Compare and Order Real Numbers

8th Grade Math Curriculum Map
Introduction
This document contains all mandated 2010 Arizona Mathematical Standards for 8th grade mathematics. The standards have been organized into
units and clusters. The units represent the major domain under which the identified standards fall. The cluster represents the collection of similar
concepts within the larger domain. Within these units and clusters the performance objectives have been sequenced to represent a logical progression
of the content knowledge. It is expected that all teachers follow the sequence of units and clusters as described in the following document.

Organization
Approximate Time
Approximate times are based on a 60-minute instructional session for grades 6-8. All units and clusters must be taught prior to the 2013 AIMS
assessment.

Essential Questions
Essential Questions are to be posed to the students at the beginning of the cluster and revisited throughout the cluster. They are designed to facilitate
conceptual development of the content and can be used as a tool for making connections, higher order thinking and inquiry. The students should be
able to answer these on their own by the end of the cluster.

Big Ideas
Big Ideas are the essential understandings that are critical for students’ learning. These are the enduring understandings we want students to carry
with them from grade level to grade level. Answering the Essential Questions is indicative of a student mastering the Big Idea, however they are not
always synonymous. Thus, in cases that the answer to the Essential Question does not include all components of the Big Idea, the Big Idea (for teacher
use) has been provided in italics.

Common Misconceptions
These are common misunderstandings students bring to the learning process. Being aware of such misconceptions allows us to plan for them during
instruction.

Content Standards and Mathematical Practices
This document has been organized by content standards and mathematical practices. The content standards are those that represent knowledge
specific to the mathematical standard (The five domains). The mathematical practices describe varieties of expertise that mathematics educators at
all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in
mathematics education. The content standards and mathematical standards have been paired to represent possible combinations of content standards
with mathematical practices. As described in the Arizona state standards, the content standards are not intended to be taught in isolation; thus, the
pairing of these standards provides a possible context for teaching these standards. Each time, the performance objective should be taught to a
deeper level of understanding and/or should be connected to the other standards in the cluster.

9/10/2012 1 Isaac Elementary School District

Common Core/Cross Curricular
The standards in the Common Core/Cross Curricular column represent possible reading, writing, math and language standards that can be reinforced
or taught through the mathematical content standards with which they are paired.

Priority
With input from grade level teachers, standards have been prioritized in two ways. The content standards have been prioritized using a three-point
scale. Essential standards represent those that are heavily weighted on state/national exams, foundational, and/or applicable in multiple contexts.
Important standards are those that are applicable in many contexts and less heavily weighted on state/national exams. Useful standards are those
with the least weight on state/national exams and are likely only useful in a specific context. This is denoted in the priority column with the codes E
(essential), I (important) and U (useful). This label applies to the content standards only. The skill/process standards that are a priority for this
grade level are highlighted in blue and are expected to be mastered at this grade level.

Key Vocabulary
The key vocabulary that should be taught for each of the performance objectives is listed under key vocabulary. These vocabulary words are coded
as tier one (1), tier two (2) or tier three (3). Tier one words are those that are very common and should not be explicitly taught. Tier two words are
high utility words that can be used across content areas or contexts. Tier three words are content specific words.

Resources
The two types of resources listed are the Web Resources resources and the Core Resources. All are suggestions that teachers may use to support
instruction. They are aligned to the standards listed in the same row. The web resources are useful Internet links that can be used for the teacher’s
edification prior to instruction or as a tool during instruction. The core resources are suggested pages from the adopted texts.

Unit/Cluster Project
The Unit/Cluster Projects are possible projects that teachers can use to support students in making connections, critical thinking, higher order thinking,
and/or spiraling curriculum. Unit projects support standards from all clusters within a unit while cluster project support the standards in a particular
cluster. While it is not required that a teacher do a project with every unit or cluster these resources will support project-based instruction and
practice should the teacher choose to implement them.

Assessment
The assessment section of the map has been left blank for teachers to plan the dates that they will give a formative assessment for the cluster. It is
expected that each cluster be assessed using a common formative assessment.

Other
Standards may appear more than once. Each time they should be taught within the context of the cluster and/or revisited to a deeper level of
knowledge. Underlined segments of a standard indicate an additional piece of the standard that was likely not covered in previous clusters.
[Brackets] will occasionally appear though out the document and indicate clarification of the Standard. Bracketed information is not a part of the
standard itself.


