Sixth Grade
|Sixth Grade | |Seventh Grade | |Eighth Grade | |6.1 |Number, operation, and quantitative reasoning. The student represents and uses rational numbers in a variety of equivalent forms. The student is expected to: |7.1 |Number, operation, and quantitative reasoning. The student represents and uses numbers in a variety of equivalent forms. The student is expected to: |8.1 |Number, operation, and quantitative reasoning. The student understands that different forms of numbers are appropriate for different situations. The student is expected to: | |6.1A |Compare and order non-negative rational numbers.
Including numbers represented as:
• Fractions
• Mixed numbers (with like and unlike denominators)
• Decimals |7.1A |Compare 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. |8.1A |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. | |
|6.1B |Generate equivalent forms of rational numbers including |7.1B |Convert between fractions, decimals, whole numbers, and |8.1B |Select and use appropriate forms of rational numbers to |
| |whole numbers, fractions, and decimals. | |percents mentally, on paper, or with a calculator. | |solve real-life problems including those involving |
| | | | | |proportional relationships. |
| |Including: | |Including mixed numbers | | |
| |Proper and improper fractions | | | |Examples include: |
| |Multiple forms within the problem | | | |Using multiple forms of fractions, decimals, percents, |
| | | | | |positive and negative integers within a single problem. |
| | |7.1C |Represent squares and square roots using geometric models. |8.1C |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. |
|6.1C |Use integers to represent real-life situations. | | |8.1D |Express numbers in scientific notation, including negative |
| | | | | |exponents, in appropriate problem situations. |
| |Including positive and negative numbers. | | | | |
| | | | | |Including: |
| | | | | |Converting numbers back to standard form |
| | | | | |Scientific notation using positive or negative exponents |
|6.1D |Write prime factorizations using exponents. | | | | |
| | | | | | |
| |Including using factor trees to find prime factorizations | | | | |
| |to be written with exponents. | | | | |
|6.1E |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. | | | | |
|6.1F |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 | | | | |
|6.2 |Number, operation, and quantitative reasoning. The student|7.2 |Number, operation, and quantitative reasoning. The student|8.2 |Number, operation, and quantitative reasoning. The student|
| |adds, subtracts, multiplies, and divides to solve problems | |adds, subtracts, multiplies, or divides to solve problems | |selects and uses appropriate operations to solve problems |
| |and justify solutions. The student is expected to: | |and justify solutions. The student is expected to: | |and justify solutions. |
|6.2B |Use addition and subtraction to solve problems involving |7.2B |Use addition, subtraction, multiplication, and division to | | |
| |fractions and decimals. | |solve problems involving fractions and decimals. | | |
| | | | | | |
| |Examples include: | |Examples include: | | |
| |Problems with mixed numbers with like and unlike | |Problems where your answer choices are models | | |
| |denominators | | | | |
| |Simplifying answers (converting improper fractions to whole| | | | |
| |or mixed numbers in lowest terms) | | | | |
| |Decimal problems with answer grids | | | | |
| | |7.2C |Use models, such as concrete objects, pictorial models, and| | |
| | | |number lines, to add, subtract, multiply, and divide | | |
| | | |integers and connect the actions to algorithms. | | |
|6.2C |Use multiplication and division of whole numbers to solve |7.2D |Use division to find unit rates and ratios in proportional |8.2D |Use multiplication by a constant factor (unit rate) to |
| |problems including situations involving equivalent ratios | |relationships such as speed, density, price, recipes, and | |represent proportional relationships. |
| |and rates. | |student-teacher ratio. | | |
| | | | | |Including: |
| |Examples include: | |Including: | |Using multiple forms of fractions, decimals, percents, |
| |Situations involving unit rate | |Fractions and decimals | |positive and negative integers within a single problem. |
| |Fractions and decimals | |Cross multiply and solve for x | |(Example: 1 gallon = 4 quarts (g = 4q)). |
| |Problems involving ratios relating numbers to the words | | | |Referring to the measurement side of the TAKS chart |
| |associated with given numbers | | | | |
| |Cross multiply and solve for x | | | | |
|6.2D |Estimate 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 cent | | | | |
