BELLE VERNON AREA SCHOOL DISTRICT

GENERAL SYLLABUS OUTLINE

**This syllabus is subject to change**

Course Name:

General Math 7

Grade:

7

1.)

Course Description:

General Math incorporates a review of topics that were initially covered in 6th grade and an introduction

of concepts that will be further developed in higher-level mathematics classes (algebra, geometry, etc)

Its purpose is to allow students to improve in the basic concepts over an extended period of time.

2.)

Learning Standards:

2.1

Numbers, Number Systems and Number Relationships

2.2

Computation and Estimation

2.3

Measurement and Estimation

2.4

Mathematical Reasoning and Connections

2.5

Mathematical Problem Solving and Communication

2.6

Statistics and Data Analysis

2.7

Probability and Predictions

2.8

Algebra and Functions

2.9

Geometry

2.10

Trigonometry

2.11

Concepts of Calculus

3.)

Student Objectives:

2.1.8     Numbers, Number Systems and Number Relationships

v

Represent and use numbers in equivalent forms (integers, fractions, decimals, percents,

exponents, scientific notation and square roots).

v

Simplify numerical expressions involving exponents, scientific notation and using order of

operations.

v

Distinguish between and order rational and irrational numbers.

v

Apply ratio and proportion to mathematical situations involving distance, rate, time,

and similar triangles.

v

Simplify and expand algebraic expressions using exponential forms.

v

Use the number line model to demonstrate integers and their applications.

v

Use the inverse relationships between addition, subtraction, multiplication, division, and

exponentiation and root extraction to determine unknown quantities in equations.

2.2.8     Computation and Estimation

v

Complete calculations by applying the order of operations.

v

Add, subtract, multiply, and divide different kinds of forms of rational numbers including

integers, decimal fractions, percents, and proper and improper fractions.

v

Solve word problems using ratio and proportion.

v

Estimate the value of irrational numbers.

v

Estimate amount of tips and discounts using ratios, proportions, and percents.

v

Determine appropriateness of overestimating or underestimating in computation.

v

Identify the difference between exact value and approximations and determine which is

appropriate for a given situation.

v

Check the reasonableness of an answer.

2.3.8     Measurement and Estimation

v

Develop formulas and procedures for determining measurements (e.g. area, volume,

distance, etc.)

v

Solve rate problems (e.g. rate x time = distance, principal x interest rate = interest, etc.)

v

Measure angles in degrees and determine relations of angles.

v

Estimate, use, and describe measures of distance, rate, perimeter, area, volume, capacity,

weight, mass, and angles.

v

Describe how a change in linear dimension of an object affects its perimeter, area, and

volume.

v

Use scale measurements to interpret maps or drawings.

v

Create and use scale models.

2.4.8     Mathematical Reasoning and Connections

v

Make conjectures based on logical reasoning and test conjectures by using

counter-examples.

v

Combine numeric relationships to arrive at a conclusion.

v

Use if…then statements to construct simple valid arguments.

v

Construct, use, and explain algorithmic procedures for computing and estimating with

whole numbers, fractions, decimals, and integers.

v

Distinguish between inductive and deductive reasoning.

v

Use measurements and statistics in family and consumer science.

2.5.8     Mathematical Problem Solving Communication

v

Invent, select, use, and justify the appropriate methods, materials, and strategies used

to solve problems.

v

Verify and interpret results using precise mathematical language, notation, and

representations, including numerical tables and equations, simple algebraic equations and

formulas, charts, graphs, and diagrams.

v

Justify strategies and defend approaches used and conclusion reached.

v

Determine pertinent information in problem situations, and whether any further information is

needed for solution.

2.6.8     Statistics and Data Analysis

v

Compare and contrast different plots of data using values of mean, median, mode,

quartiles and range.

v

Explain effects on reliability of sampling procedures and of missing or incorrect information.

v

Fit a line to the scatter plot of two quantities and describe any correlation of the variables.

v

Design and carry out a random sampling procedure.

v

Analyze the display data in stem-and leaf and box-and whisker plots.

v

Use scientific and graphing calculators and computer spreadsheets to organize and

analyze data.

v

Determine the validity of the sampling method described in studies published in local or

national newspapers.