Unit: Number Sense
Cluster: The Real Number System

Approximate Time: 1week
Essential Questions Big Ideas

 What are real numbers?  Real numbers are classified as either rational or irrational

numbers.

 What is a rational number and irrational number?  Rational numbers include all integers and non-integers (decimal

numbers) that either repeat or terminate.

 How do we compare and order real numbers?  Irrational numbers can be estimated to the nearest integer or to

a given place value to increase accuracy of the approximation.


Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources
Practices Curricular Web Resources Core
*S1C1PO1 Compare and order real Ascending order MC: Lesson 2-2
numbers including very large and Descending order
small integers and decimals and Counting number
fractions close to zero. Integers
Natural number
Real number
Whole number
*S1C1PO4 Model and solve Absolute value MC: Lesson 1-3
problems involving absolute value.

8.NS.1. Know that numbers that are 8.MP.2 8.EE.4 Approximate KA: Converting-
not rational are called irrational. 8.MP.6 8.EE.7b Estimation repeating-decimals-to-
Understand informally that every 8.MP.7 6-8.RST.4 Exponents fractions-1
number has a decimal expansion; for 6-8.RST .7 Irrational numbers
rational numbers show that the Iterative KA: Converting-
decimal expansion repeats Order repeating-decimals-to-
eventually, and convert a decimal Rational numbers fractions-2
expansion which repeats eventually Real numbers
into a rational number. Scientific notation
Square
Square root
Standard notation
8.NS.2. Use rational approximations 8.MP.2 8.G.7 Decimal KA: Estimating Square
of irrational numbers to compare the 8.MP.4 8.G.8 Fraction Roots to the Hundredths
size of irrational numbers, locate 8.MP.7 6-8.RST.5 Non-Perfect Square
them approximately on a number 8.MP.8 ET08-S1C2-01 Percent
line diagram, and estimate the value Perfect Square
of expressions (e.g., π2). For Pi
example, by truncating the decimal Repeating Decimal
expansion of √2, show that √2 is Repetend
between 1and 2, then between 1.4 Terminating Decimal
and 1.5, and explain how to continue Truncate
on to get better approximations
Unit
Project:

Assessment:



Unit: Number Sense
Cluster: Numerical Operations

Approximate Time: 1 week

 Describe how multiplying or dividing a number by less than  Estimate, compute, determine reasonable answers.

one affects the number?

 Choose real numbers to solve problems, radical, decimal, fraction, and percents.



*S1C2PO1 Solve problems with Composite number
factors, multiples, divisibility or Factor
remainders, prime numbers and Multiple
composite numbers. Divisible
Remainder
Prime number
*S1C2PO2 Describe the effect of Divide
multiplying and dividing a rational Dividend
number by: Divisor
 A number less than zero Factor
 A number between zero and one Multiply
 One Product
Quotient
 A number greater than one Rational number
*S1C2PO5 Simplify numerical Absolute value
expressions using the order of Cube root
operations that include grouping Evaluate
symbols, square roots, cube roots, Exponents
absolute values and positive Grouping symbols
exponents. Numerical
expressions
Order of operations
Radican
Simplify
Square root
*S5C1PO1 Create an algorithm to MC: Lesson 1-7
solve problems involving indirect
measurements, using proportional MC: Lesson 8-3
reasoning, dimensional analysis and
the concepts of density and rate.
Unit
Project:

Assessment:



Unit: Expressions & Equations
Cluster: Exponents and Radicals

Approximate Time: 1.5 week

 How do I evaluate an expression?  To evaluate an expression substitute in values for

given variables and follow order of operations.

 When do we use the laws of exponents?  Laws of exponents are utilized to simplify expressions

when base numbers or variables are the same.

 What are the laws of exponents?  There are three laws of exponents: product property,

the quotient property and the power property.

 How do exponents and radicals relate to one another?  Exponents and radicals are inverse operations.


*S3C3PO2 Evaluate an expression Expression MC: Lesson 1-2
containing variables by substituting Rational number
rational numbers for the variables. Substitute
Variable
8.EE.1. Know and apply the 8.MP.2 Equivalent KA: Exponent Rules Power MC: Lesson 2-9
properties of integer exponents to 8.MP.5 Evaluate to a Power
generate equivalent numerical 8.MP.6 Exponents
expressions. For example, 3 ×3 =3–
2 –5
8.MP.7 Integers KA: Exponent Rules 2
3 = 1/33 = 1/27 Numerical expression
Rational numbers
8.EE.2. Use square root and cube 8.MP.2 8.G.7 Coefficient MC: Lesson 3-1
root symbols to represent solutions to 8.MP.5 8.G.8 Constant
2
equations of the form x = p and x =
3
8.MP.6 6-8.RST.4 Cube root MC: Lesson 3-2
p, where p is a positive rational 8.MP.7 Equation
number. Evaluate square roots of Evaluate
small perfect squares and cube roots Irrational number
of small perfect cubes. Know that √2 Perfect cube
is irrational. Perfect square
Simpliest form
Simplified expression
Solution
Square root
Rational number
Unit
Project:

Assessment:



Unit: Expression and Equations
Cluster: Scientific Notation


 What is scientific notation used for?  Scientific notation is how we express the value of very large or

very small numbers.

 How do we use scientific notation to express equivalent forms of  We can convert standard notation to scientific notation and visa

rational numbers? versa.


8.EE.3. Use numbers expressed in the 8.MP.2 Base MC: Lesson 2-10
form of a single digit times an 8.MP.5 Coefficient
integer power of 10 to estimate 8.MP.6 Convert
very large or very small quantities, Estimate
and to express how many times as Mathematical
much one is than the other. For operations
example, estimate the population of Negative Exponent
8
the United States as 3×10 and the Positive Exponent
population of the world as 7×10 and Power of 10
determine that the world populations Scientific Notation
is more than 20 times larger. Standard Notation

8.EE.4. Perform operations with 8.MP.2 8.NS.1 Base
numbers expressed in scientific 8.MP.5 8.EE.1 Coefficient
notation, including problems where 8.MP.6 ET08-S6C1-03 Convert
both decimal and scientific notation Estimate
are used. Use scientific notation and Mathematical
choose units of appropriate size for operations
measurements of very large or very Negative Exponent
small quantities (e.g., use millimeters Positive Exponent
per year for seafloor spreading). Power of 10
Interpret scientific notation that has Scientific Notation
been generated by technology. Standard Notation

Unit
Project:

Assessment:



Cluster: Solving Linear Equations and Graphing Inequalities

Approximate Time: 3 weeks

 How can we use equations to represent real life sitautions?  Algebraic equations, inequalities, and graphs are

representative of real life situations.

 What are the different ways that linear equations can be expressed?  Linear equations can be expressed as a graph, an

equation, or a table of values.


*S4C4PO2 Solve geometric Cross Multiply
problems using ratios and Equivalence
proportions. Equations
Ratio
Proportions
*S3C4PO2 Solve problems involving Equation
simple interest rates. Principal
Rate
Simple interest
*S1C2PO3 Solve problems involving Interest rate KA: Finding Unit Rates
percent increase, percent decrease Mark down
and simple interest rates. Mark up KA: Solving Percent
Percent change Problems
Profit
Simple interest KA: Finding Unit Price
Tax
Tip KA: Solving Percent
Problems 2

KA: Finding a Percent of
a Number

8.EE.7 Solve linear equations in one 8.MP.2 8.F.3 Algebraic Expression KA: Solving equations MC: Lesson 1-9
variable. 8.MP.5 8.NS.1 Balance with variables on both
8.MP.6 6-8.RST Coefficient sides.
a. Give examples of linear 8.MP.7 ET08-S1C3-01 Combine Like Terms MC: Lesson1-10
equations in one variable with one Constant KA: Solving two step
solution, infinitely many solutions, or Distributive property equations
no solutions. Show which of these Equation MC: Lesson 8-1:
possibilities is the case successively Equivalent Simplifying
transforming the given equation into Inverse operations expressions
simpler forms, until an equivalent Isolate
equation of the form x = a, a = a, Like Terms
or a = b results (where a and b are Linear equations MC: Lesson 8-2:
different numbers). Multi-Step equation Two Step Equations
Non-Linear
b. Solve linear equations with Solution
rational number coefficients, Term MC: Lesson 8-4:
including equations whose solutions Equations with
require expanding expressions using variables on both
the distributive property and sides
collecting like terms.


*S3C3PO5 Graph an inequality on Coefficient KA: Graphing
a number line. Greater than (>) inequalities number line
Greater than or
equal (>)
Inequality
Isolate
Less than (<)
Less than or equal (<)
Number line
Variable
Unit
Project:

Assessment:



Unit: Geometry
Cluster: Pythagorean Theorem


 How do we apply the Pythagorean Theorem to calculate the distance of a  The Pythagorean Theorem can be used to calculate

line segment? the distance between two points.

 The Pythagorean Theorem can be used to find the

distance between two points in two-dimensional

figures and three-dimensional objects.

 How can the Pythagorean Theorem be applied to triangles?  The Pythagorean Theorem can be used to find the

missing side of a right triangle

 What is a Pythagorean Triple?  A Pythagorean Triple is set of three positive integers

that satisfy the Pythagorean Theorem.


8.G.6 Explain a proof of the 8.MP.3 6-8.WHST.2a-f Approximation KA: Introduction to the
Pythagorean Theorem and its 8.MP.4 ET08-S1C2-01 Base Pythagorean Theorem
converse. 8.MP.6 Converse
8.MP.7 Equaation
Exponents
Hypotenuse
Irrational number
Isolate
Leg
Pythagorean triples
Right triangle
Square root
Substituation
8.G.7 Apply the Pythagorean 8.MP.1 8.NS.2 Coordinate Plane KA: Pythagorean MC: Lesson 3-5, 3-
Theorem to determine unknown side 8.MP.2 ET08-S2C2-01 Equation Theorem Example 6
lengths in right triangles in real- 8.MP.4 Hypotenuse
world and mathematical problems in 8.MP.5 Inverse Operations KA: More
two and three dimensions. 8.MP.6 Isolate Pythagorean Theorem
8.MP.7 Leg Examples
Perfect Square
Pythagorean triples
Radical Sign
Radican
Right triangle
Square Root
Square root
Substituation
Three-dimension object
Two-dimensions object
8.G.8 Apply the Pythagorean 8.MP.1 8.NS.2 Converse KA: Midpoint Formula MC: Lesson 3-7
Theorem to find the distance 8.MP.2 ET08-S6C1-03 Coordinate plan
between two points in a coordinate 8.MP.4 Distance
system. 8.MP.5 Midpoint
8.MP.6 Origin
8.MP.7 Pythagorean triples
Quadrants
Right triangle
Slope
*S4C3P01: Make and test a Midpoint
conjecture about how to find the Coordinate plane
midpoint between any two points in Origin
the coordinate plane. Quadrants
Conjecture


Unit
Project:

Assessment:



Unit: Expressions and Equations
Cluster: Graphing linear equations


 How do we use linear equations in real life?  We use linear equations to represent a situation and

the situation can be expressed graphically, as a table

of values, or as an equation.

 What is slope?  Slope (m) is a change in the independent variable. In

math, it can be recognized as rise/run or .

 What are the four types of slope?  We recognize the slope by examing the relationship

between the independent and dependent variable.

 How do we use slope to make arguments?  We can use slope to make conjectures about

geometric figures as well as similarity of equations.


8.EE.5. Graph proportional 8.MP.1 8.F.2 Negative slope KA: Plotting Ordered
relationships, interpreting the unit 8.MP.2 8.F.3 Non-Linear Pairs
rate as the slope of the graph. 8.MP.3 6-8.RST.7 Origin
Compare two different proportional 8.MP.4 6- 8.WHST.2b Positive slope
relationships represented in different 8.MP.5 SC08-S5C2-01 Proportion
ways. For example, compare a 8.MP.6 SC08-S5C2-05 Proportional
distance-time graph to a distance-time 8.MP.7 relationships
equation to determine which of two 8.MP.8 Quadrants
moving objects has greater speed. Rate of change
Simpliest form
Slope-Intercept form
Solution
Term
Undefined slope
X-Intercept
Y-intercept
Zero Slope
8.EE.6. Use similar triangles to 8.MP.2 8.F.3; 8.G.4 Coordinate plane
explain why the slope m is the same 8.MP.3 6-8.RST.3 Equivalence
between any two distinct points on a 8.MP.4 6-8.WHST.1b Orgin
non-vertical line in the coordinate 8.MP.5 ET08-S1C2-01 Quadrant
plane; derive the equation y = mx 8.MP.7 ET08-S6C1-03 Rate of change
for a line through the origin and the 8.MP.8 Similar triangles
equation y = mx + b for a line Slope
intercepting the vertical axis at b. Slope-Intercept form
X-intercept
Y-intercept

Unit
Project:

Assessment:



Unit: Functions
Cluster: Evaluating Functions


 What is a function? How do you tell if a graph represents a function?  A function is a relationship between variables where

each X (input) has exactly one Y (output). We can

determine whether a graph is a function by using the

vertical line test.

 What are the different ways to represent a function?  A function can be represented with a table, a graph,

a verbal description, or an equation.