|6.2E |Use order of operations to simplify whole number |7.2E |Simplify numerical expressions involving order of | | |
| |expressions (without exponents) in problem solving | |operations and exponents. | | |
| |situations. | | | | |
| | | |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 exponents | | | | |
| | |7.2F |Select and use appropriate operations to solve problems and|8.2A |Select appropriate operations to solve problems involving |
| | | |justify the selections. | |rational numbers and justify the selections. |
| | | | | | |
| | | |Examples include: | |Including formulating equations with appropriate order of |
| | | |Problems with multiple operations | |operations. (Addition, subtraction, multiplication, |
| | | |Problems with answer grids | |division, square, and square root) with positive and |
| | | | | |negative integers, fractions, decimals, and percents. |
| | | | |8.2B |Use 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). |
| | |7.2G |Determine the reasonableness of a solution to a problem. |8.2C |Evaluate a solution for reasonableness. |
| | | | | | |
| | | |Including problems with the appropriate range | |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. |
|6.3 |Patterns, relationships, and algebraic thinking. The |7.3 |Patterns, relationships, and algebraic thinking. The |8.3 |Patterns, relationships, and algebraic thinking. The |
| |student solves problems involving direct proportional | |student solves problems involving direct proportional | |student identifies proportional or non-proportional linear |
| |relationships. The student is expected to: | |relationships. The student is expected to: | |relationships in problem situations and solves problems. |
| | | | | |The student is expected to: |
|6.3B |Represent ratios and percents with concrete models, |7.3A |Estimate and find solutions to application problems |8.3B |Estimate and find solutions to application problems |
| |fractions, and decimals. | |involving percent. | |involving percents and other proportional relationships |
| | | | | |such as similarity and rates. |
| |Including: | |Including: | | |
| |Conversions of fractions, decimals, and percents | |Percent increase | |Including: |
| |Reinforcing percent over 100 | |Percent decrease | |Ratios that may not be in lowest terms represented in a |
| |Use of strategy “of” number goes on bottom when finding | | | |table, graph, equation, verbal description and geometric |
| |percent of a number | | | |representations. |
| |Use of strategy “is” number goes on top | | | |Setting up a proportion problem from a verbal description |
| | | | | |Using data in a table |
| |IS = % (n) | | | |Dilations (Enlargements and reductions) of geometric |
| |OF 100 | | | |figures |
| | | | | |Measurements using standard and metric units |
| | | | | |Unit conversions |
|6.3C |Use ratios to make predictions in proportional situations. |7.3B |Estimate and find solutions to application problems | | |
| | | |involving proportional relationships such as similarity, | | |
| |Including: | |scaling, unit costs, and related measurement units. | | |
| |Setting up a proportion problem from a verbal description | | | | |
| |Using data in a table | |Including: | | |
| |Using conversions to express compatible time, measurement, | |Setting up a proportion problem from word problems | | |
| |and numbers | |Using data in a table | | |
| | | |Measurements using standard and metric units | | |
| | | |Unit conversions | | |
|6.4 |Patterns, relationships, and algebraic thinking. The |7.4 |Patterns, relationships, and algebraic thinking. The |8.4 |Patterns, relationships, and algebraic thinking. The |
| |student uses letters as variables in mathematical | |student represents a relationship in numerical, geometric, | |student makes connections among various representations of |
| |expressions to describe how one quantity changes when a | |verbal, and symbolic form. The student is expected to: | |a numerical relationship. The student is expected to: |
| |related quantity changes. The student is expected to: | | | | |
| | | | |8.5 |Patterns, relationships, and algebraic thinking. The |
| | | | | |student uses graphs, tables, and algebraic representations |
| | | | | |to make predictions and solve problems. The student is |
| | | | | |expected to: |
| | |7.4B |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 | | |
| | |7.4C |Use words and symbols to describe the relationship between |8.5B |Find and evaluate an algebraic expression to determine any |
| | | |the terms in an arithmetic sequence (with a constant rate | |term in an arithmetic sequence (with a constant rate of |
| | | |of change) and their positions in the sequence. | |change). |
| | | | | | |
| | | |Including: | |Including: |
