Chapter 111. Subchapter B

Chapter 111. Texas Essential Knowledge and Skills = for=20 Mathematics
Subchapter B. Middle School

Statutory Authority: The provisions of = this=20 Subchapter B issued under the Texas Education Code, =A7=A77.102(c)(4), = 28.002, and=20 28.008, unless otherwise noted.

(a) Introduction.

(1) Within a well-balanced mathematics=20 curriculum, the primary focal points at Grade 6 are using ratios to = describe=20 direct proportional relationships involving number, geometry, = measurement,=20 probability, and adding and subtracting decimals and fractions.

(2) Throughout mathematics in Grades = 6-8,=20 students build a foundation of basic understandings in number, = operation, and=20 quantitative reasoning; patterns, relationships, and algebraic thinking; = geometry and spatial reasoning; measurement; and probability and = statistics.=20 Students use concepts, algorithms, and properties of rational numbers to = explore=20 mathematical relationships and to describe increasingly complex = situations.=20 Students use algebraic thinking to describe how a change in one quantity = in a=20 relationship results in a change in the other; and they connect verbal, = numeric,=20 graphic, and symbolic representations of relationships. Students use = geometric=20 properties and relationships, as well as spatial reasoning, to model and = analyze=20 situations and solve problems. Students communicate information about = geometric=20 figures or situations by quantifying attributes, generalize procedures = from=20 measurement experiences, and use the procedures to solve problems. = Students use=20 appropriate statistics, representations of data, reasoning, and concepts = of=20 probability to draw conclusions, evaluate arguments, and make=20 recommendations.

(3) Problem solving in meaningful = contexts,=20 language and communication, connections within and outside mathematics, = and=20 formal and informal reasoning underlie all content areas in mathematics. = Throughout mathematics in Grades 6-8, students use these processes = together with=20 graphing technology and other mathematical tools such as manipulative = materials=20 to develop conceptual understanding and solve problems as they do=20 mathematics.

(b) Knowledge and skills.

(1) Number, operation, and quantitative = reasoning. The student represents and uses rational numbers in a variety = of=20 equivalent forms. The student is expected to:

(A) compare and order non-negative = rational=20 numbers;

(B) generate equivalent forms of = rational=20 numbers including whole numbers, fractions, and decimals;

(D) write prime factorizations using = exponents;

(E) identify factors of a positive = integer,=20 common factors, and the greatest common factor of a set of positive = integers;=20 and

(F) identify multiples of a positive = integer=20 and common multiples and the least common multiple of a set of positive=20 integers.

(2) Number, operation, and quantitative = reasoning. The student adds, subtracts, multiplies, and divides to solve = problems and justify solutions. The student is expected to:

(A) model addition and subtraction = situations=20 involving fractions with objects, pictures, words, and numbers;

(B) use addition and subtraction to = solve=20 problems involving fractions and decimals;

(C) use multiplication and division = of whole=20 numbers to solve problems including situations involving equivalent = ratios and=20 rates;

(D) estimate and round to = approximate=20 reasonable results and to solve problems where exact answers are not = required;=20 and

(E) use order of operations to = simplify whole=20 number expressions (without exponents) in problem solving = situations.

(3) Patterns, relationships, and = algebraic=20 thinking. The student solves problems involving direct proportional=20 relationships. The student is expected to:

(A) use ratios to describe = proportional=20 situations;

(B) represent ratios and percents = with=20 concrete models, fractions, and decimals; and

(4) Patterns, relationships, and = algebraic=20 thinking. The student uses letters as variables in mathematical = expressions to=20 describe how one quantity changes when a related quantity changes. The = student=20 is expected to:

(A) use tables and symbols to = represent and=20 describe proportional and other relationships such as those involving=20 conversions, arithmetic sequences (with a constant rate of change), = perimeter=20 and area; and

(B) use tables of data to generate = formulas=20 representing relationships involving perimeter, area, volume of a = rectangular=20 prism, etc.

(5) Patterns, relationships, and = algebraic=20 thinking. The student uses letters to represent an unknown in an = equation. The=20 student is expected to formulate equations from problem situations = described by=20 linear relationships.

