BELLE VERNON AREA SCHOOL DISTRICT

GENERAL SYLLABUS OUTLINE

**This syllabus is subject to change**

Course Name:

Title I Math

Grade:

6-8

1.)

Course Description:

This class is a supplemental math class for students experiencing difficulty with math.  Students

receive additional assistance with their math skills based on their individual needs.  Various teaching

techniques are used to address different learning styles.

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:

2.1.5     Numbers, Number Systems and Number Relationships

v

Use expanded notation to represent whole numbers as decimals.

v

Apply number theory concepts to rename a number quantity.

v

Demonstrate that mathematical operations can represent a variety of problem situations.

v

Use models to represent fractions and decimals.

v

Explain the concepts of prime and composite numbers.

v

Use simple concepts of negative numbers such as s on a number line, in counting, and

temperature.

v

Develop and apply number theory concepts (e.g. primes, factors, multiples, and

composites) to represent numbers in various ways.

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.

2.2.5     Computation and Estimation

v

Create and solve word problems involving addition, subtraction, multiplication, and division

of whole numbers.

v

Develop and apply algorithms to solve word problems that involve addition, subtraction,

and/or multiplication with decimals with and without regrouping, fractions and mixed numbers,

that include like and unlike denominators.

v

Demonstrate the ability to round numbers.

v

Determine through estimations the reasonableness of answers to problems involving

addition, subtraction, multiplication, and division of whole numbers.

v

Demonstrate skills for using fraction calculators to verify conjectures, confirm computations,

and explore complex problem solving situations.

v

Apply estimation strategies to a variety of problems including time and money.

Explain multiplication and division algorithms.

v

Select a method for computation and explain why it is appropriate.

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.

2.3.5     Measurement and Estimation

v

Select and use appropriate instruments and units for measuring quantities such as

perimeter, volume, area, weight, time, and temperature.

v

Select and use standard tools to measure the size of figures with specific accuracy,

including length, width, perimeter, and area.

v

Estimate, refine, and verify specified measurements of objects.

v

Convert linear measurements within the same system.

v

Add and subtract measurements.

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.

2.4.5     Mathematical Reasoning and Connections

v

Compare quantities and magnitudes of numbers.

v

Use models, number facts, properties, and relationships to check and verify predictions

and explain reasoning.

v

Draw inductive and deductive conclusions within mathematical contexts.

v

Distinguish between relevant and irrelevant information in a mathematical problem.

v

Interpret statements made with precise language of logic (i.e. all, every none, some, or

many).

v

Use statistics to quantify issues in social studies.

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.

2.5.5     Mathematical Problem Solving and Communication

v

Develop a plan to analyze a problem, identify the information needed to solve the problem,

carry out the plan, check whether the answer makes sense and explain how the problem

was solved.

v

Use appropriate mathematical terms, vocabulary, and language symbols and graphs to

clearly and logically explain solutions to problems.

v

Show ideas in a variety of ways, including words, numbers, symbols, pictures, charts,

graphs, tables, diagrams, and models.

v

Connect, extend, and generalize problems solutions to other concepts, problems and

circumstances in mathematics.

v

Select, use, and justify the methods, materials and strategies used to solve problems.

v

Use appropriate problem solving strategies such as solving a simpler problem or drawing

a picture or diagram.

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.

2.6.5     Statistics and Data Analysis

v

Organize and display data using pictures, tallies, tables, charts, bar graphs, and circle

graphs.

v

Describe data sets using mean, median, mode, and range.

v

Sort data using Venn diagrams.

v

Predict the likely number of times a condition will occur based on the analyzed data.

v

Construct and defend simple conclusions based on data.

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.

2.7.5     Probability and Predictions

v

Perform simulations with concrete devices (dice, spinner, etc.) to predict the chance of

an event occurring.

v

Determine the fairness of the design of a spinner.

v

Express probabilities as fractions and decimals.

v

Compare predictions based on theoretical probability and experimental results.

v

Calculate the probability of a simple event.

v

Determine patterns generated as a result of an experiment.

v

Determine the probability of an event involving "and", "or", "not".

v

Predict and determine why some outcomes are certain, more likely, less likely, equally

likely or impossible.

v

Find all possible combinations and arrangements involving a limited number of variables.

v

Make a tree diagram and list the elements in the sample space.

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.

2.8.5     Algebra and Functions

v

Recognize, reproduce, extend, create, and describe patterns, sequences and relationships

verbally, numerically, symbolically and graphically, using a variety of materials.

v

Connect patterns to geometric relations and basic number skills.

v

Form rules based on patterns (e.g., an equation that relates pairs in a sequence).

v

Use concrete objects and combinations of symbols and numbers to create expressions

that model mathematical situations.

v

Explain the use of combinations of symbols and numbers in expressions, equations, and

inequalities.

v

Describe a realistic situation using information given in equations, inequalities, tables, or

graphs.

v

Select and use appropriate strategies, including concrete materials, to solve number

v

sentences and explain the method of solution.

v

Locate and identify points on a coordinate system.

v

Generate functions from tables of data and relate data to corresponding graphs and functions.

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.

2.9.5     Geometry

v

Give formal definitions of geometric figures.

v

Classify and compare triangles and quadrilaterals according to sides or angles.

v

Identify and measure circles, their diameters and radii.

v

Describe in words how geometric shapes are constructed.

v

Construct two and three dimensional shapes and figures using Manipulatives, geoboards,

computer software.

v

Find similar solids in the environment and describe them.

v

Create an original tesselation.

v

Describe the relationship between the perimeter and area of triangles, quadrilaterals,

and circles.

v

Represent and use the concepts of line, point, and plane.

v

Define the basic properties of squares, pyramids, parallelograms, quadrilaterals,

trapezoids, polygons, rectangles, rhombi, circles, triangles, cubes, prisms, spheres, and

cylinders.

v

Analyze simple transformations of geometric figures and rotations of line segments.

v

Identify properties of geometric figures (i.e., parallel, perpendicular, similar, congruent,

symmetrical).

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.

2.10.5     Trigonometry

v

Identify and compare parts of right triangle including right angles, acute angles,

hypotenuse, and legs.

v

Create right triangles and a geoboard.

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.

2.11.5     Concepts of Calculus

v

Make comparisons of numbers such as more, less, same, least, most, greater than and

less than.

v

Identify least and greatest values represented in bar and circle graphs.

v

Identify maximum and minimum.

v

Describe the relationship between rates of change and time.

v

Estimate areas and volumes as the sums of areas of tiles and volumes of cubes.

v

Describe the relationship between the size of the unit measurement and the estimate of

the areas and volumes.

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  6th

Mathematics, Houghton-Mifflin

v  7th

Passport to Algebra and Geometry Book 2, McDougal and Little

v  8th

Passport to Algebra and Geometry, McDougal and Little

5.)

Major Units or Themes:  (Include the following)

v     Grade 6

Operations with Numbers and Decimals

Data Analysis

Fractions

Ratios Proportions and Percent

Probability

v     Grade 7

Problem Solving

Number Relations

Fractions

Ratios and Proportions

Basic Algebra

Percents and Decimals

Geometry

v     Grade 8

Number Patterns

Algebra

Data and Graphs

Ratios and Proportions

Geometry

6.)

Teaching Methods:

v     Guided Practice

v     Lightspan Adventures and Playstation

v     Cooperative Learning

v     Math Sharks

v     Demonstration

v     Tutorials

v     Hands-on Activities

v     Tutorial Software on Laptops/PC

v    Math Activities and Games

7.)

Assessment:

Assessment to track student progress only

v     Pre-Assessment Test

v     Benchmark Test

v     Post-Assessment Test