D2L Corporation
2017-01-14T16:20:32-05:00
2017-01-14T16:20:31-05:00
D2L Corporation
Arizona Mathematics Standards (Grade 7)
The Arizona Mathematics Standards are a connected body of mathematical understandings and competencies that provide a foundation for all students. These standards are coherent, focused on important mathematical concepts, rigorous, and well-articulated across the grades. Concepts and skills that are critical to the understanding of important processes and relationships are emphasized.
2016-12-22
2016
Arizona Department of Education
Domain
Ratio and Proportion
7.RP.A
Cluster
Analyze proportional relationships and use them to solve mathematical problems and problems in real-world context.
7.RP.A.1
Standard
Compute unit rates associated with ratios involving both simple and complex fractions, including ratios of quantities measured in like or different units.
7.RP.A.2
Standard
Recognize and represent proportional relationships between quantities.
7.RP.A.2.a
Component
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).
7.RP.A.2.b
Component
Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
7.RP.A.2.c
Component
Represent proportional relationships by equations.
7.RP.A.2.d
Component
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.
7.RP.A.3
Standard
Use proportional relationships to solve multi-step ratio and percent problems (e.g., simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error).
Domain
The Number System
7.NS.A
Cluster
Apply and extend previous understanding of operations with fractions to add, subtract, multiply, and divide rational numbers except division by zero.
7.NS.A.1
Standard
Add and subtract integers and other rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
7.NS.A.1.a
Component
Describe situations in which opposite quantities combine to make 0.
7.NS.A.1.b
Component
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 context.
7.NS.A.1.c
Component
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 context.
7.NS.A.1.d
Component
Apply properties of operations as strategies to add and subtract rational numbers.
7.NS.A.2
Standard
Multiply and divide integers and other rational numbers.
7.NS.A.2.a
Component
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 context.
7.NS.A.2.b
Component
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 context.
7.NS.A.2.c
Component
Apply properties of operations as strategies to multiply and divide rational numbers.
7.NS.A.2.d
Component
Convert a rational number to decimal form using long division; know that the decimal form of a rational number terminates in 0's or eventually repeats.
7.NS.A.3
Standard
Solve mathematical problems and problems in real-world context involving the four operations with rational numbers. Computations with rational numbers extend the rules for manipulating fractions to complex fractions where a/b ÷ c/d when a, b, c, and d are all integers and b, c, and d ≠ 0.
Domain
Expressions and Equations
7.EE.A
Cluster
Use properties of operations to generate equivalent expressions.
7.EE.A.1
Standard
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
7.EE.A.2
Standard
Rewrite an expression in different forms, and understand the relationship between the different forms and their meanings in a problem context.
7.EE.B
Cluster
Solve mathematical problems and problems in real-world context using numerical and algebraic expressions and equations.
7.EE.B.3
Standard
Solve multi-step mathematical problems and problems in real-world context posed with positive and negative rational numbers in any form. Convert between forms as appropriate and assess the reasonableness of answers.
7.EE.B.4
Standard
Use variables to represent quantities in mathematical problems and problems in real-world context, and construct simple equations and inequalities to solve problems.
7.EE.B.4.a
Component
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.
7.EE.B.4.b
Component
Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.
Domain
Geometry
7.G.A
Cluster
Draw, construct, and describe geometrical figures, and describe the relationships between them.
7.G.A.1
Standard
Solve problems involving scale drawings of geometric figures, such as computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
7.G.A.2
Standard
Draw geometric shapes with given conditions using a variety of methods. 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.
7.G.A.3
Standard
Describe the two-dimensional figures that result from slicing three-dimensional figures.
7.G.B
Cluster
Solve mathematical problems and problems in real-world context involving angle measure, area, surface area, and volume.
7.G.B.4
Standard
Understand and use the formulas for the area and circumference of a circle to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
7.G.B.5
Standard
Use facts about supplementary, complementary, vertical, and adjacent angles in multi-step problems to write and solve simple equations for an unknown angle in a figure.
7.G.B.6
Standard
Solve mathematical problems and problems in a real-world context involving area, of two-dimensional objects composed of triangles, quadrilaterals, and other polygons. Solve mathematical problems and problems in real-world context involving volume and surface area of three-dimensional objects composed of cubes and right prisms.
Domain
Statistics and Probability
7.SP.A
Cluster
Use random sampling to draw inferences about a population.
7.SP.A.1
Standard
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.
7.SP.A.2
Standard
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.
7.SP.B
Cluster
Draw informal comparative inferences about two populations.
7.SP.B.3
Standard
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.
7.SP.B.4
Standard
Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.
7.SP.C
Cluster
Investigate chance processes and develop, use and evaluate probability models.
7.SP.C.5
Standard
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.
7.SP.C.6
Standard
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.
7.SP.C.7
Standard
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.
7.SP.C.7.a
Component
Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.
7.SP.C.7.b
Component
Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.
Standards for Mathematical Practice
7.MP.1
Standard
Make sense of problems and persevere in solving them.
7.MP.2
Standard
Reason abstractly and quantitatively.
7.MP.3
Standard
Construct viable arguments and critique the reasoning of others.
7.MP.4
Standard
Model with mathematics.
7.MP.5
Standard
Use appropriate tools strategically.
7.MP.6
Standard
Attend to precision.
7.MP.7
Standard
Look for and make use of structure.
7.MP.8
Standard
Look for and express regularity in repeated reasoning.