Minnesota Academic Standards (adopted in 2022): Integrated Mathematics 1
Skills available for Minnesota Integrated Mathematics 1 math standards
Strand
Print skill plan
Data and Probability
Data Sciences: Identify, formulate and investigate statistical questions by collecting data, considering cultural perspectives, analyzing and interpreting data and communicating the results.
9.1.1.1 Formulate statistical investigative questions and pose hypotheses. These include questions about variation or the differences between groups, associations between quantitative and categorical variables or pairing together multiple analyses.
9.1.1.1 Formulate statistical investigative questions and pose hypotheses. These include questions about variation or the differences between groups, associations between quantitative and categorical variables or pairing together multiple analyses.
9.1.1.2 Explain how choices concerning data collection methods can affect the quality, size, speed, accessibility and cost of the data.
9.1.1.2 Explain how choices concerning data collection methods can affect the quality, size, speed, accessibility and cost of the data.
9.1.1.3 Analyze issues of bias by considering data collection methods and cultural perspectives.
9.1.1.3 Analyze issues of bias by considering data collection methods and cultural perspectives.
9.1.1.5 Analyze and explain when arguments based on data confuse correlation and causation.
9.1.1.5 Analyze and explain when arguments based on data confuse correlation and causation.
9.1.1.6 Compute using technology or estimate the correlation coefficient of a linear model. Interpret the linear model in the context of the data.
9.1.1.6 Compute using technology or estimate the correlation coefficient of a linear model. Interpret the linear model in the context of the data.
9.1.1.9 Use statistics appropriate to the shape of the data distribution to compare the center and spread of two or more data sets.
9.1.1.9 Use statistics appropriate to the shape of the data distribution to compare the center and spread of two or more data sets.
9.1.1.10 Create and analyze data displays, including scatter plots, histograms and boxplots using technology.
9.1.1.10 Create and analyze data displays, including scatter plots, histograms and boxplots using technology.
9.1.1.11 Identify, create and compare statistical models with linear and exponential functions, including linear regression. Assess the reasonableness of model fit using residuals and correlation coefficients.
9.1.1.11 Identify, create and compare statistical models with linear and exponential functions, including linear regression. Assess the reasonableness of model fit using residuals and correlation coefficients.
9.1.1.13 Analyze and interpret data using various measures, such as difference in shapes, center and spread to draw conclusions, identify trends and describe relationships, accounting for possible effects of extreme data points (outliers).
9.1.1.13 Analyze and interpret data using various measures, such as difference in shapes, center and spread to draw conclusions, identify trends and describe relationships, accounting for possible effects of extreme data points (outliers).
9.1.1.14 Evaluate reports based on published data by identifying the source of the data, the design of the study and the way the data are analyzed and displayed.
9.1.1.14 Evaluate reports based on published data by identifying the source of the data, the design of the study and the way the data are analyzed and displayed.
9.1.1.15 Identify and explain misleading uses of data along with how to use spreadsheets, tables or graphing technology to recognize and analyze distortions in data displays. Use interactive data visualizations to support and influence different points of view.
9.1.1.15 Identify and explain misleading uses of data along with how to use spreadsheets, tables or graphing technology to recognize and analyze distortions in data displays. Use interactive data visualizations to support and influence different points of view.
Checkpoint skill Checkpoint opportunity
Checkpoint skill Checkpoint opportunity
Chance and Uncertainty: Apply and explain the concepts of probability to interpret data, generate questions, predict and make informed decisions to solve problems and communicate ideas.
9.1.2.5 Construct and interpret two-way frequency tables when two categories are associated with each object being classified. Use the two-way table to decide if events are independent and to calculate conditional probabilities.
9.1.2.5 Construct and interpret two-way frequency tables when two categories are associated with each object being classified. Use the two-way table to decide if events are independent and to calculate conditional probabilities.
Checkpoint skill Checkpoint opportunity
Checkpoint skill Checkpoint opportunity
Spatial Reasoning
Measurement: Investigate measurement using a variety of tools, units, systems, processes and techniques in various cultures. Explain and reason with attributes, estimations and formulas to communicate measurement(s) and relationships effectively. Justify decisions and consider the reasonableness of the measurement.
9.2.3.1 Apply the Pythagorean Theorem and distance formula to compute perimeters of polygons and areas of right triangles and rectangles on coordinate planes.
9.2.3.1 Apply the Pythagorean Theorem and distance formula to compute perimeters of polygons and areas of right triangles and rectangles on coordinate planes.
9.2.3.6 Use units of measure and dimensional analysis to solve multi-step situations. Interpret units consistently in formulas. Interpret the scale and the origin in graphs and data displays.
Customary and metric units
Word problems
9.2.3.6 Use units of measure and dimensional analysis to solve multi-step situations. Interpret units consistently in formulas. Interpret the scale and the origin in graphs and data displays.
