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7th Grade Go Math - Advanced Pacing Guide 2016-2017 Teacher Name ________________ Pd ______This Pacing Guide is a suggestion for you to use “as a guide”. Each class should progress at its’ own pace. Although there are a few quizzes

listed in the pacing guide, teachers SHOULD quiz students as needed to check for understanding.1st 9-weeks - There are 47 teaching days

8/15/16 – 10/20/16 See individual lessons in the Lesson Plan Bank

Labor Day Holiday 9/5/16Fall Holiday 10/12/16First Day / Week Procedures Remember that you may have a fire drill and assemblies this week.Baseline – Progress Monitoring Test This Baseline should ONLY be 1 day.

1 The Baseline will be paper and pencil but the answer bubble sheets will be scanned through Data Director for scoring.

Unit 1 – The Number System ---- General Math 2 textbook to cover the topics NOT in the advanced bookLessons – HMH Go Math –7th Grade Advanced Math

Florida Standards

Benchmarks& Math Practices

MAFS

Days/ Dates

Learning Goal:“Students will be able to:”

Homework Assignment andTeacher Notes

Module 1 – Adding and Subtracting Integers

7.NS.1.17.NS.1.3

1.1 Adding Integers with the Same Sign

EQ – How do you add integers with the same sign?

7.NS.1.17.NS.1.1b

MP 5.1 Using Tools

1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers.

1.2 Adding Integers with Different Signs

EQ – How do you add integers with different signs?

NOTE: 1st day – hands on activities with 2 color counters

7.NS.1.17.NS.1.1b

MP 5.1 Using Tools

2(including

quiz)

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers.

1.3 Subtracting Integers

EQ – How do you subtract integers?

7.NS.1.1cMP 2.1

Reasoning

2 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers.

1.4 Applying Addition and Subtraction of Integers (Real World Problems)EQ – How do you solve multi-step problems involving addition and subtraction of integers?

7.NS.1.37.NS.1.1

7.NS.1.1d7.EE.2.3

MP 1.1 Problem Solving

2 Solve real world and mathematical problems involving the four operations with rational numbers.

Module 1 Review - Ready to go on? 1

Module 1 Assessment 1

Lessons – HMH Go Math –7th Grade Advanced Math

Florida Standards


MAFS

Days/ Dates



Module 2 – Multiplying and Dividing Integers

7.NS.1.27.NS.1.3

2.1 Multiplying Integers

EQ – How do you multiply integers?

7.NS.1.2MP 2.1

Reasoning

1 Multiply rational numbers given real world situations.

2.2 Dividing Integers

EQ – How do you divide integers?

7.NS.1.2MP 7.1 Using

Structure

1 Divide rational numbers given real world situations.

2.3 Applying Integer Operations (Real World Problems) Time for Quiz?EQ – How can you use integers operations to solve real-world problems?

7.NS.1.3MP 4.1

Modeling

1 Solve real world and mathematical problems

involving the four operations with rational numbers.




Florida Standards


MAFS

Days/ Dates



Module 3 – Rational Numbers 7.NS.1.17.NS.1.27.EE.2.3

3.1 Rational Numbers and Decimals

EQ – How can you convert a rational number to a decimal?

7.NS.1.2dMP 3.1 Logic

1 Convert a rational number to a decimal using long division.

3.2 Adding Rational NumbersEQ – How can you add rational numbers?

7.NS.1.1d7.NS.1.3MP 2.1

Reasoning

1 Apply properties operations as strategies to add rational numbers given real world situations.

3.3 Subtracting Rational NumbersTime for Quiz?

EQ – How do you subtract rational

7.NS.1.17.NS.1.1c

MP 2.1 Reasoning

2(including

quiz)

Understand subtraction of rational numbers as adding the inverse.

numbers?3.4 Multiplying Rational Numbers

EQ – How do you multiply rational numbers?

7.NS.1.27.NS.1.2a7.NS.1.2c

MP 2.1 Reasoning

1 Apply properties of operations as strategies to multiply rational numbers.

3.5 Dividing Rational Numbers

EQ – How do you divide rational numbers?

7.NS.1.27.NS.1.2b

7.NS.1.2c MP 4.1 Modeling

1 Apply properties of operations as strategies to divide rational numbers.

3.6 Applying Rational Number Operations (Real World Problems)

EQ – How do you use different forms of rational numbers and strategically choose tools to solve problems?

