COURSE DESCRIPTION - SEVENTH GRADE MATH

Seventh grade mathematics builds on the skills and concepts learned in the sixth grade. Concepts are presented in an integrated, interdisciplinary manner geared to prepare students for success in eighth grade and later in algebra and geometry. Topics covered include: problem solving, algebra and geometry, applying decimals, statistics: analyzing and interpreting data, using number patterns, fractions and percents, algebra: using integers and exploring equations and functions, applying fractions, using proportional reasoning, probability and geometry.

Problem Solving – Algebra, Geometry

Plan for Problem Solving (Patterns/ Interpreting Graphs)
Simplifying Numerical Expressions- Order of Operations
Evaluating Variable Expressions
Powers and Exponents – Base ten Expanded Notation Included
|Solving One Step Algebraic Equations
Geometry: Fractals & Patterns, Area of Rectangles & Parallelograms. Solving inverse equations
Problem Solving Strategies

Decimals

Place Value and Comparing Decimals
Rounding and Estimating Decimals
Problem Solving: Reasonable Answers Estimation
Basic Operations with Decimals
Powers of Ten, Scientific Notation, Metric System – Measurement
Converting Decimals to Fractions

Statistics-Analyzing Data

Constructing and Interpreting graphs and tables: Line Plots, Stem & Leaf, Box and Whisker
Measures of Central Tendency: Quartiles, Mean, Median and Mode
Making Predictions from Graphs and Misleading Statistics

Using Patterns: Fractions and Percents

Divisibility Patterns 2,3,4,5,6,8,9,10,12
Prime Factorization with Application to Determining the Greatest
Common Factor (GCF) and Least Common Multiple (LCM)
Set Method to determining (GCF) and (LCM)
Problem Solving: Sequences and Making a List
Simplifying Fractions and Ratios
Relating Fractions- Ratios to Equivalent Decimals and Percent
Probability Ratio- Simple Events
Comparing and Ordering Fractions

Algebra: Using Integers

Introduction/definition – use of number line
Comparing & Ordering Integers
Coordinate Plane – Plotting Points
Basic Operations with Integers and Order of Operations with Integers
Properties: Addition and Multiplication with integers
Problem Solving: Look for a Pattern

Algebra: Exploring Equations & Functions

Solving one and two step Algebraic Equations with Integers
Problem Solving: Working Backwards
Writing Variable Expressions and Algebraic Equations (application to geometric formulas, distance and coin problems)
Inequalities
Concepts related to Linear Equations- visual determination of Y-Intercept and Slope
Graphing Linear Equations

Applying Fractions

Estimating Fractions
Computation Operations with Fractions & Mixed Numerals
Measurement Conversions Customary Units
Geometry: Perimeter, Circles & Circumference– Use of Formulas
Application of Properties to fractional Numbers

Using Proportional Reasoning

Ratios, Rate Ratios
Writing and Solving Proportions
Drawing a Diagram, Scale Diagram
Similar Polygons – Indirect Measurement
Converting Percents – Fractions - Decimals
The Percent Proportion

Applying Percent

Percent & Estimation, Pictorial Representation of Percent
Problem Solving - Solve a Simpler Problem
Using Statistics to Predict
Percent of Change (Increase and Decrease)
Determining Tips
Construction and Interpretation of Circle Graphs (use of protractor & compass)
**(Optional) Finding Discount Amount / Sales Price/Regular Price, Simple Interest – Finding Interest / Principle / Rate / Time- Inverse Equations, Commission - Determining Commission Amount. Total Sales, Multi-Rate Commission, Taxes

Geometry: Investigating Patterns

Concepts: Points, Lines, Line Segments, Rays, Types of Lines: Intersecting,

Parallel, Perpendicular, Intersecting Skew, Angles: Acute, Right, Obtuse,
Straight, Complementary, Supplementary, Reflex, Vertical, Adjacent,
Angles on
Transversal: Interior, Exterior, Corresponding, Use of Protractor
Family of Polygons- characteristics of Triangles & Quadrilaterals
Problem Solving: Using Logical Reasoning
Tests of Congruence (Reflection, Translation and Rotation)

Circle Terms: Radius, Chord, Diameter, Secant, Tangent, Minor & Major Arc,

Semi-Circle, Determination of Pi, Circumference Formula-Finding Radius
or Diameter
(Inverse Equations)

Geometry: Area, Volume, Surface Area

Square Numbers, Square Roots, Pythagorean Theorem
Area of Square, Rectangle, Parallelogram, Trapezoid, Circle
Drawing Three Dimensional Figures
Volume and Surface Area of Rectangular Prism

**(Optional Volume & Surface Area of Cylinder and relationship to pyramids and cones)

Seventh Grade students who earn exemplary grades (ninety and above- no make-ups) and have satisfactory completion of homework, will be considered for placement in Algebra in eighth grade.

