Alexander County Schools 2012 - 2013...That non-perfect squares and cubes are irrational. That...

Unit:

8.NS.2 Work with radicals and integer exponents

8.EE.3 Express numbers using Scientific Notation

8.EE.4 Perform operations using Scientific Notation

Q1 Q2 Q3 Q4

Common Core and/or Essential Standards:

Know and apply the properties of integer exponents to generate equivalent numerical expressions.

Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number.

Evaluate square and cube roots of small perfect squares and cubes.

Use numbers expressed in scientific notation to estimate and compare very large or small quantities.

Perform operations with numbers expressed in scientific notation and choose the appropriate unit of measure

Interpret scientific notation that has generated by technology.

Transfer: Students will be able to independently use their learning to . . . Algebraic expressions and equations are used to model real-life problems and represent quantitative relationships, so that the numbers and symbols can be mindfully manipulated to reach a solution or make sense of the quantitative relationship.

Meaning

Understandings: Students will understand that . . .

The laws of exponents and their applications

Inverse operations to solve equations with exponents.

And interpret basic scientific notation and its applications. Properties of exponents, cube roots, square roots and scientific

notation can be used to solve algebraic expressions and equations.

Essential Question(s): How can algebraic expressions and equations be used to model, analyze, and solve

mathematical situations?

Acquisition

Students will know:

That the square root of 2 is irrational.

The properties of integer exponents

Bases must be same before performing operations with exponents.

Any number raised to the zero power is equal to one.

Students will be skilled at:

Applying the properties of integer exponents

Developing equivalent expressions by multiplying, dividing or raising a power to a power.

Subtracting exponents when like bases are being divided.

Expressing negative exponents as a positive when left in the

Alexander County Schools 2012 - 2013

Negative exponents occur when there are more factors in the denominator.

That several properties may be used to simplify expressions.

How to recognize perfect squares and cubes

That non-perfect squares and cubes are irrational.

That squaring or cubing a number are inverse operations of square and cube root.

That in geometry the square root of the area is the length of the side of a square and a cube root of the volume is the length of the side of the cube.

How scientific notation is expressed on various calculators or other technology.

denominator.

Adding exponents when like bases are being multiplied.

Multiplying exponents when an exponent is being raised to an exponent.

Using several properties to simplify expressions.

Solving equations containing squared or cubed numbers.

Using square and cube root information to solve geometric problems (such as area and volume).

Using scientific notation to express very large or small numbers.

Comparing and interpreting scientific notation quantities.

Solving problems using mathematical operations, expressing answers in scientific notation with and without technology.

Choosing the appropriate unit of measure for numbers expressed in scientific notation.

Essential Vocabulary: Laws of exponents, power, squaring of a number, cubing of a number, perfect squares, perfect cubes, root, square root, scientific notation, standard form of a number, inverse operations, units of measure,

IT Standards:

8.TT.1.1 Use appropriate technology tools and other resources to

access information.

8.TT.1.2 Use appropriate technology tools and other resources to organize information

IT Strategies: Use a graphing calculator, document camera, online resources to

access and organize information.

Unit Title: Grade: Subject:

STAGE 2

Understandings:

Students will

understand …

The laws of exponents and their applications

Inverse operations to solve equations with exponents.

And interpret basic scientific notation and its applications.

Properties of exponents, cube roots, square roots and scientific notation can be used to solve algebraic expressions and equations.

Essential

Questions:

Revised Blooms

Creating:

Can the student

create new product

or point of view?

assemble, construct,

create, design, develop,

formulate & write.

Evaluating:

Can the student justify a stand

or decision?

appraise, argue, defend, judge, select, support,

value & evaluate

Analyzing:

Can the student distinguish between

the different parts?

appraise, compare, contrast, criticize,

differentiate, discriminate,

distinguish, examine, experiment,

question & test.

Applying:

Can the student

use the information

in a new way?

choose, demonstrate,

dramatize, employ,

illustrate, interpret, operate, schedule,

sketch, solve,

use & write.

