Pre-Algebra Syllabus

**CALENDAR and UNITS for SEMESTER 1 of PRE-ALGEBRA.**

**This school year, we will be covering the following. All dates are according to the Akron Public Schools pacing guide, but can/will be adjusted by me as needed. Also, all assessment dates are a goal, but may be adjusted as needed. Not only will there be formal assessments, but there will be several informal assessments of learning, including observation of classwork/homework, participation in class, group work and discussions. The indicators (objectives) for each unit are numbered.GRADING PERIOD 1**

__Unit 1 Data Analysis September 1 – September 22__

You Will:

- Use, create and interpret scatterplots and other types of graphs as appropriate. [DAP8A1]

- Evaluate different graphic representations of the same data to determine which representation is the most appropriate for an identified purpose; e.g. line graph for change over time, circle graph for part-to-whole comparison, scatterplot for relationship between two variants. [DAP8B2]
- Explain the mean’s sensitivity to extremes and its use in comparison with the median and mode. [DAP8C5]

4. Compare two sets of data using measures of center (mean, mode, median) and measures of spread (range, quartiles, interquartile range, percentiles). [DAP8D4]

5. Make conjectures about possible relationship in a scatterplot and approximate line of best fit. [DAP8F6]

6. Identify different ways of selecting samples, such as survey response, random sample, representative sample, and convenience sample. [DAP8G7]

7. Describe how the relative size of a sample compared to the target population affects the validity of predictions. [DAP8E8]

**Enduring Understandings:**

Students can create a representative survey, collect data, analyze data, choose an appropriate graph to represent the data, and construct convincing arguments based on the analysis and interpretation of the data.

**Essential Questions:**

• What is data analysis?

• Why is data analysis important?

• How is data analysis used?

• Why is it important to select the appropriate graph to represent collected data?

• Why is choosing an appropriate sample important?

• What considerations should be made when selecting an appropriate sample?

Unit 1 Partial Assessment: Friday, September 17

__Unit 2: Patterns in Geometry September 23 – October 8__You Will:

1. Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two-dimensional figures and three-dimensional objects. GEO8B2

2. Use proportions in several forms to solve problems involving similar figures (part-to-part, part-to-whole, corresponding sides between figures). GEO8B3

3. Represent and analyze shapes using coordinate geometry; e.g., given three vertices and the type of quadrilateral, find the coordinates of the forth vertex. GEO8D4

4. Demonstrate understanding of the concepts of perimeter, circumference and area by using established formulas for triangles, quadrilaterals, and circles to determine the surface area and volume of prisms, pyramids, cylinders, spheres and cones. (Note: Only volume should be calculated for spheres and cones.) Mea8C9

5. Find the sum of the interior and exterior angles of regular convex polygons with and without measuring the angles with a protractor. Mea8E8

6. Find the square root of perfect squares, and approximate the square root of non-perfect squares as consecutive integers between which the root lies; e.g., is between 11 and 12. NNSO8H7

**Enduring Understandings:**

• There is a relationship among the angles within polygons or transversed lines

• Classifications of polygons

• Square roots as related to the Pythagorean Theorem

**Essential Questions:**

• Why study patterns in geometry?

• What careers directly connect to patterns in geometry?

• What is pi and why is it important to know?

• Why is it important to know about angle relationships?

• Why is it important to know about the characteristics of polygons?

• What is the relationship of finding square roots to the Pythagorean Theorem?

Unit 2 Assessment: Friday, October 8

__Unit 3 Integers and Variable Expressions October 11 – October 25__You Will:

1. Apply order of operations to simplify expressions and perform computations involving integers, exponents and radicals. (NNSO8I3)

- Explain and use the inverse and identity properties and use the inverse relationships (addition/subtraction/multiplication/division, squaring/square roots) in problem solving situations. (NNSO8C4)
- Understand how to add/subtract/multiply/divide integers without a calculator.
- Use the order of operations to evaluate an expression which contains integers, exponents, and square roots (radicals).
- Write variable expressions for word phrases.
- Use, explain and identify the properties.

**Enduring Understandings:**

Students can write variable expressions and use the properties to simplify variable expressions that include integers, exponents, and square roots (radicals).

**Essential Questions:**

• What is the purpose of using integers and variable expressions?

• When is writing a variable expression an appropriate strategy?

• Why is simplifying expressions important?

• How are the properties useful in simplifying expressions?

Grading Period closes Friday, October 29, 2010.

Nine Week Assessment Window: October 25-October 29. I will let you know the specific date when I know it.

**Grading Period 2**

__Unit 4: Writing and Solving Equations November 1-November 19__You Will:

1. Use symbolic algebra (equations and inequalities), graphs, and tables to represent situations and solve problems. [PFA8DF7]

2. Write, simplify, and evaluate algebraic expressions (including formulas) to generalize situations and solve problems. [PFA8D8]

3. Be able to write and solve multi-step equations and inequalities.

(Prerequisites: Order of operations, simplifying expressions, and the properties.)

**Enduring Understandings:**

• Identify when to write and solve an equation given a table, graph, or symbolic representation without direct instruction.

**Essential Questions:**

• What is the purpose of solving equations?

• Does every equation have an answer?

• What does the answer to an equation represent in a problem solving situation?

• How does solving equations relate to real-world situations?

Unit 4 Assessment: Friday, November 19

__Unit 5 Graphing in the Coordinate Plane November 22-December 17__You Will:

1. Relate the various representations of a relationship; i.e., relate a table to graph, description, and symbolic form. [PFA8C1]

2. Describe the relationship between the graph of a line and its equation, including being able to explain the meaning of slope as a constant rate of change and y- intercept in real-world problems. [PFA8EG6]

3. Solve linear equations and inequalities graphically, symbolically, and using technology. [PFA8F9]

4. Solve 2 by 2 systems of linear equations graphically and by simple substitution. [PFA8H10]

5. Interpret the meaning of the solution of a 2 by 2 systems of equations; i.e. point, line, no solution. [PFA8H11]

6. Compute and interpret slope, midpoint, and distance given a set of ordered pairs. [PFA8I13]

7. Describe and compare how changes in a equation affects the related graphs; e.g., for a linear equation changing the coefficient of x affects the slope and changing the constant affects the intercepts. [PFA8J15]

8. Using graphing calculators or computers to analyze change; e.g., interest compounded over time as a nonlinear growth pattern. [PFA8J16]

8. Draw the results of translation, reflections, rotations, and dilations of objects in the coordinate plane, and determine properties that remain fixed; e.g., lengths of sides remain the same under translations. [GEO8F5]

9. Extend the set of variables to include covariants where y depends on x. [PFA8D4]

**Enduring Understandings:**

Using graphs, equations, and transformations to solve problems by relating concepts of slope (constant rate of change), y-intercept, distance, midpoint, and systems to real-world situations.

**Essential Questions:**

• When is a relationship between two variables linear?

• What does a linear relationship represent?

• What are the various ways that a linear relationship can be represented?

• What is the coordinate plane and how is it useful?

Unit 5 Assessment: Wednesday, December 15

__Unit 6: Functions January 3 – January 29__You Will

1. Generalize patterns and sequences by describing how to find the nth term. [PFA8A2]

2. Identify functions as linear or nonlinear based on information given a table, graph, or equation. [PFA8B3]

3. Relate the various representations of a relationship; i.e., relate a table to graph, description, and symbolic form. [PFA8C1]

4. Solve simple quadratic equations graphically; e.g., y = x2 - 16 [PFA8G12]

5. Differentiate and explain types of changes in mathematical relationships, such as linear vs. nonlinear, continuous vs. non-continuous, direct variation vs. indirect variation. [PFA8I14]

6. Differentiate between discrete and continuous data and appropriate ways to represent each. [DAP8B3]

**Enduring Understandings:**

Identify patterns from tables, graphs, and symbolic form to represent and solve real-world problems.

**Essential Questions:**

• How can linear and nonlinear graphs be used to represent situations outside the classroom?

• How are patterns and sequences used to identify relationships?

• What is a function, and why are functions important in the study of mathematics?

Grading Period and Semester Ends January 20, 2011

Semester Exam Window: January 12- January 20, 2011. Exact Dates will be given as we get closer.

**GRADING**

Everything is on a total point system. The breakdown is below.

__Homework__: 5-10 pts, depending on length. Plan on HW every day except for Friday.

__Bellwork__: 5-10 pts., depending on length. Plan on BW every day.

__Classwork__: 5-10 points, depending on length

__Quizzes__: 20-30 points

__Assessments__: 30-100 points

A: 93-100% A-: 90-92%

B+:88-89% B: 83-87% B-: 80-82%

C+: 78-79% C: 73-77% C-:70-72%

D+: 68-69% D: 63-67% D-:60-61%

F: Below 60%

** An important note concerning homework, classwork, and bellwork:** Full credit is given for honest completion of entire assignment. I do not check right or wrong. IF YOU DO ALL OF THE WORK, YOU WILL GET ALL OF YOUR POINTS. The idea of homework, classwork and bellwork is to practice what we are learning. We will go over as many of the problems from each particular assignment as necessary in order to achieve mastery of that particular concept. Bellwork will be overall skills review in order to keep up for the OAA in the spring.

Once again, I hope you find this useful. It is long and detailed, but I do want you to be fully prepared for what is coming up this semester. I will go over the objectives with you in a way that I hope will bring understanding/comprehension.

I plan to be available for tutoring/extra help on certain days after school. I will let you know specifically when that is.

I hope this school year is a good one for you, and for the class as a whole.

Mr. Berringer