Grade 7 Math Minnesota standards Standards

Data Analysis & Probability

Geometry & Measurement

Algebra

Number & Operation

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.

Equivalence and Relational Thinking: Use concepts and properties of equivalence and relational thinking to represent and compare numerical expressions, proportional relationships, algebraic expressions and equations.

Number Relationships: Describe/Interpret and use quantities, relationships between and representations of quantities and number systems. Describe and relate operations. Use strategies and procedures accurately, efficiently and flexibly. Assess the reasonableness of the results.

Patterns and Relationships

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.

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.

Spatial Reasoning

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.

Data Sciences: Identify, formulate and investigate statistical questions by collecting data considering cultural perspectives, analyzing and interpreting data and communicating the results.

Data Analysis

Read, write, represent and compare positive and negative rational numbers, expressed as integers, fractions and decimals.

Know that every rational number can be written as the ratio of two integers or as a terminating or repeating decimal. Recognize that p is not rational, but that it can be approximated by rational numbers such as 22/7 and 3.14.

Formulate statistical investigative questions with data collection, keeping cultural perspectives in mind, which compare differences between groups, require a sample of a population and use categorical and/or numerical data. (MP3, MP6) $ ✜

Understand that division of two integers will always result in a rational number. Use this information to interpret the decimal result of a division problem when using a calculator.

Describe how statistics can be used to gain information about a population by examining a sample of the population. Explain how generalizations about a population are valid only when the sample is representative of that population and that random sampling tends to produce representative samples and support valid inferences. (MP2) ✜ ☼

Locate positive and negative rational numbers on a number line, understand the concept of opposites, and plot pairs of positive and negative rational numbers on a coordinate grid.

Make inferences using statistics about population parameters based on a random sample from that population. (MP3)

Compare positive and negative rational numbers expressed in various forms using the symbols < , > , = , ≤ , ≥.

Understand that a set of data collected to answer a statistical question has a distribution that can be described by its center, variability and overall shape. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. Justify the choice of measures of center and variability, the shape of the data distribution and the context in which the data were gathered. (MP1, MP7)

Recognize and generate equivalent representations of positive and negative rational numbers, including equivalent fractions.

Create a visualization about a data set, organizing and presenting the data in appropriate ways, including in tables, circle graphs and histograms, and incorporating any other relevant information that helps to tell a story about the data. (MP5, MP6) # μ

Compare and communicate competing explanations for data trends observed, considering cultural perspectives and reasonable alternatives given the variability in findings and sampling methods. (MP3, MP6)

Calculate with positive and negative rational numbers, and rational numbers with whole number exponents, to solve real-world and mathematical problems.

Add, subtract, multiply and divide positive and negative rational numbers that are integers, fractions and terminating decimals; use efficient and generalizable procedures, including standard algorithms; raise positive rational numbers to whole-number exponents.

Calculate probability as a fraction of sample space or as a fraction of area. Express probabilities as fractions, decimals and percentages. (MP2)

Use real-world contexts and the inverse relationship between addition and subtraction to explain why the procedures of arithmetic with negative rational numbers make sense.

Approximate the probability of a chance event, where the theoretical probability is unknown, by collecting data and observing its long-run frequency. Represent the probabilities as percentages, fractions and decimals between 0 and 1 inclusive. Use approximate probabilities to make predictions when actual probabilities are unknown. (MP4) # ☼

Understand that calculators and other computing technologies often truncate or round numbers.

Recognize that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space where the compound event occurs. (MP1)

Solve problems in various contexts involving calculations with positive and negative rational numbers and positive integer exponents, including computing simple and compound interest.

Represent sample spaces for compound events by decomposing the events using methods such as organized lists, tables and/or tree diagrams. For an event described in everyday language, identify the outcomes in the sample space that compose the event. (MP5) #

Use proportional reasoning to solve problems involving ratios in various contexts.

Design and use a simulation within a computational tool to generate frequencies for compound events. #

Demonstrate an understanding of the relationship between the absolute value of a rational number and distance on a number line. Use the symbol for absolute value.

