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
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 whole numbers, fractions, and decimals.
Including:
- Proper and improper fractions
- Multiple forms within the problem
Including mixed numbers / 8.1B / Select and use appropriate forms of rational numbers to solve real-life problems including those involving proportional relationships.
Examples include:
Using multiple forms of fractions, decimals, percents, positive and negative integers within a single problem.
7.1C / 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.
Including positive and negative numbers. / 8.1D / 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
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 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.
6.2A / Model addition and subtraction situations involving fractions with objects, pictures, words, and numbers.
Including:
- Mixed numbers
- Like and unlike denominators
Including writing or selecting the correct expression
6.2B / Use addition and subtraction to solve problems involving fractions and decimals.
Examples include:
- Problems with mixed numbers with like and unlike denominators
- Simplifying answers (converting improper fractions to whole or mixed numbers in lowest terms)
- Decimal problems with answer grids
Examples include:
Problems where your answer choices are models
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 problems including situations involving equivalent ratios and rates.
Examples include:
- Situations involving unit rate
- Fractions and decimals
- Problems involving ratios relating numbers to the words associated with given numbers
- Cross multiply and solve for x
Including:
- Fractions and decimals
- Cross multiply and solve for x
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
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 expressions (without exponents) in problem solving situations.
Including:
- Problems with both addition or subtraction and multiplication or division with and without parentheses
- Simplifying order of operation problems including the use of exponents
Including negative values
7.2F / Select and use appropriate operations to solve problems and justify the selections.
Examples include:
- Problems with multiple operations
- Problems with answer grids
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, 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.
Including problems with the appropriate range / 8.2C / 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.
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 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: / 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:
6.3A / Use ratios to describe proportional situations.
Including ratios that may or may not be in lowest terms represented in a table, equation, or verbal description. / 8.3A / 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) or geometric figures
- Measurements using standard and metric units
- Unit conversions
6.3B / Represent ratios and percents with concrete models, fractions, and decimals.
Including:
- Conversions of fractions, decimals, and percents
- Reinforcing percent over 100
- Use of strategy “of” number goes on bottom when finding percent of a number
- Use of strategy “is” number goes on top
OF 100 / 7.3A / Estimate and find solutions to application problems involving percent.
Including:
- Percent increase
- Percent decrease
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
6.3C / Use ratios to make predictions in proportional situations.
Including:
- Setting up a proportion problem from a verbal description
- Using data in a table
- Using conversions to express compatible time, measurement, and numbers
Including:
- Setting up a proportion problem from word problems
- Using data in a table
- Measurements using standard and metric units
- Unit conversions
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 / 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:
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.
Including
- Metric conversions for length
- Standard conversion for length
- Equations using variables (define)
- Line Graph
- Bar Graph
- Multiple Bar Graph
- Pictograph
- Circle Graphs
- Line Plots
- Stem & Leaf
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)
- Line Graph
- Bar Graph
- Multiple Bar Graph
- Histogram
- Scatter plot
- Pictograph
- Circle Graph
- Line Plots
- Stem and Leaf
- Venn Diagram
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:
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
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
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) (>, <, ≥, ≤)
- Line Graph
- Bar Graph
- Multiple Bar Graph
- Histogram
- Scatter Plot
- Pictographs
- Circle Graph
- Line Plots
- Stem and Leaf
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 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
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) ]
- Vocabulary: (i.e. substitute, algebraic expression, expression, rule, nth term, prediction, pattern, correlation, term, sequence)
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 / Patterns, relationships, and algebraic thinking. The student uses equations to solve problems. The student is expected to:
7.5A / Use concrete and pictorial models to solve equations and use symbols to record the actions.
Including equations with two variables
6.5A / Formulate equations from problem situations described by linear relationships.
Including:
- Equations in the form of ab=c where a and c are numbers in the problem
- Using variables to represent an unknown in an equation
- Using more than one variable in an equation
- Using multiplication in various forms (parentheses, 3n, and •)
- C = 5 (h + 25)
- X = 3n
- X = 30 • 8
- Matching an equation with a real life situation
Including prerequisites of:
- Translating word phrases to algebraic expressions
- Translating word phrases to algebraic equations.
6.6 / Geometry and spatial reasoning. The student uses geometric vocabulary to describe angles, polygons, and circles. The student is expected to: / 7.6 / Geometry and spatial reasoning. The student compares and classifies two- and three-dimensional figures using geometric vocabulary and properties. The student is expected to: / 8.6 / Geometry and spatial reasoning. The student uses transformational geometry to develop spatial sense. The student is expected to:
6.6A / 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:
- 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)
Including:
- Diagrams with multiple angles
- Prerequisite: name angles with three points
6.6B / Identify relationships involving angles in triangles and quadrilaterals.
Including:
- Understand sum of degrees in a triangle and a quadrilateral
- Understand use of ‘hash marks’ to describe congruent sides
- Define isosceles, scalene, and equilateral triangles.
Including:
- Triangle vocabulary: (i.e. acute, obtuse, right (define legs and hypotenuse), equiangular, isosceles, equilateral, and scalene)
- Quadrilateral terms: (i.e. parallelogram, rectangle, square, trapezoid, and rhombus)
7.6C / 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.
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
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
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 coordinate geometry to identify location in two dimensions. The student is expected to: / 7.7 / Geometry and spatial reasoning. The student uses coordinate geometry to describe location on a plane. The student is expected to: / 8.7 / Geometry and spatial reasoning. The student uses geometry to model and describe the physical world. The student is expected to: