# Math 8 Grade

1.0 | NUMBER AND OPERATIONS | ||

A | Understand Real Number Concepts | ||

N.ME.8.01 | Understand the meaning of a square root of a number and its connection to the square whose area is the number; understand the meaning of a cube root and its connection to the volume of a cube. | ||

N.ME.8.02 | Understand meanings for zero and negative integer exponents. | ||

N.ME.8.03 | Understand that in decimal form, rational numbers either terminate or eventually repeat, and that calculators truncate or round repeating decimals; locate rational numbers on the number line; know fraction forms of common repeating decimals. | ||

N.ME.8.04 | Understand that irrational numbers are those that cannot be expressed as the quotient of two integers, and cannot be represented by terminating or repeating decimals; approximate the position of familiar irrational numbers, e.g., √2, √3, π, on the number line. | ||

N.FL.8.05 | Estimate and solve problems with square roots and cube roots using calculators. | ||

N.FL.8.06 | Find square roots of perfect squares and approximate the square roots of non-perfect squares by locating between consecutive integers, e.g., √130 is between 11 and 12. | ||

B | Solve Problems | ||

N.MR8.07 | Understand percent increase and percent decrease in both sum and product form, e.g., 3% increase of a quantity x is x + .03x = 1.03x. | ||

N.MR.8.08 | Solve problems involving percent increases and decreases. | ||

N.FL.8.09 | Solve problems involving compounded interest or multiple discounts. | ||

N.MR.8.1 | Calculate weighted averages such as course grades, consumer price indices, and sports ratings. | ||

N.FL.8.11 | Solve problems involving ratio units, such as miles per hour, dollars per pound, or persons per square mile. | ||

2.0 | ALGEBRA | ||

C | Understand the Concept of Non-Linear Functions | ||

A.RP.08.01 | Identify and represent linear functions, quadratic functions, and other simple functions including inversely proportional relationships (y = k/x); cubics (y = ax3); roots (y = √x ); and exponentials (y = ax , a > 0); using tables, graphs, and equations.* | ||

A.PA.08.02 | For basic functions, e.g., simple quadratics, direct and indirect variation, and population growth, describe how changes in one variable affect the others. | ||

A.PA.08.03 | Recognize basic functions in problem context. | ||

A.RP.08.04 | Use the vertical line test to determine if a graph represents a function in one variable. | ||

D | Understand and represent quadratic functions | ||

A.RP.08.05 | Relate quadratic functions in factored form and vertex form to their graphs, and vice versa; in particular, note that solutions of a quadratic equation are the x-intercepts of the corresponding quadratic function. | ||

A.RP.08.06 | Graph factorable quadratic functions, finding where the graph intersects the x-axis and the coordinates of the vertex; use words “parabola” and “roots”; include functions in vertex form and those with leading coefficient –1, e.g., y = x2 – 36, y = (x – 2)2 – 9; y = – x2; y = – (x – 3)2. | ||

E | Recognize, represent, and apply common formulas | ||

A.FO.08.07 | Recognize and apply the common formulas.(a + b)2 = a2 + 2 ab + b2, (a – b)2 = a2 – 2 ab + b2, (a + b) (a – b) = a2 – b2 ; represent geometrically | ||

A.FO.08.08 | Factor simple quadratic expressions with integer coefficients. | ||

A.FO.08.09 | Solve applied problems involving simple quadratic equations. | ||

F | Understand solutions and solve equations, simultaneous equations, and linear inequalities | ||

A.FO.08.10 | Understand that to solve the equation f(x) = g(x) means to find all values of x for which the equation is true. | ||

A.FO.08.11 | Solve simultaneous linear equations in two variables by graphing, by substitution, and by linear combination; estimate solutions using graphs; include examples with no solutions and infinitely many solutions. | ||

A.FO.08.12 | Solve linear inequalities in one and two variables, and graph the solution sets. | ||

A.FO.08.13 | Set up and solve applied problems involving simultaneous linear equations and linear inequalities. | ||

3.0 | GEOMETRY | ||

G | Understand and use the Pythagorean Theorem | ||

G.GS.08.01 | Understand at least one proof of the Pythagorean Theorem; use the Pythagorean Theorem and its converse to solve applied problems including perimeter, area, and volume problems. | ||

G.LO.08.02 | Find the distance between two points on the coordinate plane using the distance formula; recognize that the distance formula is an application of the Pythagorean Theorem. | ||

H | Solve problems about geometric figures | ||

G.SR.08.03 | Understand the definition of a circle; know and use the formulas for circumference and area of a circle to solve problems. | ||

G.SR.08.04 | Find area and perimeter of complex figures by sub-dividing them into basic shapes (quadrilaterals, triangles, circles). | ||

G.SR.08.05 | Solve applied problems involving areas of triangles, quadrilaterals, and circles. | ||

I | Understand concepts of volume and surface area, and apply formulas | ||

G.SR.08.06 | Know the volume formulas for generalized cylinders ((area of base) x height), generalized cones and pyramids ( (area of base) x height), and spheres ( π (radius) 3 ) and apply them to solve problems. | ||

G.SR.08.07 | Understand the concept of surface area, and find the surface area of prisms, cones, spheres, pyramids, and cylinders. | ||

J | Visualize solids | ||

G.SR.08.08 | Sketch a variety of two-dimensional representations of three-dimensional solids including orthogonal views (top, front, and side), picture views (projective or isometric), and nets; use such two-dimensional representations to help solve problems. | ||

K | Understand and apply concepts of transformation and symmetry | ||

G.TR.08.09 | Understand the definition of a dilation from a point in the plane, and relate it to the definition of similar polygons. | ||

G.TR.08.10 | Understand and use reflective and rotational symmetries of two-dimensional shapes and relate them to transformations to solve problems. | ||

4.0 | DATA AND PROBABILITY | ||

L | Draw, explain, and justify conclusions based on data | ||

D.AN.08.01 | Determine which measure of central tendency (mean, median, mode) best represents a data set, e.g., salaries, home prices, for answering certain questions; justify the choice made. | ||

D.AN.08.02 | Recognize practices of collecting and displaying data that may bias the presentation or analysis. | ||

M | Understand probability concepts for simple and compound events | ||

D.PR.08.03 | Compute relative frequencies from a table of experimental results for a repeated event. Interpret the results using relationship of probability to relative frequency.* | ||

D.PR.08.04 | Apply the Basic Counting Principle to find total number of outcomes possible for independent and dependent events, and calculate the probabilities using organized lists or tree diagrams. | ||

D.PR.08.05 | Find and/or compare the theoretical probability, the experimental probability, and/or the relative frequency of a given event.* | ||

D.PR.08.06 | Understand the difference between independent and dependent events, and recognize common misconceptions involving probability, e.g., Alice rolls a 6 on a die three times in a row; she is just as likely to roll a 6 on the fourth roll as she was on any previous roll. |