Find probabilities of compound events using organized lists, tables, tree diagrams and/or simulation via a computational tool. (MP5) # μ ☼

Understand the concept of proportionality in real-world and mathematical situations, and distinguish between proportional and other relationships.

Understand that a relationship between two variables, x and y, is proportional if it can be expressed in the form y/x=k or y =kx . Distinguish proportional relationships from other relationships, including inversely proportional relationships ( xy =k or y=k/x ).

Understand that the graph of a proportional relationship is a line through the origin whose slope is the unit rate (constant of proportionality). Know how to use graphing technology to examine what happens to a line when the unit rate is changed.

Recognize proportional relationships in real-world and mathematical situations; represent these and other relationships with tables, verbal descriptions, symbols and graphs; solve problems involving proportional relationships and explain results in the original context.

Represent proportional relationships with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another. Determine the unit rate (constant of proportionality or slope) given any of these representations.

Solve multi-step problems involving proportional relationships in numerous contexts.

Use knowledge of proportions to assess the reasonableness of solutions.

Represent real-world or mathematical situations using equations and inequalities involving variables and positive and negative rational numbers.

Apply understanding of order of operations and algebraic properties to generate equivalent numerical and algebraic expressions containing positive and negative rational numbers and grouping symbols; evaluate such expressions.

Use properties of algebra to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols and whole number exponents. Properties of algebra include associative, commutative and distributive laws.

Demonstrate an understanding of the proportional relationship between the diameter and circumference of a circle and that the unit rate (constant of proportionality) is π. (MP1, MP2) ✜ ☼

Evaluate algebraic expressions containing rational numbers and whole number exponents at specified values of their variables.

Calculate the circumference and area of circles to solve situations in various contexts. (MP4, MP6) ✜ μ ☼

Apply understanding of order of operations and grouping symbols when using calculators and other technologies.

Calculate the arc length and area of sectors of circles (given the central angle) to solve situations in various contexts. (MP4, MP7) ✜ ☼

Calculate the surface area and volume of cylinders. Justify the formulas used. (MP3, MP8) ✜ ☼

Represent real-world and mathematical situations using equations with variables. Solve equations symbolically, using the properties of equality. Also solve equations graphically and numerically. Interpret solutions in the original context.

Represent relationships in various contexts with equations involving variables and positive and negative rational numbers. Use the properties of equality to solve for the value of a variable. Interpret the solution in the original context.

Graph and describe translations and reflections of figures on a coordinate grid. Determine the coordinates of the vertices of the figure after the transformation. Describe the properties of congruency when performing translations and reflections. (MP8)

Solve equations resulting from proportional relationships in various contexts.

Describe the properties of similarity, distinguishing between similarity and congruency, compare geometric figures for similarity and determine scale factors. (MP1, MP6) ✜ ☼

Apply scale factors, length ratios and area ratios to determine side lengths and areas of similar geometric figures. (MP5)

Use proportional reasoning and ratios to solve situations involving scale drawings and conversions of measurement units. (MP2, MP4) ✜ $ ☼

Use reasoning with proportions and ratios to determine measurements, justify formulas and solve real-world and mathematical problems involving circles and related geometric figures.

Demonstrate an understanding of the proportional relationship between the diameter and circumference of a circle and that the unit rate (constant of proportionality) is p . Calculate the circumference and area of circles and sectors of circles to solve problems in various contexts.

Calculate the volume and surface area of cylinders and justify the formulas used.

Analyze the effect of change of scale, translations and reflections on the attributes of two-dimensional figures.

Describe the properties of similarity, compare geometric figures for similarity, and determine scale factors.

Apply scale factors, length ratios and area ratios to determine side lengths and areas of similar geometric figures.

Use proportions and ratios to solve problems involving scale drawings and conversions of measurement units.

Graph and describe translations and reflections of figures on a coordinate grid and determine the coordinates of the vertices of the figure after the transformation.