Understanding:

Can the student explain ideas or

concepts?

classify, describe, discuss, explain,

identify, locate,

recognize, report, select, translate

& paraphrase

Remembering:

Can the student recall or remember

the information?

define, duplicate, list,

memorize, recall, repeat,

reproduce & state

Formative Assessments (Evidences)

Check Appropriate box

Index card summaries/questions

Hand signals

One Minute Essay

Analogy Prompt

Web or Concept Map

Misconception Check

Student Conference

3-Minute Pause

Observation

Peer/Self-Assessment

Exit Card

Portfolio Check

Quiz

Journal Entry

Choral Response

A-B-C Summaries

Debriefing

Idea Spinner (explain, evaluate)

Inside-Outside Circle

Numbered Heads Together

One Sentence Summary

Think-Pair-Share

Ticket to Leave

Turn to Your Partner

Oral Questioning

Discussion

Learning Response Logs

Graphic Organizers

Practice Presentation

Visual Representation

Kinesthetic Assessments

Individual Whiteboards

Laundry Day

Four Corners

Constructive Quizzes

Appointment Clock

As I See it

Summative Assessment

Fill in blanks with your choice of

projects found in Possible Strategies.

Multiple Choice

Grid Response

Interactive Project

_______________________

Foldable

Portfolio

Student Based Learning Project

____________________

Blog/Wiki Response

Student Presentation Model i.e…Powerpoint, Prezi, Glogster…

______________________ ______________________

How can algebraic

expressions and

equations be used to

model, analyze, and

solve mathematical

situations?

Stage 3

Approximate number of days spent on unit:

W – Where are we going? Why? What is expected?

H – How will we Hook and Hold students?

E – How will we Equip students to Explore and Experience?

R – How will we help students Rethink, Rehearse, Revise, and Refine?

E – How will student self -Evaluate and reflect on learning?

T – How will we Tailor learning to vary needs, interests, and styles?

O – How will we Organize and sequence the learning?

Resources:

Curriki

Internet

Versa-Tiles

Interactive Websites

Teacher Tube

Promethean Planet

Carnegie Learning

http://www.k12.wa.us/Mathematics/pubdocs/QuickGuide_GR8.pdf

Dee Hanlin – NW Resa

www.ixl.com – Grade 8 Online Questions

www.livebinders.com/play/play_or_edit?id=97612

Strategies:

KWL

Think-Pair-Share

Problem-Solution

Sentence Summary

Learning Logs

Content Frame

2-column Notes

3-2-1 Review

Walk Around Survey

Family Tree Project (see attached)

Exploring the Moon (see attached)

Solar System (see attached)

Scientific Notation (see attached)

http://www.k12.wa.us/Mathematics/pubdocs/QuickGuide_GR8.pdf

http://www.ixl.com/

http://www.livebinders.com/play/play_or_edit?id=97612

Alexander County Schools 2012-2013

Unit: Geometry 8.G.7 & 8.G.8 Understand and apply the Pythagorean Theorem.

Q1 Q2 Q3 Q4


Explain 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.

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

Transfer:Students will be able to independently use their learning to…

provide descriptive information about an object’s properties and position in space, support visualization, and use these descriptions for problem solving in a real world context.

Meaning

Understandings:Students will understand that…

Right triangles have unique qualities.

Using models will help demonstrate understanding.

Reasoning abstractly and quantitatively can solve problems.

Essential Question(s):

How does geometry better describe objects? How can you apply geometric properties in a real world situation?

Acquisition

Students will know:

How to use algebraic reasoning to relate the visual model to Pythagorean Theorem.

That the sum of the squares of the legs is equal to the square of the hypotenuse in a right triangle.

How to apply the Pythagorean Theorem to find an unknown length of a right triangle.

How to use a right triangle in a coordinate plane and Pythagorean Theorem to find the distance between the two


Using visual models to demonstrate the relationship of the three sides of any right triangle.

Using the Pythagorean Theorem to determine if a given triangle is a right triangle.

Drawing diagrams to find right triangles in a 3D figure and use Pythagorean Theorem to solve for dimensions and real-world problems.

Graphing points in a coordinate plane.

original points. Connecting any two points to a third so that the three make a right triangle.

Essential Vocabulary: right triangle, Pythagorean Theorem, leg, hypotenuse, converse, Pythagorean triple

IT Standards: IT Strategies:

Stage 2 Unit Title: Geometry Understand and apply the Pythagorean Theorem Grade: 8th Grade Subject: Math

Understandings:

Students will understand that…

Right triangles have unique qualities.

Using models will help demonstrate understanding.

Reasoning abstractly and quantitatively can solve problems.

Essential Questions:

How does geometry better describe

objects?

How can you apply geometric

properties in a real world situation?

Revised Blooms

Creating:

Can the student

create new product or point of view?



formulate& write.

Evaluating:

Can the student

justify a stand

or decision?

appraise, argue, defend,

judge, select, support,

value & evaluate

Analyzing:






question& test.

