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: / 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:
8.1A / Compare and order rational numbers in various forms including integers, percents, and positive and negative fractions and decimals.
Including numbers represented as fractions and decimals.
8.1B / Select and use appropriate forms of rational numbers to solve real-life problems.
Including those involving proportional relationships. / 8.1B / Select and use appropriate forms of rational numbers to solve real-life problems.
8.1C / Approximate (mentally and with calculators) the value of irrational numbers as they arise from problem situations (such asπ, √2).
Including using geometric problems using the square root of a number
Including the square root of any number less than 14.
8.1D / Express numbers in scientific notation, including negative exponents, in appropriate problem situation.
Including:
•Converting numbers back to standard form
•Scientific notation using positive or negative exponents
8.2 / Number, operation, and quantitative reasoning. The student selects and uses appropriate operations to solve problems and justify solutions. The student is expected to:
8.2A / 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.
8.2B / Use appropriate operations to solve problems involving rational numbers in problem situations.
Including problems with multi-operations (addition, subtraction, multiplication, division, square and square root) and mixed forms of rational numbers (positive and negative integers, fractions, decimals, and percents).
8.2C / Evaluate a solution for reasonableness.
Including application problems for money, measurement, and percent.
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))
•Referring to the measurement side of the TAKS chart
Including percents, fractions, and decimals.
8.3 / 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: / A.1 / Foundations for functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is expected to: / A.1 / Foundations for functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. 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: / 8.3 / 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: / 8.3 / 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:
8.5 / Geometric patterns. The student uses a variety of representations to describe geometric relationships and solve problems.The student is expected to:
A.1A / Describe independent and dependent quantities in functional relationships.
Including:
•Linear and quadratic functions
•Explaining a functional relationship by using one
variable to describe another variable.
•Selecting the independent or dependent quantity in an equation or verbal description and justifying the selection / A.1A / Describe independent and dependent quantities in functional relationships.
Including:
•Linear and quadratic functions •Explaining a functional relationship by using one variable to describe another variable.
•Selecting the independent or dependent quantity in an equation or verbal description and justifying the selection
A.1B / Gather and record data and use data sets to determine functional relationships between quantities.
Including:
•Students collecting data that models linear and quadratic functions
•Writing equations from a table of data
•Generating a list of data from a functional relationship
•Using a graphing calculator (specifically using the table function in the calculator). An option would be to teach linear regression using the calculator. / A.1B / Gather and record data and use data sets to determine functional relationships between quantities.
Including:
•Students collecting data that models linear and quadratic functions.
•Writing equations from a table of data
•Generating a list of data from a functional relationship
•Using a graphing calculator.
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
- 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, rule, expression, nth term, prediction, pattern, correlation, term, sequence)
- Number’s position in a sequence
Including:
- Areas of circles and squares
- Perimeters of squares, equilateral triangles, and circumference
- Constant rate of change (i.e. slope)
- Literal equations (a = lw solve for l)
Including describing functional relationships in writing equations or inequalities as they pertain to:
- Areas of circles and polygons
- Perimeters of polygons and circumference of circles
A.1C / Describe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations.
Including:
- Areas of circles and squares
- Perimeters of squares, equilateral triangles, and circumference
- Constant rate of change
8.3B / Estimate and find solutions to application problems involving percents and other proportional relationships such as similarity and rates.
Including:
•Ratios that may not be in lowest terms represented in a table, graph, equation, verbal description and geometric representations.
•Setting up a proportion problem from a verbal description
•Using data in a table
•Dilations (Enlargements and reductions) of geometric figures
•Measurements using standard and metric units
•Unit conversions / A.1D / Represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities.
Including quadratic relationships and linear relationships (constant rate of change) with and without a graphing calculator. / A.1D / Represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities.
Including quadratic relationships (areas of circles and squares) and linear relationships (perimeters of squares, equilateral triangles, circumference, and constant rate of change) with and without a graphing calculator.
8.3B / Estimate and find solutions to application problems involving percents and other proportional relationships such as similarity and rates.
Including linear relationships (constant rate of change, and similar figures) with and without a graphing calculator.
8.3B / Estimate and find solutions to application problems involving percents and other proportional relationships such as similarity and rates.
Including linear relationships (perimeters of squares, equilateral triangles, circumference, constant rate of change, and similar figures) with and without a graphing calculator.
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) (Example: >, <, ≤, ≥)
Graphs to include:
•Line Graph
•Bar Graph
•Multiple Bar Graph
•Pie Chart
•Histogram
•Scatter plot
•Box and Whiskers
•Pictograph
•Circle Graph
•Line Plots
•Stem and leaf
A.1E / Interpret and make decisions, predictions, and critical judgments from functional relationships.
Including linear relationships (constant rate of change) quadratic relationships communicated with concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities. / A.1E / Interpret and make decisions, predictions, and critical judgments from functional relationships.
Including linear relationships (perimeters of squares and equilateral triangles, circumference, constant rate of change, and similar figures) and quadratic relationships (area of circle and square) communicated with concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities.
8.3 / 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: / A.2 / Foundations for functions. The student uses the properties and attributes of functions. The student is expected to: / G.4 / Geometric structure. The student uses a variety of representations to describe geometric relationships and solve problems. 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: / A.2 / Foundations for functions. The student uses the properties and attributes of functions. The student is expected to:
8.12 / Probability and statistics. The student uses statistical procedures to describe data. The student is expected to:
8.3A / 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) of geometric figures
•Measurements using standard and metric units •Unit conversions / A.2A / Identify and sketch the general forms of linear (y = x) and quadratic (y = x2) parent functions.
Including :
- Investigations with and without a graphing calculator
- Specifically using the terminology “parent functions”
- Including parent functions that have been altered (for example a parabola turned upside down still belongs to the parent function y=x2)
Including investigations with and without a graphing calculator. This SE was not tested in 2003 or 2004 at this grade.
A.2B / Identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete.
Including:
•Values displayed in a table
•Values displayed by an equation
•Values displayed in a graph.
•Values displayed by an inequality.
•Values from a verbal description of everyday experiences such as temperature, money, height, etc. / A.2B / Identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete.
Including:
•A range of values displayed in a table
•A range of values displayed in a graph
•A range of values displayed by an
inequality
•A range of values from a verbal description of everyday experiences such as temperature, money, height, etc.
8.4A / The student is expected to generate a different representation of data given another representation of data (such as table, graph, equation, or verbal description).
Including:
•Multiple representations of a table, graph, equation, sequence or verbal description within a single context of a problem
•Present and future incremental predictions •Vocabulary: (i.e. Interval, scale, nth term, coordinate plane, position, sequence, trend, correlation, relationships, variables, positive, and negative
Graphs to include:
•Line Graph
•Bar Graph
•Multiple Bar Graph
•Histogram
•Scatter plot
•Pictograph
•Circle Graph
•Line Plots
•Stem and leaf
•Venn Diagram / A.2C / Interpret situations in terms of given graphs or creates situations that fit given graphs.
Including interpreting real-world situations in terms of graphs and also describing a real-world situation that fits a graph. / G.4A / The student is expected to select an appropriate representation (concrete, pictorial, graphical, verbal, or symbolic) in order to solve problems.
Including:
•Interpreting real-world geometric situations in terms of graphs, tables, and literal equations
•Describing real-world geometric situations that fit appropriate representations
A.2C / Interpret situations in terms of given graphs or creates situations that fit given graphs.
Including interpreting real-world situations in terms of graphs and also describing a real-world situation that fits a graph.
8.12B / Draw conclusions and make predictions by analyzing trends in scatter plots.
Including:
Describe the scatterplot in words (increasing/decreasing)
•Scatter plots that show no trend
•Positive, negative and no correlations or trends / A.2D / Collect and organize data, make and interpret scatter plots (including recognizing positive, negative, or no correlation for data approximating linear situations) and model, predict, and make decisions and critical judgments in problem situations.
Including organizing data that demonstrates a positive linear correlation, a negative linear correlation, and no correlation with and without a graphing calculator / A.2D / Collect and organize data, make and interpret scatter plots including recognizing positive, negative, or no correlation for data approximating linear situations) and model, predict, and make decisions and critical judgments in problem situations.
Including organizing data that demonstrates a positive linear correlation, a negative linear correlation, and no correlation with and without a graphing calculator
A.3 / Foundations for functions. The student understands how algebra can be used to express generalizations and recognizes and uses the power of symbols to represent situations. The student is expected to: / A.3 / Foundations for functions. The student understands how algebra can be used to express generalizations and recognizes and uses the power of symbols to represent situations. The student is expected to:
A.3A / Use symbols to represent unknowns and variables.
Including similarity, constant rate of change, area, perimeter, circumference, and proportions. Write an expression to represent the solution to a problem. / A.3A / Use symbols to represent unknowns and variables.
Including similarity, constant rate of change, area, perimeter, circumference, and proportions.
A.3B / Look for patterns and represent generalizations algebraically.
Including expressions in the form of, but not limited to:
- an, an±b, a/n, n/a, a/n ± b, n/a ± b, a ±n, n – a
- geometric sequence
- arithmetic sequence
- common ratios and differences
Including expressions in the form of, but not limited to:
- an, an±b, a/n, n/a, a/n ± b, n/a ± b, a ±n, n – a
- geometric sequence
- arithmetic sequence
- common ratios and differences
A.4 / Foundations for functions. The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations. The student is expected to: / A.4 / Foundations for functions. The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations. The student is expected to:
A.4A / Find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations.
Including:
•Areas of rectangles and squares.
•Factoring binomials and trinomials.
•Apply the commutative, associative, and distributive properties to solve equations.
•Substitute a value for a variable.
•Use a graphing calculator to find specific function values (e.g. zeros of quadratic functions) / A.4A / Find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations.
Including:
•Areas of rectangles and squares
•Factoring binomials and trinomials
•Apply the commutative, associative, and distributive properties to solve equations •Substitute a value for a variable
•Using a graphing calculator
A.4B / Use the commutative, associative, and distributive properties to simplify algebraic expressions. / A.4B / Use the commutative, associative, and distributive properties to simplify algebraic expressions.
A.4C / Connect equation notation with function notation, such as y = x + 1 and f(x) = x + 1.
Including examples of functions such as linear and quadratic relationships, and non-examples such as y2 = x.
A.5 / Linear functions. The student understands that linear functions can be represented in different ways and translates among their various representations. The student is expected to: / A.5 / Linear functions. The student understands that linear functions can be represented in different ways and translates among their various representations. The student is expected to:
A.5A / Determine whether or not given situations can be represented by linear functions.
Including:
•Verbal descriptions that describe a constant rate of change and a rate of change that is not constant •A table of values with a constant rate of change and a table of values in which the rate of change is not constant. / A.5A / Determine whether or not given situations can be represented by linear functions.
Including:
- Verbal descriptions that describe a constant rate of change and a rate of change that is not constant
- A table of values with a constant rate of change and a table of values in which the rate of change is not constant.
A.5B / Determine the domain and range for linear functions in given situations.
Including:
•Earning a salary and/or commission
•Speed
•Temperature, etc…
A.5C / Use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions.
Including:
•Real-world verbal descriptions of a constant rate of change such as earning an hourly wage or a constant speed.
•Connecting the graph of a line to a description of a real-world experience.
•Connecting an algebraic expression to a description of a real-world experience.
•Using a graphing calculator. / A.5C / Use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions.