# Course Syllabus

Pre Algebra is a blended learning class developed for up to 20 students age 13-15 (primarily 8th grade). The main purpose is to offer prescriptive remediation and/or enrichment to the face-to-face instruction. This is a one-semester course. Ideally, each student will work 20-40 minutes weekly on this online portion of the course, but students who are unfamiliar with navigating this type of course may find they need to schedule additional time.

The course is set up in Moodle learning management system, or LMS.

## Navigation Menu

Course Description and Objectives

Course Goals

Lesson Overview

Course Schedule and Assignments

Instruction and Community Builders

Final Project

Grading Policy

Academic Honesty

Standards

## Course Description and Objectives

This course is designed to encourage the development of mathematical problem-solving skills individually, within a group, and as a class. This course will also further develop students’ basic math skills in decimals and integers, algebraic equations and inequalities, exponents, factors, and fractions, ratios, rates, and proportions, percentages, and geometry.

The prescriptive nature of the course is to facilitate remediation or enrichment based on the diverse academic needs of the learners. The lessons will be presented in a sequential manner once the teacher opens up the lesson to the individual learners.

## Course Goals

Increase standardized test scores by following the Common Core State Standards (National Governors Association Center for Best Practices (NGA Center) and the Council of Chief State School Officers (CCSSO), 2011) . Specifically, students will demonstrate their ability to:

· Identify and compare rational and irrational numbers

· Evaluate expressions and equations

· Define, evaluate, and compare functions

· Identify foundations of geometry

· Interpret statistics & probability

### The Number System

Overview - Lesson 1.01 Rational and Irrational Numbers

Overview - Lesson 1.02 Rational and Irrational Numbers - Part 2

### Expressions and Equations

Overview - Lesson 2.01 Radicals & Integer Exponents

Overview - Lesson 2.02 Square & Cube Roots

Overview - Lesson 2.03 Using Powers of 10 when estimating,

Overview - Lesson 2.04 Scientific Notation

Overview - Lesson 2.05 Plotting Linear Equations on Cartesian Coordinate

### Functions

Overview - Lesson 3.01 Introduction to Functions

Overview - Lesson 3.02 Modeling Relationships Between Two Quantities

Overview - Lesson 3.03 Determining the Rate of Change

### Geometry

Overview - Lesson 4.01 Congruency and Similarity

Overview - Lesson 4.02 Pytahgorean Theorem

Overview - Lesson 4.03 Volume of Cylinders, Cones, and Spheres

### Statistics and Probability

Overview - Lesson 5.01 Scatter Plots

Overview - Lesson 5.02 Two-way Tables, Relative Frequencies, and Associations

## Course Schedule and Assignments:

Detailed assignments are available from within the Module. Students will have the ability to open a desired module at any time, but will be required to successfully complete the module prior to moving on to another module.

Modules and associated activities are shared below:

## Instruction & Community Builders

## Modules 1 – 5

Research Module topic using links to assigned readings and video (provided within Module)

Respond to Problem of the Week in the Discussion Forum

Post responses of two or more classmates

Submit assignment

## Final Project (required):

Create a Prezi of 20 important mathematical concepts learned throughout the year.

## Course Evaluation (Survey)

## Assignments and Grading

Assignments (discussion forum, drop box, blog, Apangea progress, etc) will be delivered at the beginning of each lesson within the Module, and are due the following Sunday night. More than one assignment can be completed weekly.

The learning log provides information on each module.

Graded assignments will be posted with comments within the grade book. Grading will be as follows:

**Points Possible**

Five Modules (200 points each whether delivered online or as an in-class activity) 1000

Respond to assigned problem in the Discussion Forum 20

Post responses of two or more classmates (Discussion Forum) 20

Online assignment (drop box submission) 50

Complete daily in-class assignments 50

Complete corresponding Apangea lesson 50

Submit Problem of the Week Blog __10__

**Total points available per module 200**

Pre-assessment (5 total) 10 points each 50

Post-assessment (5 total) 50points each 250

Weekly benchmark testing – 10 points x 20 weeks 200

Extra credit opportunities

Icebreaker and community building activities 10 points each (x 5) 50

End of course assessment (50 points extra credit) 50

A | B | C | D |
---|---|---|---|

1350-1500 | 1200-1349 | 1050-1199 | 900-1049 |

## Academic Honesty:

Online coursework is subject to the same copyright policy as face-to-face coursework. Please be especially mindful of copyright laws when posting to discussion forums and submitting assignments. All online assignments will be subject to the School’s Academic Honesty policy.

## Standards

This course is designed with the Western Governor's Common Core outcome standards in mind. The National Governors Association for Best Practices (NGA Center) and the Council of Chief State School Officers collaborated with administrators, teachers, and experts to provide a "clear and consistent framework to prepare our children for college and the workforce."

**ISTE/NETS Standards:**

**2. Communication and Collaboration**

Students use digital media and environments to communicate and work collaboratively, including at a distance, to support individual learning and contribute to the learning of others.

Students:

a. interact, collaborate, and publish with peers, experts, or others employing a variety of digital environments and media.

b. communicate information and ideas effectively to multiple audiences using a variety of media and formats.

c. develop cultural understanding and global awareness by engaging with learners of other cultures.

d. contribute to project teams to produce original works or solve problems.

**5. Digital Citizenship**

Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.

Students:

a. advocate and practice safe, legal, and responsible use of information and technology.

b. exhibit a positive attitude toward using technology that supports collaboration, learning, and productivity.

c. demonstrate personal responsibility for lifelong learning.

d. exhibit leadership for digital citizenship.

**6. Technology Operations and Concepts**

Students demonstrate a sound understanding of technology concepts, systems, and operations.

Students:

a. understand and use technology systems.

b. select and use applications effectively and productively.

c. troubleshoot systems and applications.

d. transfer current knowledge to learning of new technologies

**Common Core State Standards:**

In Grade 8, instructional time should focus on three critical areas: (1) formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations; (2) grasping the concept of a function and using functions to describe quantitative relationships; (3) analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem.

8.NS.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.

8.NS.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).

8.EE.1. Know and apply the properties of integer exponents to generate equivalent numerical expressions.

8.EE.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.

8.EE.3. Use numbers expressed in the form of a single digit times a whole-number power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.

8.EE.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.

8.EE.5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

8.EE.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.

8.EE.7. Solve linear equations in one variable.

8.EE.8. Analyze and solve pairs of simultaneous linear equations.

8.F.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.

8.F.2. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

8.F.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.

8.F.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.

8.F.5. Describe qualitatively the functional relationship between two quantities by analyzing a graph. Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

8.G.1. Verify experimentally the properties of rotations, reflections, and translations:

8.G.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.

8.G.3. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

8.G.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.

8.G.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.

8.SP.1. 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 association, linear association, and nonlinear association.

8.SP.2. 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.

8.SP.3. Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.

8.SP.4. 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 two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.

8.G.6. Explain a proof of the Pythagorean Theorem and its converse.

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

8.G.9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

#### Problem of the Week

In addition to assignments, quizzes and tests, students will develop math skills through the weekly enrichment activity, or Problem of the Week (POW). This problem will be due the last day of each week (normally Thursday). Each POW has four parts - the main problem and three exercises which further develop the strategy introduced in the main problem.