Know that every rational number can be written as the ratio of two integers and as a terminating or repeating decimal. Recognize that π is not rational but that it can be approximated by 22 rational numbers such as and 3.14. (MP8)

Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line. Recognize that the opposite of the opposite of a number is the number itself, such as –(–3) = 3. Recognize that 0 is its own opposite. (MP7)

Compare positive and negative rational numbers expressed in various forms using the symbols <, > , = , ≤ , ≥ . (MP4) $

Recognize subtraction of rational numbers as adding the additive inverse, 𝑝𝑝 − 𝑞𝑞 = 𝑝𝑝 + (−𝑞𝑞). Show that the distance between two rational numbers on the number line is the absolute value of their difference and apply this principle in contexts. (MP7, MP8) ✜ $ ☼

Create a budget using positive and negative rational numbers for an event and calculate what percentage of the total budget each category comprises. Justify choices of the allocation of the available resources. (MP1, MP4, MP5) ✜ $ μ ☼

Solve mathematical situations involving adding, subtracting, multiplying and dividing positive and negative rational numbers that are integers, fractions and terminating decimals. Use efficient and generalizable procedures. Raise positive rational numbers to whole-number exponents. (MP4) $ ☼

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. (MP1, MP4) $ ☼

Use properties of algebra to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols and whole number exponents. Properties of algebra include associative, commutative and distributive laws. (MP1)

Represent and solve contextual situations resulting in two-step equations and inequalities involving variables and positive/negative rational numbers. Graph the solution set of the inequality and interpret the solution in context. (MP4, MP5) $ ☼

Evaluate algebraic expressions, including expressions containing rational numbers, absolute value and whole number exponents, by applying computational hierarchy of operations at specified values of their variables. (MP7) #

Solve multi-step situations involving proportional relationships in numerous contexts using models, such as tables of equivalent ratios involving scaling up and down, tape diagrams, double number lines or equations. (MP4, MP7) ✜ $ μ ☼

Solve multi-step financial literacy situations including simple interest, tax, markups and markdowns, tips and commissions, fees, percent increase and decrease and percent error. Distinguish between sales tax and income tax for earned wages. Situations include finding the whole, the part and the percent. (MP7, MP8) $ μ ☼

Represent proportional relationships with tables, verbal descriptions, symbols, equations and graphs. Translate from one representation to another. Determine the unit rate (constant of proportionality or rate of change) given any of these representations. (MP4, MP5) ✜ $ ☼

Express a relationship between two variables, the independent (x) and the dependent (y), as 𝑦𝑦 proportional if it can be written in the form = 𝑥𝑥 𝑘𝑘 or 𝑦𝑦 = 𝑘𝑘𝑥𝑥. Distinguish proportional relationships from non-proportional relationships, including relationships where the x and y value are not 0. (MP8) $

Determine whether two quantities are in a proportional relationship by testing for equivalent ratios in a table or graphing on a coordinate plane and by observing whether the graph is a straight line through the origin. Use graphing technology to examine the relationship between the unit rate and the line for a given situation. (MP1) ✜ μ ☼

Use mean, median and range to draw conclusions about data and make predictions.

Design simple experiments and collect data. Determine mean, median and range for quantitative data and from data represented in a display. Use these quantities to draw conclusions about the data, compare different data sets, and make predictions.

Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. Know how to create data displays using a spreadsheet to examine this impact.

Display and interpret data in a variety of ways, including circle graphs and histograms.

Use reasoning with proportions to display and interpret data in circle graphs (pie charts) and histograms. Choose the appropriate data display and know how to create the display using a spreadsheet or other graphing technology.

Calculate probabilities and reason about probabilities using proportions to solve real-world and mathematical problems.

Use random numbers generated by a calculator or a spreadsheet or taken from a table to simulate situations involving randomness, make a histogram to display the results, and compare the results to known probabilities.

Calculate probability as a fraction of sample space or as a fraction of area. Express probabilities as percents, decimals and fractions.

Use proportional reasoning to draw conclusions about and predict relative frequencies of outcomes based on probabilities.