Grade 8 Mathematics Curriculum Pacing Guide 2018-2019...Grade 8 Mathematics – Curriculum Pacing Guide – 2018-2019 Anderson School District Two Page 5 2018-2019 Unit 2 – Rational

Grade 8 Mathematics – Curriculum Pacing Guide – 2018-2019

Anderson School District Two Page 1 2018-2019

Math 8 Pacing

Quarter Unit # Topic # of Days

1 1 Integer Review and Matrices 7

2 Rational and Irrational Numbers 11

3 Integer Exponents 9

4 Scientific Notation 7

5 Proportional Relationships, Lines, and Linear Equations 15

2 6 Linear Functions 15

7 Linear Equations in One Variable 14

8 Linear Inequalities in One Variable 8

9 Volume and Surface Area 7

3 10 Reasoning in Geometry 8

11 Congruence 14

12 Similarity 14



13 Using the Pythagorean Theorem 7

4 14 Scatterplots 5

15 Analyzing Categorical Data 14

16 Systems of 2 Linear Equations 15

SC Ready Review

Unit 1 – Integer Review and Matrices (7 days) 8.DSP.5 Organize data in matrices with rational numbers and apply to real-world and mathematical situations. 8.DSP.5a Understand that a matrix is a way to organize data.

8.DSP.5b Recognize that a m x n matrix has m rows and n columns. 8.DSP.5c Add and subtract matrices of the same size. 8.DSP.5d Multiply a matrix by a scalar.

Unit 1 – Integer Review and Matrices (7 days)

Essential Tasks/Key Concepts Learning Targets Resources (Suggested Activities)

MDC Formative Assessment Lessons

● Organize data in matrices

(using rational numbers) in both mathematical and real world contexts

➢ Identify dimensions of

matrices

➢ Use matrix vocabulary of element, row,

column

I can organize data into matrices using rational numbers in both mathematical and real world

context. I can identify dimensions, element,

row and column in a matrix

● Slides (last slide has links

to Khan Academy videos

and exercises)

● Khan Academy

● https://www.khanacademy.org/math/algebra2/alg2-matrices/basic-matrix-operations-

alg2/v/introduction-to-the-

https://docs.google.com/presentation/d/11T0oAKsjo5c8ltR8o9DPk5599vPsCQnicuUQS90248s/copy




https://www.khanacademy.org/math/precalculus/precalc-matrices

https://www.khanacademy.org/math/algebra2/alg2-matrices/basic-matrix-operations-alg2/v/introduction-to-the-matrix







matrix

● Add matrices I can add matrices of the same

size.

● http://www.mathworksheets4kids.com/matrices/add-

sub.html ● http://www.virtualnerd.com/al

gebra-2/matrices/add-example.php

● Subtract matrices I can subtract matrices of the same

size.

● http://www.mathworksheets4kids.com/matrices/add-sub.html

● http://www.virtualnerd.com/algebra-2/matrices/subtract.php

● Scalar multiplication I can multiply a matrix by a scalar.

● https://www.khanacademy.org/math/algebra2/alg2-

matrices/basic-matrix-operations-alg2/e/scalar_matrix_multiplic

ation ● http://www.virtualnerd.com/al

gebra-2/matrices/scalar-multiply-example.php

● Use matrices as a vehicle to

review the integer operations

I can use integer operations to add, subtract, and multiply

matrices.

● http://amby.com/educate/math/integer.html

● https://quizlet.com/6952820/integer-operation-rules-flash-

cards/ ● http://www.math-

drills.com/integers.shtml

Unit Review and Test

● Matrix Activity ● Matrices Quiz


http://www.mathworksheets4kids.com/matrices/add-sub.html



http://www.virtualnerd.com/algebra-2/matrices/add-example.php






http://www.virtualnerd.com/algebra-2/matrices/subtract.php

http://www.virtualnerd.com/algebra-2/matrices/subtract.php

https://www.khanacademy.org/math/algebra2/alg2-matrices/basic-matrix-operations-alg2/e/scalar_matrix_multiplication






http://www.virtualnerd.com/algebra-2/matrices/scalar-multiply-example.php



http://amby.com/educate/math/integer.html

http://amby.com/educate/math/integer.html

https://quizlet.com/6952820/integer-operation-rules-flash-cards/



http://www.math-drills.com/integers.shtml

http://www.math-drills.com/integers.shtml

https://docs.google.com/document/d/1Hl6mpJifu1Dh1wHnpD8Aye2kbR8i2p4xFwTOMFRdYgE/copy

https://docs.google.com/document/d/1Agi--y1M5UfvUl0CEtgyePvQKhn9TEyj_DTYJAodpro/copy





Unit 2 – Rational and Irrational Numbers (11 days) 8.NS.1 Explore the real number system and its appropriate usage in real-world situations.

8.NS.1a Recognize the differences between rational and irrational numbers. 8.NS.1b Understand that all real numbers have a decimal expansion. 8.NS.1c Model the hierarchy of the real number system, including natural, whole, integer, rational, and irrational numbers.

8.NS.2 Estimate and compare the value of irrational numbers by plotting them on a number line. 8.NS.3 Extend prior knowledge to translate among multiple representations of rational numbers (fractions, decimal numbers, percentages).

Include the conversion of repeating decimal numbers to fractions.

Unit 2 – Rational and Irrational Numbers (11 days)



Classifying Numbers

● Convert fractions to decimals and decimals to fractions and compare. (prior knowledge)

● Be able to classify and give examples of integers, rational, irrational, whole, and natural numbers.

I can translate among multiple representations of rational numbers.

I can model the hierarchy of the real number system.

● iReady Lesson 3: Understand Rational and Irrational Numbers

● iReady Standards Mastery

● www.khanacademy.org/commoncore - 8.NS.1 – videos and exercises

FAL: Translating Between Repeating Decimals and Fractions

Expressing Rational Numbers with Decimal Expansions ● Express rational numbers

using decimal expansions that terminate in 0s or eventually repeat.

● Describe decimals that do and

do not terminate. ● Compare rational numbers by

using decimal expansions that

terminate in 0s or eventually repeat.

I can understand that all real numbers have a decimal

expansion.

● iReady Lesson 3: Understand

Rational and Irrational

Numbers ● iReady Standards Mastery ● www.khanacademy.org/comm

oncore - 8.NS.1 – videos and exercises

● Stress using a calculator to do the conversion vs. doing it by

hand.

http://www.khanacademy.org/commoncore


http://map.mathshell.org/lessons.php?unit=8105&collection=8







Exploring Irrational Numbers ● Apply and extend

understanding of rational numbers and decimal expansions to describe the characteristics of irrational

numbers. ● Describe irrational numbers. ● Apply and extend

understanding of decimal expansions to identify rational and irrational numbers.

● Apply and extend

understanding of rational numbers to identify rational and irrational numbers.

● Apply and extend understanding of rational numbers and decimal expansions to identify which

subset(s) of the real number system a number belongs to.

I can estimate and compare the value of of irrational numbers by plotting on a number line.


Rational and Irrational Numbers

● iReady Standards Mastery ● www.khanacademy.org/comm

oncore - 8.NS.1 – videos and exercises

Perfect Squares and Perfect Cubes ● Understand the meaning of

square and cube roots and understand that they represent rational and

irrational numbers. ● Understand the relationship

between area and square roots.

● Understand the relationship between volume and cube roots.

● Recall the perfect squares and cubes.

● Truncate decimal expansions

I can explain the meaning of square and cube and the inverse operations.


Rational and Irrational Numbers

● iReady Lesson 2: Square Roots and Cube Roots


oncore - 8.NS.1 – videos and

exercises







of irrational roots and cubes. ● Recall the value of pi and

know that this is an irrational number.

● Understand that every number on a number line is either

rational or irrational.

● Comparing rational and

irrational numbers using <, >,

≤, and ≥.

Approximating Irrational Numbers

● Estimate the value of an irrational number to the nearest integer.

● Estimate the value of an irrational number to the nearest tenth and/or hundredth.

● Estimate the value of an irrational number to solve real-world problems.

I can estimate irrational numbers.



Numbers ● iReady Lesson 2: Square

Roots and Cube Roots ● iReady Standards Mastery

● www.khanacademy.org/commoncore - 8.NS.2 – videos and exercises





Comparing and Ordering Rational and Irrational Numbers

● Compare and order rational and irrational numbers.

