BELLE VERNON AREA SCHOOL DISTRICT

GENERAL SYLLABUS OUTLINE

**This syllabus is subject to change**

Course Name:

Title I Math

Grade:

1-5

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:

2.1.3     Numbers, Number Systems and Number Relationships

v

Count using whole numbers (to 10,000) and by 2's, 3's, 5's, 10's, 25's and 100's.

v

Use whole numbers and fractions to represent quantities.

v

Represent equivalent forms of the same number through the use of concrete objects,

drawings, word names, and symbols.

v

Use drawings, diagrams, or models to show the concept of fraction as part of a whole.

v

Count, compare, and make change using a collection of coins and one-dollar bills.

v

Apply number patterns (even and odd) and compare values of numbers on the hundred

board.

v

Use concrete objects to count, order, and group.

v

Demonstrate understanding of one-to-one correspondence.

v

Apply place-value concepts and numeration to counting, ordering, and grouping.

v

Estimate, approximate, round, or use exact numbers as appropriate.

v

Describe the inverse relationship between addition and subtraction.

v

Demonstrate knowledge of basic facts in four basic operations.

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.

2.2.3     Computation and Estimation

v

Apply addition and subtraction situations using concrete objects.

v

Solve singe and double digit addition and subtraction problems with regrouping in vertical

form.

v

Demonstrate concept of multiplication as repeated addition and arrays.

v

Demonstrate concept of division as repeated subtraction and as sharing.

v

Use estimation skills to arrive at conclusions.

v

Determine the reasonableness of calculated answers.

v

Explain addition and subtraction algorithms with regrouping.

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.

2.3.3     Measurement and Estimation

v

Compare measurable characteristics or different objects on the same dimensions (time,

temperature, area, length, weight, capacity, perimeter).

v

Determine the measurement of objects with non-standard (e.g., US customary and metric)

units.

v

Determine and compare elapsed times.

v

Tell time (analog and digital) to the minute.

v

Determine appropriate unit of measure.

v

Use concrete objects to determine area and perimeter.

v

Estimate and verify measurements.

v

Demonstrate that a single object has different attributes that can be measured in different

ways (e.g., length, mass/weight, time, area, temperature, capacity, and perimeter).

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.

2.4.3     Mathematical Reasoning and Connections

v

Make, check, and verify predictions about the quantity, size, and shape of objects and

groups of objects.

v

Use measurements to determine the geography of the school building.

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.

2.5.3     Mathematical Problem Solving and Communication

v

Use appropriate problem solving strategies such as guess and check and working

backwards.

v

Determine when sufficient information is present to solve a problem and explain how to

solve a problem.

v

Select and use an appropriate method, materials, and strategy to solve problems, including

mental mathematics, paper and pencil, and concrete objects.

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.

2.6.3     Statistics and Analysis

v

Gather, organize, and display data using pictures, tallies, charts, bar graphs, and pictographs.

v

Formulate and answer questions based on data shown on graphs.

v

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

v

Form and justify an opinion on whether a given statement is reasonable based on a

comparison to data.

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.

2.7.3     Probability and Predictions

v

Predict and measure the likelihood of events and recognize that the results of an

experiment may not match predicted outcomes.

v

Design a fair and an unfair spinner.

v

List or graph the possible results of an experiment.

v

Analyze data using the concepts of largest, smallest, most often, least often, and middle.

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.

2.8.3     Algebra and Functions

v

Recognize, describe extend, create, and replicate a variety of patterns including attribute,

activity, number and geometric patterns.

v

Use concrete objects and trial and error to solve number sentences and check if solutions

are sensible and accurate.

v

Substitute a missing addend in a number sentence.

v

Create a story to match a given combination of symbols and numbers.

v

Use concrete objects and symbols to model the concepts of variables, expressions,

equations, and inequalities.

v

Explain the meaning of solutions and symbols.

v

Gather information and display it in the form of a table or chart.

v

Describe and interpret the data shown in tables and charts.

v

Demonstrate simple function rules.

v

Analyze simple functions and relationships and locate points on a simple grid.

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.

2.9.3     Geometry

v

Name and label geometric shapes in two and three dimensions (circle/sphere, square/

cube, triangle/pyramid, rectangle/prism).

v

Build geometric shapes using concrete objects (manipulatives).

drawings, word names, and symbols.

v

Draw two and three dimensional geometric shapes and construct rectangles, squares,

and triangles on the geoboard and on graph paper satisfying specific criteria.

v

Find and describe geometric figures in real life.

v

Identify and draw lines of symmetry in geometric figures.

v

Identify symmetry in nature.

v

Fold paper to demonstrate the reflections about a line.

v

Show relationships between and among figures using reflections.

v

Predict how shapes can be changed by combining or dividing them.

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).

2.10.3     Trigonometry

v

Identify right angles in the environment.

v

Model right angles and right triangles using concrete objects.

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.

2.11.3     Concepts of Calculus

v

Identify whole number quantities and measurements from least to most and greatest

value.

v

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

v

Categorize rates of change as faster and slower.

v

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

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.

4.)

Course Text:

v  The following materials are used as needed:

v  Houghton-Mifflin Mathematics 2002

v  PSSA Mathematics Coach

5.)

Major Units or Themes:  (Include the following)

v     Grade 1

v     Grade 2

Addition Concepts

Addition & Subtraction Facts

Subtraction Concepts

Numbers & Patterns to 100

Addition & Subtraction Facts to 10

Data and Graphing

Data and Graphing

Money

Numbers and Patterns to 100

Adding two-digit numbers

Addition and Subtraction Facts to 12

Subtracting two-digit numbers

Money

Geometry, Fractions, and Probability

Geometry, Fraction, and Probability

Multiplication and Division

Addition and Subtraction Facts to 20

Measurement

Measurement

Time and Calendar

Time and Calendar

Numbers and Patters to 100

Two-digit Addition and Subtraction

Adding & Subtracting three-digit numbers

v     Grade 3

v     Grade 4

Place Value

Place Value and Money

Money and Time

Addition and Subtraction

Addition and Subtraction

Relating Multiplication and Division

Measurement

Multiplication of Whole Numbers

Multiplication Concepts

Division of one-digit Divisors

Multiplication Facts

Measurement and Negative Numbers

Geometry and Measurement

Fractions and Mixed Numbers

Division Concepts

Decimals

Division Facts

Statistics and Probability

Data and Probability

Geometry and Measurement

Fractions and Decimals

Graphing and Algebra

Multiplying and Dividing Greater Numbers

Division by two-digit numbers

v     Grade 5

Whole Numbers, Decimals, and Integers

Addition, Subtraction, and Equations

Multiplication

Division and Equations

Measurement and Integers

Data, Statistics, and Probability

Number Theory and Addition and Subtraction of Fractions

Multiplication and Division of Fractions

Multiplication and Division of Decimals

Geometry and Measurement

Ratio and Percent

Integers and the Coordinate Plane

6.)

Teaching Methods:

v     ETA Versa Tiles

v     Lightspan Adventures and Playstation

v     Computers

v     Math Sharks

v     Worksheets

v     Board Work

v     Games

v     Guided Practice

v     Cooperative Learning

v     Direct Instruction

7.)

Assessment:

v     Pre-Assessment Test

v     Benchmark Test

v     Post-Assessment Test

v     Diagnostic Test