Last updated: 6/2/2015 ## Math- 8 Core Map Quarter 1

The Number System, Expressions and Order of Operations

Order of Operations

Classify Real Numbers

Powers and Exponents

Multiply and Divide Monomials

Zero Exponent

Negative Exponent

Scientific Notation

Computing in Scientific Notation

Roots

Roots of perfect squares

Roots of non-perfect squares

Comparing Real Numbers

Solving Equations

Examine properties of real numbers and their use in solving equations

Solving Equations with Rational Equivalence

Solving Two-step Equations

Write Two-Step Equations

Solving Equations with variables on both sides

Solving Multi-Step Equations

Determining the equations with all or no solutions

Cubed and Square Root Equations

Linear Equations

Cartesian, coordinate plane

Examine standard form of Linear Equation

Determine independent and dependent variables

Solving for y-in terms of x

Solving for missing coordinates given a linear equation

Graphing lines, from list of points (either given or found using equation)

Determine slope of line from graph (given any points on the line or graphed)

Determining slope from two sets of coordinates (using slope formula)

Notice parallelism with equivalent slopes

Examine the no and zero slope linear equations

Finding the missing coordinate given the slope, a pair of coordinates and one other coordinate

Slope triangles

Examining the intercepts

Writing equations of lines using slope and y-intercept

Graphing lines, given slope and y-intercept

Graphing lines, given the equation of a line in slope-intercept form

Determining and interpreting intercepts-graphically and algebraically

Quarter 1

The Number System, Expressions and Order of Operations

Variables and Expressions

Difference between Expressions and Equations

Using Substitution Property of Equality to evaluate expressions

Order of Operations with Rational numbers

Order of Operations with Absolute Value Groups

Order of Operations with fractions (Numerator and Denominator -groups)

Reading Algebraic Expressions (use opposite for negations)

Evaluating Expressions using Substitution Property of Equality

Complex fractions within Expressions

The Number Systems and their subsets

Classifying numbers as Rational and Irrational

Stating the sets of Real Number sets a number belongs to

Recognizing Powers

Recognizing the base of powers

Distinguishing the difference between a negative base and a negated power

Expanding powers

Determining the sign of a negative power base to even or odd exponents

Understanding the directives when asked to either evaluate, simplify, write results using powers

Explore the employ the product rule with powers of the same base

Explore and employ power to exponent rule

Explore and employ quotient rule with powers of the same base

Multiplying monomials using Laws of Exponents

Finding quotients with numerical coefficients and using Laws of exponents

Discovering the meaning of the zero exponent

Simplifying expressions with exponents

Demonstrate use of commutative and associative properties evaluating expressions with exponents

Discover the meaning of negative exponents

Using Product, Quotient and Power Laws of exponents with negative exponents

Rewriting products and quotients as powers with positive exponents

Evaluating expressions with complex fractions

Expanding numbers with sums of powers of ten with integer exponents

Writing numbers in scientific notation from standard form

Writing numbers in standard form from scientific notation

Comparing numbers in scientific notation

Computing products in scientific notation

Computing quotients in scientific notation

Computing sum and differences in scientific notation

Real life situations computing in scientific notation

Squares and Square Roots

Cubes and Cube Roots

Estimating square roots of non-perfect squares

Determining which two consecutive integers a root falls between

Comparing and ordering real numbers

Determining the roots of perfect squares and perfect cubes

Estimate the value of roots on non-perfect squares and roots

Density Property

Equations

Examining equivalence

Solving for the solution that makes the math statement true

Literal Equations

Rewriting Formulas

Geometric applications of solving equations

Determine the value of the missing coordinate of a given linear equation

Plot line from a list of coordinates

Determine slope of line from the graph and from two points

Determine slope using slope formula

Discerning slope and y-intercept from graph

Explore the x and y intercepts and what their corresponding coordinates are

Interpreting the x and y intercepts

Reading slope and intercept from equation and graphing from equation

Writing linear equations in standard and slope intercept form

The Number System, Expressions and Order of Operations

How do we calculate the value of expressions that contains multiple operations?

What happens when you add, subtract, multiply and divide numbers?

How do we classify real numbers?

How do we define rational and irrational numbers?

Why is it useful to write numbers in different ways?

How can you use exponents to write numbers?

How can we multiply/divide powers with the same base?

How do we define the zero and negative exponent?

How do you read numbers written in scientific notation?

How can we compute numbers written in scientific notation?

How do we use scientific notation in the real world?

