Grade 7 Math Michigan standards Standards

Statistics and Probability

Expressions and Equations

The Number System

Ratios and Proportional Relationships

Geometry

Standards for Mathematical Practice

Solving Expressions and Equations

Students solve increasingly complex mathematical problems, making productive use of algebra and functions.

Statistics and Probability

Students demonstrate increasingly complex understanding of measurement, data and analytic procedures.

Geometry

Students demonstrate increasingly complex spatial reasoning and understanding of geometric principles.

The Number System

Ratios and Proportional Relationships

Students demonstrate increasingly complex understanding of number sense.

Use properties of operations to generate equivalent expressions.

Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.

Draw, construct, and describe geometrical figures and describe the relationships between them.

Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

Describe situations in which opposite quantities combine to make 0.

Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

Apply properties of operations as strategies to add and subtract rational numbers.

Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.

Apply properties of operations as strategies to multiply and divide rational numbers.

Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

Solve real-world and mathematical problems involving the four operations with rational numbers.

Analyze proportional relationships and use them to solve real-world and mathematical problems.

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

Recognize and represent proportional relationships between quantities.

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Represent proportional relationships by equations.

Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Use proportional relationships to solve multistep ratio and percent problems.

Use random sampling to draw inferences about a population.

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.

Draw informal comparative inferences about two populations.

Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability.

Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.

Investigate chance processes and develop, use, and evaluate probability models.

Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.

Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.

Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event.

Design and use a simulation to generate frequencies for compound events.

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

Use the properties of operations as strategies to demonstrate that expressions are equivalent.

Identify an arithmetic sequence of whole numbers with a whole-number common difference.

Use the concept of equality with models to solve one-step addition and subtraction equations.

The student can recognize an arithmetic sequence of numbers with and without decimals (e.g., 2, 4, 6; 2.5, 4.5, 6.5) with a whole-number common difference

The student can solve one-step addition and subtraction equations with an unknown represented with a box. (e.g., box + 5 = 10; box – 2 = 3).

The student can recognize the number that comes next in a sequence of numbers to 10 in sequential order with a difference of 1.

The student can identify how much is “one more” or when one is “taken away” from a quantity up to 5 with a model.

The student can recognize an arithmetic sequence of whole numbers with and without a model and limited to 2s, 5s, and 10s.

The student can solve one-step addition and subtraction equations, where the unknown is the sum or difference, paired with pictures or objects. (e.g., 5 + 5 = box; 5 – 2 = box)

Match two similar geometric shapes that are proportional in size and in the same orientation.

Recognize geometric shapes with given conditions.

Match a two-dimensional shape with a three-dimensional shape that shares an attribute.

Determine the perimeter of a rectangle by adding the measures of the sides.

Recognize angles that are acute, obtuse, and right.

Determine the area of a rectangle using the formula for length × width, and confirm the result using tiling or partitioning into unit squares.

The student can identify two similar two- and three-dimensional shapes that are proportional in size and in the same orientation.

The student can recognize geometric shapes with specified attributes.

The student can determine the perimeter of a rectangle by adding the measures of the sides.

The student can recognize an angle as being greater than or less than a right angle when given a model of a right angle.

The student can find the area of a rectangle when given the formula of length x width, a model, and the dimensions of the rectangle up to 40 square units.

The student can match a similar two-dimensional shape with an object that is proportional in size and in the same orientation; limited to round and square (e.g., an analog clock and a coin).

The student can differentiate between round/circle and square or sphere and cube.

The student can match objects to their outlines.

The student can differentiate between a shape that has corners and one that does not.

The student can count unit squares to find the area of a model of a rectangle up to 6 square units.

The student can identify two similar two-dimensional shapes or objects that are proportional in size and in the same orientation; limited to square, circle, and triangle. (e.g., a postage stamp and a picture frame).

The student can identify common two-dimensional shapes (e.g., square, circle, triangle, and star).

The student can use a model to determine the perimeter of a rectangle by adding the side lengths; lengths limited to 1, 2, or 3.

The student can match an angle to a shape that has the same angle.

The student can use unit squares to determine the area of a model of a rectangle up to 20 square units.

Add fractions with like denominators (halves, thirds, fourths, and tenths) with sums less than or equal to one.

Solve multiplication problems with products to 100.

Solve division problems with divisors up to five and also with a divisor of 10 without remainders.

Express a fraction with a denominator of 10 as a decimal.

Compare quantities represented as decimals in real-world examples to tenths.

The student can add fractions with common denominators with sums less than or equal to 1.

The student can solve a simple multiplication problem (one factor times another) using concrete objects or a calculator.

The student can solve division problems with a divisor of 2, 5, or 10 or where the dividend is less than 30 using concrete objects or a calculator.

The student can express a fraction with a denominator of 10 as a decimal. (Functional skill is expressing money as a fraction/decimal of a dollar, limited to tenths of a dollar: $0.10, $0.20, etc.)

The student can compare quantities represented as decimals in real-world examples to tenths (e.g., a combination of bills and coins, a discount of 10 percent = .10).

The student can identify that the sum of two halves is equal to 1 whole.

The student can identify double the amount of specified quantity (limited to 1, 2, 3 or 4).

The student can identify a larger set of up to 10 that has been divided into 2 or 3 equal subsets.

The student can use models to identify the fractions one-half and one-fourth.

The student can differentiate coins and bills from each other and from other similar objects.

The student can add fractions with common denominators with sums less than or equal to 1 and limited to halves, thirds, and fourths (fractions shown as models).

The student can solve a simple multiplication problem (one factor times another) with products up to 30 using concrete objects and/or a calculator.

The student can solve division problems with a divisor of 2, 5, or 10 or where the dividend is 20 or less using concrete objects and/or a calculator.

The student can identify that one-half equals .50 and one-fourth equals .25 with models as support. (e.g., model of .50 is the same as one-half of a dollar.)

The student can identify a combination of coins and bills up to $5 using decimal notation. (e.g., $2.50 is equal to two one-dollar bills and two quarters).

Use a ratio to model or describe a relationship.

The student can complete a ratio using numbers to describe a relationship.

The student can recognize a 1:1 relationship of a given modeled ratio.

The student can use a simple ratio to describe a relationship.

Answer a question related to the collected data from an experiment, given a model of data, or from data collected by the student.

Compare two sets of data within a single data display such as a picture graph, line plot, or bar graph.

Describe the probability of events occurring as possible or impossible.

The student can solve problems using data presented within a single data display: tables, bar graphs, circle graphs, tallies, and pictographs, including graphs and charts that have more than one set of data.

The student can describe the probability of events occurring as possible or impossible.

The student can identify the quantity of data, limited to 1, 2, or 3 on a pictograph.

The student can identify when activities are likely to happen (e.g., go to school in the morning, eat lunch at noon).

The student can compare sets of data within two similar data displays (2 bar graphs or 2 picture graphs) to determine whether two quantities are the same, more than, or less than.

The student can identify possible events that occur in the natural environment (e.g., possible: sun produces warmth; rain results in wet).