Ref: GIS Math G 8 A, B, E, F. 2017-2018

2011-2012

SUBJECT : Math TITLE OF COURSE : Algebra 1, Geometry

GRADE LEVEL : 8

DURATION : ONE YEAR

NUMBER OF CREDITS : 1.25

Goals:

The Number System 8.NS Know that there are numbers that are not rational, and approximate them by

rational numbers. 1. Know that numbers that are not rational are called irrational.

Understand informally that every number has a decimal expansion; for rational numbers show

that the decimal expansion repeats eventually, and convert a decimal expansion which repeats

eventually into a rational number.

2. Use rational approximations of irrational numbers to compare the size of irrational numbers,

locate them approximately on a number line diagram, and estimate the value of expressions (e.g.,

π2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2,

then between 1.4 and 1.5, and explain how to continue on to get better approximations.

Expressions and Equations 8.EE Work with radicals and integer exponents. 1. Know and apply the properties of integer exponents to generate equivalent numerical

expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27.

2. Use square root and cube root symbols to represent solutions to equations of the form x2 = p

and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares

and cube roots of small perfect cubes. Know that √2 is irrational.

3. 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.

For example, estimate the population of the United States as 3×108 and the population of the

world as 7 × 109, and determine that the world population is more than 20 times larger.

4. Perform operations with numbers expressed in scientific notation, including problems where

both decimal and scientific notation are used. Use scientific notation and choose units of

appropriate size for measurements of very large or very small quantities (e.g., use millimeters per

year for seafloor spreading). Interpret scientific notation that has been generated by technology.

Understand the connections between proportional relationships, lines, and linear

equations. 5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare

two different proportional relationships represented in different ways. For example, compare a

distance-time graph to a distance-time equation to determine which of two moving objects has

greater speed.

6. Use similar triangles to explain why the slope m is the same between any two distinct points

on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the

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

Analyze and solve linear equations and pairs of simultaneous linear equations. 7. Solve linear equations in one variable.

a. Give examples of linear equations in one variable with one solution, infinitely many solutions,

or no solutions. Show which of these possibilities is the case by successively transforming the

given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b

results (where a and b are different numbers).

b. Solve linear equations with rational number coefficients, including equations whose solutions

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

8. Analyze and solve pairs of simultaneous linear equations.

a. Understand that solutions to a system of two linear equations in two variables correspond to

points of intersection of their graphs, because points of intersection satisfy both equations

simultaneously.

b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by

graphing the equations.

Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x +

2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

c. Solve real-world and mathematical problems leading to two linear equations in two variables.

For example, given coordinates for two pairs of points, determine whether the line through the

first pair of points intersects the line through the second pair.

Functions 8.F Define, evaluate, and compare functions. 1. 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.1

2. Compare properties of two functions each represented in a different way (algebraically,

graphically, numerically in tables, or by verbal descriptions). For example, given a linear

function represented by a table of values and a linear function represented by an algebraic

expression, determine which function has the greater rate of change.

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

give examples of functions that are not linear.

For example, the function A = s2 giving the area of a square as a function of its side length is not

linear because its graph contains the points (1,1),(2, 4) and (3, 9), which are not on a straight line.

Use functions to model relationships between quantities. 4. Construct a function to model a linear relationship between two quantities. Determine the rate

of change and initial value of the function from a description of a relationship or from two (x, y)

values, including reading these from a table or from a graph. Interpret the rate of change and

initial value of a linear function in terms of the situation it models, and in terms of its graph or a

table of values.

5. 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.

Geometry 8.G Understand congruence and similarity using physical models, transparencies, or

geometry software. 1. Verify experimentally the properties of rotations, reflections, and translations:

a. Lines are taken to lines, and line segments to line segments of the same length.

b. Angles are taken to angles of the same measure.

c. Parallel lines are taken to parallel lines.

2. 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.

3. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional

figures using coordinates.

4. 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.

5. 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. For example, arrange three copies of the same triangle so that the sum

of the three angles appears to form a line, and give an argument in terms of transversals why this

is so.

Understand and apply the Pythagorean Theorem. 6. Explain a proof of the Pythagorean Theorem and its converse.

7. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-

world and mathematical problems in two and three dimensions.

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

system.

Solve real-world and mathematical problems involving volume of cylinders, cones,

and spheres. 9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve

real-world and mathematical problems.

Resources: 1- HMH Algebra 1, Geometry text book.

2- Online resources

3- HMH attached resources CD’S (lesson tutorial videos, power point presentations, one

stop planer,…..)

4- Internet.

5- E-games and links

6- Teacher’s Handouts

Course Content and Objectives:

Algebra 1 Unit 1: Quantities and Modeling

Module 2: Algebraic Models

2.2: Creating and solving equations

Creating Equations from Verbal Descriptions

Creating and Solving Equations Involving the Distributive Property

Creating and Solving Equations with Variables on Both Sides

Constructing Equations from an Organized Table

2.3: Solving for a variable

Rearranging Mathematical Formulas

Rearranging Scientific Formulas

Rearranging Literal Equations

2.4: Creating and solving inequalities

Creating Inequalities from Verbal Descriptions

Creating and Solving Inequalities Involving the Distributive Property

Creating and Solving Inequalities with Variables on Both Sides

2.5: Creating and solving compound inequalities

Solving Compound Inequalities Involving AND

Solving Compound Inequalities Involving OR

Creating Compound Inequalities From Graphs

Expressing Acceptable Levels with Compound Inequalities

Unit 2: Understanding functions

Module 3: Functions and models

3.1: Graphing relationships

Interpreting Graphs

Relating Graphs to Situations

Sketching Graphs for Situations

3.2: Understanding relations and functions

Understanding Relations

Recognizing Functions

Understanding the Vertical Line Test

3.3: Modeling with functions

Identifying Independent and Dependent Variables

Applying Function Notation

Modeling Using Function Notation

Choosing a Reasonable Domain and Range

3.4: Graphing functions

Graphing Functions Using a Given Domain

Graphing Functions Using a Domain of All Real Numbers

Using a Graph to Find Values

Modeling Using a Function Graph

Unit 3: Linear functions, equations, and inequalities

Module 5: Linear functions

5.1: Understanding linear functions

Recognizing Linear Functions

Proving Linear Functions Grow by Equal Differences Over Equal Intervals

Graphing Linear Functions Given in Standard Form

Modeling with Linear Functions

5.2: Using intercepts

Identifying Intercepts

Determining Intercepts of Linear Equations

Interpreting Intercepts of Linear Equations

Graphing Linear Equations Using Intercepts

5.3: Interpreting rate of change and slope

Determining Rates of Change

Determining the Slope of a Line

Determining Slope Using the Slope Formula

Interpreting Slope

Module 6: Forms of linear equations

6.1: Slope- intercepts form

Graphing Lines Given Slope and y-Intercept

Creating Linear Equations in Slope-Intercept Form

Graphing from Slope-Intercept Form

Determining Solutions of Equations in Two Variables

6.2: Point-slope form

Deriving Point-Slope Form

Creating Linear Equations Given Slope and a Point

Creating Linear Models Given Slope and a Point

Creating Linear Equations Given Two Points

Creating A Linear Model Given Two Points

6.3: Standard form

Comparing Forms of Linear Equations

Creating Linear Equations in Standard Form Given Slope and a Point

Creating Linear Equations in Standard Form Given Two Points

Creating Linear Models in Standard Form

6.4: Transforming Linear Functions

Building New Linear Functions by Translating

Building New Linear Functions by Stretching, Shrinking, or Reflecting E

Understanding Function Families

Interpreting Parameter Changes in Linear Models

6.5: Comparing properties of linear functions

Comparing Properties of Linear Functions Given Algebra and a Description

Comparing Properties of Linear Functions Given Algebra and a Table

Comparing Properties of Linear Functions Given a Graph and a Description

Unit 5: Linear systems and piecewise-defined functions

Module 11: Solving systems of linear equations

11.1: Solving linear systems by graphing

Solving Consistent, Independent Linear Systems by Graphing

Solving Special Linear Systems by Graphing

Estimating Solutions of Linear Systems by Graphing

Interpreting Graphs of Linear Systems to Solve Problems

11.2: Solving linear systems by substitution Exploring the Substitution Method of Solving Linear Systems

Solving Consistent, Independent Linear Systems by Substitution

Solving Special Linear Systems by Substitution

Solving Linear System Models by Substitution

11.3: Solving linear systems by adding or subtracting Exploring the Effects of Adding Equations

Solving Linear Systems by Adding or Subtracting

Solving Special Linear Systems by Adding or Subtracting

Solving Linear System Models by Adding or Subtracting

11.4: Solving linear systems by multiplying first

Understanding Linear Systems and Multiplication

Proving the Elimination Method with Multiplication

Solving Linear Systems by Multiplying First

Solving Linear System Models by Multiplying First

Module 12: Modeling with linear systems

12.1: Creating systems of linear equations

Creating Linear System Models by Changing Parameters

Creating Linear System Models from Verbal Descriptions

Creating Linear System Models from Tables

Creating Linear System Models from Graphs

12.2: Graphing systems of linear inequalities Determining Solutions of Systems of Linear Inequalities

Solving Systems of Linear Inequalities by Graphing

Graphing Systems of Inequalities with Parallel Boundary Lines

12.3: Modeling with linear systems

Modeling Real-World Constraints with Systems

Modeling Real-World Constraints with Systems of Linear Equations

Modeling Real-World Constraints with Systems of Linear Inequalities

Unit 7: Polynomial Operations

Module 17: Adding and subtracting polynomials

17.1: Understanding polynomial expressions

Identifying Monomials

Classifying Polynomials

Writing Polynomials in Standard Form

Simplifying Polynomials

Evaluating Polynomials

17.2: Adding polynomials expressions Adding Polynomials Using a Vertical Format

Adding Polynomials Using a Vertical Format

Adding Polynomials Using a Horizontal Format

Modeling with Polynomials

17.3 Subtracting polynomial expressions

Subtracting Polynomials Using a Vertical Format

Subtracting Polynomials Using a Horizontal Format

Modeling with Polynomials

18.1 Multiplying Polynomial Expressions by Monomials

Multiplying Monomials

Multiplying a Polynomial by a Monomial

Multiplying a Polynomial by a Monomial to Solve a Real-World Problem

18.2 Multiplying polynomial expressions

Modeling Binomial Multiplication

Multiplying Binomials Using the Distributive Property

Multiplying Binomials Using FOIL

Multiplying Polynomials

Modeling with Polynomial Multiplication

18.3 Special Products of Binomials

Multiplying (a + b)2

Multiplying (a - b)2

Multiplying (a + b)(a − b)

Modeling with special products

Geometry

Unit 1: Transformations and congruence

Module 1 Tools of Geometry

1.1: Segment length and midpoints.

Exploring Basic Geometric Terms

Constructing a Copy of a Line Segment

Using the Distance Formula

Finding a Midpoint

Finding Midpoints on the Coordinate Plane

1.2 Angle Measures and Angle Bisectors.

Constructing a Copy of an Angle

Naming Angles and Parts of an Angle

Measuring Angles

Constructing an Angle Bisector

1.3 Representing and Describing Transformations

Performing Transformations Using Coordinate Notation

Describing Rigid Motions Using Coordinate Notation

Describing Non rigid Motions Using Coordinate Notation

1.4 Reasoning and Proof.

Exploring Inductive and Deductive Reasoning

Introducing Proofs

Using Postulates about Segments and Angles

Using Postulates about Lines and Planes

Module 2 Transformations and symmetry

2.1 Exploring translations

Translating Figures using vectors

Drawing translations on a coordinate plane

Specifying Translation vectors

2.2Reflections

Exploring reflections

Reflection figures using graph paper

Drawing reflections on a coordinate plane

Specifying Lines of reflection

Applying reflections

2.3 Rotations

Exploring Rotations

Rotating figures using a ruler and protractor

Drawing rotations on a coordinate plane

Simplifying rotation Angles

2.4 Investigating Symmetry

Identifying Line symmetry

Identifying rotational symmetry

Describing Symmetries

Module 3 Congruent Figures

3.1Sequences of transformations

Combining rotations or reflections

Combining rigid transformations

Combining non rigid transformations

Predicting the effect of transformations

3.2 Proving figures are congruent using rigid motions

Confirming congruence

Determining if figures are congruent

Finding a sequence of rigid motions

Investigating Congruent segments and angles

3.3 Corresponding Parts of Congruent Figures are Congruent

Exploring Congruence of Parts of Transformed Figures

Exploring Congruence of Parts of Transformed Figures.