● Use rational approximations of irrational numbers to compare

the size of rational and irrational numbers and locate them approximately on a

number line diagram. ● Use rational approximations of

irrational numbers to order positive rational and irrational

numbers using a number line diagram.

● Use rational approximations of

irrational numbers to order positive and negative rational and irrational numbers using a number line diagram.

I can compare and order of rational and irrational numbers.



Numbers ● iReady Standards Mastery ● www.khanacademy.org/comm

oncore - 8.NS.2 – videos and

exercises






Unit 3 – Integer Exponents (9 days)

8.EEI.1 Understand and apply the laws of exponents (i.e. product rule, quotient rule, power to a power, product to a power,

quotient to a power, zero power property, negative exponents) to simplify numerical expressions that include integer exponents. 8.EEI.2 Investigate concepts of square and cube roots.

8.EEI.2a Find the exact and approximate solutions to equations of the form x2 = p and x3 = p where p is a positive rational

number. 8.EEI.2b Evaluate square roots of perfect squares.

8.EEI.2c Evaluate cube roots of perfect cubes. 8.EEI.2d Recognize that square roots of non-perfect squares are irrational.

Unit 3 – Integer Exponents (9 days)



Perfect Squares, Square Roots, and Equations of the form x2 = p (8.EEI.2) 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. Know

that the square root of 2 is irrational.

● Evaluate square

roots of small perfect squares (suggest knowing 1-15, 20 and 25 without a calculator).

● Apply knowledge

of square numbers to compare algebraic expressions involving exponents.

● Solve equations of

the form x2 = p, where p is a positive perfect square

I can use square roots symbols to represent solutions to equations of

the form x^2 = p, where p is a positive rational number.

● iReady Lesson 1: Properties of

Integer Exponents ● iReady Standards Mastery

● www.khanacademy.org/commoncore - 8.EEI.2 - videos and exercises

FAL: Applying Properties of

Exponents







rational number. ● Solve equations of

the form x2 = p, where p is a positive rational number but not a perfect square.

Perfect Cubes, Cube Roots, and Equations of the form x3 = p

(8.EE.2) ● Evaluate cube

roots of small perfect cubes (suggest knowing the first 6

without a calculator). ● Use area and

volume to compare square

numbers and cube numbers. ● Solve equations of

the form x3 = p, where p is a positive perfect cube rational

number. ● Solve equations of

the form x3 = p, where p is a

positive rational number but not a perfect cube.

I can use cube roots symbols to represent solutions to equations of

the form x^3 = p, where p is a positive rational number.

● iReady Lesson 2: Square Roots and Cube Roots


oncore - 8.EEI.2 - videos and exercises





Exponents and Multiplication (8.EEI.1)

● Describe and apply properties of exponents.

● Know and apply the product rule of exponents

with the same base to generate equivalent expressions.

● Know and apply the power to a power property to generate equivalent expressions.

● Know and apply the product to a power property to generate

equivalent expressions.

I can understand and apply the laws of exponents to simplify numerical expressions that include

integer exponents.


Integer Exponents ● iReady Standards Mastery ● www.khanacademy.org/comm

oncore - 8.EEI.1 – videos and exercises Activity for Exponent Rules

● Activity for Exponent Rules

Exponents and Division (8.EEI.1) ● Review dividing

common factors in a division problem.

● Know and apply the quotient rule of exponents

with the same base to generate equivalent expressions.

● Know and apply

the power of a quotient to a power equivalent expressions.

I can understand and apply the

laws of exponents to simplify numerical expressions that include integer exponents.



● www.khanacademy.org/commoncore - 8.EEI.1 – videos and exercises Activity for Exponent Rules




http://staff.rogersschools.net/modules/groups/homepagefiles/cms/1004854/File/8th%20Grade%20Teacher%20Resources/8th%20MATH%20Resources/Unit%204/unit%204%20grade%208.EE.1-Multiplying+Exponents.pdf?sessionid=932570ef7c6cbd4ede3f4fce5092a50c






Zero and Negative Exponents (8.EE.1)

● Use patterns to describe values of zero and negative exponents.

● Know and apply

the zero power property to generate equivalent expressions.

● Know and apply the negative exponent property to generate equivalent expressions.

● Know and apply the properties of integer exponents to classify

numerical expressions involving exponents.

I can understand and apply the laws of exponents to simplify

numerical expressions that include integer exponents.

● iReady Lesson 1: Properties of Integer Exponents


oncore - 8.EEI.1 – videos and exercises Activity for Exponent Rules


Comparing Expressions with

Exponents (8.EEI.1) ● Apply properties

of integer exponents to write different expressions.

● Know and apply the properties of integer exponents to write equivalent

numerical expressions involving exponents.

● Know and apply the properties of integer

exponents to compare numerical expressions involving exponents with the

same base. ● Know and apply

the properties of integer

I can apply the properties of

integer exponents to compare and rewrite expressions.








exponents to compare numerical expressions

involving exponents with different bases.




Unit 4 – Scientific Notation (7 days)

8.EEI.1 Understand and apply the laws of exponents (i.e. product rule, quotient rule, power to a power, product to a power,

quotient to a power, zero power property, negative exponents) to simplify numerical expressions that include integer exponents. 8.EEI.3 Explore the relationship between quantities in decimal and scientific notation.

8.EEI.3a Express very large and very small quantities in scientific notation in the form a x 10b = p where 1 ≤ a < 10 and b is an

integer. 8.EEI.3b Translate between decimal notation and scientific notation. 8.EEI.3c Estimate and compare the relative size of two quantities in scientific notation.

8.EEI.4 Apply the concepts of decimal and scientific notation to solve real-world and mathematical problems. 8.EEI.4a Multiply and divide numbers expressed in both decimal and scientific notation. 8.EEI.4b Select appropriate units of measure when representing answers in scientific notation.

8.EEI.4c Translate how different technological devices display numbers in scientific notation.

Unit 4 – Scientific Notation (7 days)

Essential Tasks/Key Concepts Learning Targets Resources (Suggested

Activities)

MDC Formative Assessment

Lessons

Exploring Scientific Notation (8.EEI.3, 8.EEI.4)

● Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very

large or very small quantities. ● Translate how

different technological devices

display numbers in scientific notation.

● Compare and order numbers expressed in

decimal notation and scientific notation.

● Recognize

numbers that are expressed in scientific notation.

I can express very large and very small quantities in scientific notation in the form a X 10b = p

where 1< a < 10 and b is an integer.

I can estimate and compare the relative size of two quantities in scientific notation.

● iReady Lesson 4: Scientific

Notation


FAL: Estimating Length Using

Scientific Notation





● Understand how multiplying by a power of 10

affects the values of numbers.

Using Scientific Notation to Describe Very Large Quantities

(8.EEI.3, 8.EEI.4) ● 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 is than the other.

● Rewrite very large numbers in scientific notation.

● Rewrite very large numbers in decimal notation.

I can estimate and compare the relative size of two very large

quantities in scientific notation. I can translate between very large quantities expressed in decimal

notation and scientific notation.

● iReady Lesson 4:

Scientific Notation


● www.khanacademy.org/commoncore, 8.EEI.3,

8.EEI.4 – videos and exercises





Using Scientific Notation to Describe Very Small Quantities (8.EEI.3, 8.EEI.4)

● 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 is than the

other ● Rewrite very small

numbers in scientific notation.

● Rewrite very small numbers in decimal notation.

I can estimate and compare the relative size of two small large

quantities in scientific notation. I can translate between very small quantities expressed in decimal

notation and scientific notation.

● iReady Lesson 4: Scientific Notation

● iReady Standards

Mastery ● www.khanacadem

y.org/commoncore, 8.EEI.3, 8.EEI.4 – videos and

exercises

Operating with Numbers Expressed in Scientific Notation

(8.EEI.3, 8.EEI.4) ● Use numbers

expressed in the form of a single digit times an integer

power of 10 to estimate very large or very small quantities.

● Perform

operations with numbers expressed in scientific notation, including problems where both decimal and

scientific notation are used. ● Perform

multiplication with numbers

expressed in scientific notation.

● Perform division with numbers expressed in

I can multiply and divide numbers

expressed in both decimal and scientific notation.


Operations and Scientific Notation



y.org/commoncore, 8.EEI.3, 8.EEI.4 – videos and

exercises







scientific notation.




Unit 5 – Proportional Relationships, Lines, and Linear Equations (15 days)

8.EEI.5 Apply concepts of proportional relationships to real-world and mathematical situations.

8.EEI.5a Graph proportional relationships. 8.EEI.5b Interpret unit rate as the slope of the graph. 8.EEI.5c Compare two different proportional relationships given multiple representations, including tables, graphs, equations,

diagrams, and verbal descriptions.

8.EEI.6 Apply concepts of slope and y-intercept to graphs, equations, and proportional relationships.

8.EEI.6a Explain why the slope, m, is the same between any two distinct points on a non-vertical line using similar triangles.

8.EEI.6b Derive the slope-intercept form (y = mx + b) for a non-vertical line.

8.EEI.6c Relate equations for proportional relationships (y = kx) with the slope-intercept form (y = mx + b) where b = 0.

Unit 5 – Proportional Relationships, Lines, and Linear Equations (15 days)

Essential Tasks/Key Concepts

Learning Targets Resources (Suggested Activities)


Graphing Proportional Relationships

● Graph

proportional relationships, interpreting the unit rate as the slope of the

graph. ● Graph a

proportional relationship given numerical values

and describe its real-world meaning.

● Graph a

proportional relationship where the data is discrete, and use the unit rate to slope a

problem.

I can graph proportional relationships.

● iReady

Lesson 11: Represent

Proportional Relationships


● www.khanacademy.org/commoncore - 8.EE.5 – videos, 8.EE.6 – videos and

exercises

FAL: Comparing Lines and Linear Equations FAL: Defining Lines by Points, Slopes

and Equations FAL: Matching Situations, Graphs, and Linear Equations

FAL: Comparing Fuel Consumption: Buying Cars

FAL: Interpreting Distance-Time Graphs















● Graph a relationship involving

percents and determine if the relationship is proportional.

● Graph a

relationship involving a negative rate of change and determine if the

relationship is proportional.

Linear Equations: y = mx ● Define the

equation y = mx for a line through the origin.

● Compare two different

proportional relationships represented in different

ways. ● Compare

and contrast proportional

relationships represented on a graph.

● Derive the

equation y = mx for proportional situation shown in a graph.

● Derive the

equation y = mx for proportional situation described verbally and then graph the situation.

● Compare

I can relate equations for proportional relationships (y = kx) with the slope-

intercept form (y = mx + b) where b = 0.


Understand the Slope-Intercept Equation for a Line


Mastery ● www.khanacademy.org

/commoncore - 8.EE.5

– videos, 8.EE.6 – videos and exercises





two different proportional

relationships where one is represented by an equation and the other is represented by a

graph.

The Slope of a Line ● Graph


graph. ● Compare

and contrast shapes in

the coordinate plane that have the same slope.

● Identify the

slope of the line given a graph.

● Identify the

slope of the line given two points on the line.

● Compare the slopes of two real-

world objects to solve a problem.

I can apply concepts of slope and y-

intercept to graphs, equations, and proportional relationships.

I can explain why the slope, m, is the same between any two distinct points on a non-vertical line using similar

triangles.

● iReady Lesson 12: Understand the Slope-Intercept Equation of a

Line ● iReady Standards

Mastery ● www.khanacademy.org/

commoncore - 8.EE.5 – videos, 8.EE.6 – videos and exercises





Unit Rates and Slope ● Graph


graph. ● Compare

two different

proportional relationships represented in different ways.

● Describe and compare given lines on a graph with a focus

on slope. ● Given a

graph of a proportional relationship, interpret

the unit rate as the slope of the graph.

● Graph a real-world proportional

relationship, interpreting the unit rate as the slope of the graph.

● Given a graph of a non-proportional relationship, interpret the slope of the

graph as the unit rate.

I can interpret unit rate as the slope of

the graph. I can compare two different proportional

relationships given multiple representations, including tables, graphs, equations, diagrams, and verbal descriptions.

● iReady Lesson 11: Represent Proportional Relationships

● www.khanacademy.org/

commoncore - 8.EE.5 – videos, 8.EE.6 – videos and exercises





The y-intercept of a Line ● Define the

equation y = mx + b for a line intercepting the vertical axis at b.

● Describe

and compare given lines on a graph with a focus on the y-intercept.

● Find the y-intercept of a line given a graph of a line that intercepts the vertical

axis at b. ● Find the y-

intercept of a line given

a graph of a line that intercepts the vertical axis at b or an equation of a line.

● Given a graph of a real-world context, explain the y-intercept in the context

of the situation

I can apply concepts of slope and y-

intercept to graphs, equations, and proportional relationships.

● iReady Lesson 12: Understand the Slope-Intercept Equation for a Line


Linear Equations: y = mx + b

● Define the equation y = mx + b for a line intercepting the vertical axis at b.

● Look for patterns in graphed lines and equations to identify

the slope and y-intercept from an equation.

● Derive an

I can derive the slope-intercept form (y= mx + b) for a non-vertical line.

I

I can apply concepts of proportional relationships to real-world and mathematical situations.


Understand the Slope-Intercept Equation for a Line


Mastery ● www.khanacademy.org/

commoncore - 8.EE.5 –

videos, 8.EE.6 – videos and exercises





equation in the form y = mx + b given a graph

that intercepts the vertical axis at b.

● Derive an equation in the form y =

mx + b given a graph of a real-world situation that intercepts the

vertical axis at b. ● Given a

linear equation in slope-intercept form, use the

y-intercept and the slope to graph the line.

● Derive the

equation y = mx + b for any non-vertical line (convert from ax + by = c to y = mx + b).


END OF FIRST NINE WEEKS



Unit 6 – Linear Functions (15 days)

8.F.1 Explore the concept of functions.

8.F.1a Understand that a function assigns to each input exactly one output.

8.F.1b Relate inputs (x-values or domain) and outputs (y-values or range) to independent and dependent variables.

8.F.1c Translate among the multiple representations of a function, including mappings, tables, graphs, equations, and verbal descriptions. 8.F.1d Determine if a relation is a function using multiple representations, including mappings, tables, graphs, equations, and

verbal descriptions. 8.F.1e Graph a function from a table of values. Understand that the graph and table both represent a set of ordered pairs of that function.

8.F.2 Compare multiple representations of two functions, including mappings, tables, graphs, equations, and verbal descriptions, in order to draw conclusions. 8.F.3 Investigate the differences between linear and nonlinear functions using multiple representations (i.e. tables, graphs, equations, and verbal descriptions).

8.F.3a Define an equation in slope-intercept form (y = mx + b) as being a linear function.

8.F.3b Recognize that the graph of a linear function has a constant rate of change. 8.F.3c Provide examples of nonlinear functions. 8.F.4 Apply the concepts of linear functions to real-world and mathematical situations.

8.F.4a Understand that the slope is the constant rate of change and the y-intercept is the point where x = 0.

8.F.4b Determine the slope and the y-intercept of a linear function given multiple representations, including two points, tables,

graphs, equations, and verbal descriptions.

8.F.4c Construct a function in slope-intercept form that models a linear relationship between two quantities.

8.F.4d Interpret the meaning of the slope and the y-intercept of a linear function in the context of the situation.

8.F.4e Explore the relationship between linear functions and arithmetic sequences. 8.F.5 Apply the concepts of linear and nonlinear functions to graphs in real-world and mathematical situations. 8.F.5a Analyze and describe attributes of graphs of functions (e.g., constant, increasing/decreasing, linear/nonlinear,

maximum/minimum, discrete/continuous). 8.F.5b Sketch the graph of a function from a verbal description. 8.F.5c Write a verbal description from the graph of a function with and without scales.









Unit 6 – Linear Functions (15 days)


Activities)


Lessons

Defining a Linear Function Rule ● Define a function

as a rule that assigns to each

input exactly one output. ● Classify a linear

function as a rule defined by

an equation of the form y = mx + b, whose graph is a straight line.

● Match a functional

relationship with its appropriate graphical representation.

● Classify a linear function as a rule defined by an equation of the form y = mx, whose graph is a straight

line. ● Classify a linear

function as a rule defined by an equation of the form y =

mx + b, whose graph is a straight line.

● Identify a function

that models a linear relationship between two quantities.

I can define an equation in slope-intercept form (y=mx+b) as being a linear function.

I can explore concepts of functions.

I can understand that a function assigns to each input exactly one output.

I can relate inputs and outputs to independent and dependent variables.


Functions ● iReady Lesson 7: Compare

Functions

● iReady Lesson 8: Understand Linear Functions

● iReady Standards Mastery ● www.khanacademy.org/com

moncore - 8.F.1, 8.F.3, 8.F.5 – videos and exercises

FAL: Comparing Lines and Linear Equations

FAL: Defining Lines by Points, Slopes and Equations FAL: Matching Situations, Graphs,

and Linear Equations FAL: Comparing Fuel Consumption: Buying Cars

FAL: Interpreting Distance-Time Graphs















Comparing Two Linear Functions ● Compare the

properties of two functions when each is represented in a different way.

● Compare the

meanings of two linear functions represented on a graph.

● Compare the rates of change of functions represented in different ways, a verbal description, a table,

and an equation. ● Compare the y-

intercept of functions

represented in different ways, a verbal description, a table, and an equation.

I can compare multiple representations of two functions, including mappings, tables,

graphs, equations, and verbal descriptions in order to draw conclusions.

● iReady Lesson 9: Analyze Linear Functions


moncore - 8.F.2 – exercises

Sketching a Function Graph

● Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

● Sketch a graph of a function from a verbal description.

● Sketch a graph that exhibits the qualitative features of a function and illustrates a real-world context

when given a verbal description.

● Match a sketch of

a function with its verbal description.

● Sketch the graph

I can graph a function from a

table of values. I can sketch the graph of a function from verbal description.

● iReady Lesson 10: Graphs of

Functional Relationships ● iReady Standards Mastery ● www.khanacademy.org/com

moncore - 8.F.3, 8.F.5 –

videos and exercises



http://www.khanacademy.org/commoncore%20-%208.F.3





of a function from a verbal description.

Attributes of Graphs of Functions ● Analyze a graph for

increasing,decreasing, constant, discrete/continuous

I can analyze and describe attributes of graphs including

increasing, decreasing, constant, discrete, continuous, linear, nonlinear, maximum, and

minimum.

● iReady Lesson 10: Graphs of Functional Relationships







Unit 7 – Linear Equations in One Variable (14 days) 8.EEI.7 Extend concepts of linear equations and inequalities in one variable to more complex multi-step equations and inequalities in real-

world and mathematical situations. 8.EEI.7a Solve linear equations and inequalities with rational number coefficients that include the use of the distributive property, combining

like terms, and variables on both sides.

8.EEI.7b Recognize the three types of solutions to linear equations: one solution (x = a), infinitely many solutions (a = a), or no solutions

(a = b).

8.EEI.7c Generate linear equations with the three types of solutions.

8.EEI.7d Justify why linear equations have a specific type of solution.

Unit 7 – Linear Equations in One Variable (14 days)



Solving Two-Step Equations ● Solve two-step linear

equations with rational number coefficients.

● Solve a two-step real-world problem with a variable on

one side. ● Write and solve two-step

linear equations with rational

number coefficients from real-world situations.

● Solve linear equations with rational number coefficients,

including equations whose solutions require collecting like terms.

I can solve linear equations with rational number coefficients that include the use of combining like

terms.

● iReady Lesson 13: Solve

Linear Equations with Rational

Coefficients ● iReady Standards Mastery ● www.khanacademy.org/comm

oncore - 8.EE.7, 8.EE.7a, 8.EE.7b – videos and exercises

FAL: Solving Linear Equations in One Variable FAL: Building and Solving Linear

Equations









Solving Equations with Variables on Both Sides

● Solve linear equations in one variable.

● Solve a two-step real-world problem with a

variable on both sides. ● Solve linear

equations in one variable, with

variables on both sides of the equal sign, using Algebra Tiles.

● Write and solve

linear equations in one variable, with variables on both sides of the equal sign,

from real-world situations. ● Solve linear

equations with rational number coefficients, and with

variables on both sides of the equal sign, including equations whose solutions require collecting like terms.

I can solve linear equations with rational number coefficients that include the use of combining like

terms and variables on both sides.

● iReady Lesson 13: Solve Linear Equations with Rational

Coefficients ● iReady Standards Mastery ● www.khanacademy.org/comm


Solving Equations Using the Distributive Property

● Match expressions

using the Distributive Property.

● Solve linear equations with integer

coefficients, including equations whose solutions require expanding expressions

using the distributive property and collecting like terms.

● Solve linear

I can solve linear equations with rational number coefficients that include the use of the distributive

property, combining like terms and variables on both sides.


Linear Equations with Rational Coefficients









equations with rational number coefficients, including

equations whose solutions require expanding expressions using the distributive property and collecting like terms.

● From problem situations, write and solve linear equations with rational

number coefficients, including equations whose solutions require expanding expressions using the distributive property.

Solutions – One, None, and infinitely Many

● Evaluate two

expressions and compare them.

● Determine whether a linear equation in

one variable has one solution (x = a), infinitely many solutions (a = a), or no solution (a = b).

● Transform linear equations in one variable into simpler forms until an

equivalent equation with no solution (a = b) results.

● Transform linear equations in one variable into

simpler forms until an equivalent equation with infinitely many solutions (a =

a).

I can recognize the three types of solutions to linear equations: one solution (x = a), infinitely many

solutions (a = a), or no solution (a = b).

● iReady Lesson 14: Solutions of Linear Equations










Unit 8 – Linear Inequalities in One Variable (8 days) 8.EEI.7a Solve linear equations and inequalities with rational number coefficients that include the use of the distributive property, combining

like terms, and variables on both sides.

Unit 8 – Linear Inequalities in One Variable (8 days)



Solving Two-Step Inequalities

● Solve two-step linear inequalities with rational number coefficients.

● Solve a two-step real-world inequality problem with a variable on one side.

● Write and solve two-step

linear inequality with rational number coefficients from real-world situations.

● Solve linear inequalities with rational number coefficients, including inequalities whose solutions require collecting like

terms.

I can solve linear inequalities with rational number coefficients that

include the use of combining like terms.

● Instructional video on solving two step inequalities

https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-variables-expressions/cc-7th-

inequalities/v/solving-inequalities

● Suggested websites to find worksheets:

➢ http://www.mathworkshe

ets4kids.com/inequalities.html

➢ https://www.kutasoftwar

e.com/free.html

➢ http://www.math-aids.com/Algebra/Pre-

Algebra/Inequalities/

➢ http://www.softschools.com/math/algebra/inequali

ties/

➢ http://www.mathworksheetsland.com/6/27eq.html

● Instructional video on

constructing and solving two

https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-variables-expressions/cc-7th-inequalities/v/solving-inequalities






http://www.mathworksheets4kids.com/inequalities.html



https://www.kutasoftware.com/free.html

https://www.kutasoftware.com/free.html

http://www.math-aids.com/Algebra/Pre-Algebra/Inequalities/



http://www.softschools.com/math/algebra/inequalities/



http://www.mathworksheetsland.com/6/27eq.html

http://www.mathworksheetsland.com/6/27eq.html

https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-variables-expressions/cc-7th-inequalities/v/interpreting-inequalities




step inequalities

Solving Inequalities with Variables on Both Sides

● Solve a two-step real-world inequality problem with a variable on both sides.

● Solve linear inequalities in one

variable, with variables on both sides of the equal sign.

● Write and solve linear

inequalities in one variable, with variables on both sides of the inequality, from real-world situations.

● Solve linear inequalities with rational number coefficients, and with variables on both

sides of the inequality, including inequalities whose

I can solve linear inequalities with rational number coefficients that

include the use of combining like terms and variables on both sides.

● Instructional video on solving multi-step inequalities with variable on both sides (distributive property)

➢ https://www.khanacademy.org/math/algebra/linear_inequalities/inequalities/

v/multi-step-inequalities

➢ https://www.khanacademy.org/math/algebra/linear

_inequalities/inequalities/v/multi-step-inequalities-2

➢ https://www.khanacadem

y.org/math/algebra/linear_inequalities/inequalities/v/multi-step-inequalities-3


https://www.khanacademy.org/math/algebra/linear_inequalities/inequalities/v/multi-step-inequalities




https://www.khanacademy.org/math/algebra/linear_inequalities/inequalities/v/multi-step-inequalities-2










solutions require collecting like terms.

Solving Inequalities Using the Distributive Property

● Solve linear inequalities with integer coefficients, including inequalities whose solutions require expanding expressions

using the distributive property and collecting like terms.

● Solve linear inequalities with

rational number coefficients, including inequalities whose solutions require expanding expressions using the

distributive property and collecting like terms.

● From problem situations, write

and solve linear inequalities with rational number coefficients, including inequalities whose solutions

require expanding expressions using the distributive property.

I can solve linear inequalities with rational number coefficients that include the use of the distributive property and combining like terms.






Unit 9 – Volume and Surface Area (7 days)

8.GM.9 Solve real-world and mathematical problems involving volumes of cones, cylinders, and spheres and the surface area of

cylinders.

Unit 9- Volume and Surface Area (7 days)



***You do not need to calculate surface area of

cones and spheres. Surface Areas of Cylinders

● Apply and extend understanding of three-

dimensional figures to define the properties of cones, cylinders, and spheres.

● Use the formulas for the surface areas of cylinders, cones, and spheres to solve real-world and

mathematical problems. ● Determine the

approximate lateral area of a

cylinder. ● Apply and extend

understanding of three-dimensional figures to define

the properties of cylinders and use their nets to find surface areas.

● Use the formula for the surface area of a cylinder to solve mathematical problems.

I can solve real-world and mathematical problems involving the surface area of cylinders.


Problems with Cylinders,

Cones, and Sphers ● iReady Standards Mastery ● www.khanacademy.org/com

moncore - 8.GM.9 – videos

and exercises

FAL: Modeling: Making Matchsticks

FAL: Sampling and Estimating: How Many Jellybeans








● Use the formula for the surface area of a

cylinder to solve real-world problems

Volumes of Cylinders ● Apply and extend

understanding of three-dimensional figures to define the properties of cones, cylinders, and spheres.

● Use the formula for the volume of a cone to solve real-world and

mathematical problems. ● Apply knowledge

of volume of right rectangular prisms to solve a problem

about volume of a cylinder. ● Use the formula

for the volume of a cylinder to

solve mathematical problems. ● Use the formula

for the volume of a cylinder to solve real-world problems

I can solve real-world and mathematical problems involving volumes of cylinders.


Understand Volume of Cylinders, Cones, and Spheres

● iReady Lesson 27: Solve Problems with Cylinders, Cones, and Sphers


● www.khanacademy.org/commoncore - 8.GM.9 – videos and exercises





● Use the formula for the volume of a cylinder to

find the radius when the volume is known.

Volumes of Cones ● Use the formulas

for the volumes of cylinders, cones, and spheres to solve real-world and mathematical problems.

● Apply knowledge of volume of cylinders to solve a problem about volume of

cones. ● Use the formula

for the volume of a cone to solve mathematical problems.

● Use the formula for the volume of a cone to solve real-world problems.

● Use the formula for the volume of a cone to find the radius when the volume is known.

I can solve real-world and mathematical problems involving volumes of cones.

● iReady Lesson 26: Understand Volume of Cylinders, Cones, and

Spheres ● iReady Lesson 27: Solve

Problems with Cylinders, Cones, and Sphers




Volume of Spheres (not hemi-spheres)

● Apply and extend understanding of three-dimensional figures to define the properties of cones,

cylinders, and spheres. ● Use the formulas

for the volumes of cylinders,

cones, and spheres to solve real-world and mathematical problems.

● Apply knowledge

of volume of cylinders to solve a problem about volume of spheres.

● Use the formula for the volume of a sphere to solve real-world and mathematical problems when

the radius is known. ● Use the formula

for the volume of a sphere to solve real-world and

mathematical problems when the diameter is known.

● Use the formula

for the volume of a sphere to find the radius when the volume is known.

I can solve real-world and mathematical problems involving

volumes of spheres.

● iReady Lesson 26: Understand Volume of Cylinders, Cones, and

Spheres ● iReady Lesson 27: Solve

Problems with Cylinders, Cones, and Sphers


moncore - 8.GM.9 – videos and exercises


END OF SECOND NINE WEEKS







Unit 10 – Reasoning in Geometry (8 days)

8.GM.4 Apply the properties of transformations (rotations, reflections, translations, dilations).

8.GM.4a Dilate geometric figures using scale factors that are positive rational numbers. 8.GM.4b Recognize that two-dimensional figures are only similar if a series of transformations can be performed to map the pre-image to the image.

8.GM.4c Given two similar figures, describe the series of transformations that justifies this similarity. 8.GM.4d Use proportional reasoning to find the missing side lengths of two similar figures. 8.GM.5 Extend and apply previous knowledge of angles to properties of triangles, similar figures, and parallel lines cut by a transversal.

8.GM.5a Discover that the sum of the three angles in a triangle is 180 degrees. 8.GM.5b Discover and use the relationship between interior and exterior angles of a triangle. 8.GM.5c Identify congruent and supplementary pairs of angles when two parallel lines are cut by a transversal. 8.GM.5d Recognize that two similar figures have congruent corresponding angles.

Unit 10 – Reasoning in Geometry (8 days)


Activities)


Lessons

***The stress throughout this topic is on DISCOVERY and IDENTIFY AND

RECOGNIZE.*** Angles, Lines, and Transversals

● Use facts about

the angles created when parallel lines are cut by a transversal to solve problems.

● Make conjectures

about angles formed by parallel lines and a transversal.

● Identify corresponding angles and alternate interior angles created when lines are cut by

I can identify congruent and supplementary pairs of angles when two parallel lines are cut by

a transversal.


Understand Angle Relationships



FAL: Identifying Similar Triangles






a transversal. ● Find measures of

corresponding angles created when parallel lines are cut by a transversal.

● Find measures of

alternate interior angles created when parallel lines are cut by a transversal.

Reasoning and Parallel Lines ● Use facts about

the angles created when lines are cut by a transversal to decide whether the lines are parallel.

● Justify that two line segments are parallel.

● Use facts about

the corresponding angles created when lines are cut by a transversal to decide whether the lines are parallel.

● Use facts about the alternate interior angles created when lines are cut by

a transversal to decide whether the lines are parallel.

● Use facts about the angles created when two

lines are cut by two transversals to decide whether

I can extend and apply previous knowledge of angles to properties of triangles, similar figures, and

parallel lines cut by a transversal.

● iReady Lesson 21: Understand Angle Relationships

● iReady Lesson 22: Understand Angle Relationships in Triangles







the lines are parallel.

Interior Angles of Triangles ● Use facts about

the angle sum of triangles to

solve problems. ● Prove the sum of

angle measures in a triangle.

● Use facts about the angle sum of triangles to solve problems in which two angle measures are given and

the third is unknown. ● Use facts about

the angle sum of triangles to

solve problems in which one acute angle measure in a right triangle is given and the other is unknown.

● Use facts about the angle sum of triangles to solve problems in which angle

measures are given in terms of algebraic expressions.

I can discover and use the relationship between interior and exterior angles of a triangle.

● iReady Lesson 21: Understand Angle

Relationships ● iReady Lesson 22:

Understand Angle Relationships in Triangles




Exterior Angles of Triangles ● Use facts about

the angle sum of triangles to solve problems.

● Use facts about the exterior angles of triangles

to solve problems. ● Use angle

relationships to make a

deduction about the exterior angle of a triangle.

● Identify exterior angles and remote interior

angles of triangles. ● Use facts about

the exterior angles of triangles

to solve problems in which two angle measures are given and either an exterior angle measure or a remote interior

angle measure is unknown. ● Use facts about

the exterior angles of triangles to solve problems in which

two angle measures are given in terms of algebraic expressions.

I can discover and use the relationship between interior and exterior angles of a triangle.






Angle-Angle Triangle Similarity ● Determine

whether two figures are similar by deciding if the second can be obtained from the first by a sequence of

rotations, reflections, translations, and dilations.

● Use facts about

the angle-angle criterion for similarity of triangles to solve problems.

● Determine

whether two triangles are similar.

● Use facts about

the angle-angle criterion for similarity of triangles to solve problems involving two separate triangles.

● Use facts about the angle-angle criterion for similarity of triangles to solve problems involving two

triangles configured so that there are vertical angles.

● Use facts about

the angle-angle criterion for similarity of triangles to solve problems involving two overlapping triangles.

● Determine whether two figures are similar by deciding if the

second can be obtained from the first by a sequence of rotations, reflections,

I can recognize that two similar figures have congruent corresponding angles.




● www.khanacademy.org/commoncore - 8.GM.4, 8.GM.5 – videos and exercises





translations, and dilations. ● Use facts about

the angle-angle criterion for similarity of triangles to solve problems.

● Use facts about

the angle-angle criterion for similarity of triangles to solve problems involving two

triangles configured so that there are vertical angles




Unit 11 - Congruence (14 days) 8.GM.1 Investigate the properties of rigid transformations (rotations, reflections, translations) using a variety of tools (e.g., grid paper,

reflective devices, graphing paper, technology). 8.GM.1a Verify that lines are mapped to lines, including parallel lines. 8.GM.1b Verify that corresponding angles are congruent.

8.GM.1c Verify that corresponding line segments are congruent. 8.GM.2 Apply the properties of rigid transformations (rotations, reflections, translations). 8.GM.2a Rotate geometric figures 90, 180, and 270 degrees, both clockwise and counterclockwise, about the origin.

8.GM.2b Reflect geometric figures with respect to the x-axis and y-axis.

8.GM.2c Translate geometric figures vertically and/or horizontally.

8.GM.2d Recognize that two-dimensional figures are only congruent if a series of rigid transformations can be performed to map the pre-image to the image.

8.GM.2e Given two congruent figures, describe the series of rigid transformations that justifies this congruence.

Unit 11 - Congruence (14 days)



***Throughout this topic, the terms “pre-image” and “image” should be stressed.

Translations ● Explore the

properties of translations.

● Use coordinates to describe the effect of dilations, translations, rotations, and reflections on two-dimensional

figures. ● Complete and

describe a translation on a grid.

● Identify translations.

I can apply the properties of rigid transformations (translations).

I can verify that corresponding angles and line segments are congruent.

I can translate geometric figures vertically and/or horizontally.

● iReady Lesson 18: Understand Properties of Transformations

● iReady Lesson 19: Transformations and Congruence


● www.khanacademy.org/commoncore - 8.G.1c – exercises

FAL: Representing and Combining

Transformations FAL: Transforming 2D Figures









● Use coordinates to graph a translation of a two-

dimensional figure. ● Use coordinates to

write a rule for a translation of a two-dimensional figure.

Reflections ● Explore the

properties of reflections over

the x axis and y axis (no other lines eg do not reflect over the line y = 2 or x = 4).

● Use coordinates to

describe the effect of reflections on two-dimensional figures.

● Complete and describe a reflection on a grid.

● Identify reflections.

● Describe a reflection of a two-dimensional figure.

I can apply the properties of rigid transformations (reflections).

I can verify that corresponding angles and line segments are congruent.

I can reflect geometric figures with respect to the x-axis and y-axis..

● www.khanacademy.org/commoncore - 8.G.1c – exercises

Rotations

● Explore the properties of rotations.

● Use coordinates to

describe the effect of rotations on two-dimensional figures.

● Complete and describe a rotation on a grid.

● Identify rotations. ● Explore properties

of rotations for 90, 180 and

270 degrees both clockwise and counterclockwise about the origin

I can apply the properties of rigid transformations (rotations). I can verify that corresponding

angles and line segments are congruent.

I can rotate geometric figures 90, 180, and 270 degrees, both clockwise and counterclockwise, about the origin.

● iReady Lesson 18: Understand Properties of

Transformations ● iReady Lesson 19:

Transformations and

Congruence ● iReady Standards Mastery ● www.khanacademy.org/com

moncore - 8.G.1c – exercises







● Use coordinates to graph a rotation of a two-

dimensional figure.

Congruent Figures ● Determine

whether two figures are

congruent by deciding if the second can be obtained from the first by a sequence of

rotations, reflections, and translations.

● Given congruent figures, describe a sequence

of rotations, reflections, and translations that exhibits the congruence between them.

● Determine whether one figure is congruent to another by deciding if the second can be

obtained from the first by a sequence of rigid motions.

● Given congruent triangles, describe a sequence

of rigid motions that exhibits the congruence between them.

● Given congruent quadrilaterals, describe a sequence of rigid motions that exhibits the congruence

between them. ● Determine

whether one triangle is

congruent to another triangle by deciding if the second can be obtained from the first by a

I can recognize that two-dimensional figures are only

congruent if a series of rigid transformations can be performed to map the pre-image to the image.

I can describe the series of rigid transformations that justifies when

two congruent figures are congruent.

● iReady Lesson 18: Understand Properties of

Transformations ● iReady Lesson 19:

Transformations and Congruence


moncore - 8.G.1c – exercises ● www.khanacademy.org/com

moncore - 8.G.2 – exercises







sequence of rigid motions.




Unit 12 - Similarity (14 days)





8.GM.1 Investigate the properties of rigid transformations (rotations, reflections, translations) using a variety of tools (e.g., grid paper, reflective devices, graphing paper, technology).

8.GM.1a Verify that lines are mapped to lines, including parallel lines. 8.GM.1b Verify that corresponding angles are congruent. 8.GM.1c Verify that corresponding line segments are congruent.

8.GM.3 Investigate the properties of transformations (rotations, reflections, translations, dilations) using a variety of tools (e.g., grid paper, reflective devices, graphing paper, dynamic software).

8.GM.3a Use coordinate geometry to describe the effect of transformations on two-dimensional figures. 8.GM.3b Relate scale drawings to dilations of geometric figures.

8.GM.4 Apply the properties of transformations (rotations, reflections, translations, dilations). 8.GM.4a Dilate geometric figures using scale factors that are positive rational numbers. 8.GM.4b Recognize that two-dimensional figures are only similar if a series of transformations can be performed to map the pre-image to the

image. 8.GM.4c Given two similar figures, describe the series of transformations that justifies this similarity. 8.GM.4d Use proportional reasoning to find the missing side lengths of two similar figures.



Unit 12 - Similarity (14 days)


Activities)


Lessons

Dilations ● Use coordinates to describe

the effect of dilations,

translations, rotations, and reflections on two-dimensional figures.

● Identify dilations, translations, rotations, and reflections.

● Explain whether a figure is drawn to scale.

● Identify dilations. ● Identify enlargements and

reductions of two-dimensional

figures in the coordinate plane.

● Graph a dilation of a two-dimensional figure in the

coordinate plane. ● Dilate geometric figures using

scale factors that are positive rational numbers

I can apply the properties of dilations.

I can dilate geometric figures using scale factors that are positive real numbers.

I can relate scale drawings to dilations of geometric figures.


Transformations and Similarity


FAL: Identifying Similar Triangles




Similar Figures ● Determine

whether two figures are similar by deciding if the second can be obtained from the first by a sequence of

rotations, reflections, translations, and dilations.

● Given similar

figures, describe a sequence of rotations, reflections, translations, and dilations that exhibits the similarity between

them. ● Determine

whether figures are similar to

one another by deciding if one can be obtained from another by a sequence of rigid motions and dilations.

● Given similar triangles, describe a sequence of rigid motions and dilations that exhibits the similarity

between the triangles. ● Given similar

quadrilaterals, describe a

sequence of rigid motions and dilations that exhibits the similarity between the quadrilaterals.

● Determine whether one triangle is similar to another triangle by deciding

if the second can be obtained from the first by a sequence of rigid motions and dilations.

I can recognize that two-dimensional

figures are only similar if a series of transformations can be performed

to map the pre-image to the image.


Transformations and Similarity

● iReady Standards Mastery ● www.khanacademy.org/co

mmoncore - 8.GM.4 – videos and exercises





Relating Similar Triangles and Slope

● 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. ● Determine whether right

triangles are proportional to

one another by deciding if they have the same height to base ratio.

● Use similar triangles to

compare the slopes between two pairs of distinct points on a non-vertical line in the

coordinate plane. ● Compare ratios of side lengths

of triangles to the slope of a non-vertical line in the

coordinate plane.

I can explain why the slope, m, is

the same between any two distinct points on a non-vertical line using similar triangles.

● iReady Lesson 20: Transformations and Similarity

● iReady Standards Mastery ● www.khanacademy.org/co

mmoncore - 8.GM.3,

8.GM.4, 8.EEI.6 – videos and exercises






Unit 13 – Using the Pythagorean Theorem (7 days) 8.GM.6 Use models to demonstrate a proof of the Pythagorean Theorem and its converse.

8.GM.7 Apply the Pythagorean Theorem to model and solve real-world and mathematical problems in two and three dimensions involving right triangles.

8.GM.8 Find the distance between any two points in the coordinate plane using the Pythagorean Theorem.

Unit 13 – Using the Pythagorean Theorem (7 days)



The Pythagorean Theorem ● Use models to demonstrate a

proof of the Pythagorean Theorem and its converse.

● Apply the Pythagorean Theorem to determine unknown side lengths in right

triangles in real-world and mathematical problems in two and three dimensions.

● Describe geometric

relationships that lead to the Pythagorean Theorem.

● Apply the Pythagorean

Theorem to determine the length of the hypotenuse in a right triangle, where the length of the hypotenuse is a

whole number. ● Apply the Pythagorean

Theorem to determine the

length of the hypotenuse in a right triangle, where the length of the hypotenuse is an irrational number.

I can use models to demonstrate a proof of the Pythagorean

Theorem. I can apply the Pythagorean

Theorem to model and solve real-world and mathematical problems.


Understand the Pythagorean Theorem

● iReady Lesson 24: Solve Problems Using the Pythagorean Theorem


moncore - 8.GM.6, 8.GM.7 – videos and exercises

FAL: Discovering the Pythagorean

Theorem FAL: Finding the Shortest Route: A

Schoolyard Problem










● Apply the Pythagorean Theorem to determine the

slant height of a pyramid.

Finding Unknown Leg Lengths ● Apply the Pythagorean

Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two

and three dimensions. ● Apply the Pythagorean

Theorem to determine

unknown side lengths in a right triangle.

● Apply the Pythagorean Theorem to determine the

length of a leg in a right triangle, where the length of the leg is a whole number.

● Apply the Pythagorean Theorem to determine the length of a leg in a right

I can use models to demonstrate a proof of the Pythagorean Theorem.

I can apply the Pythagorean Theorem to model and solve real-world and mathematical problems.


Understand the Pythagorean Theorem


Problems Using the Pythagorean Theorem







triangle, where the length of the leg is an irrational number.

● Apply the Pythagorean Theorem to determine the height of a pyramid.

The Converse of the Pythagorean Theorem

● Explore a proof of the Pythagorean Theorem and its converse.

● Apply the Converse of the

Pythagorean Theorem to determine if a triangle is a right triangle.

● Describe geometric relationships that lead to the Converse of the Pythagorean Theorem.

● Apply the Converse of the Pythagorean Theorem to determine if a triangle with

side lengths that are rational numbers is a right triangle.

● Apply the Converse of the Pythagorean Theorem to

determine if a triangle with side lengths that are rational and irrational numbers is a

I can use models to demonstrate a proof of the Pythagorean Theorem and its converse.

● iReady Lesson 23: Understand the Pythagorean Theorem

● iReady Lesson 24: Solve Problems Using the Pythagorean Theorem







right triangle.

Distance in the Coordinate Plane ● Apply the Pythagorean

Theorem to find the distance between two points in a coordinate system.


Theorem to solve a mathematical problem related to distance in the coordinate

plane. ● Apply the Pythagorean

Theorem to find the distance between two points in a

coordinate system, where the distance is a rational number.


Theorem to find the distance between two points in a coordinate system, where the distance is an irrational

number.

I can find the distance between

any two points in the coordinate plane using the Pythagorean Theoerm.

● iReady Lesson 25: Distance in

the Coordinate Plane ● iReady Standards Mastery ● www.khanacademy.org/com

moncore - 8.GM.8 – videos

and exercises






END OF THIRD NINE WEEKS



Unit 14 – Scatter Plots (5 days) 8.DSP.1 Investigate bivariate data.

8.DSP.1a Collect bivariate data. 8.DSP.1b Graph the bivariate data on a scatter plot. 8.DPS.1c Describe patterns observed on a scatter plot, including clustering, outliers, and association (positive, negative, no correlation, linear,

nonlinear). 8.DSP.2 Draw an approximate line of best fit on a scatter plot that appears to have a linear association and informally assess the fit of the line

to the data points. 8.DSP.3 Apply concepts of an approximate line of best fit in real-world situations.

8.DSP.3a Find an approximate equation for the line of best fit using two appropriate data points. 8.DSP.3b Interpret the slope and intercept. 8.DSP.3c Solve problems using the equation.

Unit 14 – Scatter Plots (5 days)



Interpreting a Scatter Plot ● Interpret scatter plots for

bivariate measurement data to investigate patterns of

association between two quantities.

● Draw two conclusions based

on data given on a scatter plot.

● Identify the basic elements of a scatter plot.

● Classify statements as true or false based on an existing scatter plot.

I can investigate bivariate data. I can collect bivariate data.

I can graph bivariate data on a scatter plot.

● iReady Lesson 28: Scatter Plots




Constructing a Scatter Plot ● Construct scatter

plots for bivariate measurement data to investigate patterns of association between two

quantities. ● Collect bivariate

data and construct a scatter

plot for a given situation. ● Construct a

scatter plot for given data when the axes and scales are

given. ● Construct a

scatter plot for given data,

when the axes and scales are not already given.

● Construct a scatter plot for given data

using a data and graphs tool.

I can graph bivariate data on a scatter plot.





Investigating Patterns – Clustering

and Outliers ● Construct scatter plots for

bivariate measurement data to investigate patterns of

association between two quantities.

● Collect data and construct a

scatter plot for a given situation.

● Construct a scatter plot for given data when the axes and

scales are given. ● Construct a scatter plot for

given data, when the axes and

scales are not already given. ● Construct a scatter plot for

given data using a data and graphs tool.

I can describe patterns observed

on a scatter plot, including clustering, outliers, and association (positive, negative, no correlation, linear, nonlinear).





Investigating Patterns - Association

● Describe patterns in scatter plots such as clustering, outliers, positive or negative association, linear association,

and nonlinear association. ● For a given situation, collect

data, construct a scatter plot,

and describe any relationships in the plotted points.

● Describe patterns in scatter plots such as positive

association, negative association or no correlation.

● Consider the possibility of

patterns in scatter plots such as positive association, negative association and no correlation, when only given

the verbal descriptions of the data categories.

● Describe patterns in scatter plots such as linear or

nonlinear associations. ● Explain whether given lines

accurately reflect an

association on a scatter plot. ● For scatter plots that suggest

a linear association, choose a reasonable trend line from

several drawn on the graph. ● For scatter plots that suggest

a linear association, informally

draw/fit a straight line. ● For scatter plots that suggest

a linear association, informally

I can describe patterns observed on a scatter plot, including clustering, outliers, and association (positive, negative, no

correlation, linear, nonlinear).

● iReady Lesson 28: Scatter

Plots ● iReady Standards Mastery ● www.khanacademy.org/co

mmoncore - 8.DSP.2 –






fit a straight line using technology tools.

Linear Models – Line of Best Fit ● 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.

● Describe how scatter plots can be used to make a prediction.

● Use the equation of a linear model to estimate a value between two known values.

● Use the equation of a linear

I can draw an approximate line of best fit on a scatter plot that

appears to have a linear association and informally assess the fit of the line to the data

points.

● iReady Lesson 29: Scatter

Plots and Linear Models

● iReady Lesson 30: Solve Problems with Linear Models


moncore - 8.DSP.1 – videos and exercises





model to predict a value outside the range of known

values. ● Find an approximate equation

for the line of best fit using two appropriate data points.

● Interpret the slope and intercept

Using the Equation of a Linear Model ● Use the equation of a linear

model to solve problems in the context of bivariate measurement data, interpreting the slope and

intercept.

I can apply the concepts of an approximate line of best fit in real-world situations.

● iReady Lesson 29: Scatter Plots and Linear Models


Problems with Linear Models ● iReady Standards Mastery ● www.khanacademy.org/com

moncore - 8.SP.2, 8.SP.3 – videos and exercises


Unit 15 – Analyzing Categorical Data (14 days) 8.DSP.4 Investigate bivariate categorical data in two-way tables.

8.DSP.4a Organize bivariate categorical data in a two-way table. 8.DSP.4b Interpret data in two-way tables using relative frequencies. 8.DSP.4c Explore patterns of possible association between the two categorical variables.





Unit 15 – Analyzing Categorical Data (14 days)



Organize Bivariate Categorical Data ● Apply and extend understanding of data to

define the characteristics of bivariate categorical data.

● Describe the possible reasons for asking a survey question.

● Apply and extend understanding of data to

determine if data are categorical data or measurement data.

● Apply and extend understanding of bivariate categorical data to determine if a survey is

designed to collect bivariate categorical data.

● Apply and extend understanding of bivariate

categorical data to design a survey to collect categorical, not measurement, data. Then identify the variables, categories, and groups that describe the data.

I can organize bivariate categorical data in a two-way table.


Categorical Data in Frequency Tables

● iReady Standards Mastery ● www.khanacademy.org/c

ommoncore – 8.DSP.4 – videos

FAL: Using Data: Testing a

New Product FAL: Interpreting and Using

Data: Setting Taxi

Fares

Interpreting Two-Way Frequency Tables ● Construct a two-way table summarizing

data on two categorical variables collected from the same subjects. Use relative

frequencies calculated for rows or columns to describe possible association between the two variables.

● Analyze how to use relative frequencies instead of frequencies in a two-way table.

● Construct a two-way relative frequency table for the total population summarizing

data on two categorical variables collected from the same subjects.

● Construct a two-way relative frequency

table for the row populations summarizing

I can interpret data in two-way

tables using relative frequencies.

● iReady Lesson 31: Categorical Data in Frequency Tables

● iReady Standards Mastery ● www.khanacademy.org/c

ommoncore – 8.DSP.4












data on two categorical variables collected from the same subjects.

Interpreting Two-Way Relative Frequency Tables

● Interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe

possible association between the two variables.

● Construct a two-way table summarizing

data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the

two variables.

I can interpret data in two-way tables using relative frequencies.

● iReady Lesson 31: Categorical Data in

Frequency Tables ● iReady Standards Mastery ● www.khanacademy.org/c

ommoncore – 8.DSP.4 –

videos





Choosing a Measure of Frequency ● Interpret a two-way table summarizing data

on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two

variables. ● Construct a two-way table summarizing

data on two categorical variables collected

from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.

● Choose a type of two-way table to display a given data set, and justify that choice.

● Justify if a two-way frequency table or

relative frequency table summarizing data on two categorical variables collected from the same subjects would be more useful to find the answer to a question.

● Determine which two-way relative frequency table (total relative frequency table, row relative frequency table, or column relative frequency table)

summarizing data on two categorical variables collected from the same subjects you should construct to answer a given

question. ● Construct a two-way relative frequency

table summarizing data on two categorical variables collected from the same subjects,

choosing to use relative frequencies calculated for rows or columns to describe a possible association between the two

variables.

I can explore patterns of possible association between the two categorical variables.

● iReady Lesson 31: Categorical Data in

Frequency Tables ● iReady Standards Mastery ● www.khanacademy.org/c

ommoncore – 8.DSP.4 –

videos






Unit 16 – System of Two Linear Equations (15 days)

8.EEI.8 Investigate and solve real-world and mathematical problems involving systems of linear equations in two variables with

integer coefficients and solutions. 8.EEI.8a Graph systems of linear equations and estimate their point of intersection. 8.EEI.8b Understand and verify that a solution to a system of linear equations is represented on a graph as the point of intersection of the two lines.

8.EEI.8c Solve systems of linear equations, algebraically, including methods of substitution and elimination, or through inspection. 8.EEI.8d Understand that systems of linear equations can have one solution, no solution, or infinitely many solutions.

Unit 16 – System of Two Linear Equations (15 days)





What is a System of Linear Equations in Two Variables?

● Apply and extend understanding of linear equations in two variables to define a system of two linear

equations in two variables. ● Solve real-world

and mathematical problems

leading to two linear equations in two variables.

● Solve a real-world problem involving two

quantities and two linear relationships.

● Apply and extend

understanding of linear equations and expressions in two variables to recognize a system of two linear equations

in two variables. ● Apply and extend

understanding of linear equations in two variables to

determine if an ordered pair is a solution of a system of two linear equations in two

variables. ● Write a system of

linear equations in two variables to represent real-

world problems. ***For each method of

solving, students should understand that systems of linear equations can have no

I can solve real-world and mathematical problems involving systems of linear equations in two

variables with integer coefficients and solutions. I can determine that systems of

linear equations can have one solution, no solution, or infinitely many solutions.


Systems of Equations ● iReady Standards Mastery ● www.khanacademy.org/comm

oncore - 8.EE.8, 8.EE.8a,

8.EE.8b, 8.EE.8c – videos and exercises

FAL: Classifying Solutions to Systems of Equations







solution, one solution or infinitely many solutions.

Solving Systems of Linear Equations by Graphing

● Solve systems of two linear equations in two variables by graphing the two equations in the same

rectangular coordinate plane and naming the coordinates of the point of intersection of the

two lines. ● Estimate solutions

systems of two linear equations in two variables by

graphing the equations. ● Represent

systems of linear equations in

two variables by graphing and writing equations.

I can graph systems of linear

equations and estimate their point of intersection.

I can determine that systems of linear equations can have one solution, no solution, or infinitely many solutions.


Solve Problems Using Systems of Equations



y.org/commoncore - 8.EE.8, 8.EE.8a, 8.EE.8b, 8.EE.8c –






● Identifying the coordinates of the point of

intersection of two linear equations in two variables.

● Estimating the solution to a system of two

linear equations in two variables by graphing.

● Solve real-world

problems leading to two linear equations in two variables by graphing.

Solving Systems of Linear Equations Using Substitution

● Analyze and solve pairs of simultaneous linear equations.

● Solve systems of

two linear equations in two variables algebraically using substitution.

● Solve a system of linear equations in two variables using your own method.

● Solve systems of two linear equations in two variables using the

substitution method. ● Solve real-world

problems leading to two linear equations in two variables

using substitution.

I can solve systems of linear equations, algebraically, through substitution.

● iReady Lesson 16: Solve Systems of Equations Algebraically

● iReady Lesson 17: Solve Problems Using Systems of Equations




Solving Systems of Linear Equations Using Addition


equations in two variables. ● Analyze and solve

pairs of simultaneous linear

equations. ● Solve a problem in

preparation for adding two linear equations in two

variables. ● Analyze pairs of

simultaneous linear equations

to determine the most efficient method to use to solve the equations.


two linear equations in two variables algebraically using addition.


problems leading to two linear equations in two variables using addition.

I can solve systems of linear

equations, algebraically, through elimination.

● iReady Lesson 16: Solve Systems of Equations

Algebraically ● iReady Lesson 17:

Solve Problems Using

Systems of Equations ● iReady Standards


y.org/commoncore - 8.EE.8, 8.EE.8a, 8.EE.8b, 8.EE.8c – videos and exercises





Solving Systems of Linear Equations Using Subtraction


equations in two variables. ● Analyze and solve

pairs of simultaneous linear

equations. ● Solve a problem in

preparation for subtracting two linear equations in two

variables. ● Analyze pairs of

simultaneous linear equations

to determine the most efficient method to use to solve the equations.


two linear equations in two variables algebraically using subtraction.


problems leading to two linear equations in two variables using subtraction.

I can solve systems of linear

equations, algebraically, through elimination.

● iReady Lesson 16: Solve Systems of Equations Algebraically

● iReady Lesson 17: Solve Problems Using Systems of Equations


Mastery


END OF FOURTH NINE WEEKS



Documents

Grade 8 Mathematics Curriculum Pacing Guide 2018-2019...Grade 8 Mathematics – Curriculum Pacing Guide – 2018-2019 Anderson School District Two Page 5 2018-2019 Unit 2 – Rational