| | | |The nth term table | |Expressions in which the constant rate of change is |
| | | |Finding the nth term | |expressed as a fraction or a decimal |
| | | |Using nth term to find a specific term | |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) ] |
| | | | | |Vocabulary: (i.e. substitute, algebraic expression, |
| | | | | |expression, rule, nth term, prediction, pattern, |
| | | | | |correlation, term, sequence) |
|6.5 |Patterns, relationships, and algebraic thinking. The |7.5 |Patterns, relationships, and algebraic thinking. The | | |
| |student uses letters to represent an unknown in and | |student uses equations to solve problems. The student is | | |
| |equation. The student is expected to: | |expected to: | | |
|6.5A |Formulate equations from problem situations described by |7.5B |Formulate problem situations when given a simple equation | | |
| |linear relationships. | |and formulate an equation when given a problem situation. | | |
| | | | | | |
| |Including: | |Including prerequisites of: | | |
| |Equations in the form of ab=c where a and c are numbers in | |Translating word phrases to algebraic expressions | | |
| |the problem | |Translating word phrases to algebraic equations. | | |
| |Using variables to represent an unknown in an equation | | | | |
| |Using more than one variable in an equation | |Including focusing on operational vocabulary (Examples: | | |
| |Using multiplication in various forms (parentheses, 3n, and| |difference, total, product, and quotient) | | |
| |•) | | | | |
| | | | | | |
| |Examples include: | | | | |
| |C = 5 (h + 25) | | | | |
| |X = 3n | | | | |
| |X = 30 • 8 | | | | |
| |Matching an equation with a real life situation | | | | |
|6.6 |Geometry and spatial reasoning. The student uses geometric|7.6 |Geometry and spatial reasoning. The student compares and |8.6 |Geometry and spatial reasoning. The student uses |
| |vocabulary to describe angles, polygons, and circles. The| |classifies two- and three-dimensional figures using | |transformational geometry to develop spatial sense. The |
| |student is expected to: | |geometric vocabulary and properties. The student is | |student is expected to: |
| | | |expected to: | | |
|6.6B |Identify relationships involving angles in triangles and |7.6B |Use properties to classify triangles and quadrilaterals | | |
| |quadrilaterals. | | | | |
| | | |Including: | | |
| |Including: | |Triangle vocabulary: (i.e. acute, obtuse, right (define | | |
| |Understand sum of degrees in a triangle and a quadrilateral| |legs and hypotenuse), equiangular, isosceles, equilateral, | | |
| |Understand use of ‘hash marks’ to describe congruent sides | |and scalene) | | |
| |Define isosceles, scalene, and equilateral triangles. | |Quadrilateral terms: (i.e. parallelogram, rectangle, | | |
| | | |square, trapezoid, and rhombus) | | |
| | |7.6C |Use properties to classify three-dimensional figures, | | |
| | | |including pyramids, cones, prisms, and cylinders. | | |
| | | | | | |
| | | |Including vocabulary (i.e. faces, edges, vertices, bases, | | |
| | | |and lateral face) | | |
| | |7.6D |Use critical attributes to define similarity. |8.6A |Generate similar figures using dilations including |
| | | | | |enlargements and reductions. |
| | | |Include: | | |
| | | |All polygons | |Including: |
| | | |Corresponding sides are proportional | |Figures graphed on a coordinate grid |
| | | |Corresponding angles are congruent | |Figures with dimensions labeled in the diagram |
| | | |Using proportions to find missing sides | |Vocabulary: (i.e. similar, dilation, enlargement, |
| | | |Identifying pictorially similar figures | |reduction, coordinate, plane, vertex, dimension, |
| | | |Students needing to identify corresponding angles and sides| |proportional, corresponding side, scale factor) |
| | | |by a similarity statement. Example: ∆ABC similar ~ ∆DEF | |Multiply to solve for dilations by using the scale factor |
| | | | | |Enlargements – scale factor greater than 1 |
| | | | | |Reductions – scale factor less than 1 |
|6.6C |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 | | | | |
|6.7 |Geometry and spatial reasoning. The student uses |7.7 |Geometry and spatial reasoning. The student uses |8.7 |Geometry and spatial reasoning. The student uses geometry |
| |coordinate geometry to identify location in two dimensions.| |coordinate geometry to describe location on a plane. The | |to model and describe the physical world. The student is |
| |The student is expected to: | |student is expected to: | |expected to: |
| | |7.7B |Graph reflections across the horizontal or vertical axis |8.6B |Graph dilations, reflections, and translations on a |
| | | |and graph translations on a coordinate plane. | |coordinate plane. |
| | | | | | |