Customary and metric units
Word problems
Checkpoint skill Checkpoint opportunity
Checkpoint skill Checkpoint opportunity
Geometry: Analyze characteristics of geometric shapes to make mathematical arguments and justifications about geometric relationships. Use visualization and geometric modeling to compare, solve problems and communicate ideas.
9.2.4.4 Apply properties of congruent figures to solve situations and logically justify results.
9.2.4.4 Apply properties of congruent figures to solve situations and logically justify results.
9.2.4.12 Make geometric constructions with a variety of tools, including dynamic geometric technology, to examine theorems, make and test conjectures, represent transformations and develop mathematical reasoning skills in multi-step situations.
Angles
Points, lines, and segments
Polygons
9.2.4.12 Make geometric constructions with a variety of tools, including dynamic geometric technology, to examine theorems, make and test conjectures, represent transformations and develop mathematical reasoning skills in multi-step situations.
Angles
Points, lines, and segments
Polygons
9.2.4.13 Create and compare rigid and non-rigid transformations, and connect the preimage and image to congruence.
Classify and compare transformations
Translations
Reflections and rotations
Congruence
Dilations
9.2.4.13 Create and compare rigid and non-rigid transformations, and connect the preimage and image to congruence.
Classify and compare transformations
Translations
Reflections and rotations
Congruence
Dilations
9.2.4.14 Describe the steps used to show various sequences of transformations, applying reflections, rotations, translations and/or dilations of geometric figures that map one figure onto the other.
9.2.4.14 Describe the steps used to show various sequences of transformations, applying reflections, rotations, translations and/or dilations of geometric figures that map one figure onto the other.
Checkpoint skill Checkpoint opportunity
Checkpoint skill Checkpoint opportunity
Patterns and Relationships
Number Relationships: Describe, interpret and use quantities, relationships between quantities, representations of quantities, and number systems. Describe operations and the relationship between operations. Use strategies and procedures accurately, efficiently and flexibly. Assess the reasonableness of the results.
9.3.5.1 Add, subtract, multiply and divide numbers in scientific notation.
9.3.5.1 Add, subtract, multiply and divide numbers in scientific notation.
9.3.5.3 Apply knowledge of number systems extending from whole numbers to integers, from integers to rational numbers, from rational numbers to real numbers and from real numbers to complex numbers to solve equations.
One- and two-step linear equations
Multi-step linear equations
Solutions to linear equations
Exponential equations
9.3.5.3 Apply knowledge of number systems extending from whole numbers to integers, from integers to rational numbers, from rational numbers to real numbers and from real numbers to complex numbers to solve equations.
One- and two-step linear equations
Multi-step linear equations
Solutions to linear equations
Exponential equations
9.3.5.5 Estimate and verify the cost of an item, including multiple discounts and taxes. Show an understanding of the order of operations.
Money and percents
Evaluate expressions
9.3.5.5 Estimate and verify the cost of an item, including multiple discounts and taxes. Show an understanding of the order of operations.
Money and percents
Evaluate expressions
9.3.5.6 Assess the reasonableness of a solution in its given context, including financial literacy applications. Compare the solution to appropriate graphical or numerical estimates. Interpret a solution in the original context.
Word problems
Tables and graphs
9.3.5.6 Assess the reasonableness of a solution in its given context, including financial literacy applications. Compare the solution to appropriate graphical or numerical estimates. Interpret a solution in the original context.
Word problems
Tables and graphs
9.3.5.7 Use the structure of an expression, equation and/or formula to create an equivalent form that is more helpful given the situation. Rearrange formulas to highlight a quantity of interest, using the same reasoning in solving equations.
9.3.5.7 Use the structure of an expression, equation and/or formula to create an equivalent form that is more helpful given the situation. Rearrange formulas to highlight a quantity of interest, using the same reasoning in solving equations.
9.3.5.8 Use the structure of an expression to write it in multiple ways.
9.3.5.8 Use the structure of an expression to write it in multiple ways.
9.3.5.10 Compute the time it takes to pay off a loan given the interest rate, loan amount and monthly payment. Determine the change in cost by the variation in loan amount, fixed or variable interest rates and payment amounts. Use technology, including spreadsheets.
9.3.5.10 Compute the time it takes to pay off a loan given the interest rate, loan amount and monthly payment. Determine the change in cost by the variation in loan amount, fixed or variable interest rates and payment amounts. Use technology, including spreadsheets.
9.3.5.11 Compute the total payments to pay off a loan given the interest rate, loan amount and monthly payment. Compare the total payments for various monthly payments and various interest rates. Use technology, including spreadsheets.