Applying:

Can the student

use the information in a new way?


dramatize, employ, illustrate, interpret,

operate, schedule,

sketch, solve, use & write.

Understanding:


concepts?


identify, locate,

recognize, report, select, translate

& paraphrase

Remembering:


the information?



reproduce & state

Formative Assessments

(Evidences)

Check Appropriate box Index card summaries/questions

Hand signals

One Minute Essay

Analogy Prompt

Web or Concept Map

Misconception Check

Student Conference

3-Minute Pause

Observation


Exit Card

Portfolio Check

Quiz

Journal Entry

Choral Response

A-B-C Summaries

Debriefing





Think-Pair-Share

Ticket to Leave


Oral Questioning

Discussion


Graphic Organizers





Laundry Day

Four Corners


Appointment Clock

As I See it


Fill in blanks with your choice of projects found in Possible Strategies.

Multiple Choice

Grid Response

Interactive Project _______________

Foldable

Portfolio

Student Based Learning Project _______________

Blog/Wiki Response

Student Presentation Model i.e…Powerpoint, Prezi, Glogster…

_______________

Stage 3

Approximate number of days spent on unit: 15 days








Resources:

www.curriki.org (video clips)

mathinmind.com

AIMS

Coordinate Plane for distance problems

Pythagorean Theorem Worksheets

http://www.learnnc.org/lp/pages/3650

https://sites.google.com/site/paulgrimes1924/web-2-

0-project-based-assessment

http://wveis.k12.wv.us/teach21/public/project/

Guide.cfm?upid=3320&tsele1=2&tsele2=108

Strategies:

Know the definition of right triangles and hypotenuse.

Use the Pythagorean Theorem to derive the distance formula.

Ladder Problems

Baseball Diamond word problems

Distance from one point on a map to the other.

Problem Centered Lesson (see attached)

Project Based Assessment (see attached)

Teach 21 Project (see attached)

http://www.curriki.org/

http://www.learnnc.org/lp/pages/3650

https://sites.google.com/site/paulgrimes1924/web-2-0-project-based-assessment

https://sites.google.com/site/paulgrimes1924/web-2-0-project-based-assessment

http://wveis.k12.wv.us/teach21/public/project/


Unit: 8.F.1, 8.F.2, 8.F.3 Functions Define, evaluate, and compare functions

Q1 Q2 Q3 Q4


Understand that a function is a rule that assigns to each input exactly one output

The graph of a function is the set of ordered pairs consisting of an input and the corresponding output

Compare the properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions)

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line

Give examples of functions that are not linear.

Transfer: Students will be able to independently use their learning to…

Use the characteristics of functions and their representations to make sense of patterns and solve problems involving quantitative relationships in real world situations

Meaning

Understandings: Students will understand that…

a function is a rule that assigns to each input exactly one output

graphs of functions are the set of ordered pairs consisting of an input and the corresponding output

functions can be represented in different ways (algebraically, graphically, numerically in tables or verbal descriptions)

a straight line is defined as a linear function using the equation y = mx + b

the slope and y-intercept can be interpreted in relation to the function

some functions are not linear

the rate of change between input and output values can be used to determine if the function is linear or non-linear

Essential Question(s): How are functions useful?

Acquisition

Students will know:

the rules of a function is x as the input and y as the output

that functions occur when exactly one y-value is associated with any x-value

how to recognize equations as functions or not a function


Identifying functions from equations, graphs, and table/ordered pairs

Recognizing graphs that are functions and those that are not functions

how to compare two functions from different representations

y = mx + b is an equation used to define a linear function, whose graph is a straight line

how to determine whether a function is linear or non-linear

linear functions have a constant rate of change between any two points

Reading tables or looking at a set of ordered pairs to determine functions and identify equations where there is only one output for each input

Recognizing equations such as y = x as functions; whereas, equations such as x2 + y2 = 25 is not a function

Compare functions to determine which has the greater rate of change

Compare two linear functions to determine which has a negative slope

Using equations, graphs and tables to categorize functions as linear or non-linear

Identifying slope and y-intercept from tables, graphs, equations, or verbal descriptions to write a linear functions.

Sketching a graph to model that situation given a verbal description.

Providing a verbal description from a given graph.

Essential vocabulary: function, linear function, rate of change, y-value, x-value, vertical line test, input, output, non-linear function


Unit Title: Grade: Subject: Define, evaluate, and compare functions 8th Math

Stage 2

Understandings: Students will understand …

a function is a rule that assigns to each input exactly one output

graphs of functions are the set of ordered pairs consisting of an input and the corresponding output

functions can be represented in different ways (algebraically, graphically, numerically in tables or verbal descriptions)

a straight line is defined as a linear function using the equation y = mx + b

the slope and y-intercept can be interpreted in relation to the function

some functions are not linear

the rate of change between input and output values can be used to determine if the function is linear or non-linear

Essential Questions: How are functions useful?