| | | |Include all four quadrants | |Including: |
| | | |Reflection across x-axis (x,y) → (x,-y) | |All four quadrants |
| | | |Reflection across y-axis (x,y) → (-x,y) | |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) |
| | |7.8 |Geometry and spatial reasoning. The student uses geometry |8.7 |Geometry and spatial reasoning. The student uses geometry |
| | | |to model and describe the physical world. The student is | |to model and describe the physical world. The student is |
| | | |expected to: | |expected to: |
| | |7.8B |Make a net (two-dimensional model) of the surface area of a| | |
| | | |three-dimensional figure. | | |
| | | | | | |
| | | |Include figures such as: | | |
| | | |Cylinders | | |
| | | |Cones | | |
| | | |Prisms | | |
| | | |Pyramids | | |
| | | |Cube | | |
| | |7.8C |Use geometric concepts and properties to solve problems in |8.7B |Use geometric concepts and properties to solve problems in |
| | | |fields such as art and architecture. | |fields such as art and architecture. |
| | | | | | |
| | | |Include all two- and three-dimensional figures listed on | |Include: |
| | | |the formula chart and combinations of figures such as a | |Using the given data to solve for perimeter, circumference,|
| | | |half circle and rectangle pieced together. | |area, volume, or dimension |
| | | | | |Various representations of limits of measures |
| | | | |8.7C |Use 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) |
|6.8 |Measurement. The student solves application problems |7.9 |Measurement. The student solves application problems |8.8 |Measurement. The student uses procedures to determine |
| |involving estimation and measurement of length, area, time,| |involving estimation and measurement. The student is | |measures of three-dimensional figures. The student is |
| |temperature, volume, weight, and angles. The student is | |expected to: | |expected to: |
| |expected to: | | | | |
| | |7.9B |Connect models for volume of prisms (triangular and |8.8B |Connect models of prisms, cylinders, pyramids, spheres, and|
| | | |rectangular) and cylinders to formulas of prisms | |cones to formulas for volume of these objects. |
| | | |(triangular and rectangular) and cylinders. | | |
| | | | | |Including: |
| | | |Including matching nets and models to appropriate formulas | |Matching nets and models to appropriate formulas to problem|
| | | |to problem solve. | |solve |
| | | | | |Real-life models (i.e. sphere-basketball) |
|6.8B |Select and use appropriate units, tools, or formulas to |7.9C |Estimate measurements and solve application problems |8.8C |Estimate measurements and use formulas to solve application|
| |measure and to solve problems involving length (including | |involving volume of prisms (rectangular and triangular) and| |problems involving lateral and total surface area and |
| |perimeter), area, time, temperature, volume, and weight. | |cylinders. | |volume. |
| | | | | | |
| |Including: | | | |Including: |
| |Measure with the ruler on the mathematics chart | | | |Measurements in metric and standard units for cubes, |
| |Utilize the conversions and formulas on the mathematics | | | |cylinders, cone, spheres, and prisms |
| |chart to solve problems | | | |Rounding all dimensions to whole numbers |
| |Recognize abbreviations of measurement units | | | |Using “3” for (pi symbol) |
| |Use of answer grid | | | |The capital B on the formula chart is the area of the base |
| |Recall degree scale of a thermometer | | | |Vocabulary: (i.e. surface area, prism, rectangular prism, |
| |Use the given dimensions of a figure to solve problems | | | |triangular prism, cylinder, pyramid, lateral surface area, |
| |Find perimeter of regular and irregular polygons | | | |edge, face, vertex, height, base, total surface area, net, |
| |Find area of the following geometric shapes: squares, | | | |volume) |
| |parallelograms, rectangles, triangles, trapezoids, and | | | |Real-life models (i.e. rectangular prism = a present or a |
| |circles | | | |shoe box) |
|6.8C |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 | | | | |
|6.8D |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 |Measurement. The student uses indirect measurement to |
| | | | | |solve problems. The student is expected to: |
| | | | |8.9B |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) |
| | | | |8.10 |Measurement. The student describes how changes in |
| | | | | |dimensions affect linear, area, and volume measurements. |
| | | | | |The student is expected to: |
| | | | |8.10B |Describe the resulting effect on volume when dimensions of |
| | | | | |a solid are changed proportionally. |
|6.9 |Probability and statistics. The student uses experimental |7.10 |Probability and statistics. The student recognizes that a |8.11 |Probability and statistics. The student applies concepts |
