Model and solve one-variable, one-step equations and inequalities that represent problems, including geometric concepts.
Determine if the given value(s) make(s) one-variable, one-step equations or inequalities true.
Identify independent and dependent quantities from tables and graphs.
Write an equation that represents the relationship between independent and dependent quantities from a table.
Represent a given situation using verbal descriptions, tables, graphs, and equations in the form y = kx or y = x + b.
Generate equivalent numerical expressions using order of operations, including whole number exponents and prime factorization.
Distinguish between expressions and equations verbally, numerically, and algebraically.
Determine if two expressions are equivalent using concrete models, pictorial models, and algebraic representations.
Generate equivalent expressions using the properties of operations: inverse, identity, commutative, associative, and distributive properties.
Extend previous knowledge of triangles and their properties to include the sum of angles of a triangle, the relationship between the lengths of sides and measures of angles in a triangle, and determining when three lengths form a triangle.
Model area formulas for parallelograms, trapezoids, and triangles by decomposing and rearranging parts of these shapes.
Write equations that represent problems related to the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers.
Determine solutions for problems involving the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers.
Write one-variable, one-step equations and inequalities to represent constraints or conditions within problems.
Represent solutions for one-variable, one-step equations and inequalities on number lines.
Write corresponding real-world problems given one-variable, one-step equations or inequalities.
The student applies mathematical process standards to use coordinate geometry to identify locations on a plane. The student is expected to graph points in all four quadrants using ordered pairs of rational numbers.
Represent numeric data graphically, including dot plots, stem-and-leaf plots, histograms, and box plots.
Use the graphical representation of numeric data to describe the center, spread, and shape of the data distribution.
Summarize numeric data with numerical summaries, including the mean and median (measures of center) and the range and interquartile range (IQR) (measures of spread), and use these summaries to describe the center, spread, and shape of the data distribution.
Summarize categorical data with numerical and graphical summaries, including the mode, the percent of values in each category (relative frequency table), and the percent bar graph, and use these summaries to describe the data distribution.
Interpret numeric data summarized in dot plots, stem-and-leaf plots, histograms, and box plots.
Distinguish between situations that yield data with and without variability.
Compare the features and costs of a checking account and a debit card offered by different local financial institutions.
Distinguish between debit cards and credit cards.
Balance a check register that includes deposits, withdrawals, and transfers.
Explain why it is important to establish a positive credit history.
Describe the information in a credit report and how long it is retained.
Describe the value of credit reports to borrowers and to lenders.
Explain various methods to pay for college, including through savings, grants, scholarships, student loans, and work-study.
Compare the annual salary of several occupations requiring various levels of post-secondary education or vocational training and calculate the effects of the different annual salaries on lifetime income.
Apply mathematics to problems arising in everyday life, society, and the workplace.
Add and Subtract Decimal Up to 100
Ratios
Unit Rates
Equivalent Ratios
Compare Ratios
Percents of Numbers
Divide Fractions and Mixed Numbers
Divide Numbers Ending in Zeroes
Mixed Equations with Whole Numbers
Mixed Equations with Decimals
GCF and LCM
Add and Subtract Integers
Two-Variable Equations
Linear Function
Write Variable Expressions
Write Variable Equations to Represent
Coordinate Graphs as Maps
Maps with Decimal Distances
Percents of Numbers and Money Amounts
Compare and Convert Customary Units with Numbers Up to 20
Convert, Compare and Subtract Mixed Customary Units
Compare and Convert Metric Units
Convert Between Celsius and Fahrenheit
Working with Temperatures Above and Below Zero
Multiply and Divide Mixed Customary Units
Customary Unit Conversions Involving Fractions and Mixed
Convert Between Metric and Customary Units
Which Is the Better Coupon?
Unit Prices with Customary Unit Conversions and Fractions
Unit Prices with Customary Unit Conversions Up to 100
Consumer Math: Unit Prices
Unit Prices: Which Is the Better Buy?
Sale Prices
Sale Prices: Find the Original Price
Calculate Tip, Markup and Commission
Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.
Variable Inequalities
Reciprocals
Inequalities with Decimal Division
Inequalities with Decimal Multiplication
Solve One-Step Linear Inequalities
Mean, Median, Mode, and Range: Find the Missing Number
Simplify Variable Expressions
Exponents: Solve for the Variable
Solve One-Step Equations with Decimals and Fractions
Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.