(6) Geometry and spatial reasoning. The = student=20 uses geometric vocabulary to describe angles, polygons, and circles. The = student=20 is expected to:

(A) use angle measurements to = classify angles=20 as acute, obtuse, or right;

(B) identify relationships involving = angles in=20 triangles and quadrilaterals; and

(7) Geometry and spatial reasoning. The = student=20 uses coordinate geometry to identify location in two dimensions. The = student is=20 expected to locate and name points on a coordinate plane using ordered = pairs of=20 non-negative rational numbers.

(8) Measurement. The student solves = application=20 problems involving estimation and measurement of length, area, time,=20 temperature, volume, weight, and angles. The student is expected to:

(A) estimate measurements (including = circumference) and evaluate reasonableness of results;

(B) select and use appropriate = units, tools,=20 or formulas to measure and to solve problems involving length (including = perimeter), area, time, temperature, volume, and weight;

(D) convert measures within the same = measurement system (customary and metric) based on relationships between = units.

(9) Probability and statistics. The = student uses=20 experimental and theoretical probability to make predictions. The = student is=20 expected to:

(A) construct sample spaces using = lists and=20 tree diagrams; and

(B) find the probabilities of a = simple event=20 and its complement and describe the relationship between the two.

(10) Probability and statistics. The = student uses=20 statistical representations to analyze data. The student is expected = to:

(A) select and use an appropriate=20 representation for presenting and displaying different graphical = representations=20 of the same data including line plot, line graph, bar graph, and stem = and leaf=20 plot;

(B) identify mean (using concrete = objects and=20 pictorial models), median, mode, and range of a set of data;

(D) solve problems by collecting, = organizing,=20 displaying, and interpreting data.

(11) Underlying processes and = mathematical tools.=20 The student applies Grade 6 mathematics to solve problems connected to = everyday=20 experiences, investigations in other disciplines, and activities in and = outside=20 of school. The student is expected to:

(A) identify and apply mathematics = to everyday=20 experiences, to activities in and outside of school, with other = disciplines, and=20 with other mathematical topics;

(B) use a problem-solving model that = incorporates understanding the problem, making a plan, carrying out the = plan,=20 and evaluating the solution for reasonableness;

(C) select or develop an appropriate = problem-solving strategy from a variety of different types, including = drawing a=20 picture, looking for a pattern, systematic guessing and checking, acting = it out,=20 making a table, working a simpler problem, or working backwards to solve = a=20 problem; and

(D) select tools such as real = objects,=20 manipulatives, paper/pencil, and technology or techniques such as mental = math,=20 estimation, and number sense to solve problems.

(12) Underlying processes and = mathematical tools.=20 The student communicates about Grade 6 mathematics through informal and=20 mathematical language, representations, and models. The student is = expected=20 to:

(A) communicate mathematical ideas = using=20 language, efficient tools, appropriate units, and graphical, numerical,=20 physical, or algebraic mathematical models; and

(B) evaluate the effectiveness of = different=20 representations to communicate ideas.

(13) Underlying processes and = mathematical tools.=20 The student uses logical reasoning to make conjectures and verify = conclusions.=20 The student is expected to:

(A) make conjectures from patterns = or sets of=20 examples and nonexamples; and

(B) validate his/her conclusions = using=20 mathematical properties and relationships.

Source: The provisions of this =A7111.22 adopted = to be=20 effective September 1, 1998, 22 TexReg 7623; amended to be effective = August 1,=20 2006, 30 TexReg 1930.

(a) Introduction.

(1) Within a well-balanced mathematics=20 curriculum, the primary focal points at Grade 7 are using direct = proportional=20 relationships in number, geometry, measurement, and probability; = applying=20 addition, subtraction, multiplication, and division of decimals, = fractions, and=20 integers; and using statistical measures to describe data.

(b) Knowledge and skills.

(1) Number, operation, and quantitative = reasoning. The student represents and uses numbers in a variety of = equivalent=20 forms. The student is expected to:

(A) compare and order integers and = positive=20 rational numbers;

(B) convert between fractions, = decimals, whole=20 numbers, and percents mentally, on paper, or with a calculator; and

(2) Number, operation, and quantitative = reasoning. The student adds, subtracts, multiplies, or divides to solve = problems=20 and justify solutions. The student is expected to:

(A) represent multiplication and = division=20 situations involving fractions and decimals with models, including = concrete=20 objects, pictures, words, and numbers;

(B) use addition, subtraction, = multiplication,=20 and division to solve problems involving fractions and decimals;

(C) use models, such as concrete = objects,=20 pictorial models, and number lines, to add, subtract, multiply, and = divide=20 integers and connect the actions to algorithms;

(D) use division to find unit rates = and ratios=20 in proportional relationships such as speed, density, price, recipes, = and=20 student-teacher ratio;

(E) simplify numerical expressions = involving=20 order of operations and exponents;

(F) select and use appropriate = operations to=20 solve problems and justify the selections; and

(G) determine the reasonableness of = a solution=20 to a problem.

(3) Patterns, relationships, and = algebraic=20 thinking. The student solves problems involving direct proportional=20 relationships. The student is expected to:

(A) estimate and find solutions to = application=20 problems involving percent; and

(B) estimate and find solutions to = application=20 problems involving proportional relationships such as similarity, = scaling, unit=20 costs, and related measurement units.

(4) Patterns, relationships, and = algebraic=20 thinking. The student represents a relationship in numerical, geometric, = verbal,=20 and symbolic form. The student is expected to:

(A) generate formulas involving unit = conversions within the same system (customary and metric), perimeter, = area,=20 circumference, volume, and scaling;

(B) graph data to demonstrate = relationships in=20 familiar concepts such as conversions, perimeter, area, circumference, = volume,=20 and scaling; and

(C) use words and symbols to = describe the=20 relationship between the terms in an arithmetic sequence (with a = constant rate=20 of change) and their positions in the sequence.

(5) Patterns, relationships, and = algebraic=20 thinking. The student uses equations to solve problems. The student is = expected=20 to:

(A) use concrete and pictorial = models to solve=20 equations and use symbols to record the actions; and

(B) formulate problem situations = when given a=20 simple equation and formulate an equation when given a problem = situation.

(6) Geometry and spatial reasoning. The = student=20 compares and classifies two- and three-dimensional figures using = geometric=20 vocabulary and properties. The student is expected to:

(A) use angle measurements to = classify pairs=20 of angles as complementary or supplementary;

(B) use properties to classify = triangles and=20 quadrilaterals;

(D) use critical attributes to = define=20 similarity.

(7) Geometry and spatial reasoning. The = student=20 uses coordinate geometry to describe location on a plane. The student is = expected to:

(A) locate and name points on a = coordinate=20 plane using ordered pairs of integers; and

(B) graph reflections across the = horizontal or=20 vertical axis and graph translations on a coordinate plane.

(8) Geometry and spatial reasoning. The = student=20 uses geometry to model and describe the physical world. The student is = expected=20 to:

(A) sketch three-dimensional figures = when=20 given the top, side, and front views;

(B) make a net (two-dimensional = model) of the=20 surface area of a three-dimensional figure; and

(9) Measurement. The student solves = application=20 problems involving estimation and measurement. The student is expected = to:

(A) estimate measurements and solve=20 application problems involving length (including perimeter and = circumference)=20 and area of polygons and other shapes;

(B) connect models for volume of = prisms=20 (triangular and rectangular) and cylinders to formulas of prisms = (triangular and=20 rectangular) and cylinders; and

(C) estimate measurements and solve=20 application problems involving volume of prisms (rectangular and = triangular) and=20 cylinders.

(10) Probability and statistics. The = student=20 recognizes that a physical or mathematical model (including geometric) = can be=20 used to describe the experimental and theoretical probability of = real-life=20 events. The student is expected to:

(A) construct sample spaces for = simple or=20 composite experiments; and

(B) find the probability of = independent=20 events.

(11) Probability and statistics. The = student=20 understands that the way a set of data is displayed influences its=20 interpretation. The student is expected to:

(A) select and use an appropriate=20 representation for presenting and displaying relationships among = collected data,=20 including line plot, line graph, bar graph, stem and leaf plot, circle = graph,=20 and Venn diagrams, and justify the selection; and

(B) make inferences and convincing = arguments=20 based on an analysis of given or collected data.

(12) Probability and statistics. The = student uses=20 measures of central tendency and variability to describe a set of data. = The=20 student is expected to:

(A) describe a set of data using = mean, median,=20 mode, and range; and

(B) choose among mean, median, mode, = or range=20 to describe a set of data and justify the choice for a particular = situation.

(13) Underlying processes and = mathematical tools.=20 The student applies Grade 7 mathematics to solve problems connected to = everyday=20 experiences, investigations in other disciplines, and activities in and = outside=20 of school. The student is expected to:

(A) identify and apply mathematics = to everyday=20 experiences, to activities in and outside of school, with other = disciplines, and=20 with other mathematical topics;

(B) use a problem-solving model that = incorporates understanding the problem, making a plan, carrying out the = plan,=20 and evaluating the solution for reasonableness;

(D) select tools such as real = objects,=20 manipulatives, paper/pencil, and technology or techniques such as mental = math,=20 estimation, and number sense to solve problems.

(14) Underlying processes and = mathematical tools.=20 The student communicates about Grade 7 mathematics through informal and=20 mathematical language, representations, and models. The student is = expected=20 to:

(A) communicate mathematical ideas = using=20 language, efficient tools, appropriate units, and graphical, numerical,=20 physical, or algebraic mathematical models; and

(B) evaluate the effectiveness of = different=20 representations to communicate ideas.

(15) Underlying processes and = mathematical tools.=20 The student uses logical reasoning to make conjectures and verify = conclusions.=20 The student is expected to:

(A) make conjectures from patterns = or sets of=20 examples and nonexamples; and

(B) validate his/her conclusions = using=20 mathematical properties and relationships.

Source: The provisions of this =A7111.23 adopted = to be=20 effective September 1, 1998, 22 TexReg 7623; amended to be effective = August 1,=20 2006, 30 TexReg 1930; amended to be effective February 22, 2009, 34 = TexReg=20 1056.

(a) Introduction.

(1) Within a well-balanced mathematics=20 curriculum, the primary focal points at Grade 8 are using basic = principles of=20 algebra to analyze and represent both proportional and non-proportional = linear=20 relationships and using probability to describe data and make = predictions.

(b) Knowledge and skills.

(1) Number, operation, and quantitative = reasoning. The student understands that different forms of numbers are=20 appropriate for different situations. The student is expected to:

(A) compare and order rational = numbers in=20 various forms including integers, percents, and positive and negative = fractions=20 and decimals;

(B) select and use appropriate forms = of=20 rational numbers to solve real-life problems including those involving=20 proportional relationships;

(C) approximate (mentally and with=20 calculators) the value of irrational numbers as they arise from problem=20 situations (such as p, =D62);

(D) express numbers in scientific = notation,=20 including negative exponents, in appropriate problem situations; and

(E) compare and order real numbers = with a=20 calculator.

(2) Number, operation, and quantitative = reasoning. The student selects and uses appropriate operations to solve = problems=20 and justify solutions. The student is expected to:

(A) select appropriate operations to = solve=20 problems involving rational numbers and justify the selections;

(B) use appropriate operations to = solve=20 problems involving rational numbers in problem situations;

(D) use multiplication by a given = constant=20 factor (including unit rate) to represent and solve problems involving=20 proportional relationships including conversions between measurement=20 systems.

(3) Patterns, relationships, and = algebraic=20 thinking. The student identifies proportional or non-proportional linear = relationships in problem situations and solves problems. The student is = expected=20 to:

(A) compare and contrast = proportional and=20 non-proportional linear relationships; and

(B) estimate and find solutions to = application=20 problems involving percents and other proportional relationships such as = similarity and rates.

(4) Patterns, relationships, and = algebraic=20 thinking. The student makes connections among various representations of = a=20 numerical relationship. The student is expected to generate a different=20 representation of data given another representation of data (such as a = table,=20 graph, equation, or verbal description).

(5) Patterns, relationships, and = algebraic=20 thinking. The student uses graphs, tables, and algebraic representations = to make=20 predictions and solve problems. The student is expected to:

(A) predict, find, and justify = solutions to=20 application problems using appropriate tables, graphs, and algebraic = equations;=20 and

(B) find and evaluate an algebraic = expression=20 to determine any term in an arithmetic sequence (with a constant rate of = change).

(6) Geometry and spatial reasoning. The = student=20 uses transformational geometry to develop spatial sense. The student is = expected=20 to:

(A) generate similar figures using = dilations=20 including enlargements and reductions; and

(B) graph dilations, reflections, = and=20 translations on a coordinate plane.

