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Explore how each subject becomes a coherent sequence of knowledge, reasoning, practice, and transfer—not a disconnected checklist.

Grade 8 Math

28 curriculum outcomes with explicit teaching progressions

Select a record to inspect its progression

Number System · 8.NS.A.1

Distinguish rational from irrational numbers

Independently know that numbers that are not rational are called irrational. understand informally that every number has a decimal expansion; for rational numbers, show that the decimal expansion repeats eventually and convert a repeating decimal expansion into a rational number. across representations and contexts.

Component progression

  1. 1I can determine whether a given decimal expansion repeats eventually or continues without a repeating pattern.
  2. 2I can convert a repeating decimal into an equivalent rational number written as a fraction.
  3. 3I can classify a given number as rational or irrational based on whether its decimal expansion terminates, repeats, or does neither.
Number System · 8.NS.A.2

Approximate and compare irrational numbers

Independently use rational approximations of irrational numbers to compare their size, locate them approximately on a number line, and estimate the value of expressions involving them. across representations and contexts.

Component progression

  1. 1I can use nearby perfect squares to determine a reasonable rational approximation for a square root, such as showing √28 is between 5 and 6.
  2. 2I can plot the approximate location of an irrational number on a number line using its rational approximation.
  3. 3I can compare the size of two irrational numbers and estimate the value of an expression involving an irrational number using rational approximations.
Expressions Equations · 8.EE.A.1

Apply integer exponent properties

Independently know and apply the properties of integer exponents to generate equivalent numerical expressions, including expressions with negative exponents. across representations and contexts.

Component progression

  1. 1I can apply the product-of-powers and quotient-of-powers rules to simplify expressions with the same base.
  2. 2I can simplify expressions using the rule that a nonzero number to the zero power is 1, and that a negative exponent indicates a reciprocal.
  3. 3I can use integer exponent properties together to rewrite a numerical expression in an equivalent, simplified form.
Expressions Equations · 8.EE.A.2

Solve equations using square and cube roots

Independently 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. evaluate square roots of small perfect squares and cube roots of small perfect cubes, and know that √2 is irrational. across representations and contexts.

Component progression

  1. 1I can evaluate the square roots of small perfect squares and the cube roots of small perfect cubes without a calculator.
  2. 2I can solve equations of the form x² = p and x³ = p for a positive rational number p, representing solutions with root symbols and accounting for both solutions when squaring.
  3. 3I can explain why the square root of a number that is not a perfect square, such as √2, is irrational.
Expressions Equations · 8.EE.A.3

Use scientific notation to estimate quantities

Independently use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one quantity is as another. across representations and contexts.

Component progression

  1. 1I can express a very large or very small quantity as a single digit times a power of 10 to estimate its size.
  2. 2I can compare two quantities expressed in this form by comparing their powers of 10.
  3. 3I can determine how many times as much one quantity is as another when both are expressed as a single digit times a power of 10.
Expressions Equations · 8.EE.A.4

Operate with scientific notation

Independently perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. choose units of appropriate size for measurements of very large or very small quantities, and interpret scientific notation generated by technology. across representations and contexts.

Component progression

  1. 1I can multiply and divide numbers expressed in scientific notation, applying integer exponent rules to the powers of 10.
  2. 2I can add and subtract numbers expressed in scientific notation, first rewriting them with a common power of 10.
  3. 3I can choose units of appropriate size for a real-world quantity and interpret scientific notation as displayed by calculators or computer software.
Expressions Equations · 8.EE.B.5

Graph proportional relationships and compare unit rates

Independently graph proportional relationships, interpreting the unit rate as the slope of the graph, and compare two different proportional relationships represented in different ways. across representations and contexts.

Component progression

  1. 1I can graph a proportional relationship given as a table, equation, or verbal description.
  2. 2I can identify the unit rate of a proportional relationship as the slope of its graph.
  3. 3I can compare two proportional relationships presented in different forms (graph, table, equation, description) by comparing their unit rates.
Expressions Equations · 8.EE.B.6

Derive y = mx and y = mx + b using similar triangles

Independently 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, and derive the equation y = mx for a line through the origin and y = mx + b for a line intercepting the vertical axis at b. across representations and contexts.

Component progression

  1. 1I can construct right triangles between two pairs of points on a line and use similarity to show the rise-over-run ratio is the same for both pairs.
  2. 2I can use the constant-slope argument to derive the equation y = mx for a proportional (through-the-origin) line.
  3. 3I can extend the argument to a line that intercepts the vertical axis at b, deriving the equation y = mx + b.
Expressions Equations · 8.EE.C.7

Solve linear equations in one variable

Independently solve linear equations in one variable with rational number coefficients, including equations whose solutions require combining like terms and using the distributive property, and recognizing equations with one solution, infinitely many solutions, or no solutions. across representations and contexts.

Component progression

  1. 1I can solve linear equations in one variable that require combining like terms on one or both sides.
  2. 2I can solve linear equations in one variable that require applying the distributive property before combining terms.
  3. 3I can determine whether a linear equation has exactly one solution, infinitely many solutions, or no solution, and justify the classification.
Expressions Equations · 8.EE.C.8

Solve systems of two linear equations

Independently understand that solutions to a system of two linear equations correspond to points of intersection of their graphs; solve simple systems by inspection, and solve systems in two variables algebraically and graphically, including systems that arise from real-world problems. across representations and contexts.

Component progression

  1. 1I can explain that the solution to a system of two linear equations is the point where their graphs intersect, and identify solutions by inspection for simple systems.
  2. 2I can solve a system of two linear equations by graphing both lines and identifying the intersection point.
  3. 3I can solve a system of two linear equations algebraically and use systems to solve real-world problems.
Functions · 8.F.A.1

Understand functions as input-output rules

Independently understand that a function is a rule that assigns to each input exactly one output. the graph of a function is the set of ordered pairs consisting of an input and the corresponding output. across representations and contexts.

Component progression

  1. 1I can determine whether a given rule, table, or mapping assigns exactly one output to each input.
  2. 2I can generate input-output ordered pairs from a function rule.
  3. 3I can explain that a function's graph is the set of all its input-output ordered pairs.
Functions · 8.F.A.2

Compare functions across representations

Independently compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). across representations and contexts.

Component progression

  1. 1I can determine a specific property, such as rate of change or a particular output value, from a function given algebraically, graphically, numerically, or verbally.
  2. 2I can compare a specific property between two functions given in different representations.
  3. 3I can draw and justify a conclusion, such as which function has the greater rate of change, based on the comparison.
Functions · 8.F.A.3

Interpret y = mx + b as a linear function

Independently interpret the equation y = mx + b as defining a linear function whose graph is a straight line; give examples of functions that are not linear. across representations and contexts.

Component progression

  1. 1I can identify a function as linear when it can be written in the form y = mx + b, and identify its slope and y-intercept.
  2. 2I can verify that a linear function has a constant rate of change by checking a table of values.
  3. 3I can identify functions that are not linear, such as those with a squared term, and give original examples.
Functions · 8.F.B.4

Construct a linear function from a description

Independently construct a function to model a linear relationship between two quantities. determine the rate of change and initial value from a description, a table, or a graph, and interpret them in terms of the situation. across representations and contexts.

Component progression

  1. 1I can determine the rate of change and initial value of a linear relationship from a verbal description, table, or two given points.
  2. 2I can construct a linear function modeling the relationship using the determined rate of change and initial value.
  3. 3I can interpret the rate of change and initial value of the constructed function in terms of the original real-world situation.
Functions · 8.F.B.5

Describe and sketch functional relationships qualitatively

Independently describe qualitatively the functional relationship between two quantities by analyzing a graph, and sketch a graph that exhibits the qualitative features of a function described verbally. across representations and contexts.

Component progression

  1. 1I can describe in words how a quantity changes over the domain shown in a graph, including where it increases, decreases, or stays constant.
  2. 2I can sketch a graph showing the general shape described verbally, without needing exact values.
  3. 3I can match a verbal description of a changing relationship to the graph that correctly represents it, and explain why others do not fit.
Geometry · 8.G.A.1

Verify properties of rotations, reflections, and translations

Independently verify experimentally the properties of rotations, reflections, and translations: lines are taken to lines and line segments to line segments of the same length; angles are taken to angles of the same measure; and parallel lines are taken to parallel lines. across representations and contexts.

Component progression

  1. 1I can verify experimentally that translating a figure preserves segment lengths and angle measures.
  2. 2I can verify experimentally that rotating or reflecting a figure preserves segment lengths and angle measures.
  3. 3I can verify experimentally that rigid motions map parallel lines to parallel lines.
Geometry · 8.G.A.2

Determine congruence via a sequence of rigid motions

Independently understand 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 that exhibits the congruence. across representations and contexts.

Component progression

  1. 1I can apply a specified rigid motion to a figure and draw its image.
  2. 2I can determine whether two given figures are congruent by identifying whether a sequence of rigid motions maps one onto the other.
  3. 3I can describe a specific sequence of rotations, reflections, and translations that maps one given figure onto a congruent figure.
Geometry · 8.G.A.3

Describe transformation effects using coordinates

Independently describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. across representations and contexts.

Component progression

  1. 1I can use coordinate rules to find the image of a figure under a given translation or reflection.
  2. 2I can use coordinate rules to find the image of a figure under a 90°, 180°, or 270° rotation about the origin.
  3. 3I can use coordinates to find the image of a figure under a dilation with a given center and scale factor.
Geometry · 8.G.A.4

Determine similarity via a sequence of transformations

Independently understand 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 figures, describe a sequence that exhibits the similarity. across representations and contexts.

Component progression

  1. 1I can explain the difference between similar figures (same shape, possibly different size) and congruent figures (same shape and size).
  2. 2I can determine whether two given figures are similar by identifying whether a sequence of rigid motions and dilations maps one onto the other.
  3. 3I can describe a specific sequence of transformations, including at least one dilation, that maps one figure onto a similar figure.
Geometry · 8.G.A.5

Use informal arguments for angle relationships

Independently 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. across representations and contexts.

Component progression

  1. 1I can use an informal argument (such as rearranging angles along a line) to show a triangle's interior angles sum to 180° and that an exterior angle equals the sum of the two remote interior angles.
  2. 2I can use an informal argument to establish that alternate interior angles and corresponding angles are congruent when a transversal crosses parallel lines.
  3. 3I can use an informal argument to explain why two triangles with two pairs of congruent angles must be similar.
Geometry · 8.G.B.6

Prove the Pythagorean Theorem and its converse

Independently explain a proof of the pythagorean theorem and its converse. across representations and contexts.

Component progression

  1. 1I can explain a specific proof (such as an area-based rearrangement proof) that a2 + b2 = c2 for a right triangle's legs and hypotenuse.
  2. 2I can explain how the converse, which states that a triangle with a2 + b2 = c2 must be a right triangle, follows from the original theorem.
  3. 3I can use the pythagorean theorem and its converse together to solve a problem involving verifying a right angle and finding a missing measurement.
Geometry · 8.G.B.7

Apply the Pythagorean Theorem to find unknown lengths

Independently apply the pythagorean theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. across representations and contexts.

Component progression

  1. 1I can apply the pythagorean theorem to find a missing side length in a two-dimensional right triangle, correctly identifying the hypotenuse.
  2. 2I can apply the pythagorean theorem to solve real-world problems modeled by a right triangle.
  3. 3I can apply the pythagorean theorem, potentially twice, to find an unknown length in a three-dimensional figure such as a rectangular prism's diagonal.
Geometry · 8.G.B.8

Find distance between points using the Pythagorean Theorem

Independently apply the pythagorean theorem to find the distance between two points in a coordinate system. across representations and contexts.

Component progression

  1. 1I can determine the horizontal and vertical distances between two points on a coordinate plane, forming the legs of a right triangle.
  2. 2I can use the pythagorean theorem with the horizontal and vertical distances to find the straight-line distance between two points.
  3. 3I can apply this method to solve a real-world problem involving the distance between two locations plotted on a coordinate grid.
Geometry · 8.G.C.9

Apply volume formulas for cones, cylinders, and spheres

Independently know the formulas for the volumes of cones, cylinders, and spheres, and use them to solve real-world and mathematical problems. across representations and contexts.

Component progression

  1. 1I can use the formula v = πr²h to find the volume of a cylinder given its radius and height.
  2. 2I can use the formulas for the volume of a cone and a sphere to find their volumes given the necessary measurements.
  3. 3I can solve a real-world problem requiring computation of, or solving for an unknown dimension from, a volume of a cone, cylinder, or sphere.
Statistics Probability · 8.SP.A.1

Construct and interpret scatter plots

Independently construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities, including clustering, outliers, positive or negative association, linear association, and nonlinear association. across representations and contexts.

Component progression

  1. 1I can construct a scatter plot from a bivariate measurement data set.
  2. 2I can identify clusters and outliers in a scatter plot.
  3. 3I can describe a scatter plot's association as positive, negative, or none, and as linear or nonlinear.
Statistics Probability · 8.SP.A.2

Informally fit and assess a linear model

Independently know that straight lines are widely used to model relationships between two quantitative variables. 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. across representations and contexts.

Component progression

  1. 1I can determine whether a scatter plot's pattern suggests a linear association appropriate for a straight-line model.
  2. 2I can draw a straight line that appears to fit a scatter plot's linear pattern reasonably well.
  3. 3I can judge how closely the data points cluster around the fitted line and describe the quality of the fit.
Statistics Probability · 8.SP.A.3

Use a linear model to solve problems

Independently use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and the intercept. across representations and contexts.

Component progression

  1. 1I can interpret the slope and y-intercept of a fitted linear model in terms of the real-world quantities being compared.
  2. 2I can use the equation of a linear model to predict a value of one variable given the other.
  3. 3I can evaluate whether a prediction made using the model is reasonable, considering the range of the original data.
Statistics Probability · 8.SP.A.4

Analyze patterns in bivariate categorical data

Independently understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects, and use relative frequencies calculated for rows or columns to describe possible association between the two variables. across representations and contexts.

Component progression

  1. 1I can construct a two-way frequency table summarizing bivariate categorical data.
  2. 2I can calculate relative frequencies from a two-way table, by row, column, or overall total.
  3. 3I can use relative frequencies to describe a possible association between the two categorical variables.
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