7.EE.2.37.NS.1.3

MP 1.1 Problem Solving

1 Solve multi step real world problems involving positive and negative rational numbers.


Module 3 Assessment 1UNIT 1 Review & Assessment OPTIONAL


Florida Standards


MAFS

Days/ Dates



Unit 2 – Ratios and Proportional RelationshipsModule 4 – Rates and Proportionality 7.RP.1.1

7.RP.1.24.1 Unit Rates

EQ – How do you find and use unit rates?

7.RP.1.1MP 4.1

Modeling

1 Compute unit rates associated with ratios of fractions, lengths, areas and other quantities.

4.2 Constant Rates of Change

EQ – How can you identify and represent proportional relationships?

7.RP.1.27.RP.1.2a7.RP.1.2b7.RP.1.2c

MP 2.1 Reasoning

1 Recognize and represent proportional relationships between quantities.

4.3 Proportional Relationships and Graphs

EQ – How can you use graphs to represent and analyze proportional relationships?

7.RP.1.2a7.RP.1.2b7.RP.1.2c7.RP.1.2d

MP 4.1

1 Decide whether two quantities are in a proportional relationship by graphing

ModelingModule Review - Ready to go on? 1

Module 4 Assessment 1Lessons – HMH Go Math –7th Grade Advanced Math

Florida Standards


MAFS

Days/ Dates



Module 5 – Proportions and Percent 7.RP.1.27.RP.1.3

5.1 Percent Increase and DecreaseEQ – How do you use Percents to describe change?

7.RP.1.3MP.2.1 - Reason abstractly and quantitatively.

1 Use percent and proportions to find the amount by which real-world quantities have increased or decreased.

5.2 Rewriting Percent Expressions

EQ – How can you rewrite expressions to help you solve markup and markdown problems?

7.EE.1.2MP.5.1 - Using

appropriate tools.

2 Understand that rewriting an expression in different

forms in a problem context can shed light on the problem and how the quantities in it are related.

5. 3 Applications of Percent

EQ – How do you use Percents to solve problems?

7.RP.1.3MP.4.1 - Model

with mathematics.

Use percent and proportions to find the amount by which real-world quantities have increased or decreased.

Module Review - Ready to go on? p. 159 1Module 5 Assessment 1

You are NOW working in the Advanced Math 2 textbook!


Florida Standards

Benchmarks& Math PracticesMAFS

Days/ Dates



Unit 1 – Expressions, Equations and InequalitiesModule 1 – Expressions and Equations 7.EE.1.1

7.EE.1.27.EE.2.4

7.EE.2.4a1.1 Algebraic Expressions

EQ – How do you add, subtract, factor, and multiply algebraic expressions?

7.EE.1.17.EE.1.2

MP.4.1 - Model with

mathematics

2 Apply properties of operations as strategies to add, subtract, factor and expand linear expressions with rational coefficients.

Understand that rewriting an expression in different forms in a problem context can shed light on the

“Clue Words” Includes Distributive Property

problem and how the quantities in it are related.

1.2 One-Step Equations

EQ – How do you use one-step equations with rational coefficients to solve problems?Time for Quiz? Hands On Equations Includes all 4 operations and rational

coefficients

7.EE.2.4MP.7.1 - Look for and make

use of structure.

3(including

quiz)

Use variables to represent quantities in a real-world or mathematical problem, and construction simple equations…to solve problems by reasoning about the quantities.

1.3 Writing Two-Step Equations

EQ – How do you write a two-step equation?

7.EE.2.4MP.1.1 - Make

sense of problems and persevere in

solving them.

2


1.4 Solving Two-Step Equations EQ – How do you solve a two-step equation? Hands On Equations Ready to go on?

7.EE.2.4aMP.4.1 - Model

with Mathematics


Module 1 Review 1


Teachers should be here by October 20, 2016Teacher Planning Day 10/21/162nd 9-weeks -- There are 33 teaching days and 3 exam days / Early Release Days

10/24/16 – 12/16/16

Veteran’s Day 11/11/16Thanksgiving Holiday 11/23/16 – 11/25/16Middle School Exams – Mid-Year Progress Monitoring Test - (Early Release Days)

12/14/16 12/15/16 & 12/16/16


Florida Standards


Days/ Dates



Module 2 – Inequalities 7.EE.2.4b2.1 Writing and Solving One-Step 7.EE.2.4b Use variables to represent quantities in a real-world

Inequalities

EQ – How do you write and solve one-step inequalities?

MP.1.1 - Make sense of

problems and persevere in

solving them.

1 or mathematical problem, and construct simple … inequalities to solve problems by reasoning about the quantities.

2.2 Writing Two-Step Inequalities

EQ – How do you write a two-step inequality?

7.EE.2.4MP.2.1 - Reason

abstractly & quantitatively

2 Use variables to represent quantities in a real-world

or mathematical problem, and construction simple equations…to solve problems by reasoning about the quantities.

2.3 Solving Two-Step Inequalities

EQ – How do you solve a two-step inequality?

7.EE.2.4bMP 5.1 Using

Tools


Module Review - Ready to go on? 1


Unit 1 Review & Assessment OPTIONAL


Florida Standards


Days/ Dates



Unit 2 – GeometryModule 3 – Modeling Geometric Figures

7.G.1.17.G.1.27.G.1.37.G.2.5

3.1 Similar Shapes and Scale DrawingsTime for Quiz?EQ – How can you use scale drawings to solve problems?

7.G.1.1MP.4.1 - Model

with mathematics.

2-3(including

quiz)

Solve problems involving scale drawings of geometric figures, including computing actual lengths & areas from a scale drawing & reproducing a scale drawing at a different scale.

3.2 Geometric Drawings

EQ – How can you draw shapes that satisfy given conditions?

7.G.1.2MP.5.1 - Using

appropriate tools.

1 Draw…geometric shapes, with given conditions. Focus on constructing triangles.

3.3 Cross Sections

EQ – How can you identify cross sections of three-dimensional figures?

7.G.1.3MP.4.1 - Model

with mathematics

1 Describe the two-dimensional figures that result from slicing three-dimensional figures…

3.4 Angle Relationships 7.G.2.5MP.2.1 - Reason

2 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem

EQ – How can you use angle relationships to solve problems?

abstractly and quantitatively.

to write & solve simple equations for an unknown angle in a figure.

Module Review - Ready to go on? 1



Florida Standards


MAFS

Days/ Dates



Module 4 – Circumference, Area, and Volume

7.G.2.47.G.2.6

4.1 Circumference

EQ: How do you find and use the circumference of a circle?

7.G.2.4MP7.1 Using

Structure

1 Find the circumference of a circle.

4.2 Area of Circles

EQ: How do you find the area of a circle?

7.G.2.4MP.4.1 Modeling

1 Know the formulas for the area and circumference of a circle and use them to solve problems.

4.3 Area of Composite Figures

EQ: How do you find the area of composite figures?

7.G.2.6MP.5.1 Using

Tools

2 Solve real-world and mathematical problems involving area, volume, and surface area of two- and three- dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

4.4 Solving Surface Area ProblemsTime for Quiz?EQ: How can you find the surface area of a figure made up of cubes and prisms?

7.G.2.6MP.4.1

Modeling

3(including

quiz)

Solve real-world and mathematical problems involving area, volume, and surface area of two- and three- dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms

4.5 Solving Volume Problems

EQ: How can you find the volume of a figure made of cubes and prisms?

7.G.2.6MP.7.1 Using

Structure

2 Solve real world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.



Semester Exams – Early Release DaysMid-Year Progress Monitoring Test

12/14/16 & 12/15/1612/16/16

Winter Holidays 12/17/16 – 1/2/173rd 9-weeks -- There are 47 teaching days.

1/4/17 – 3/10/17

Teacher Planning Day 1/3/17Martin Luther King Day 1/16/17


Florida Standards


MAFS

Days/ Dates



Unit 3 – Statistics and Sampling

Module 5 – Random Samples and Populations

7.SP.1.17.SP.1.2

5.1 - Populations and Samples

EQ: How can you use a sample to fain information about a population?

7.SP.1.1MP.6.1 Precision

1 Understand that random sampling tends to produce representative samples & support valid inferences.

5.2 - Making Inferences from a Random Sample

EQ: How can you use a sample to gain information about a population?

NOTE: Students will create and make inferences from dot plots and box plots.

7.SP.1.17.SP.1.27.SP.1.2c

MP.4.1 - Model with

mathematics

1 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest.

5.3 Generating Random Samples

EQ – How can you generate and use random samples to represent a population?

7.SP.1.2MP.5.1 Using

Tools

1 Use data from a random sample to draw inferences about a population.

Module 5 Review – Ready to Go On? p163 1


Teachers should be here by 12/9/16 Mid-Year Progress Monitoring ends here…Lessons – HMH Go Math –7th Grade Advanced Math

Florida Standards


MAFS

Days/ Dates



MODULE 6 - ANALYZING & COMPARING DATA

7.SP.2.37.SP.2.4

Lesson 6.1 - Comparing Data Displayed in Dot PlotsEQ: How can you compare two sets of data

7.SP.2.37.SP.2.4

MP.7.1 - Look 1

Use measures of center and measures of variability…to draw informal comparative inferences about two populations.

displayed in dot plots?NOTE: Pull a worksheet from 6th grade lesson 16.4

for & make use of structure.

Lesson 6.2 - Comparing Data Displayed in Box Plots

EQ: How can you compare data displayed in box plots?NOTE: Pull a worksheet from 6th grade lesson 16.3

7.SP.2.37.SP.2.4

MP.2.1- Reason abstractly and quantitatively.

1 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities.

Lesson 6.3 - Using Statistical Measures to Compare Populations

EQ: How can you use statistical measures to compare populations?MAD – Mean Absolute DeviationNOTE: Pull a worksheet from 6th grade lesson 16.2.

7.SP.2.37.SP.2.4

MP.6.1 - Attend to Precision.

2 Informally assess…two numerical data distributions…measuring the difference between the centers by expressing it as a multiple of a measure of variability.

Module 6 Review –Ready to Go On? pg. 163

1




Florida Standards


Days/ Dates



Module 7 – Experimental ProbabilityModule 8 – Theoretical Probability and Simulations

TEACHERS: We have combined these 2 modules. We felt that experimental and theoretical probability should be taught together … not as two separate modules.

You will have to prepare the lessons together ahead of time.

Use “REAL WORLD PROBLEMS” as often as possible because that is how the students will be tested!

**Check with Denise Williams if you need to check out sets of regular dice and/or Polyhedra dice for your students to preform experiments.

She also has worksheets for the experiments (including frequency tables) and graphs to represent those experiments if you wish to use them.

Experiments with dice, coins, and marbles would be helpful in showing the different in theoretical probability (what “should” happen) with the experimental probability (what happens in “real life”).

7.1 - Probability

EQ: How can you describe the likelihood of an event?

7.SP.3.57.SP3.7a

MP.6.1 - Attend to Precision.

1 Understand that the probability of a chance event is a number between 0 & 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood.

Dice Experiment(use the data from the experiments to illustrate theoretical vs experimental probabilities)

1

8.1 Theoretical Probability of Simple Events

EQ: How can you find the theoretical probability of a simple event?

7.SP.3.77.SP.3.7a

MP7.1 Using Structure 2

(including quiz)

Develop a probability model and use the model to determine probabilities of events.

Approximate the probability of an event by collecting data, observing its frequency, and predict the relative frequency.

7.2 - Experimental Probability of Simple Events

Time for Quiz?

EQ: How do you find the experimental probability of a simple event?

7.SP.3.67.SP.3.7b

MP.4.1 - Model with

mathematics

Approximate the probability of a chance event by collecting data on the chance process that produces it & observing its long-run relative frequency.

8.2 Theoretical Probability of Compound Events

EQ: How do you find the theoretical probability of a compound event?

7.SP.3.87.SP.3.8a7.SP.3.8b

MP.2.1 Reasoning

1 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulations.

Lesson 7.3 - Experimental Probability of Compound Events

Time for Quiz?

EQ: How do you find the experimental probability of a compound event?

7.SP.3.87.SP.3.8a7.SP.3.8b7.SP.3.8c

MP.2.1 - Reason abstractly and quantitatively

2

(including quiz)

Find probabilities of compound events using tables and simulations.

Lesson 7.4 - Making Predictions with Experimental Probability

EQ: How do you make predictions using experimental probability?

7.SP.3.6MP.4.1 - Model

with mathematics

1 Approximate the probability of a chance event by collecting data on the chance process that produces it…, and predict the approximate relative frequency given the probability.

8.3 Predictions with Theoretical Probability 7.SP.3.6 1 Approximate the probability of a chance by collecting

EQ: How do you make predictions using theoretical probability?

7.SP.3.7aMP.4.1 -

Modeling

data, observing its relative frequency, and predicting the relative frequency given the probability.

Probability Review 1

Probability Test 1



Florida Standards


MAFS

Days/ Dates

Learning Goal: “Students will be able to:”


Unit 5 – Real Numbers, Exponents, and Scientific NotationModule 9 - Real Numbers 8.NS.1.1

8.NS.1.2

9.1 Rational and Irrational NumbersEQ: How do you rewrite rational numbers and decimals, take square roots and cube roots?

NOTE: NO calculator

Students should “know” perfect square numbers and perfect cube numbers up through 12² and 6³

8.NS.1.18.NS.1.28.EE.1.2

2 Know and understand characteristics of rational and irrational numbers. Understand that every number has a decimal expansion.

Use rational approximations of irrational numbers to compare size of irrational numbers, locate them on a number line (approx.) and estimate the value of expressions (e.g. squared)

Use square and cube root symbols to represent solutions to equations.

Know that √2 is irrational.

9.2 Sets of Real Numbers

EQ: How can you describe relationships between sets of real numbers?

8.NS.1.1MP.7.1 Using

Structure

1 Know and understand characteristics of rational and irrational numbers. Understand that every number has a decimal expansion.

9.3 Ordering Real Numbers

EQ: How do you order a set of real numbers?

8.NS1.2MP.4.1

Modeling

1 Compare size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g.π2)

Module 9 Review - Ready to Go On? 1

Module 9 Test 1



Days/ Dates


Homework Assignment and

Florida Standards MAFS Teacher NotesModule 10 Exponents and Scientific Notation

8.EE.1.18.EE.1.38.EE.1.4

10.1 Integer Exponents

EQ: How can you develop and use the properties of integer exponents?

Positive and Negative Exponents

8.EE.1.1MP.8.1 Patterns

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

10.2 Scientific Notation with Positive Powers of 10

EQ: How can you use scientific notation to express very large numbers?

8.EE.1.3MP.4.1

Modeling

1 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small numbers, and to express how many times as much one is than the other.

10.3 Scientific Notation with Negative Powers of 10

EQ: How can you use scientific notation to express very small numbers?

8.EE.1.3 MP.2.1 Reasoning

1 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small numbers, and to express how many times as much one is than the other.

10.4 Operations with Scientific Notation

EQ: How do you add, subtract, multiply, and divide using scientific notation?

8.EE.1.4MP.1.1 Problem

Solving

2 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used.

Module 10 ReviewReady to Go On?

1




Florida Standards


MAFS

Days/ Dates



Review Modules before FSA Testing in April

Review Module 1 These Modules are all in the 7th Grade General Book.Review Module 2

Review Module 3

Review Module 4

Review Module 5

Review Module 6

Review Module 1 These Modules are all in the 7th Grade Advanced Book.Review Module 2

Review Module 3

Review Module 4

Review Module 5

Review Module 6

Review Module 7

Review Module 8

Teachers – Use the time both during and after the FSA to either dig deeper into an area from during the year, or move on to the next grade level of lessons. Below is s suggested option which begins in Module 9 of the Advanced 2, 7th.

Spring Break 3/13/17 – 3/17/17

Teacher Planning Day 3/20/17

4th 9-weeks Dates - There are 47 teaching days and 3 Exam / Early Release Days

3/21/17 – 5/30/17

Middle School Exams (Early Release Days) 5/25/17 & 5/26/17 & 5/30/17


Florida Standards


MAFS

Days/ Dates



Unit 6 – Proportional and Nonproportional Relationships and Functions

Module 11 – Proportional Relationships 8.EE.2.58.EE.2.68.F.1.28.F.2.4

11.1 Representing Proportional Relations

EQ – How can you use tables, graphs, and

8.EE.2.68.F.2.4

1 Use tables, graphs, and equations to represent proportional situations.

equations to represent proportional relationships?

y=kx

MP 4.1 Modeling

11.2 Rate of Change and Slope

EQ – How do you find a rate of change or a slope?NOTE: Discuss that rate of change and slope are the SAME thing…

8.F.2.4 2

11.3 Interpreting the Unit Rate and Slope

EQ – How do you interpret the unit rate as slope?

8.EE.2.58.F.1.28.F.2.4MP 4.1

Modeling

2 Interpret the unit rate as slope.

Module Review - Ready to Go On? 1Module 11 Assessment 1


Florida Standards


MAFS

Days/ Dates



Module 12 – Nonproportional Relationships

8.EE.2.68.F.1.28.F.1.38.F.2.4

12.1 Representing Linear Nonproportional Relationships

EQ – How can you use tables, graphs, and equations to represent linear nonproportional situations?

NOTE: Model writing equations both from tables and from graphs.

y=kx and y=mx+b

8.F.1.3MP 4.1

Modeling

2 Interpret the equation y=mx+b as defining a linear function, whose graph is a straight line: give examples of nonlinear functions.

12.2 Determining Slope and y-intercept

EQ - How do you find a rate of change or a slope?Time for Quiz?

8.NS.1.18.NS.1.28.EE.1.2MP 7.1

Structure

2(including quiz)

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.

12.3 Graphing Linear Non-Proportional Relationships using slope and y-intercept?

8.NS.1.1

MP 6.1

1 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two

EQ – How can you graph a line using the slope and y-intercept?

Precision populations. 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.

12.4 Proportional and Nonproportional Situations

EQ – How can you distinguish between proportional and nonproportional situations?

8.NS.1.18.NS.1.28.EE.1.2

MP 6.1 Precision

1 Compare 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 nonlinear functions.

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.

Module Review - Ready to Go On? 1Module 12 Assessment 1 Great Opportunity for an Activity or Project to Assess Student Learning

These lessons can be taught after the FSA…Lessons – HMH Go Math –7th Grade Advanced Math

Florida Standards


MAFS

Days/ Dates



Module 19 – Angle Relationships in Parallel Lines and Triangles

E.Q.- How can you use angle relationships in parallel likes and triangles to solve real-world problems?

8.EE.2.68.EE.3.7

8.EE.3.7b8.G.1.5

Lesson 19.1- Parallel Lines cut by Transversal(include complementary, supplementary, vertical and adjacent)

8.G.1.5 MP.6.1- Precision

2 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

E.Q.- What can you conclude about the angles formed by parallel lines that are cut by a transversal?

transversal, and the angle-angle criterion for similarity of triangles.

Lesson 19.2- Angle Theorems for Triangles

E.Q.- What can you conclude about the measures of the angles of a triangle?

8.EE.3.78.EE.3.7b8.G.1.5

MP.5.1- Using Tools

2 Solve linear equations in one variable. Solve linear equations with rational number

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

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.

Lesson 19.3- Angle –Angle Similarity

E.Q.- How can you determine when two triangles are similar?

8.EE.2.68.EE.3.7

8.G.1.5 MP.4.1- Modeling

2 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y=mx for a line through the origin and the equation y=mx+b for a line intercepting the vertical axis at b.

Solve linear equations in one variable. 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.

Module 19 Review 1 Great Opportunity for an Activity or Project to Assess Student Learning



Florida Standards


MAFS

Days/ Dates



Module 20 The Pythagorean Theorem

E.Q. - How can you use the Pythagorean Theorem to solve real-world problems?

8.G.2.68.G.2.78.G.2.8

Lesson 20.1- The Pythagorean Theorem

E.Q. - How can you prove the Pythagorean Theorem and use it to solve problems?

8.G.2.68.G.2.7

MP.5.1- Using Tools

1-2 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.

Lesson 20.2- Converse of the Pythagorean Theorem

E.Q. - How can you test the converse of the Pythagorean Theorem and use it to solve problems?

8.G.2.6MP.7.1-

Structure

1 Explain a proof of the Pythagorean Theorem and its converse.

Lesson 20.3- Distance Between Two Points

E.Q. - How can you use the Pythagorean Theorem to find the distance between two points on a coordinate plane?

8.G.2.8MP.2.1-

Reasoning

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

Module 20 Review 1

Module 20 Assessment 1 Great Opportunity for an Activity or Project to Assess Student Learning

Final Exam Days – (Early Release Days)

5/25/175/26/175/30/17

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