| |and theoretical probability to make predictions. The | |physical or mathematical model can be used to describe the | |of theoretical and experimental probability to make |
| |student is expected to: | |experimental and theoretical probability of real-life | |predictions. The student is expected to: |
| | | |events. The student is expected to: | | |
|6.9B |Find the probabilities of a simple event and its complement|7.10B |Find the probability of independent events. |8.11A |Find the probabilities of dependent and independent events.|
| |and describe the relationship between the two. | | | | |
| | | |Including: | |Including: |
| |Including: | |Flipping a coin | |Displaying the results as a fraction or a decimal or |
| |Vocabulary: (i.e. theoretical probability, experimental | |Drawing an object from a box without looking | |percent |
| |probability, complement, simple event, outcome, likely, and| |Compound events: Drawing an object from a box without | |Working the problem from a verbal description |
| |random) | |looking, replacing the object, and drawing another object | |Analyzing data from a table or graph |
| |Flipping a coin | |(and/or situations) | |Using experimental results and comparing those results with|
| |Drawing an object from a box without looking | | | |the theoretical results. |
| | | | |8.11B |Use 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. |
| | | | |8.11C |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 the theoretical |
| | | | | |results (such as using spinners, dice, and/or marbles in a |
| | | | | |sack in a probability event) |
|6.10 |Probability and statistics. The student uses statistical |7.11 |Probability and statistics. The student understands that |8.12 |Probability and statistics. The student uses statistical |
| |representations to analyze data. The student is expected | |the way a set of data is displayed influences its | |procedures to describe data. The student is expected to: |
| |to: | |interpretation. The student is expected to: | | |
| | |7.11B |Make inferences and convincing arguments based on an |8.12B |Draw conclusions and make predictions by analyzing trends |
| | | |analysis of given or collected data. | |in scatter plots. |
| | | | | | |
| | | |Including using the data to make predictions. | |Including: |
| | | | | |Scatter plots that show no real trend |
| | | | | |Positive, negative, and no correlations or trends |
| | | | | |Describe the scatter plot in words (increasing and |
| | | | | |decreasing) |
| | |7.12 |Probability and statistics. The student uses measures of |8.12 |Probability and statistics. The student uses statistical |
| | | |central tendency and range to describe a set of data. The | |procedures to describe data. The student is expected to: |
| | | |student is expected to: | | |
| | |7.12B |Choose among mean, median, mode, or range to describe a set|8.12A |Select the appropriate measure of central tendency or range|
| | | |of data and justify the choice for a particular situation. | |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 | |Including: |
| | | |of central tendency to describe that data | |Finding mean, median, mode and range to justify an answer |
| | | | | |The effects of changing data on mean, median, mode, and |
| | | | | |range |
|6.10C |Sketch circle graphs to display data. | | | | |
| | | | | | |
| |Including knowledge of relationship between percent and | | | | |
| |fractions. | | | | |
|6.10D |Solve problems by collecting, organizing, displaying, and | | | | |
| |interpreting data. | | | | |
| | | | |8.13 |Probability and statistics. The student evaluates |
| | | | | |predictions and conclusions based on statistical data. The|
| | | | | |student is expected to: |
| | | | |8.13B |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. |
|6.11 |Underlying processes and mathematical tools. The student |7.13 |Underlying processes and mathematical tools. The student |8.14 |Underlying processes and mathematical tools. The student |
| |applies Grade 6 mathematics to solve problems connected to | |applies Grade 7 mathematics to solve problems connected to | |applies Grade 8 mathematics to solve problems connected to |
| |everyday experiences, investigations in other disciplines, | |everyday experiences, investigations in other disciplines, | |everyday experiences, investigations in other disciplines, |
| |and activities in and outside of school. The student is | |and activities in and outside of school. The student is | |and activities in and outside of school. The student is |
| |expected to: | |expected to: | |expected to: |