KEY TEXT

Middle School Math: Course 2, McDougal Littel

SUPPLEMENTAL TEXT

Algebra, Houghton, Mifflin and Amesco

COURSE DESCRIPTION - PRE-ALGEBRA

The Pre-Algebra track is an accelerated course combining both grade 7 and grade 8 mathematics. Sixth grade students are recommended for Pre-Algebra by their sixth grade teacher based on student achievement, level of organization, consistency of effort, CMT scores and performance on placement tests. Students in Pre-Algebra must display a level of satisfactory understanding of all material presented through their achievement on tests and quizzes ( eighty percent or higher – no make-ups) in order to earn a recommendation to Algebra in eighth grade.

The following topics are covered in Pre-Algebra:

Tools for Algebra

Problem Solving Strategies – Patterns
Simplifying Numerical Expressions – Order of Operations
Writing and Evaluating Variable Expressions
Identifying and Using Properties
Distributive Property – Bases of Multiplication, Factoring, Collecting Like Terms
Solving one & Two Step Algebraic Equations
Coordinate Plane – Plotting Points
Writing and Evaluating Inequalities
Gathering & Recording Data, Interpretation & Construction of Frequency
Distributions and Histograms

Exploring Integers

Integers & Absolute Value
Graphing – Statistical Line Plots
Comparing & Ordering Integers
Adding, Subtracting, Multiplying and Dividing Integers

Rules for Positive & Negative Exponents

Solving One & Two Step Algebraic Equations and Inequalities

Problem Solving Strategy: Eliminate Possibilities
Solving One & Two Step Inverse Equations & Inequalities
Using Algebra to solve for any variable in a formula
Problem Solving Area & Perimeter (Both Length and Width Variable Expressions)
Problem Solving: Writing and Solving Equations and Inequalities to solve

Exploring Factors and Fractions

Factors & Monomials / Rules of Divisibility
Evaluating Expressions with Exponents – Using the Graphing Calculator
Problem Solving strategy- Draw a Diagram
Prime Factorization (Factor trees) with algebraic expressions
Greatest Common Factor (GCF) with Algebraic Expressions using both the Set Method & Prime Factorization – Venn Diagram
Simplifying Fractions (Algebraic expressions)
Least Common Multiple (LCM) with algebraic expressions, both Set and Prime Factorization
Multiplying and Dividing Monomials

Rational: Patterns in Addition, Subtraction, Multiplication & Division

Rational Numbers ( Changing decimals & repeating decimals to fractions)
Estimating Sums, Differences, Products, Quotients
Operations with Decimals (Add., Sub., Mul.,Div.)
Operations with Fractions (like and unlike)
Solving Equations & Inequalities with Decimals / Fractions one & two step
Problem Solving: Using Logical Reasoning
Sequences: Arithmetic & Geometric
Statistics: Measures of Central Tendency (Mean, Median, Mode)
Graphing Calculator – creating spreadsheet for measures of central tendency
Scientific Notation

Solving Equations And Inequalities

Problem Solving: Work Backward
Problem Solving: Two Step Equations Applications: Coin, Area, Perimeter
Integration: Geometry Circles & Circumference
Solving Equations with Variables on Both Sides
Solving Multi-Step Inequalities
Using The Metric System

Functions and Graphing

Relations and Functions
Scatter Plots using the Graphing Calculator
Graphing Linear Equations and Inequalities
Visual and Formula for Determining Slope
Y & X Intercepts
Writing an Linear Equation from a graph
Graphing Systems of Equations

Proportional Reasoning and Percent

Ratio & Rates
Problem Solving: Make a Table
Simple Probability
Fair and Unfair Games
Problem Solving: Using Proportion
Similar Triangles/ Polygons & Indirect Measurement
Conversion of Fractions / Decimals / Percent
Using the Percent Proportion to solve problems
Percent Proportion Using Statistics to Predict
Percent & Estimation
Percent of Change : Increase and Decrease
Problem Solving (Discount, Regular Price, Sales Price, Discount Amount & Rate, Commission, Sales, Rate, Multi-Rate Commission, Taxes, Tips, Simple & Compound Interest

Statistics

Interpretation and Construction of Circle Graphs – Project
Stem & Leaf Plots
Measures of Variation, Quartiles, Measures of Central Tendency using the Graphing Calculator
Displaying Data, Box and Whisker
Misleading Statistics

Geometry

Concepts: Points, Lines, Planes, Line Segments, Rays
Types of Lines: Parallel, Perpendicular, Intersecting, Skew
Angle Relationships / Classification: Acute, Right, Obtuse, Straight, Supplementary, Complementary, Vertical, Adjacent Angles on Transversal: Alternate Interior, Exterior, Corresponding
Triangles Classified by Angles & Sides, Congruent Triangles
Square Numbers, Square Roots, application to Pythagorean Theorem
Family of Quadrilaterals/ Characteristics
Polygons
Transformations
Circles- Circumference, Radius, Diameter, Chord, Secant, Tangent, Arcs
Area: Squares, Rectangles, Parallelograms, Triangles, Trapezoids, Irregular Polygons
Surface Area and Volume of Prisms and Cylinders relationship to Cones & Pyramids

KEY TEXT

Pre-Algebra: An Integrated Transition to Algebra and Geometry, Glencoe, McGraw Hill.

SUPPLEMENTAL TEXT

Algebra, Houghton, Mifflin and Amesco