Creating: can the

student create new

product or point of view?


create, design,

develop, formulate, write.

Evaluating: can the

student justify a stand

or decision?

appraise, argue,

defend, judge, select, support,

value, evaluate

Analyzing: can the

student distinguish between the different

parts?

appraise, compare,

contrast, criticize,


distinguish,

examine, experiment,

question, test.

Applying: can the student use the

information in a new

way?

choose,

demonstrate,

dramatize, employ,

illustrate, interpret, operate, schedule,

sketch, solve, use,

write.

Understanding: can

the student explain ideas or concepts?

classify, describe,

discuss, explain, identify, locate,

recognize, report,

select, translate, paraphrase

Remembering: can the

student recall or remember the

information?

define, duplicate,

list, memorize, recall, repeat,

reproduce state

Revised Blooms Formative Assessments

(Evidences) Check Appropriate box


Hand signals

One Minute Essay

Analogy Prompt

Web or Concept Map

Misconception Check

Student Conference

3-Minute Pause

Observation


Exit Card

Portfolio Check

Quiz

Journal Entry

Choral Response

A-B-C Summaries

Debriefing





Think-Pair-Share

Ticket to Leave


Oral Questioning

Discussion


Graphic Organizers





Laundry Day

Four Corners


Appointment Clock

As I See it

Summative Assessment Fill in blanks with your choice of projects found in possible strategies

Multiple choice

Grid response

Interactive Projects ___________________

Foldable

Portfolio

Student based Learning Projects __________________

Blog/Wiki Response

Powerpoint presentations

___________________

___________________

Unit Title: Define, evaluate, and compare functions Grade: 8th Subject: Math

STAGE 3






E – How will student self Evaluate and reflect on learning?

T – How will we Tailor learning to varied needs, interests, styles?


Resources:

“Teaching the Common Core Math Standards” with Hands-On Activities” by Jossey Bass Teacher

“Bridge to Algebra” by Carnegie Learning

AIMS Activities Grades 6-9

www.nsdl.org – Grade 8 Math



Strategies:

Pages 183-190 of “Teaching the Common Core Math Standards”

Pages 419-440 in “Bridge to Algebra” in Carnegie Learning.

“Looking at Lines” in the AIMS Integrating Math and Science Series.

http://www.nsdl.org/

http://www.ixl.com/



Unit: 8.F.4 Functions Use Functions to model relationships between quantities.

Q1 Q2 Q3 Q4


Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Transfer: Students will be able to independently use their learning to… Use the characteristics of functions and their representations to make sense of patterns and solve problems involving quantitative relationships in real world situations.

Meaning


As they construct functions to model a linear relationship that the function has meaning.

Measuring, Collecting, and Graphing Data can show patterns that can be analyzed to make use of in real-life situations.

Essential Question(s): How are functions useful?

Acquisition

Students will know:

That the equation, y=mx + b, represents the relationship between the x and y value.

That slopes can be undefined or zero.

That the y-intercept is when x = 0.

That slope can be determined by finding the change between two y and x values.

In linear equations, y=mx+b, the coefficient of x is the slope and the constant is the y-intercept.


Identifying and interpret the rate of change (slope) from tables, graphs, equations, or verbal descriptions to write a function.

Identifying and interpret the initial value (y-intercept) from tables, graphs, equations, or verbal descriptions to write a function.

Identifying the slope and y-intercept on a graph and write the equation that models the linear relationship.

Converting equations into y=mx+b form.

Writing equations given slope and a point, and two ordered pairs.

Using their graphing calculator.

Essential vocabulary: interpret, linear relationship, nonlinear, rate of change, slope, initial value, y-intercept


Unit Title: Functions Use Functions to model Grade 8 Subject: Math

relationships between quantities

Stage 2


Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Essential Questions: How are functions useful?

Creating: can the

student create new product or point of

view?


create, design, develop, formulate,

write.

Evaluating: can the student justify a stand

or decision?

appraise, argue,

defend, judge,

select, support, value, evaluate

Analyzing: can the student distinguish

between the different

parts?

appraise, compare,

contrast, criticize, differentiate,

discriminate,

distinguish, examine,

experiment,

question, test.