2.7.8     Probability and Predictions

v

Determine the number of combinations and permutations of an event.

v

Present the results of an experiment using visual representations (tables, charts, and

graphs).

v

Analyze predictions such as election polls.

v

Compare and contrast from observations and mathematical models.

v

Make valid inferences, predictions and arguments based on probability.

2.8.8     Algebra and Functions

v

Apply simple algebraic patterns to basic number theory and to spatial relations.

v

Discover, describe, and generalize patterns, including linear, exponential and simple

quadratic relationships.

v

Create and interpret expressions, equations, or inequalities that model problem situations.

v

Use concrete objects to model algebraic concepts.

v

Select and use a strategy to solve an equation or inequality, explain the solution and check

the solution for accuracy.

v

Solve and graph equations and inequalities using scientific and graphing calculators and

computer spreadsheets.

v

Represent relationships with tables, graphs in the coordinate plane, and verbal or

symbolic rules.

v

Graph a linear function for a rule or table.

v

Generate a table or graph from a function and using graphing calculators and computer

spreadsheets to graph and analyze functions.

v

Show that an equality relationship between two quantities remains the same as long as

the same change is made to both quantities; and explain how a change in one quantity

determines another quantity in a functional relationship.

2.9.8     Geometry

v

Construct figures incorporating perpendicular and parallel lines, the perpendicular

bisector of a line segment and an angle bisector using computer software.

v

Draw, label, measure and list the properties of complementary, supplementary, and

vertical angles.

v

Classify familiar polygons as regular or irregular up to a decagon.

v

Identify, name, draw and list all properties of squares, cubes, pyramids, parallelograms,

quadrilaterals, trapezoids, polygons, rectangles, rhombi, circles, spheres, triangles,

prisms, and cylinders.

v

Construct parallel lines, draw a transversal, measure and compare angles formed such as

alternate interior and exterior angles.

v

Distinguish between similar and congruent polygons.

v

Approximate the value of π (pi) through experimentation.

v

Use simple geometric figures such as triangles to create, through rotation, transformational

figures in three dimensions.

v

Generate transformations using computer software.

v

Analyze geometric patterns, such as tessellations and sequences of shapes, and develop

descriptions of the patterns.

v

Analyze objects to determine if they illustrate tesselations, symmetry, congruence,

similarity, and scale.

2.10.8     Trigonometry

v

Compute measures of sides and angles using proportions, the Pythagorean Theorem, and

right triangle relationships.

v

Solve problems requiring indirect measurement for lengths of sides of triangles.

2.11.8     Concepts of Calculus

v

Analyze graphs of related quantities for minimum and maximum values and justify.

v

Describe concept of unit rates, ratios, and slope in the context of rate of change.

v

Continue a pattern of numbers or objects that could be extended infinitely.

4.)

Course Text:

v  Passport to Mathematics--McDougal, Littel

5.)

Major Units or Themes:  (Include the following)

v     Problem Solving

Diagrams

Experiments

Guess and Check

Write an Equation

Logical Reasoning

v     Number Relations and Fractions

Order of Operations

Powers and Exponents

Divisibility Rules

Prime Factorization

Greatest Common Factor

Least Common Multiple

v     Fraction Operations

Mixed Numbers and Improper Fractions

Add, Subtract, Multiply, and Divide Fractions

v     Algebra and Integers

Scatter Plots and the Coordinate Plane

Add, Subtract, Multiply, and Divide Integers

v     Data Analysis and Statistics

Measures of Central Tendency

Histograms

Box-and-Whisker Plots

Probability

v     Ratio and Proportions

Ratios

Rates

Proportions

Similar Polygons

Scale Drawings

v     Percents and Decimals

Finding Percents

The Percent Proportion

Large and Small Percents

Percent Increase and Decrease

v     Geometry in the Plane

Parallel Lines

Angle Relationships

Circumference and Area

6.)

Teaching Methods:

v     Cooperative Learning

v     Demonstration

v     Guided Practice

v     Lecture/Discussion

7.)

Assessment:

v     Tests/Quizzes

v     Homework

v     Take Home Graded Assignments