 8.12 the theoretical results (such as using spinners, dice, and/or marbles in a sack in a probability event) Probability and statistics. The student uses statistical procedures to describe data. The student is expected to: Select 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) Draw 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) Probability and statistics. The student uses statistical procedures to describe data. The student is expected to: 22 and pictorial models), median, mode, and range of a set of data. median, mode, and range. 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. 7.12B Choose among mean, median, mode, or range to describe a set of data and justify the choice for a particular situation. 8.12A Including problems such as: Given a set of data the student selects the “best” measure of central tendency to describe that data 6.10C Sketch circle graphs to display data. 6.10D Including knowledge of relationship between percent and fractions. Solve problems by collecting, organizing, displaying, and interpreting data. Select 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 range 8.13 8.13A Probability and statistics. The student evaluates predictions and conclusions based on statistical data. The student is expected to: Evaluate methods of sampling to 23 determine validity of an inference made from a set of data. 8.13B 6.11 6.11A 6.11B Underlying 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: Identify 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. Use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution 7.13 7.13A 7.13B Underlying 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: Identify 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. Use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution 8.14 8.14A 8.14B Including biased sampling due to methods of collecting the data. Recognize 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. Underlying 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: Identify 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. Use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution 24 6.11C 6.11D 6.12 6.12A for reasonableness. for reasonableness. for reasonableness. This student expectation can be tested in every strand including one or more than one TEKS at a time. Select 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. Select 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. Select 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. Select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems. Underlying processes and mathematical tools. The student communicates about Grade 6 mathematics through informal and mathematical language, representations, and models. The student is expected to: Communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models. 7.13C 7.13D 7.14 7.14A This student expectation can be tested in every strand including one or more than one TEKS at a time. Select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems. Underlying processes and mathematical tools. The student communicates about Grade 7 mathematics through informal and mathematical language, representations, and models. The student is expected to: Communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models. 8.14C 8.14D 8.15 8.15A This student expectation can be tested in every strand including one or more than one TEKS at a time. Select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems. Underlying processes and mathematical tools. The student communicates about Grade 8 mathematics through informal and mathematical language, representations, and models. The student is expected to: Communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models. 25 6.12B 6.13 6.13A 6.13B This student expectation can be tested in every strand including one or more than one TEKS at a time. Evaluate the effectiveness of different representations to communicate ideas. Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to: Make 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-examples Validate 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. 7.14B 7.15 7.15A 7.15B This student expectation can be tested in every strand including one or more than one TEKS at a time. Evaluate the effectiveness of different representations to communicate ideas. Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to: Make 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-examples Validate 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. 8.15B 8.16 8.16A 8.16B This student expectation can be tested in every strand including one or more than one TEKS at a time. Evaluate the effectiveness of different representations to communicate ideas. Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to: Make 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-examples Validate 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. 26