 How can functions be used to serve real world problems?  A function can be utilized to make conjectures about

predicted outcomes.


8.F.1 Understand that a function is a rule 8.MP.1 SC08-S5C2-05 Function KA: Testing if a MC: Lesson 9-2:
that assigns to each input exactly one 8.MP.2 Function table relationship is a function Functions
output. The graph of a function is the set of 8.MP.6 Input
ordered pairs consisting of an input and the Ordered pair KA: Graphical Relations
corresponding output (Function notation is Origin and Functions MC: Lesson 9-3:
not required in Grade 8). Output Graphing
Slope PM: Determining if a functions
X-Intercept relationship is a function
Y-Intercept
8.F.3 Interpret the equation y = mx + b as 8.MP.2 8.EE.5; 8.EE.7a Function KA: Graphing a line in MC: Lesson 10-1:
defining a linear function, whose graph is a 8.MP.4 6-8.WHST.1b Interpret slope intercept form Linear &
straight line; give examples of functions that 8.MP.5 ET08-S6C1-03 Linear functions Nonlinear
are not linear. For example, the function A = 8.MP.6 Non-linear functions Functions
2
s giving the area of a square as a function of 8.MP.7 Ordered pair
its side length is not linear because its graph Origin
contains the points (1,1), (2,4) and (3,9), Quadrant
which are not on a straight line. Rate of change
Slope
8.F.2 Compare properties of two functions 8.MP.1 8.EE.5; 8.F.2 Algebraic expression
each represented in a different way 8.MP.2 6-8.RST.7 Domain
(algebraically, graphically, numerically in 8.MP.3 6-8.WHST.1b Function
tables, or by verbal descriptions). For 8.MP.4 ET08-S1C3-01 Function table
example, given a linear function represented 8.MP.5 Linear equation
by a table of values and a linear function 8.MP.6 Linear function
represented by an algebraic expression, 8.MP.7 Non-Linear function
determine which function has the greater rate 8.MP.8 Point-Slope form
of change. Proportional
Quadratic function
Range
Rate of change
Standard form
8.F.4. Construct a function to model a linear 8.MP.1 8.EE.5 Function
relationship between two quantities. 8.MP.2 8.SP2 Function table
Determine the rate of change and initial 8.MP.3 8.SP.3 Initial value
value of the function from a description of a 8.MP.4 ET08-S1C2-01 Intercept
relationship or from two (x, y) values, 8.MP.5 SC08-S5C2-01 Interpret
including reading these from a table or 8.MP.6 SC08-S1C3-02 Linear relationship
from a graph. Interpret the rate of change 8.MP.7 Ordered pair
and initial value of a linear function in terms 8.MP.8 Origin
of the situation it models, and in terms of its Quadrant
graph or a table of values. Rate of change
Slope

8.F.5. Describe qualitatively the functional 8.MP.2 6-8.WHST.2a-f Analyzing MC: Lesson 9-6:
relationship between two quantities by 8.MP.3 ET08-S1C2-01 Decreasing Graphing in
analyzing a graph (e.g., where the function 8.MP.4 SC08-S5C2-05 Function slope-intercept
is increasing or decreasing, linear or 8.MP.5 Increasing form
nonlinear). Sketch a graph that exhibits the 8.MP.6 Linear relationship
qualitative features of a function that has 8.MP.7 Nonlinear
been described verbally. relationship
Qualitative
8.SP.3. Use the equation of a linear model 8.MP.2 8.EE.5 Bivariate MC: Lesson 9-4:
to solve problems in the context of bivariate 8.MP.4 8.F.3 measurement Slope
measurement data, interpreting the slope 8.MP.5 8.F.4 Equation
and intercept. For example, in a linear model 8.MP.6 ET08-S1C3-03 Interpreting
for a biology experiment, interpret a slope of 8.MP.7 ET08-S2C2-01 Linear nmodel MC: Extend 9-5
1.5 cm/hr as meaning that an additional hour Slope
of sunlight each day is associated with an Y-Intercept
additional 1.5 cm in mature plant height.
Unit
Project:

Assessment:



Cluster: System of Equations


 What is a system of equations?  A system of equations is a collection of equations who

are utilizing the same variables—we use systems of

equations to find a solution whose answer will satisfy

each condition.

 What are the ways to solve systems of equations?  There are three methods for solving system of

equations: Graphing, Substitution and Elimination.