Applying: can the

student use the

information in a new way?

choose,

demonstrate,


operate, schedule,

sketch, solve, use, write.

Understanding: can the student explain

ideas or concepts?


identify, locate,

recognize, report, select, translate,

paraphrase

Remembering: can the

student recall or

remember the

information?

define, duplicate,

list, memorize,

recall, repeat,

reproduce state

Revised Blooms Formative Assessments

(Evidences) Check Appropriate box


Hand signals

One Minute Essay

Analogy Prompt

Web or Concept Map

Misconception Check

Student Conference

3-Minute Pause

Observation


Exit Card

Portfolio Check

Quiz

Journal Entry

Choral Response

A-B-C Summaries

Debriefing





Think-Pair-Share

Ticket to Leave


Oral Questioning

Discussion


Graphic Organizers





Laundry Day

Four Corners


Appointment Clock

As I See it

Summative Assessment Fill in blanks with your choice of projects found in possible strategies

Multiple choice

Grid response

Interactive Projects ___________________

Foldable

Portfolio


Blog/Wiki Response


___________________

___________________

Unit Title: Grade: Subject: Functions Use Functions to model

relationships between quantities 8th Math

STAGE 3






E – How will student self Evaluate and reflect on learning?

T – How will we Tailor learning to varied needs, interests, styles?


Resources:

“Teaching the Common Core with Hands-On Activities” by Jossey Bass Teacher

“Looking at Lines” from AIMS Activities

www.nsdl.org – Grade 8 Math



Strategies:

Pages 191-200 of “Teaching the Common Core with Hands-On Activities”

http://www.nsdl.org/

http://www.ixl.com/



Unit: 8.EE.5, 8.EE.6 Understand the connections between proportional relationships, lines, and linear equations.

Q1 Q2 Q3 Q4


Graph proportional relationships, interpreting the unit rate as the slope of the graph.

Compare two different proportional relationships represented in different ways

Use similar triangles to explain why slope is the same between any two distinct points on a non-vertical line.

Derive the equation y= mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

Transfer: Students will be able to independently use their learning to… Algebraic expressions and equations are used to model real-life

problems and represent quantitative relationships, so that the numbers and symbols can be mindfully manipulated to reach a solution or make sense of the quantitative relationship.

Meaning


Identify the unit rate (slope) in graphs, tables, and equations to compare two or proportional relationships

Triangles are similar when there is a constant rate of proportion between them.

Essential Question(s): How can algebraic expressions and equations be used to model, analyze, and solve mathematical situations?

Acquisition

Students will know:

A graph is a proportional relationship in the coordinate plane.

The interpretation of unit rate of a proportional relationship as the slope of the graph.

Justification of a graph of proportional relationship will always intersects to the origin of the graph.

A graph, a table, or an equation to determine the unit of a proportional relationship and use the unit rate to make comparison between various proportional relationships.

Right triangles by drawing a horizontal line segment and a vertical line segment from any two points on a non-vertical line.

Right triangles are similar by comparing the ratios of the lengths of the corresponding legs.

Similar triangles, ratios of all corresponding hypotenuses, representing the slope of the line will be equivalent.

Equations in the form y = mx +b will represent a graph of proportional relationship with a slope of m and y-intercept of 0.


Graphing proportional relationships in the coordinate plane.

Interpreting the unit rate of a proportional relationship as the slope of a graph.

Justifying that the graph of a proportional relationship will always intersect at the origin.

Using a graph, table or an equation to determine the unite rate of a proportional relationship

Using unit rate to make comparisons between various proportional relationships.

Creating right triangles by drawing horizontal line segment and a vertical line segment from any two points on a non-vertical line.

Justifying that right triangles are similar by comparing the ratios of the lengths of the corresponding legs.

Justifying that an equation in the form y = mx will represent the graph of a proportional relationship with a slope of m and y-intercept of 0.

Equations in the form y = mx + b represents the graph of a linear relationship with a slope of m and a y-intercept of b.

Justifying that an equation in the form of y = mx + b represents the graph of a linear relationship with a slope of m and and y-intercept of b.

Essential vocabulary: Proportional relationship, unit rate, slope, right triangle, leg, hypotenuse, similar triangles, ratio, y-intercept.



Unit: Unit: 8.EE.7 & 8.EE.8 Analyze and solve linear equations and pairs of simultaneous linear equations.

Q1 Q2 Q3 Q4


Solve one variable equations with the variable being on both sides of the equals sign.

Analyze and solve pairs of simultaneous linear equations.


Algebraic expressions and equations are used to model real-life problems and represent quantitative relationships, so that the numbers and symbols can be mindfully manipulated to reach a solution or make sense of the quantitative relationship.

Meaning


Linear relationships in one variable with one solution, many solutions or no solutions

Linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.


How can algebraic expressions and equations be used to model, analyze, and solve mathematical situations?

Acquisition

Students will know:

Properties of real numbers to determine the solution of linear equations.

Process for simplifying a linear equation by using the distributive property and or coming like terms.

Linear equations may have one solution, infinitely many solutions or no solutions.


Using the properties of real numbers to determine the solution of a linear equation.

Simplifying a linear equation by using a distributive property

Simplifying a linear equation by combining like terms.

Solving equations with one solution, infinitely many solutions or no solution.

Essential Vocabulary: Linear equations, equivalent equations, rational number, coefficient, like terms, solutions


x

Unit Title: 8.EE.7 & 8.EE.8Analyze and solve

linear equations and pairs of simultaneous linear equations. Grade: 8th Subject: Math

STAGE 2

Understandings:

Linear relationships in one variable with one solution, many solutions or no solutions

Linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.


How can algebraic expressions and

equations be used to model,

analyze, and solve mathematical

situations?

Revised Blooms

Creating:

Can the student




formulate & write.

Evaluating:

Can the student

justify a stand

or decision?



value & evaluate

Analyzing:






question & test.

Applying:

Can the student




operate, schedule,


Understanding:


concepts?


identify, locate,

recognize, report,

select, translate

& paraphrase

Remembering:


the information?



reproduce & state


(Evidences)


Hand signals

One Minute Essay

Analogy Prompt

Web or Concept Map

Misconception Check

Student Conference

3-Minute Pause

Observation


Exit Card

Portfolio Check

Quiz

Journal Entry

Choral Response

A-B-C Summaries

Debriefing





Think-Pair-Share

Ticket to Leave


Oral Questioning

Discussion


Graphic Organizers





Laundry Day

Four Corners


Appointment Clock

As I See it


Fill in blanks with your

choice of projects found in

possible strategies

Multiple choice

Grid response

Interactive Projects __________________

Foldable

Portfolio


Blog/Wiki Response


__________________

STAGE 3









Resources:

I. AIMS: Solving Equations: A Conceptual Approach

II .Teaching the Common core Math Standards with Hands-on Activities

III. Prentice Hall: Skills and Concepts Review

IV. Harcourt Brace Enrichment Stretching Your Thinking

http://illuminations.nctm.org/LessonDetail.aspx?id=L744


Solving Systems of Linear Equations in Two Variables

http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut19_systwo.htm

Strategies:

I. AIMS: What’s in the Bank? Page 13 Widgets, page 23; Backtracking ESP, page 63 & 71; ESP Extraordinary Solution Prediction, page 81; Equality In the Balance page 91

II. p. 176- 182 of “Teaching the Common Core Math Standards with Hands-on Activities”

III. Review concepts pages 34-47 IV. Stretching Your Thinking pages 25-34






Unit: Statistics and Probability 8.SP.1, 8. SP.2, 8.SP.3, 8.SP.4 Investigate Patterns of Association in Bivariate Data

Q1 Q2 Q3 Q4


Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative associations, and nonlinear association.

Know that straight lines are widely used to model relationships between two quantitative variables. 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.

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.

Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on a two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether 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?

Transfer: Students will be able to independently use their learning to… Understand how the rules of probability can lead to more valid and reliable predictions about the likelihood of an event occurring in real-life.

x

Meaning


Associations of two-variable data can be determined and analyzed using graphs and tables.

Problems in context can be solved using the analysis of graphs and tables.


How is the probability used to make informed decisions about uncertain events? How are predictions made from data?

Acquisition

Students will know:

That bivariate data refers to two-variable data.

That outliers are points that That lie away from the other points and can affect the linear model.

That straight lines are used to model relationships between two variables.

How to use the equation of the best-fit line to solve problems in context.

How to interpret the slope and y-intercept from the line of best-fit equation.

That a two-way table provides a way to organize data between two categories.

How to determine patterns associated with the data presented in a two-way table.


Construct and interpret scatter plots to investigate patterns between two quantities.

Describe clustering, outliers, positive or negative association, linear or nonlinear association.

Graphing data on an x and y axis (coordinate plane).

Fitting a straight line that comes closest to most data points to represent the linear association.

Informally assessing the model by judging the closeness of the data points to the line.

Determining the equation of the line of best fit using slope and y-intercept.

Solving problems using a linear model (predictions). Calculating relative frequencies to describe associations.

Essential Vocabulary:

scatter plot, bivariate, clustering, outliers, positive and negative association, linear and nonlinear association, clustering, two-way table, categorical data, relative frequency, line of best fit


Unit Title: Statistics and Probability Grade: 8 Subject: Math

STAGE 2

Understandings:

Associations of two-variable data can be determined and analyzed using graphs and tables.

Problems in context can be solved using the analysis of graphs and tables.


How is probability used to make

informed decisions about uncertain

events?

How are predictions made from data?

Revised Blooms

Creating:

Can the student




formulate & write.

Evaluating:

Can the student

justify a stand

or decision?



value & evaluate

Analyzing:






question & test.

Applying:

Can the student




operate, schedule,


Understanding:


concepts?


identify, locate,

recognize, report,

select, translate

& paraphrase

Remembering:


the information?



reproduce & state


(Evidences)


Hand signals

One Minute Essay

Analogy Prompt

Web or Concept Map

Misconception Check

Student Conference

3-Minute Pause

Observation


Exit Card

Portfolio Check

Quiz

Journal Entry

Choral Response

A-B-C Summaries

Debriefing





Think-Pair-Share

Ticket to Leave


Oral Questioning

Discussion


Graphic Organizers





Laundry Day

Four Corners


Appointment Clock

As I See it


Fill in blanks with your choice of projects.

Multiple Choice

Grid Response

Interactive Project: ________________

Foldable

Portfolio

Student Based Learning Project: ________________

Blog/Wiki Response

Student Presentation Model: ________________________________________________________________

STAGE 3









Resources:

“Teaching the Common Core Math Standards with Hands-

On Activities”; Grades 6-8; pages 237-246

“Carnegie Learning Series, Course 3”; Chapters 15, 16, 17;

pages 795-924

“Carnegie Learning Algebra I”; Chapter 6; pages 249-295

NWRESA – Dee Hanlin

Strategies:

Collecting Data

Graphing Calculator Functions

Analyzing and Interpreting Data


Unit: Geometry 8.G.1, 8.G.2, 8.G.3, 8.G.4 Understand congruence and similarity using physical models, transparencies, or geometry software.

Q1 Q2 Q3 Q4


Verify experimentally the properties of rotations, reflections, and translations.

Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations.

Given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.


provide descriptive information about an object’s properties and position in space, support visualization, and use these descriptions for problem solving in a real world context

Meaning


Using their knowledge of angles and distance will help them to analyze 2D and 3D figures to solve problems.

Using logical thinking that is expressed in words to develop an understanding of similarity and congruency.

Through this understanding of symmetry and congruency, conclusions can be made about the relationships of line segments and angles with figures.


How does geometry better describe objects?

Acquisition

x

Students will know:

Characteristics of figures; lengths of line segments, angle measures, and parallel lines.

That these transformations produce images of exactly the same size and shape as their pre-image and are known as rigid transformations.

That congruent figures have the same shape and size.

That translations, reflections, and rotations are examples of rigid transformations.

That a rigid transformation (translation, reflection, or rotation) is one in which angles and corresponding line segments remain congruent.

That the relationship between the coordinates of the pre-image, the image, and the scale factor for a dilation.

That similar figures have congruent angles and sides that are proportional, produced from dilations


Using compasses, protractors and rulers or technology to explore figures created from translations, reflections, and rotations.

Recognizing the symbol for congruency and writing statements of congruency.

Examining two figures to determine congruency by identifying that after the translation, reflection, or rotation that he corresponding parts are the same measure and corresponding parallel lines remain parallel.

Identifying resulting coordinates from translations, reflections, and rotations.

Recognizing the relationship between the coordinates and the transformation.

Using the coordinates to identify the scale factor and understand how the scale factor produces an enlargement or reduction.

Using transformations to prove that two figures are similar.

Informally proving that the sum of a triangle’s interior angles have the same measure as a straight line.

Informally proving that the sum of a polygon’s exterior angles will be 360 degrees.

Stating the relationships and measurements of the angles created when two parallel lines are cut by a transversal

Essential Vocabulary: : translations, rotations, reflections, line of reflection, center of rotation, clockwise, counterclockwise, parallel lines, betweenness, congruence, reading A’ as “A prime”, similarity, dilations, pre-image, image, rigid transformation, exterior angles, interior angles, alternate interior angles, angle-angle criterion, deductive reasoning, vertical angles, adjacent angles, supplementary, complementary, corresponding, scale factor, transversal parallel


STAGE 2

Unit Title: Grade: Subject:

Understandings:


Revised Blooms

Creating:

Can the student




formulate & write.

Evaluating:

Can the student

justify a stand

or decision?



value & evaluate

Analyzing:






question & test.

Applying:

Can the student




operate, schedule,


Understanding:


concepts?


identify, locate,

recognize, report,

select, translate

& paraphrase

Remembering:


the information?



reproduce & state


(Evidences)


STAGE 3









Resources:

Strategies:


Unit: Solve Real-World and mathematical problems involving volume of cylinders, cones and spheres. 8.G.9

Q1 Q2 Q3 Q4


Students will know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Transfer: Students will be able to independently use their learning to… Provide descriptive information about an object’s properties and position in space and support visualization and problem solving in a real-world context.

Meaning


They will build upon understandings of circles and volume from the 7th grade to find the volume of cylinders, cones, and spheres.

They will apply geometric formulas to solve real-world problems.

Geometric formulas for cylinders, cones, and spheres are related to one another.


How does geometry better describe objects?

Acquisition

Students will know:

How to identify a cylinder, cone, and sphere.

What number is used to represents pi.

What is the radius of a circle.

The relationship between radius and diameter.

The concept of volume.

How to determine the height of cones and cylinders.

The formulas for the volume of a cylinder, cone, and sphere.

The volume of a cylinder is 3 times the volume of a cone having the same base area and height, or the volume of a cone is 1/3 the volume of a cylinder having the same base area and height.

The volume of a sphere is 4/3 the the volume of a cylinder with the same radius and height.

The height of the cylinder is the same as the diameter of the sphere or 2r.


To find the volume of a cylinder you have to find the area of the base (circle) and multiply by how many layers (height) are present.

Describing the similarity between finding the volume of a cylinder and the volume of a right prism.

Recalling the formula to find the volume of a cylinder.

Informally proving the relationship between the volume of a cylinder and the volume of a cone with the same base.

Recalling the formula to find the volume of a cone.

Informally proving the relationship between the volume of a sphere and the volume of a circumscribed cylinder.

Recalling the formula to find the volume of a sphere.

Using the formulas to find the volume of cylinders, cones and spheres.

Solving real-world problems involving the volume of cylinders, cones, and spheres.

X

Essential Vocabulary:

Cylinder, cone, sphere, volume radius, diameter, height, pi, base area


Unit Title: Solve Real-World and Mathematical problems involving volume of cyliners, cones, and spheres. Grade: 8 Subject: Math

STAGE 2

Understandings:

They will build upon understandings of circles and volume from the 7th grade to find the volume of cylinders, cones, and spheres.

They will apply geometric formulas to solve real-world problems.

Geometric formulas for

cylinders, cones, and

spheres are related to one

another.


How does geometry better describe

objects?

Revised Blooms

Creating:

Can the student




formulate & write.

Evaluating:

Can the student

justify a stand

or decision?



value & evaluate

Analyzing:






question & test.

Applying:

Can the student




operate, schedule,


Understanding:


concepts?


identify, locate,

recognize, report,

select, translate

& paraphrase

Remembering:


the information?



reproduce & state


(Evidences)


Hand signals

One Minute Essay

Analogy Prompt

Web or Concept Map

Misconception Check

Student Conference

3-Minute Pause

Observation


Exit Card

Portfolio Check

Quiz

Journal Entry

Choral Response

A-B-C Summaries

Debriefing





Think-Pair-Share

Ticket to Leave


Oral Questioning

Discussion


Graphic Organizers





Laundry Day

Four Corners


Appointment Clock

As I See it


Fill in blanks with your choice of projects

found in possible strategies

o Multiple choice o Grid response o Interactive Projects

___________________ o Foldable o Portfolio o Student based Learning

Projects __________________

o Blog/Wiki Response o Powerpoint presentations o ___________________ o ___________________

STAGE 3









Resources:

“Teaching the Common Core Math Standards with Hands-

On Activities”; pages 234-236

“Carnegie Learning Series, Course 3”; Chapter 14; pages

745-796

NWRESA – Dee Hanlin

Flashdrive 8.6 “Modeling: Making Matchsticks” – Dee

Hanlin

www.figurethis.org

Video:

www.coll_HeyMath/VolumeofCone

Strategies:

KWL

Think-Pair-Share

Learning Logs

2-Column Notes

Exit Cards

http://www.figurethis.org/

http://www.coll_heymath/VolumeofCone

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