How can we determine sides of a square when given the area?

Why and when do you need to use cube and square roots?

Where are irrational numbers on the number line?

Between any two numbers on the number line, are their other real numbers?

Equations

What is equivalence?

How do we determine the values that make two expressions equivalent?

What properties maintain equivalence?

How can you solve a multi-step equations?

How can you be sure your solution is reasonable?

Can we determine the correctness of our solution, how?

Can we solve equations with variables on both sides?

Why would we need to rewrite formulas?

How can we find points on a line given the equation of the line?

Can we determine errors in solving equations from plotted points found from the same linear equation?

Can we predict another point on the line, without using the equation, once we know three points on the line?

Can you determine if lines are parallel from their slopes?

What must we consider when a line has no run, or no rise?

How can you recognize a linear equation?

How do the solutions to a linear equation relate to the line?

How can we use the slope of a line to describe the line?

Can we rewrite equations of lines to reveal information about the line?

Would a point not on the line be a solution to the linear equation?

 (1) 8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 * 3-5 = 3-3=1 / 33 – 1 / 27. (1) 8.EE.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. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. (1) 8.EE.3 Use numbers expressed in the form of a single digit times a whole-number power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 times 108 and the population of the world as 7 times 109, and determine that the world population is more than 20 times larger. (1) 8.EE.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 appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. (1) 8.EE.6 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; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. (1) 8.EE.7 Solve linear equations in one variable. (1) 8.EE.7.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 x = a, a = a, or a = b results (where a and b are different numbers). (1) 8.EE.7.b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. (1) 8.F.3 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. For example, the function A = s2 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. (1) 8.F.4 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 (x, y) 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. (1) 8.NS.1 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 decimal expansion which repeats eventually into a rational number. (1) 8.NS.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 (e.g., π2). For example, 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.

The Number System, Expressions and Order of Operations

Classify real numbers as rational or irrational

Evaluate expressions with absolute value, powers, fractional expressions and radicals

Recognize the base of a power

Determine if the base of a power is negative or positive

Determine the sign if a negative base power will result in a positive or negative product, based on whether the exponent is odd or even

Expand powers

Evaluate powers

Write products as powers

Multiply and divide powers of the same base

Determine the product of a power raised to an exponent

Multiply and divide monomials

Write numbers in scientific notation

Write numbers written in scientific notation to standard form

Compute in scientific notation

Determine operations to be used in applications of scientific notation

Comparing numbers in scientific notation

Find another real number between two given numbers on the number line

Equations

Recognize that an equation is a statement of equality and truth

Simplify each side of an equation and employ inverse properties to solve multi-step equations

Solve single step equations

Solve equations with variables on both sides

Solve multi-step equations

Using order of operatoins to check validity of solutions

Determine the solutions that make a statement true

Rewrite a formula to determine that value of a variable

Perform geometric and real world applications by solving equations

Solve linear equations by substituting in a coordinate and solving for the other

Find points on a line, by building a chart of ordered pairs that are on given linear equation

Plot points and determine correctness of line, from slope and collinear behavior

Determine and interpret x and y intercepts

Find x and y intercepts algebraically

Graph lines using slope and y-intercept

Graph lines whose slopes are zero or no slopes (vertical, horizontal)

Rewrite linear equations from slope intercept form to standard form

Determine the slope of a line from a graph

Determine the slope of a line from two points

Determine the slope of a line using the formula

Find the missing coordinate, give the slope and two points, containing one variable

Real numbers

Rational numbers

Irrational numbers

Perfect squares

Square roots

Terminating decimal

Repeating decimal

Simple fraction

Complex fraction

Integers

Whole Numbers

Natural and Counting Numbers

Power

Base

Exponent

Product

Quotient

Expanded form

Order of Operations

Monomial

Factors

Coefficient

Laws of Exponents

Zero Exponent

Negative Exponent

Scientific Notation

Base 10

Place Value

Non-perfect squares

Perfect Cubes

Non-Perfect Cubes

Roots

Principle Root

Density Property

equivalence

terms

like terms

null set

empty set

identity equation

all solutions

no solutions

set

multiplicative inverses

reciprocal

properties

distributive property

Check

Cartesian, coordinate plane

Intersection of number lines

Origin

abscissa

ordinate

coordinates

line

collinear points

slope

linear equation

slope intercept form of a linear equation

standard form of a linear equation

parallelism

Writing Assessment

Unit Assessment

Benchmark Assessment

IXL-technology informal assessment

Glencoe Course 3 Text 