8.EE.8. Analyze and solve pairs of 8.MP.1 6-8.RST.7 Coefficient KA: Graphing system of MC: Lesson 9-7:
simultaneous linear equations. 8.MP.2 ET08-S1C2-01 Consistent equations word Solving by
8.MP.3 ET08-S1C2-02 Dependent problems graphing
a. Understand that solutions to a 8.MP.4 Elimination
system of two linear equations in two 8.MP.5 Substitution KA:
variables correspond to points of 8.MP.6 Graphing Systems of equations:
intersection of their graphs, because 8.MP.7 Equations determining number of
points of intersection satisfy both 8.MP.8 Function Table solutions
equations simultaneously. Graph
Inconsistent
b. Solve systems of two linear Independent
equations in two variables Infinite solutions
algebraically, and estimate solutions Intersect
by graphing the equations. Solve Linear equation
simple cases by inspection. For Linear function
example, 3x + 2y = 5 and 3x + 2y No solution
= 6 have no solution because 3x + Ordered pair
2y cannot simultaneously be 5 and 6. Proportional
Simultaneous
c. Solve real-world and Slope
mathematical problems leading to Slope-Intercept form
two linear equations in two Solution
variables. For example, given Standard form
coordinates for two pairs of points, Variable
determine whether the line through the X-intercept
first pair of points intersects the line Y-intercept
through the second pair.

Unit
Project:

Assessment:



Unit: Geometry
Cluster: Surface Area & Volume

Approximate Time: 1.5 weeks

 What is volume?  Volume is the amount of 3 dimensional space inside an

object (length x width x height)

 What is the difference between volume and surface area?  Volume is labeled with units cubed and surface area is

labeled in units squared.

 Composite shapes can be decomposed into several

different figures (such as circles or any polygon).


*S4C1PO1 Identify the attributes of Central Angle
circles: radius, diameter, chords, Chord
tangents, secants, inscribed angles, Circumference
central angles, intercepted arcs, Diameter
circumference, and area. Inscribed Angle
Intercepted Arc
Major Arc
Minor Arc
Pi
Radius
Secant
Tangent
*S4C4PO3 Calculate the surface Cylinder MC: Lesson 7-7, 7-
area and volume of rectangular Diameter 8: Surface Area
prisms, right triangular prisms and Edge
cylinders. Face
Lateral Surface Area
Net
Pi
Radius
Rectangular Prism
Right Triangle
Surface Area
Triangular prism
Vertex
Volume
*S4C4PO2 Predict results of Area
combining, subdividing, and Composite shapes
changing shapes of plane figures Diameter
and solids. Pi
Plane figures
Radius
Solids
8.G.9. Know the formulas for the 8.MP.1 6-8.RST.3 Base KA: Volume of a sphere MC: Lesson 7-5:
volumes of cones, cylinders, and 8.MP.2 6-8.RST.7 Combine Volume of Cylinder
spheres and use them to solve real- 8.MP.3 ET08-S2C2-01 Cones KA:
world and mathematical problems. 8.MP.4 ET08-S1C4-01 Edge Volume of a cylinder
8.MP.5 Face MC: Lesson 7-6:
8.MP.6 Height Volume of Cone
8.MP.7 Pi
8.MP.8 Radius
Sphere
Volume
Vertex

Unit
Project:

Assessment:



Unit: Geometry
Cluster: Congruence, Similarity and Transformations


 What is the difference between similarity and congruence?  When two figures have the same shape and same

dimensions, they are congruent. When two figures

have the same shape, but different dimensions, they

are similar.

 What are the different types of geometric transformations?  Congruent transformations will never change a shape’s

dimensions. There are congruent transformations

(reflection, rotations, translations) and similar

transformations (dilations).


8.G.2. Understand that a two- 8.MP.2 6-8.WHST.2b,f Congruency KA: Congruent Triangles MC: Lesson 6-4
dimensional figure is congruent to 8.MP.4 ET08-S6C1-03 Congurent figures
another if the second can be 8.MP.6 Coordinate Plane
obtained from the first by a 8.MP.7 Ordered pairs
sequence of rotations, reflections, Origin
and translations; given two Quadrants
congruent figures, describe a Reflections
sequence that exhibits the Rotations
congruence between them. Sequence
Translations
Two-dimensional
figure
8.G.3. Describe the effect of 8.MP.3 6-8.WHST.2b,f Coordinate Plane MC: Lesson 4-7, 4-
dilations, translations, rotations, and 8.MP.4 ET08-S6C1-03 Dilations 8: Similarity
reflections on two-dimensional 8.MP.5 Ordered pairs
figures using coordinates. 8.MP.6 Origin MC: Lesson 6-6:
8.MP.7 Quadrants Reflections
Reflections
Rotations
Translations MC: Lesson 6-7:
Two-dimensional Translations
figure
8.G.1. Verify experimentally the 8.MP.4 Angle
properties of rotations, reflections, 8.MP.5 Line segment
and translations: 8.MP.6 Parallel lines
8.MP.7 Quadrant
a. Lines are taken to lines, and line 8.MP.8 Reflection
segments to line segments of the Rotation
same length. Transformations
Translation
b. Angles are taken to angles of the Verify
same measure.

c. Parallel lines are taken to parallel
lines.
8.G.4. Understand that a two- 8.MP.2 8.EE.6 Coordinate plane KA: Similar Triangles
dimensional figure is similar to 8.MP.4 6-8.WHST.2b,f Dilations
another if the second can be 8.MP.5 ET08-S6C1-03 Orgin
obtained from the first by a 8.MP.6 ET08-S1C1-01 Quadrants
sequence of rotations, reflections, 8.MP.7 Reflections
translations, and dilations; given two Rotaitons
similar two-dimensional figures, Sequence
describe a sequence that exhibits the Similar figures
similarity between them. Transformation

Translations
Two-dimensional

*S4C2PO3 Identify lines of Lines of symmetry
symmetry in plane figures or classify Reflective symmetry
types or symmetries of 2 dimensional Rotational symmetry
figures. Line of feflection
Unit
Project:

Assessment:



Unit: Geometry
Cluster: Geometric arguments

Approximate Time: 1.5 weeks

 What are the types of angle relationships?  The types of angle relationships are vertical,

complementary, supplementary, alternate interior,

alternate exterior, corresponding.

 How can you use angle relationships to solve real world problems?  Once you have one or more pieces of information

about an angle relationship, you can deduce an

unknown angle measure.


8.G.5. Use informal arguments to 8.MP.3 6-8.WHST.2b,f Alternate exterior KA: Finding Missing
establish facts about the angle sum 8.MP.4 6-8.WHST.1b Alternate interior Angles
and exterior angle of triangles, 8.MP.5 ET08-S6C1-03 Angle
about the angles created when 8.MP.6 ET08-S1C1-01 Complementary KA: Angles of Parallel
parallel lines are cut by a 8.MP.7 ET08-S1C3-03 Congruent Lines
transversal, and the angle-angle Corresponding angle
criterion for similarity of triangles. Equation KA: Angles Formed
For example, arrange three copies of Exterior When a Transversal
the same triangle so that the sum of Interior Intersects a Parallel Line
the three angles appears to form a Parallel lines
line, and give an argument in terms of Similar triangles KA: Angles Formed
transversals why this is so. Supplementary Between Transversals
Transversal and Parallel Lines
Triangle
Vertical angles KA: Angles at the
Intersection of Two Lines

KA: Finding Angles in a
Triangle with Exterior
Angles

KA: Finding Angles in a
Triangle

Unit
Project:

Assessment:



Unit: Statistics & Probability
Cluster: Compound Probabilities and Combinations


 How does understanding probability help us to make informed predictions?  The more trial an experiment conducts the closer the

experimental probability and the theoretical

probabily become.

 Probability ranges from 0 to 1 or impossible to

certain.

 Probability can be expressed as a decimal, percent,

or a fraction.

 What is the difference between a permutation and a combinations?  If the order of an arrangement matters, it is a

permutation. If the order of an arraggement does not

matter it is a combination. In other words, a

permutation is an ordered combination.


*S2C2PO1 Determine theoretical Compound events
and experimental conditional Conditional
probabilities in compound prodbability
probabilities in compound Dependent events
probability experiments. Experimental
probability
Favorable outcome
Independent events
Mutually exclusive
Possible outcome
Sample space
Theoretical
probability
*S2C2PO2 Interpret probabilities Experimental
within a given context and compare probability
the outcome of an experiment to the Outcome
predictions made prior to Prediction
performing the experiment. Theoretical
probabilithy

*S2C2PO3 Use all possible Dependent events
outcomes (sample space) to Independent events
determine the probability of Possible outcomes
dependent and independent events. Probability
Sample Space
Tree diagram
*S2C3PO1 Represent, analyze and Combinations
solve counting problems with or Factorial noation
without ordering and repetitions. Fundamental counting
principle
Permutations
*S2C3PO2 Solve counting problems Combinations
and represent counting principles Factorial notation
algebraically including factorial Permutations
notation.
Unit
Project:

Assessment:



Cluster: Graphical Displays of Data

Approximate Time: Two weeks

 At what benchmarks do associations become strong and very strong  Scatter plots are used to show the assocations

associations? between two variables (independent variable and the

 How can different data representations be used to manipulate data? dependent variable).

 Associations can be seen in bivariate categorical data

by displaying frequency in a two-way table.

 Directed graphs are created to represent the

reletionship between items.


8.SP.1. Construct and interpret 8.MP.2 6-8.WHST.2b,f Bivariate MC: Lesson 9-9:
scatter plots for bivariate 8.MP.4 ET08-S1C3-01 measurement data Interpreting scatter
measurement data to investigate 8.MP.5 ET08-S1C3-02 Clusters plots/line of fit
patterns of association between two 8.MP.6 ET08-S6C1-03 Correlation
quantities. Describe patterns such as 8.MP.7 SS08-S4C1-01 Frequency
clustering, outliers, positive or SS08-S4C2-03 Intervals
negative association, linear SS08-S4C1-05 Line of best fit
association, and nonlinear SC08-S1C3-02 Linear association
association. SC08-S1C3-03 Mesaures of central
tendency
Negative assocation
No association
Nonlinear assocation
Outliers
Positive association
Scatter plot
8.SP.2. Know that straight lines are 8.MP.2 8.EE.5 Dependent variable
widely used to model relationships 8.MP.4 8.F.3 Independent variable
between two quantitative variables. 8.MP.5 ET08-S1C3-01 Line of best fit
For scatter plots that suggest a 8.MP.6 ET08-S6C1-03 Linear relationship
linear association, informally fit a 8.MP.7 SS08-S4C1-05 Negative association
straight line, and informally assess No association
the model fit by judging the Nonlinear relationship
closeness of the data points to the Positive association
line. Scatter plots
8.SP.4. Understand that patterns of 8.MP.2 6-8.WHST.2b,f Associations
association can also be seen in 8.MP.3 ET08-S1C1-01 Bivariate categorical
bivariate categorical data by 8.MP.4 ET08-S1C3-02 data
displaying frequencies and relative 8.MP.5 ET08-S1C3-03 Dependent variable
frequencies in a two-way table. 8.MP.6 SS08-S4C2-03 Independent variable
Construct and interpret a two-way 8.MP.7 SS08-S4C1-05 Line of best fit
table summarizing data on two SC08-S1C3-02 Linear relationship
categorical variables collected from Negative association
the same subjects. Use relative No association
frequencies calculated for rows or Nonlinear relationship
columns to describe possible Positive association
association between the two Scatter plots
variables. For example, collect data Summaring
from students in your class on whether Variables
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?

*S2C1PO1Solve problems by Box and whisker plot
selecting, constructing, interpreting, Dependent variable
and calculating with displays of First quartile
data, including box and whicker Independent variable
plots and scatter plots. Inter-quartile range
Lower extreme
Median
Outliners
Quartiles
Range
Scatter plots
Stem and leaf plot
Third quartile
Upper extreme
*S2C4PO1 Use directed graphs to Directed graph
solve problems. Eulter circuit
Eulter path
Hamilton circuit
Hamilton path
Unit
Project:

Assessment:



Cluster: Evaluation of Experimental Design


 How can the design of a survey be biased?  The design of an experiment is important to obtain

accurate, reliable, and valid data.

 Why would someone want to design a biased survey?  Surveys can be biased or unbiased based on their

design.

 Data displays can be manipulated to avance an

argument or a particular view point.


*S2C1PO3 Describe how summary Extreme values
statistics relate to the shape of the Interquartile range
distribution. Mean
Median
Mode
Outliers
Quartiles
Range
*S2C1PO4 Determine whether Bar graphs
information is represented Box and whisker plot
effectively and appropriately given Circle graph
a graph or a set of data by Frequency
identifying sources of bias and Histrogram
compare and contrast the Line graph
effectiveness of different Multi-bar graphs
representations of data. Multi-line graphs
Pictographs
Scatter plot
Stem and leaf plot
Tally charts
*S2C1PO5 Evaluate the design of Biased
an experiment. Experimental design
Random sampling
Sample
Surveys
Unbiased
Unit
Project:

Assessment:


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