Corresponding Parts of Congruent Figures Are Congruent

Applying the Properties of Congruence.

Using Congruent Corresponding Parts in a Proof.

Unit 2: Lines angles and triangles

Module 4 Lines and Angles

4.1 Angles Formed by Intersecting Lines.

Exploring Angle Pairs Formed by Intersecting Lines

Exploring Angle Pairs Formed by Intersecting Lines

Proving the Vertical Angles Theorem

Using Vertical Angles

Using Supplementary and Complementary Angles.

4.2 Transversals and Parallel Lines.

Exploring Parallel Lines and Transversals

Proving that Alternate Interior Angles are Congruent.

Proving that Corresponding Angles are Congruent.

Using Parallel Lines to Find Angle Pair Relationships.

4.3 Proving Lines are Parallel.

Writing Converses of Parallel Line Theorems

Proving that Two Lines are Parallel

Constructing Parallel Lines

Using Angle Pair Relationships to Verify Lines are Parallel

4.4 Perpendicular Lines

Constructing Perpendicular Bisectors and Perpendicular Lines.

Proving the Perpendicular Bisector Theorem Using Reflections

Proving the Converse of the Perpendicular Bisector Theorem

Proving Theorems about Right Angles

4.5 Equations of Parallel and Perpendicular Lines

Exploring Slopes of Lines

Writing Equations of Parallel Lines

Writing Equations of Perpendicular Lines

Module 5 Triangle Congruence Criteria

5.1 Exploring What Makes Triangles Congruent

Transforming Triangles with Congruent Corresponding Parts

Deciding If Triangles are Congruent by Comparing Corresponding Parts

Applying Properties of Congruent Triangles

5.2 ASA Triangle Congruence

Drawing Triangles Given Two Angles and a Side

Justifying ASA Triangle Congruence

Deciding Whether Triangles Are Congruent Using ASA Triangle Congruence

Proving Triangles Are Congruent Using ASA Triangle Congruence

5.3 SAS Triangle Congruence

Drawing Triangles Given Two Sides and an Angle

Justifying SAS Triangle Congruence

Deciding Whether Triangles are Congruent Using SAS Triangle Congruence

Proving Triangles Are Congruent Using SAS Triangle Congruence

5.4 SSS Triangle Congruence

Constructing Triangles Given Three Side Lengths

Justifying SSS Triangle Congruence

Proving Triangles Are Congruent Using SSS Triangle Congruence

Applying Triangle Congruence

Module 6 Applications of Triangle Congruence

6.1 Justifying Constructions

Using a Reflective Device to Construct a Perpendicular Line

Justifying the Copy of an Angle Construction

Proving the Angle Bisector and Perpendicular Bisector Constructions

6.2 AAS Triangle Congruence

Exploring Angle-Angle-Side Congruence

Justifying Angle-Angle-Side Congruence

Using Angle-Angle-Side Congruence.

Applying Angle-Angle-Side Congruence

6.3 HL Triangle Congruence

Is There a Side-Side-Angle Congruence Theorem?

Justifying the Hypotenuse-Leg Congruence Theorem

Applying the HL Triangle Congruence Theorem

Course Sequence.

Algebra 1 Term 1

Module 2: Algebraic Models 2.2: Creating and solving equations

2.3: Solving for a variable

2.4: Creating and solving inequalities

2.5: Creating and solving compound inequalities

Module 3: Functions and models

3.1: Graphing relationships

3.2: Understanding relations and functions

3.3: Modeling with functions

3.4: Graphing functions

Module 5: Linear functions

5.1: Understanding linear functions

5.2: Using intercepts

Term 2

Module 5: Linear functions

5.3: Interpreting rate of change and slope

Module 6: Forms of linear equations

6.1: Slope intercept form

6.2: Point-slope form

6.3: Standard form

Module 11: Solving systems of linear equations

11.1: Solving linear systems by graphing

11.2: Solving linear systems by substitution

11.3: Solving linear systems by adding or subtracting

11.4: Solving linear systems by multiplying first

Term 3

Module 12: Modeling with Linear Systems

12.1 : Creating Systems of Linear Equations

12.2 : Graphing Systems of Linear Inequalities

12.3 : Modeling with Linear Systems

Module 17: Adding and subtracting polynomials

17.1: Understanding polynomial expressions

17.2: Adding polynomials expressions

17.3: Subtracting polynomial expressions

Module 18: Multiplying polynomials

18.1: Multiplying polynomial expressions

18.2: Multiplying polynomial expressions

18.3: Special products of binomials

Geometry

Term 1

Module 1 Tools of Geometry

1.1: Segment length and midpoints.

1.2 Angle Measures and Angle Bisectors.

1.3 Representing and Describing Transformations

1.4 Reasoning and Proof.

Module 2: Transformations and symmetry 2.1: Translations

2.2: Reflections

2.3: Rotations

2.4: Investigating Symmetry

Module 3: Congruent figures

3.1: Sequences of transformations

3.2: Proving figures are congruent using rigid motions

Term 2

Module 3: Congruent figures

3.3: Corresponding parts of congruent figures are congruent. Module 4 Lines and Angles

4.1 Angles Formed by Intersecting Lines.

4.2 Transversals and Parallel Lines.

4.3 Proving Lines are Parallel

4.4 Perpendicular Lines

4.5 Equations of Parallel and Perpendicular Lines

Module 5 Triangle Congruence Criteria

5.1 Exploring What Makes Triangles Congruent

5.2 ASA Triangle Congruence

5.3 SAS Triangle Congruence

5.4 SSS Triangle Congruence Term 3

Module 6 Applications of Triangle Congruence

6.1 Justifying Constructions

6.2 AAS Triangle Congruence

6.3 HL Triangle Congruence

Assessment Tools and Strategies:

Strategieso 1st The students will be provided with study guides or mock tests on the school

website in the students portal, based on our curriculum manual, bench marks and

objectives before every quiz, test, or exam.

o 2nd The students will be tested based on what they have practiced at home from

the study guides or mock tests mentioned before.

o 3rd The evaluation will be based on what objectives did the students achieve, and

in what objectives do they need help, through the detailed report that will be sent

to the parents once during the semester and once again with the report card.

Tests and quizzes will comprise the majority of the student’s grade. There will be one major test

given at the end of each chapter.

Warm-up problems for review, textbook assignments, worksheets, etc. will comprise the majority of

the daily work.

Home Works and Assignments will provide students the opportunity to practice the concepts

explained in class and in the text.

Students will keep a math notebook. In this notebook students will record responses to daily warm-

up problems, lesson activities, post-lesson wrap-ups, review work, and daily textbook

assignments.

Class work is evaluated through participation, worksheets, class activities and group work done in

the class.

Passing mark 60 %

Grading Policy:

Term 1 Terms 2 and 3

Weigh

t

Frequency Weight Frequency

Class Work (Should

include MAP to Khan

and Beyond the

20% Formative (For

every New

lesson) and

Class Work (Should

include MAP to Khan

and Beyond the

25% Formative

(For every

New

standard Questions). Summative

(once a term)

standard Questions). lesson) and

Summative

(once a

term)

Homework 5% At least 4

times

Homework 5% At least 4

times

Quizzes (Should

include MAP to Khan

and Beyond the

standard Questions).

30% 2 / term Quizzes (Should

include MAP to Khan

and Beyond the

standard Questions).

40% 2/term

Project Based

Learning

10% Once in a term. Project Based

Learning

15% Once in a

term.

POP Quizzes

MAP (Based

on students

results)

Student’s/Gr

oup work.

10%

5%

Bonus

(3 %)

At least 5

times per

term.

Once per term.

POP Quizzes

MAP (Based

on students

results)

Student’s/Gro

up work.

10%

5%

Bonus (3 %)

At least 5

times per

term.

Once per

term

Mid-Year Exam 20%

Total 100 Total 100

Performance Areas (skills).

Evaluation, graphing, Application, and Analysis of the Mathematical concepts and relating them to daily life, through solving exercises, word problems and applications...

Communication and social skills: through group work, or presentation of their own work.

Technology skills: using digital resources and graphic calculators or computers to solve problems or present their work.

Note: The following student materials are required for this class:

Graph paper.

Scientific Calculator (Casio fx-991 ES Plus)

Done by Femi Antony Math teacher