Grade 7 Math Colorado standards Standards

Geometry

Statistics & Probability

Expressions & Equations

The Number System

Ratios & Proportional Relationships

Standards for Mathematical Practice

Use properties of operations to generate equivalent expressions.

Expressions & Equations: 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.

Apply properties of operations as strategies to add and subtract linear expressions with whole number coefficients. For example, 2x + 3x is 5x.

Demonstrate 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.

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

For example, if 3 people at lunch spend $21 for sandwiches, the expression $7 x 3 tells us that it was 7 dollars for each of the 3 sandwiches.

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

Expressions & Equations: 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.

Solve multi-step real-life and mathematical problems posed with whole numbers, benchmark fractions, and/or decimals to two decimal places. Numbers should combine cleanly for simpler calculations.

For example, if a sandwich costs $6.50 and a drink costs $1.50, but you have a coupon to save 1 off the total, how much will you spend for the 4 sandwich and the drink?

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 real-world or mathematical problems using simple equations containing variables.

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, px±q ≥ r, 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.

For example, if x number of glasses of water plus 2 glasses of water makes 8 glasses of water total, then x must be 6 glasses of water.

Represent the problems using objects or drawings and match the situations to equations (in this case, x + 2 = 8).

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

Geometry: 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.

Match corresponding parts of scale drawings of geometric figures and compare given lengths and areas.

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.

Create triangles with given conditions and recognize that some combinations of side lengths and/or angles cannot be made into a triangle.

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

Describe rectangular cross-sections from right rectangular prisms.

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

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

State 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 the formula for the area and circumference of a circle to solve problems.

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

Recognize angles that are acute, obtuse, and right (EE.7.G.B.5).

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.

Solve real-world and mathematical problems involving the area of triangles, rectangles, and circles, and the volume and surface area of right rectangular prisms.

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

The Number System: 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.

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers with single-digit numerators and denominators up to at least 12.

Describe situations in which opposite quantities combine to make 0.

Represent addition and subtraction on a horizontal or vertical number line diagram. For example, add - 1 + 3 to get 1 .

Demonstrate 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.

Demonstrate 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.

Apply and extend previous understandings of multiplication and division and or fractions to multiply and divide rational numbers with single-digit numerators and denominators up to at least 12, e.g., by using visual fraction models or equations to represent the problem.

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.

For example, dividing 3 of a pizza into pieces the size of 1 of the whole 4 4 pizza can be written as 3 divided by 1 , and it yields 3 pieces.

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.

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

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

Ratios & Proportional Relationships: 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.

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

For example, if a person walks 6 miles in 2 hours, compute the unit rate as the fraction 6 , equivalently 3 miles per hour.

Identify and represent proportional relationships between quantities.

Represent proportional relationships between quantities using a table.

Determine 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 proportional relationships to solve simple ratio and percent problems.

Examples: simple interest, tax, markups and markdowns, and gratuities.

Use random sampling to draw inferences about a population.

Statistics & Probability: 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; explain that generalizations about a population from a sample are valid only if the sample is representative of that population. Explain that random sampling tends to produce representative samples and support valid inferences.

Understand that statistics usually involves measuring something about a sample to learn something about a problem.

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.

Use data from a sample to answer a statistical question.

For example, conclude from a sample of the class that most students like chocolate ice cream.

Draw informal comparative inferences about two populations.

Statistics & Probability: 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.

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

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

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

For example, if the average height of a class of 8th graders is 5 feet 5 inches, and the average height of a class of 7th graders is 5 feet 2 inches, which population is more likely taller on average, 8th graders of 7th graders?

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

Statistics & Probability: Investigate chance processes and develop, use, and evaluate probability models.

Explain 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 ½ indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

Indicate an understanding that the probability of a chance event can be 0, for things that never happen, between 0 and 1, for things that sometimes happen, or 1, for things that always happen.

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.

Collect data on a chance process (e.g., flipping a coin, rolling a die) and observe its long-run relative frequency.

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.

Compare probabilities from a model to observed frequencies and identify when agreement is not good.

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

For example, given that the probability of flipping heads is 0.5, getting 8 heads out of 10 flips is not good agreement with the model.

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.

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

Explain 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.

Algebra and Functions

Data, Statistics, and Probability

Geometry

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.

Number and Quantity