(7) Geometry and spatial reasoning. The = student=20 uses geometry to model and describe the physical world. The student is = expected=20 to:

(A) draw three-dimensional figures = from=20 different perspectives;

(B) use geometric concepts and = properties to=20 solve problems in fields such as art and architecture;

(D) locate and name points on a = coordinate=20 plane using ordered pairs of rational numbers.

(8) Measurement. The student uses = procedures to=20 determine measures of three-dimensional figures. The student is expected = to:

(A) find lateral and total surface = area of=20 prisms, pyramids, and cylinders using concrete models and nets = (two-dimensional=20 models);

(B) connect models of prisms, = cylinders,=20 pyramids, spheres, and cones to formulas for volume of these objects; = and

(C) estimate measurements and use = formulas to=20 solve application problems involving lateral and total surface area and=20 volume.

(9) Measurement. The student uses = indirect=20 measurement to solve problems. The student is expected to:

(A) use the Pythagorean Theorem to = solve=20 real-life problems; and

(B) use proportional relationships = in similar=20 two-dimensional figures or similar three-dimensional figures to find = missing=20 measurements.

(10) Measurement. The student describes = how=20 changes in dimensions affect linear, area, and volume measures. The = student is=20 expected to:

(A) describe the resulting effects = on=20 perimeter and area when dimensions of a shape are changed = proportionally;=20 and

(B) describe the resulting effect on = volume=20 when dimensions of a solid are changed proportionally.

(11) Probability and statistics. The = student=20 applies concepts of theoretical and experimental probability to make=20 predictions. The student is expected to:

(A) find the probabilities of = dependent and=20 independent events;

(B) use theoretical probabilities = and=20 experimental results to make predictions and decisions; and

(12) Probability and statistics. The = student uses=20 statistical procedures to describe data. The student is expected to:

(A) use variability (range, = including=20 interquartile range (IQR)) and select the appropriate measure of central = tendency to describe a set of data and justify the choice for a = particular=20 situation;

(B) draw conclusions and make = predictions by=20 analyzing trends in scatterplots; and

(C) select and use an appropriate=20 representation for presenting and displaying relationships among = collected data,=20 including line plots, line graphs, stem and leaf plots, circle graphs, = bar=20 graphs, box and whisker plots, histograms, and Venn diagrams, with and = without=20 the use of technology.

(13) Probability and statistics. The = student=20 evaluates predictions and conclusions based on statistical data. The = student is=20 expected to:

(A) evaluate methods of sampling to = determine=20 validity of an inference made from a set of data; and

(B) recognize misuses of graphical = or=20 numerical information and evaluate predictions and conclusions based on = data=20 analysis.

(14) Underlying processes and = mathematical tools.=20 The student applies Grade 8 mathematics to solve problems connected to = everyday=20 experiences, investigations in other disciplines, and activities in and = outside=20 of school. The student is expected to:

(A) identify and apply mathematics = to everyday=20 experiences, to activities in and outside of school, with other = disciplines, and=20 with other mathematical topics;

(B) use a problem-solving model that = incorporates understanding the problem, making a plan, carrying out the = plan,=20 and evaluating the solution for reasonableness;

(D) select tools such as real = objects,=20 manipulatives, paper/pencil, and technology or techniques such as mental = math,=20 estimation, and number sense to solve problems.

(15) Underlying processes and = mathematical tools.=20 The student communicates about Grade 8 mathematics through informal and=20 mathematical language, representations, and models. The student is = expected=20 to:

(A) communicate mathematical ideas = using=20 language, efficient tools, appropriate units, and graphical, numerical,=20 physical, or algebraic mathematical models; and

(B) evaluate the effectiveness of = different=20 representations to communicate ideas.

(16) Underlying processes and = mathematical tools.=20 The student uses logical reasoning to make conjectures and verify = conclusions.=20 The student is expected to:

(A) make conjectures from patterns = or sets of=20 examples and nonexamples; and

(B) validate his/her conclusions = using=20 mathematical properties and relationships.

Source: The provisions of this =A7111.24 adopted = to be=20 effective September 1, 1998, 22 TexReg 7623; amended to be effective = August 1,=20 2006, 30 TexReg 1930; amended to be effective February 22, 2009, 34 = TexReg=20 1056.