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Course Title:
School/District: GWMS Grade: 8
Unit: Expression and Equation
Unit: GeometryUnit: FunctionsUnit: Number SystemConcepts/TopicsConcepts/TopicsConcepts/TopicsConcepts/Topics
Order of operations
Variables and Expressions
Equations
Problem Solving
Adding and Subtracting integers
Multiplying and Dividing integers
Number properties
Distributive property
Solving equations using adding, subtracting, multiplying, dividing
Two step equations
Solving inequalities
Rules of exponents
Negative and zero exponents
Scientific notationAngles
Triangles
Polygons
Reflections
Translations
Rotations
Similarity and dilation
Square roots
Pythagorean Theorem
Right triangles
Trigonometry (if time)
Area
Three D Figures
Volume of cones, cylinders, prisms, pyramidsMultistep equations
Solve equations w/variables on both sides
Inequalities (if time)
Writing and solving proportions
Functions
Equations in two variables
Linear equations
Intercepts
Slope
Slopeintercept form
Systems of equations (found in advanced book)Fractions and decimals
Adding/subtracting decimals
Multiplying/dividing decimals
Skills/StandardsSkills/StandardsSkills/StandardsSkills/Standards use the properties of integer exponents to simply expressions. (CCSS: 8.EE.1)
use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p , where p is a positive rational number. (CCSS: 8.EE.2)
evaluate the square root of a perfect square (CCSS: 8.EE.2)
evaluate the cube root of a perfect cube. (CCSS: 8.EE.2)
justify that the square root of a nonprefect square will be irrational. (CCSS: 8.EE.2)
write an estimation of a large quantity by expressing it as the product of a singledigit number and a positive power of ten. (CCSS: 8.EE.3)
write an estimation of a very small quantity by expressing it as the product of a singledigit number and a negative power of ten. (CCSS: 8.EE.3)
compare quantities written as the product of a singledigit number and a power of ten by stating their multiplicative relationships. (CCSS: 8.EE.3)
perform operations (addition/subtraction/multiplication/division) with two numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. (CCSS: 8.EE.4)
use scientific notation and choose units of appropriate size for measurements of very large or very small quantities.(CCSS: 8.EE.4)
interpret scientific notation that has been generated by technology. (CCSS: 8.EE.4)
simplify a linear equation by using the distributive property and/or combining like terms. (CCSS: 8.EE.7a)
give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. (CCSS: 8.EE.7a)
solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. (CCSS: 8.EE.7b)verify by measuring and comparing lengths, angle measures, and parallelism, of a figure and its image that after a figure has been translated, or reflected, or rotated corresponding lines and line segments remain the same length, corresponding angles have the same measure, and corresponding parallel lines remain parellel.1 (CCSS: 8.G.1.1a.1b.1c.)
demonstrate that a twodimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations. (CCSS: 8.G.2)
Given two congruent figures, describe a sequence of transformations that exhibits the congruence between them. (CCSS: 8.G.2)
describe the changes occurring to the xand y coordinates of a figure after a: translation, reflection, rotation, dilation. (CCSS: 8.G.3)
explain how transformation can be used to prove that two figures are similar. (CCSS: 8.G.4)
describe a sequence of transformations to prove or disprove that two given figures are similar. (CCSS: 8.G.4)
informally prove that the sum of any triangle's interior angles will be the same measure as a straight angle (180 degrees). (CCSS: 8.G.5) informally prove that the sum of any polygon's exterior angles will be 360 degrees. (CCSS: 8.G.5)
make conjectures regarding the relationships and measurements of the angles created when two parallel lines are cut be a transversal. (CCSS: 8.G.5)
use the Pythagorean Theorem to determine if the given triangle is a right triangle. (CCSS: 8.G.6)
use algebraic reasoning to relate the visual model to the Pythagorean Theorem. (CCSS: 8.G.6)
apply the Pythagorean Theorem to find an unknown side length of a right triangle. (CCSS: 8.G.7)
draw a diagram and use the Pythagorean Theorem to solve real world problems involving right triangles. (CCSS: 8.G.7)
draw a diagram to find right triangles in a threedimensional figure and use the Pythagorean Theorem to calculate various dimensions. (CCSS: 8.G.7)
connect any two points on a coordinate grid to a third point so that the three points form a right triangle. (CCSS: 8.G.7)
use the right triangle and the Pythagorean Theorem to find the distance between the original two points. (CCSS: 8.G.7)
connect any two points on a coordinate grid to a third point so that the three points form a right triangle. (CCSS: 8.G.8)
use the right triangle and the Pythagorean Theorem to find the distance between the original two points. (CCSS: 8.G.8)
state the formulas for the volumes of cones, cylinders, and spheres and use them to solve realworld and mathematical problems. (CCSS: 8.G.9)
describe the similarity between finding the volume of a cylinder and the volume of a right prism. (CCSS: 8.G.9)
informally prove the relationship between the volume of a cylinder and the volume of a cone with the same base. (CCSS: 8.G.9)