|6.11B |Use a problem-solving model that incorporates understanding|7.13B |Use a problem-solving model that incorporates understanding|8.14B |Use a problem-solving model that incorporates understanding|
| |the problem, making a plan, carrying out the plan, and | |the problem, making a plan, carrying out the plan, and | |the problem, making a plan, carrying out the plan, and |
| |evaluating the solution for reasonableness. | |evaluating the solution for reasonableness. | |evaluating the solution for reasonableness. |
| | | | | | |
| |This student expectation can be tested in every strand | |This student expectation can be tested in every strand | |This student expectation can be tested in every strand |
| |including one or more than one TEKS at a time. | |including one or more than one TEKS at a time. | |including one or more than one TEKS at a time. |
|6.11C |Select or develop an appropriate problem-solving strategy |7.13C |Select or develop an appropriate problem-solving strategy |8.14C |Select or develop an appropriate problem-solving strategy |
| |from a variety of different types, including drawing a | |from a variety of different types, including drawing a | |from a variety of different types, including drawing a |
| |picture, looking for a pattern, systematic guessing and | |picture, looking for a pattern, systematic guessing and | |picture, looking for a pattern, systematic guessing and |
| |checking, acting it out, making a table, working a simpler | |checking, acting it out, making a table, working a simpler | |checking, acting it out, making a table, working a simpler |
| |problem, or working backwards to solve a problem. | |problem, or working backwards to solve a problem. | |problem, or working backwards to solve a problem. |
| | | | | | |
| |This student expectation can be tested in every strand | |This student expectation can be tested in every strand | |This student expectation can be tested in every strand |
| |including one or more than one TEKS at a time. | |including one or more than one TEKS at a time. | |including one or more than one TEKS at a time. |
|6.11D |Select tools such as real objects, manipulatives, |7.13D |Select tools such as real objects, manipulatives, |8.14D |Select tools such as real objects, manipulatives, |
| |paper/pencil, and technology or techniques such as mental | |paper/pencil, and technology or techniques such as mental | |paper/pencil, and technology or techniques such as mental |
| |math, estimation, and number sense to solve problems. | |math, estimation, and number sense to solve problems. | |math, estimation, and number sense to solve problems. |
|6.12 |Underlying processes and mathematical tools. The student |7.14 |Underlying processes and mathematical tools. The student |8.15 |Underlying processes and mathematical tools. The student |
| |communicates about Grade 6 mathematics through informal and| |communicates about Grade 7 mathematics through informal and| |communicates about Grade 8 mathematics through informal and|
| |mathematical language, representations, and models. The | |mathematical language, representations, and models. The | |mathematical language, representations, and models. The |
| |student is expected to: | |student is expected to: | |student is expected to: |
|6.12B |Evaluate the effectiveness of different representations to |7.14B |Evaluate the effectiveness of different representations to |8.15B |Evaluate the effectiveness of different representations to |
| |communicate ideas. | |communicate ideas. | |communicate ideas. |
|6.13 |Underlying processes and mathematical tools. The student |7.15 |Underlying processes and mathematical tools. The student |8.16 |Underlying processes and mathematical tools. The student |
| |uses logical reasoning to make conjectures and verify | |uses logical reasoning to make conjectures and verify | |uses logical reasoning to make conjectures and verify |
| |conclusions. The student is expected to: | |conclusions. The student is expected to: | |conclusions. The student is expected to: |
|6.13B |Validate his/her conclusions using mathematical properties |7.15B |Validate his/her conclusions using mathematical properties |8.16B |Validate his/her conclusions using mathematical properties |
| |and relationships. | |and relationships. | |and relationships. |
| | | | | | |
| |This student expectation can be tested in every strand | |This student expectation can be tested in every strand | |This student expectation can be tested in every strand |
| |including one or more than one TEKS at a time. | |including one or more than one TEKS at a time. | |including one or more than one TEKS at a time. |
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VERTICAL ALIGNMENT
MATH: GRADE 6 – GRADE 8
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