Department/Grade:  Math/Grade 6        Course:  6th Grade Math           Revision Date:  April 2008

 

Required/Elective:  Required                 Course Length:  1 year  Pre-requisite: 5th  Grade Math

 

Course Description: 

 

COURSE OBJECTIVES

CONTENT OUTLINE

1.  Students will develop an understanding of numbers, number systems and number relationships.

 

 

 

 

 

 

 

 

Pennsylvania Academic Standards for Mathematics

2.1.  Numbers, Number Systems and Number Relationships

1.  Use expanded notations to represent whole numbers to infinity

     Represent, use and compare whole numbers in equivalent forms (fraction, decimals, percents, whole numbers, mixed numbers, improper fractions) Common percents are 1,10,25,50,75,100

     Develop and apply ratios and proportions to mathematical problem situations

     Use models to order and compare integers (positive and negative numbers) and represent percents through 100

     Find the value of a number written in exponential form.

    Apply number theory concepts (factor, multiples, divisibility rules for 2,3,5, and 10)

    Complete equations by using the following properties:  associative, cumulative, distributive and identity

 

 

2.  Students will apply computation and estimation skills in mathematical operations.

 

 

 

 

 

 

 

 

 

 

 

Pennsylvania Academic Standards for Mathematics

2.2.  Computation and Estimation

2.   Add, subtract, multiply and divide whole numbers, decimals, and fractions.

     Find the GCF and LCM of two numbers through 50

      Find the percent of a number

      Demonstrate through estimation the reasonableness of answers to problems involving fractions, decimals, and whole numbers (up to 2 digit divisors and 4 operations)

     Determine and apply algorithms (input and output tables) needed to solve problems that involve all operations with whole, decimal and fractional numbers

     Create and solve word problems involving all operations with whole, decimals through thousandths, and fractional numbers using materials such as diagrams, manipulatives, estimations, paper and pencil and calculators

     Use models to represent addition and multiplication of integers and percents

 

3.  The students will demonstrate an understanding of true and estimated measurements.

 

 

 

 

 

 

 

 

Pennsylvania Academic Standards for Mathematics

2.3.  Measurement and Estimation

3.  Estimate and measure objects with standard units (US Customary to the nearest 1/16th of an inch and Metric to the nearest millimeter) to find radius, diameter, length, width, perimeter, circumference, temperature

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

     Select and use appropriate instruments of measurement with specified accuracy

     Measure angles in degrees and draw angles at specified degrees

     Compare and/or determine elapsed time to the minute (time may cross a.m to p.m. or more than 1 day)

 

 

 

 

4.  The students will communicate their use of mathematical reasoning and problem solving.

 

 

 

 

 

 

 

 

Pennsylvania Academic Standards for Mathematics

2.4  Mathematical Reasoning and Connections

2.5  Mathematical Problem Solving and Communication

4.  Solve problems by developing a plan, analyzing the problem, identifying the information needed to solve the problem, carrying out the plan, checking whether the answer makes sense and is complete and explaining how the problem was solved

     Select and justify strategies necessary to solve problems

     Verify and interpret results using precise mathematical language, notation, and representations, including numerical tables and equations, formulas, charts and diagrams

     Determine when given information is relevant, pertinent, and sufficient to make conjectures based on logical reasoning and then test the conjectures

    

 

 

 

 

 

 

5.  The students will predict and interpret data they have gathered and organized.

 

 

 

 

 

 

 

 

 

 

 

Pennsylvania Academic Standards for Mathematics

2.6  Statistics and Data Analysis

2.7  Probability and Predictions

5.  Collect, organize and display data using pictures. tallies, charts, spreadsheets, frequency tables, histograms, circle graphs (including center points and tic marks), bar or double bar graphs, line or double line graphs, or line plots models, number facts, properties and relationships using correct title, label and scales

     Analyze data using mean, median, range and mode

     Perform simulations, calculate probabilities in lowest terms and make valid inferences, predictions and arguments based on theoretical probability and experimental results

     Compare and display predictions based on theoretical probability and experimental results

     Determine/show all possible combinations involving no more than 20 total arrangements (e.g., tree diagram, table, grid)

 

 

 

 

6.  The students will use algebra and functions.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Pennsylvania Academic Standards for Mathematics

2.8.    Algebra and Functions

6.  Show that an equality relationship between two quantities remains the same as long as the same change is made to both quantities

     Identify and plot ordered pairs on a coordinate system

     Select and use a strategy to solve an equation, explain the solution and check the solution for accuracy

     Recognize, reproduce, extend, create or find missing elements and describe patterns, sequence, and relationships, verbally, numerically, symbolically and graphically using a variety of materials

     Use concrete objects to model algebraic concepts

     Interpret equations and inequalities

     Create, extend or find a missing element in a pattern displayed in a table, chart, or graph (pattern mush show at least 3 repetitions-may use up to 2 operations with whole numbers

     Match an equation or expression involving one variable to a verbal math situation (one operation only)

     Solve a one-step equation (i.e. using the inverse operation-whole numbers only)

 

 

 

 

 

 

 

7.       The students will demonstrate knowledge of basic geometric and

Trigonometry concepts.

 

 

 

 

 

 

 

 

 

 

 

 

Pennsylvania Academic Standards for Mathematics

2.9  Geometry

       2.10 Trigonometry

7.  Determine when/how to find/use perimeter, area or volume in a given situation

     Solve problems requiring indirect measurement for lengths of sides of triangles (e.g. find heights of objects using shadow proportions)

     Identify, name, draw and list all properties of polygons, circles, triangles (obtuse, right, acute, scalene, equilateral, and isosceles) quadrilateral, spheres, cylinders, prisms and pyramids and identify them in the environment

     Approximate the value of (pi) through experimentation

     Use concrete objects to distinguish between similar and congruent polygons

     Use tools of geometry including compass, protractor, straightedge, ruler

     Identify, describe and/or label parallel, perpendicular or intersecting lines

     Identify, draw, and/or label points, planes, lines, line segments, rays, angles (right, acute and obtuse) and vertices

     Plot, locate or identify points in Quadrant 1 and/or on  the x and y axes (with intervals of 1,2,5, or 10 units) 

8.  The students will demonstrate basic concepts of calculus.

 

Pennsylvania Academic Standards for Mathematics

2.11.  Concepts of Calculus

8.  Find and graph data that describes the relationships between rates of change and time

     Introduce the concepts of unit rates and ratios

     Determine the repeating decimal equivalent of a fraction (1/3, 2/3, 1/9, 1/11)

 

 

RESOURCE MATERIALS

ASSESSMENT

·          McDougal-Littell Mathematics Textbook

·          Teacher Resource Package

·          Calculators

·          Geoboards

·          Cm cubes; cm squares

·          Metric measuring tools (liquid and linear)

·          US Customary Measuring Tools (liquid and linear)

·          Pattern blocks

·          Polygon blocks

·          Available computer Software/Printers

·          Tangrams

·          Compasses

·          Protractors

·          Other Manipulatives

·          Teacher Made Test and Quizzes

·          Text Book Tests and Quizzes

·          Student Written Responses

·          Teacher Observations

·          Student Oral Responses

·          Student Demonstrations