9.3.5.11 Compute the total payments to pay off a loan given the interest rate, loan amount and monthly payment. Compare the total payments for various monthly payments and various interest rates. Use technology, including spreadsheets.
9.3.5.12 Compare different types of retirement plans, considering after tax or pretax contributions, employer match contributions, the benefit of starting contributions early and the consequences of use prior to retirement.
9.3.5.12 Compare different types of retirement plans, considering after tax or pretax contributions, employer match contributions, the benefit of starting contributions early and the consequences of use prior to retirement.
Patterns and Relationships: Represent and connect mathematical patterns and relationships using verbal descriptions, generalizations, tables and graphs. Use representations to generate questions, make predictions and solve mathematical problems.
9.3.7.1 Represent and solve situations in various contexts, including financial literacy, using systems of linear equations, systems of linear inequalities and exponential and quadratic functions.
Solutions of systems of equations
Solve a system of equations by graphing
Solve a system of equations by substitution
Solve a system of equations by elimination
Solve a system of equations using any method
Linear inequalities
System of linear inequalities
Exponential functions
9.3.7.1 Represent and solve situations in various contexts, including financial literacy, using systems of linear equations, systems of linear inequalities and exponential and quadratic functions.
Solutions of systems of equations
Solve a system of equations by graphing
Solve a system of equations by substitution
Solve a system of equations by elimination
Solve a system of equations using any method
Linear inequalities
System of linear inequalities
Exponential functions
9.3.7.2 Translate between graphs of quadratic, exponential and other functions (including absolute value, rational and polynomial), tables and symbolic representations. Sketch graphs and use graphing technology to graph functions.
Linear functions
Exponential functions
Linear and exponential functions
Compare functions
9.3.7.2 Translate between graphs of quadratic, exponential and other functions (including absolute value, rational and polynomial), tables and symbolic representations. Sketch graphs and use graphing technology to graph functions.
Linear functions
Exponential functions
Linear and exponential functions
Compare functions
9.3.7.3 Determine how vertical/ horizontal reflecting, translating and scaling affect the symbolic and graphical forms of a function. Use graphing technology to examine transformations.
9.3.7.3 Determine how vertical/ horizontal reflecting, translating and scaling affect the symbolic and graphical forms of a function. Use graphing technology to examine transformations.
9.3.7.4 Express the terms in an arithmetic or geometric sequence recursively and by giving an explicit formula.
Number sequences
Recursive and explicit formulas
9.3.7.4 Express the terms in an arithmetic or geometric sequence recursively and by giving an explicit formula.
Number sequences
Recursive and explicit formulas
9.3.7.5 Express recursive patterns using recursive formulas. Calculate sequences defined by recursive formulas.
9.3.7.5 Express recursive patterns using recursive formulas. Calculate sequences defined by recursive formulas.
9.3.7.6 Find the domain and range of functions defined symbolically, graphically or in a context, including piecewise and step functions. Express solutions and recognize that some answers obtained may not be valid, including cases where the function inputs are discrete instead of continuous.
Linear functions
Exponential functions
9.3.7.6 Find the domain and range of functions defined symbolically, graphically or in a context, including piecewise and step functions. Express solutions and recognize that some answers obtained may not be valid, including cases where the function inputs are discrete instead of continuous.
Linear functions
Exponential functions
9.3.7.7 Describe the graph of a function using key features such as intercepts, maxima/minima, intervals of increase and decrease and end behavior. Draw conclusions from graphs of functions and other relations.
Linear functions
Exponential functions
Linear and exponential functions
Word problems
9.3.7.7 Describe the graph of a function using key features such as intercepts, maxima/minima, intervals of increase and decrease and end behavior. Draw conclusions from graphs of functions and other relations.
Linear functions
Exponential functions
Linear and exponential functions
Word problems
9.3.7.8 Define the compounding of interest n times per year according to a recursive formula. Compare the recursive definition of interest to the recursive definition of a geometric sequence t(n) = r(t(n – 1)). Compare the interest formula A = P(1 + r/n)nt to the general form of an exponential function y = a(b)x. Explain the purpose of each part of the interest formula.
9.3.7.8 Define the compounding of interest n times per year according to a recursive formula. Compare the recursive definition of interest to the recursive definition of a geometric sequence t(n) = r(t(n – 1)). Compare the interest formula A = P(1 + r/n)nt to the general form of an exponential function y = a(b)x. Explain the purpose of each part of the interest formula.
9.3.7.10 Use the concept of a function as a connection between inputs and outputs to find function values and use function notation.
Identify functions
Evaluate functions
Interpret functions
Function tables
9.3.7.10 Use the concept of a function as a connection between inputs and outputs to find function values and use function notation.
Identify functions
Evaluate functions
Interpret functions
Function tables
Checkpoint skill Checkpoint opportunity
Checkpoint skill Checkpoint opportunity