Estimate Quotients When Dividing Mixed Numbers
Estimate Quotients
Estimate Sums and Differences of Decimals Up to 100
Estimate Products of Decimal Numbers
Evaluate Exponents
Write Multiplication Expressions Using Exponents
Exponents with Decimal Bases
Exponents with Fractional Bases
Divide by Fractions with Models
Divide by Fractions with Models
Understanding Integers
Absolute Value and Opposite Integers
Evaluate Expressions Involving Integers
Mixed Equations with Decimals
Mixed Fraction Equations with Mixed Numbers Up to 500
Mixed Fraction Equations Up to 500
Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
Evaluate Variable Expressions with Whole Numbers
Evaluate Variable Expressions with Decimals and Fractions
Evaluate Multi-Variable Expressions
Write Variable Expressions
Evaluate Expressions with Decimals
Convert Scientific Notation
Factors of Multiplication
Greatest Common Factors (GCF)
Identify Factors
Understanding Decimals Expressed in Words
Compare Rational Numbers
Ratio Tables
Describe Pictures as Ratios
What Percentage Is Illustrated?
Identify Terms, Coefficients, and Monomials
Add and Subtract Like Terms
Solve Mixed Equations
Graph Linear Functions
Nets of 3-Dimensional Figures
Area of Complex Figures
Compare Area and Perimeter of Two Figures
Area of Right Triangles
Volume of Cubes and Rectangular Prisms
Classify Quadrilateral Shapes
Types of Triangles
Identify Angles by Type
Circles
Create and use representations to organize, record, and communicate mathematical ideas.
Function Tables
Interpret Pictographs
Create Pictographs
Interpret Line Plots with Up to 5 Data Points
Create Line Plots
Create Line Plots II
Create Frequency Tables
Interpret Bar Graphs
Create Bar Graphs
Interpret Double Bar Graphs
Create Double Bar Graphs Using Tables
Create Histograms
Circle Graphs with Fractions
Interpret Circle Graphs
Interpret Line Graphs
Create Line Graphs
Interpret Double Line Graphs
Create Double Line Graphs Using Tables
Stem-And-Leaf Plots
Interpret Box-And-Whisker Plots
Interpret Charts to Find Mean, Median, Mode, and Range
Analyze mathematical relationships to connect and communicate mathematical ideas.
Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Classify whole numbers, integers, and rational numbers using a visual representation such as a Venn diagram to describe relationships between sets of numbers.
Identify a number, its opposite, and its absolute value.
Locate, compare, and order integers and rational numbers using a number line.
Order a set of rational numbers arising from mathematical and real-world contexts.
Extend representations for division to include fraction notation such as a/b represents the same number as a � b where b ? 0.
Recognize that dividing by a rational number and multiplying by its reciprocal result in equivalent values.
Determine, with and without computation, whether a quantity is increased or decreased when multiplied by a fraction, including values greater than or less than one.
Represent integer operations with concrete models and connect the actions with the models to standardized algorithms.
Add, subtract, multiply, and divide integers fluently.
Multiply and divide positive rational numbers fluently.
Compare two rules verbally, numerically, graphically, and symbolically in the form of y = ax or y = x + a in order to differentiate between additive and multiplicative relationships.
Apply qualitative and quantitative reasoning to solve prediction and comparison of real-world problems involving ratios and rates.
Give examples of ratios as multiplicative comparisons of two quantities describing the same attribute.
Give examples of rates as the comparison by division of two quantities having different attributes, including rates as quotients.
Represent ratios and percents with concrete models, fractions, and decimals.
Represent benchmark fractions and percents such as 1%, 10%, 25%, 33 1/3%, and multiples of these values using 10 by 10 grids, strip diagrams, number lines, and numbers.
Generate equivalent forms of fractions, decimals, and percents using real-world problems, including problems that involve money.
Convert units within a measurement system, including the use of proportions and unit rates.
Represent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions.
Solve real-world problems to find the whole given a part and the percent, to find the part given the whole and the percent, and to find the percent given the part and the whole, including the use of concrete and pictorial models.
Use equivalent fractions, decimals, and percents to show equal parts of the same whole.