informally prove the relationship between the volume of a sphere and the volume of a circumscribed cylinder. (CCSS: 8.G.9)
solve real world problems involving the volume of cylinders, cones, and spheres. (CCSS: 8.G.9) define a function as a rule that assigns to each input exactly one output. (CCSS: 8.F.1)
show the relationship between the inputs and outputs of a function by graphing them as ordered pairs on a coordinate grid. (CCSS: 8.F.1)
determine the properties of a function written in algebraic form (rate of change, meaning of yintercept, linear, nonlinear). (CCSS: 8.F.2)
determine the properties of a function given the inputs and outputs in a table. (CCSS: 8.F.2)
compare the properties of two functions that are represented differently (equation, a table, graphically, or verbal representation). (CCSS: 8.F.2)
explain why the equation y=mx+b represents a linear function and interpret the slope and yintercept in relation to the function. (CCSS: 8.F.3)
give examples of relationships that are nonlinear functions. (CCSS: 8.F.3)
create a table of values that can be defined as a nonlinear function. (CCSS: 8.F.3)
construct a function to model a linear relationship between two quantities. (CCSS: 8.F.4)
determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. (CCSS: 8.F.4)
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. (CCSS: 8.F.4)
match the graph of function to a given situation. (CCSS: 8.F.5)
I sketch a graph that exhibits the qualitative features of a function that has been described verbally. (CCSS: 8.F.5)
write a story that describes the functional relationship between two variables depicted on a graph. (CCSS: 8.F.5)
graph proportional relationships, interpreting the unit rate as the slope of the graph. (CCSS: 8.EE.5)
justify that the graph of a proportional relationship will always intersect the origin (0,0) of the graph. (CCSS: 8.EE.5)
use a graph, a table, or an equation to determine the unit rate of a proportional relationship an use the unit rate to make comparisons between various proportional relationships. (CCSS: 8.EE.5)
use similar triangles to explain why the slope m is the same between any two distinct points on a nonvertical line in the coordinate plane. (CCSS: 8.EE.6)
justify that an equation in a form of y=mx will represent the graph of a proportional relationship with a slope of m and yintercept of 0. (CCSS: 8.EE.6)
justify that an equation in the form of y=mx + b represents the graph of a linear relationship with a slope of m and a yintercept of b. (CCSS: 8.EE.6)
analyze and solve pairs of simultaneous linear equations. (CCSS: 8.EE.8)
explain that 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. (CCSS: 8.EE.8a)
solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations.
solve simple cases by inspection. (CCSS: 8.EE.8b)
solve realworld and mathematical problems leading to two linear equations in two variables intersecting. (CCSS: 8.EE.8c)demonstrate that every number has a decimal expansion. (CCSS: 8.NS.1)
convert a repeating decimal into a rational number. (CCSS: 8.NS.1)
For rational numbers show that the decimal expansion repeats eventually. (CCSS: 8.NS.1)
convert a decimal expansion which repeats eventually into a rational number. (CCSS: 8.NS.1)
use rational approximations of irrational numbers to compare the size of irrational numbers, locate and plot them approximately on a number line diagram, and estimate the value of expressions. (CCSS: 8.NS.2)
use estimated values to compare two or more irrational numbers. (CCSS: 8.NS.2)
Course Title:
School/District: Grade:
Unit: Statistics and Probability
Unit:Unit:Unit:Concepts/TopicsConcepts/TopicsConcepts/TopicsConcepts/Topics
Data displays
Scatter plots
Probability and odds
Independent and dependent events
Skills/StandardsSkills/StandardsSkills/StandardsSkills/Standards plot ordered pairs on a coordinate grid representing the relationship between two data sets. (CCSS: 8.SP.1)
describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. (CCSS: 8.SP.1)
recognize whether or not data plotted on a scatter plot have a linear association. (CCSS: 8.SP.2)
draw a straight trend line to approximate the linear relationship between the plotted points of two data sets. (CCSS: 8.SP.2)
determine the equation of a trend line that approximates the linear relationship between the plotted points of two data sets. (CCSS: 8.SP.3)
interpret the yintercept of the equation in the context of the collected data. (CCSS: 8.SP.3)
interpret the slope of the equation in the context of the collected data. (CCSS: 8.SP.3)
use the equation of the trend line to summarize the given data and make predictions regarding additional data points. (CCSS: 8.SP.3)
create a twoway table to record the frequencies of bivariate categorical values. (CCSS: 8.SP.4)
determine the relative frequencies for rows and/or columns of a twoway table. (CCSS: 8.SP.4)
use the relative frequencies and context of the problem to describe possible associations between the two sets of data. (CCSS: 8.SP.4)
Course Title:
School/District: Grade:
Unit:
Unit:Unit:Unit:Concepts/TopicsConcepts/TopicsConcepts/TopicsConcepts/Topics
Skills/StandardsSkills/StandardsSkills/StandardsSkills/Standards
Course Title:
School/District: Grade:
Unit:
Unit:Unit:Unit:Concepts/TopicsConcepts/TopicsConcepts/TopicsConcepts/Topics
Skills/StandardsSkills/StandardsSkills/StandardsSkills/Standards
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