Fifth Grade 

Number and Operations

• write numbers in standard, expanded, and exponent notation

• understand the relationship of the place-value structure of  the base-ten numeration system to represent and compare whole numbers and decimals
• master the four fundamental operations with whole numbers (addition, subtraction, multiplication, and division)
• use numbers less than 0 in everyday applications
• describe classes of numbers according to characteristics such as the nature of their factors
• add and subtract decimal and common fractions with the same denominators using models and drawings
• develop and use strategies to estimate and check reasonableness of results in computational problems

Algebra

• represent patterns, relations, and functions in a variety of ways

• understand and use properties of operations (commutative, associative, and distributive)

• use variables to represent numbers and solve application problems
• identify and describe how change in one variable can cause a predictable change in a dependent variable

 Geometry

• investigate and describe the results of transforming shapes
• plot points in quadrants I through IV
• find the distance between points that lie on a horizontal or vertical line in the coordinate plane
• identify both line and rotational symmetry in two- and three-dimensional shapes

• recognize, analyze, and explain the properties of common two- and three-dimensional figures
• use basic geometric terms (rays, angles, line segments, sides, edges, vertices, faces, radius, diameter, perpendicular, parallel, intersecting)
• explain congruence and give examples

Measurement                         

• do simple conversion inside a measurement system (examples:  centimeters to meters and feet to inches)
• understand that measurements are approximations
• measure perimeter and area of regular and irregular figures
• use benchmarks to estimate perimeter and area of geometric figures
• use the correct tools and units to measure length, area, weight, time, temperature, and angles
• develop methods to calculate perimeter
• develop procedures (formulas) to calculate the area of rectangles and squares

Data Analysis and Probability

• collect and display in a variety of ways data from observations, surveys, and experiments
• recognize the difference between categorical and numerical data
• analyze data using measures of central tendency (mean, mode, and median)

and dispersion (range)

• make conclusions and predictions based on data information
• make predictions of possible outcomes before collecting the information
• develop the concept that probability predictions should range from 0 (Never will happen.) to 1 (Always will happen.)

Sixth Grade  

Number and Operations

• maintain computational skills with whole numbers by solving application and investigation problems
• review addition and subtraction of decimals and develop an understanding of multiplication and division of decimals
• understand and be able to explain and use the correct placement of decimal points in all operations
• use factors, multiples, and prime numbers in problem solving
• convert between the three types of fractions (common, decimal, and percent)
• add and subtract fractions with like and unlike denominators using manipulatives and drawings
• identify proportions as two equal ratios
• begin the study of proportional relationships including numerical and geometric
• solve percent problems using proportions
• develop an understanding of integers and the four fundamental operations using models
• develop estimation skills with rational numbers

Algebra

• develop an initial concept of the use of variables
• solve one-step equations using models
• generalize a variety of patterns
• use graphs and charts in problem solving

Geometry

• describe the relationships between two- and three-dimensional figures
• describe sizes, positions, and orientations of shapes using transformations such as flips, turns, slides, scaling
• apply geometric ideas to situations outside of mathematics class, such as art, design, science, and life
• use the Cartesian coordinate system to solve problems

Measurement

·        know and use the metric and customary systems of measurement

·        calculate the perimeter of regular and irregular figures

·        calculate the area of rectangles, squares, parallelograms, and triangles

·        add and subtract units within the same system of measurement

Data Analysis and Probability

• use charts, tables, and a variety of graphs to organize and interpret data
• select topics, collect data, and organize a statistical study
• use data to assist in forming opinions and making decisions
• use measures of central tendency and dispersion

Seventh and Eighth Grade: Pre-Algebra 

Number and Operations

• use decimal operations in application and problem solving problems
• compare and order fractions, decimals, and percents
• develop the skills necessary to multiply and divide fractions
• extend the knowledge of integers and compare their relative value

• use the associative, commutative, and distributative properties as an aid in computation
• expand the knowledge of percent to include percents less than 1% and greater than 100%

      *    work fluently with fractions, decimals, percents, and integers

*    demonstrate an understanding of  very large and very small numbers

*    use appropriate notation including exponential and scientific

      *    use properties of operations and inverse relations to simplify computation

Algebra

• continue the development of an understanding of variables
• write algebraic phrases
• relate different ways to represent relationships
• use a variety of problem solving techniques such as equations, graphs, charts, and tables

*    solve equations and write equations for application problems

      *    explore the relationship between linear equations and the slope and intercepts of their graphs

Geometry

• use geometric ideas and relationships to investigate congruence, similarity, and the Pythagorean theorem
• use coordinate geometry to investigate special geometric shapes
• use visual tools such as nets to solve problems
• draw three-dimensional solids in two-dimensions

*    use the formal definition of similar figures as having proportional sides      

      and congruent angles to identify figures as similar and not similar and find the lengths of      corresponding sides

*    apply the principles of geometry to applications

Measurement

·     use the customary and metric system of measures to calculate the area of trapezoids, circles, and irregular figures

·        develop the concept of volume and cubic units to compute the volume of three-dimensional figures (rectangular prisms, cones, cubes, pyramids, cylinders)

*    calculate volume and surface area of  three-dimensional  geometric figures

*    solve problems involving scale factors

Data Analysis and Probability

• compute simple theoretical probabilities

·        design probability experiments, predict results, experiment, record results, compare to   theoretical probability

• use counting techniques, tree diagrams, area models, and tables to solve probability problems
• represent probabilities in multiple ways (common, decimal, and percent fractions)
• construct and interpret displays of data (tables, circle graphs, line plots, stem-and-leaf plots, scatter plots, and box-and-whiskers plots)

    *    understand and use correct terminology (sample space, event, outcome,   

          complementary events, and mutually exclusive events

      *   compute probabilities for compound events

           *Optional Topics

Eighth Grade: Algebra I 

Rational Numbers

• relate rational numbers to positions on the number line

• add, subtract, multiply, and divide integers and other rational numbers

·        estimate square roots

·        review order of operations rules

Equations and Inequalities

• use algebraic expressions and  simplify polynomials

• solve and check linear multi-step equations
• use formulas
• solve linear inequalities
• represent inequality solutions using set notation and number lines
• solve application problems using equations and inequalities

  Coordinate Plane and Graphing

• learn the terminology of graphing
• graph linear equations and simple inequalities
• develop the concept of slope and intercepts
• discover the relationship between slope and y-intercept and the slope-intercept form for the equation of a line
• calculate the slope of the graph of a linear equation
• write equations for lines given the slope and intercept, slope and pair of coordinates, and two pairs of coordinates

Systems of Equations

• solve systems of equations by graphing using graph paper or a graphing calculator
• solve systems of equations by substitution
• solve system of equations by the elimination method

Exponents

• understand the meaning of exponents
• use exponents in scientific notation
• perform operations involving integer exponents

Polynomials and Factoring

• add and subtract polynomials
• multiply polynomials (monomials x monomials, monomials x polynomials, polynomials x polynomials)
• divide polynomials (monomial by monomial, polynomial by monomial, polynomial by polynomial)
• factor polynomials (common monomials, binomials, trinomials)

Quadratic Equations

• solve quadratic equations by factoring and use of the quadratic formula
• solve quadratic equations by graphing
• apply quadratic equations to real world problems 

Rational Expressions

• simplify rational expressions
• multiply and divide rational numbers
• add and subtract rational expressions with like denominators

Radical Expressions

• simplify radical expressions

• compute with radicals
• use the Pythagorean theorem
• use the distance formula

Data and Algebra

work with variables and data

·        organize data using matrices and spreadsheets

             graph data