BELLE VERNON AREA SCHOOL DISTRICT

GENERAL SYLLABUS OUTLINE

**This syllabus is subject to change**

Course Name:

Mathematics

Grade:

5

1.)

Course Description:

Fifth grade mathematics is a course designed to develop grade level mathematics concepts and skills.

The focus on problem solving and reasoning provides opportunities for students to demonstrate and

apply their understanding.  Students are prompted to explain their thinking, share their strategy, or

identify a more efficient strategy.  Instruction focuses on the why and the how of mathematics so that

students see connections, make generalizations, and use knowledge effectively.

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.

2.2.5     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.

2.3.5     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.

2.4.5     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.

2.5.5     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.

2.6.5     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.

2.7.5     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.

2.8.5     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.

2.9.5     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).

2.10.5     Trigonometry

v

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

hypotenuse, and legs.

v

Create right triangles and a geoboard.

2.11.5     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  Houghton Mifflin Mathematics, Boston--Morris Plains, N.J.

v  PSSA Mathematics Coach, Grade 5--Jerome D. Kaplan, Ed.D.

(Supplemental Material)

5.)

Major Units or Themes:  (Include the following)

v     Place Value Concepts with Whole Numbers

Read, Write, and Identify Place Value in Whole Numbers Through Billions, and Decimals

Through Thousandths

Compare Positive and Negative Integers and Positive and Negative Decimals

v     Addition, Subtraction, and Equations

Adding and Subtracting Whole Numbers Through Hundred Millions

Adding and Subtracting Decimals Through Thousandths

Writing and Evaluating Expressions, Using Algebra with Variables

v     Multiplication

Multiplying by 1 and 2 Digit Numbers

Multiplying With Zeros

Mental Math--Multiplying by 10, 100, or 1,000

v     Division

Dividing by 1 and 2 Digit Divisors

Dividing into 4 and 5 Digit Dividends

Estimating Quotients

Finding the Mean

v     Measurement

Measuring Customary and Metric Units of Length

Measuring Area, Perimeter, Weight, and Capacity

Adding and Subtracting Units of Time

v     Data, Statistics, and Probability

Making and Gathering Information from Stem-and-Leaf Plots, Bar Graphs, and Histograms

Finding Mean, Median, Mode, and Range

Defining and Determining Probability

v     Addition and Subtraction of Fractions

Writing and Comparing Fractions with Equivalent Fractions

Adding and Subtracting Fractions with Like and Unlike Denominators

Adding and Subtracting Mixed Numbers

Solving Problems Using Patterns

Identifying Prime and Composite Numbers

v     Geometry

Identifying Basic Properties of Plane Figures

Classifying Plane Figures

Identifying Parallel and Perpendicular Lines and Angles

Identifying Symmetry

v     Multiplication and Division of Fractions

Multiplying Fractions and Mixed Numbers

Dividing Fractions and Mixed Numbers

Choosing Operation to Solve a Problem

Problem Solving Using Circle Graphs

v     Multiplication and Division of Decimals

Multiplying and Dividing Decimals by Whole Numbers

6.)

Teaching Methods:

7.)

Assessment:

v     Cooperative Learning

v     Informal Observation

v     Demonstration

v     Mid-Chapter Evaluations

v     Guided Practice

v     End of Chapter Evaluations

v     Lecture/Discussion

v   Teacher Made Assessments (Quizzes)

v     Facilitated Inquiry

v     Homework Assignments

v     Using Manipulatives

v     Open-Ended Questions