Common Planner
K–12 Standards

Grade 8

Other Iowa Mathematics sets

The Number System8.NS

  • 1

    Work with numbers that are not rational, and approximate them by rational numbers.8.NS.A

    1. 1

      Classify and explain numbers as rational or irrational. For rational numbers show that the decimal expansion repeats eventually and convert a decimal expansion which repeats eventually into a rational number. 8.NS.A.1

    2. 2

      Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions. For example, estimate the value of √2. By truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue - on to get better approximations.  8.NS.A.2

Expressions and Equations8.EE

  • 1

    Work with radicals and integer exponents.8.EE.A

    1. 1

      Apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3−5 = 3−3 = 1 33 = 1 27 .8.EE.A.1

    2. 2

      Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Students evaluate square roots of small perfect squares and cube roots of small perfect cubes. Use bases 1 through 5 and 10 for cubes.8.EE.A.2

    3. 3

      Use numbers expressed in the form of a single digit times an integer power of 10 to estimate exceptionally large or small quantities and to express how many times as much one is than another. For example, estimate the population of the United States as 3 times 10 8 and the population of the world as 7 times 10 9, and determine that the world population is more than 20 times larger.8.EE.A.3

    4. 4

      Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of convenient size for quantities. For example, use millimeters per year for seafloor spreading. Interpret scientific notation that has been generated by technology. 8.EE.A.4

  • 2

    Understand the connections between proportional relationships, lines, and linear equations. 8.EE.B

    1. 1

      Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. 8.EE.B.5

    2. 2

      Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane. 8.EE.B.6

      1. a

        Derive from this principle the equation 𝑦𝑦 = 𝑚𝑚𝑚𝑚 for a line through the origin.8.EE.B.6.a

      2. b

        Derive from this principle the equation 𝑦𝑦 = 𝑚𝑚𝑚𝑚 + 𝑏𝑏 for a line intercepting the vertical axis at 𝑏𝑏.  8.EE.B.6.b

  • 3

    Analyze and solve linear equations and pairs of simultaneous linear equations.8.EE.C

    1. 1

      Solve linear equations in one variable.8.EE.C.7

      1. a

        Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form 𝑥𝑥 = 𝑎𝑎, 𝑎𝑎 = 𝑎𝑎, or 𝑎𝑎 = 𝑏𝑏 results (where 𝑎𝑎 and 𝑏𝑏 are different numbers).8.EE.C.7.a

      2. b

        Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.8.EE.C.7.b

    2. 2

      Analyze and solve pairs of simultaneous linear equations.8.EE.C.8

      1. a

        Describe how the solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.8.EE.C.8.a

      2. b

        Solve systems of two linear equations in two variables algebraically and estimate solutions by graphing the equations. Solve simple (by inspection) cases. For example, 3𝑥𝑥 + 2𝑦𝑦 = 5 and 3𝑥𝑥 + 2𝑦𝑦 = 6 have no solution because 3𝑥𝑥 + 2𝑦𝑦 cannot simultaneously be 5 and 6; 𝑥𝑥 − 𝑦𝑦 = 11 and 2𝑥𝑥 + 𝑦𝑦 = 19.8.EE.C.8.b

      3. c

        Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. 8.EE.C.8.

Functions8.F

  • 1

    Define, evaluate, and compare functions.8.F.A

    1. 1

      Describe a function as a rule that assigns to each input exactly one output and the graph of a function is the set of ordered pairs consisting of an input and the corresponding output. Function notation is not required in grade 8.8.F.A.1

    2. 2

      Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. 8.F.A.2

    3. 3

      Interpret the equation 𝑦𝑦 = 𝑚𝑚𝑚𝑚 + 𝑏𝑏 as defining a function that assigns to each input value x the output value 𝑚𝑚𝑚𝑚 + 𝑏𝑏; this is a linear function whose graph is a straight line. Give examples of functions that are not linear. For example, the function 𝐴𝐴 = 𝑠𝑠2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.8.F.A.3

  • 2

    Use functions to model relationships between quantities.8.F.B

    1. 1

      Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝑥𝑥, 𝑦𝑦) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models and in terms of its graph or a table of values.8.F.B.4

    2. 2

      Describe qualitatively the functional relationship between two quantities by analyzing a graph. For example, identify where the function is increasing or decreasing, and if it is linear or nonlinear. Sketch a graph that shows the qualitative features of a function that has been described verbally.  8.F.B.5

Geometry8.G

  • 1

    Demonstrate congruence and similarity using physical models, patty paper or geometry software.8.G.A

    1. 1

      Verify experimentally the properties of rotations, reflections, and translations:8.G.A.1

      1. a

        Lines are taken to lines, and line segments to line segments of the same length.8.G.A.1.a

      2. b

        Angles are taken to angles of the same measure.8.G.A.1.b

      3. c

        Parallel lines are taken to parallel lines. 8.G.A.1.c

    2. 2

      Explain that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations. Given two congruent figures, describe a sequence of rigid transformations that proves the congruence between them.8.G.A.2

    3. 3

      Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.8.G.A.3

    4. 4

      Explain that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that demonstrates the similarity between them.  8.G.A.4

    5. 5

      Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.8.G.A.5

  • 2

    Explain and apply the Pythagorean Theorem.8.G.B

    1. 1

      Explain a proof of the Pythagorean Theorem and a proof of its converse. 8.G.B.6

    2. 2

      Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two- and three-dimensions. 8.G.B.7

    3. 3

      Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. 8.G.B.8

  • 3

    Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. 8.G.C

    1. 1

      Apply the formulas for the volume of cones, cylinders, and spheres to solve real-world and mathematical problems.8.G.C.9

Statistics and Probability8.SP

  • 1

    Investigate patterns of association in bivariate data.8.SP.A

    1. 1

      Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. 8.SP.A.1

    2. 2

      For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. 8.SP.A.2

    3. 3

      Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 𝑐𝑐𝑐𝑐 ℎ𝑟𝑟 has meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. 8.SP.A.3

    4. 4

      Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?8.SP.A.4

Frequently asked questions

What grade levels do these standards cover?
Grade 8
Where can I read the official document?
Iowa Academic Standards for Mathematics

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