Millikan’s Mathematics Department

Millikan’s Math Department Philosophy October 2008 Millikan’s Mathematics Department

Millikan Math Department Staff Ms. D’Aloisio - Math Department Administrator

Curriculum

Algebra, Ratios, Percents, Proportions Fractions, Decimals, Integers, Exponents Perimeter/Area Calculations, Properties Add/Subtract Facts Multiplication Tables Geometry/ Vocabulary Basic Math Pyramid

6th Grade FOCUS STANDARDS for 6th Grade: NUMBER SENSE 1.0: Students compare and order positive and negative fractions, decimals, and mixed numbers. Students solve problems involving fractions, ratios, proportions, and percentages. NUMBER SENSE 2.0: Students calculate and solve problems involving addition, subtraction, multiplication, and division. ALGEBRA AND FUNCTIONS 1.0: Students write verbal expressions and sentences as algebraic expression and equations; they evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results. ALGEBRA AND FUNCTIONS 2.0: Students analyze and use tables, graphs, and rules, to solve problems involving rates and proportions. ALGEBRA AND FUNCTIONS 3.0: Students investigate geometric patterns and describe them algebraically. MEASUREMENT AND GEOMETRY 1.0: Students deepen their understanding of the measurement of plane and solid shapes that use this understanding to solve problems. MEASUREMENT AND GEOMETRY 2.0: Students identify and describe the properties of two dimensional figures. STATISTICS, DATA ANALYSIS, AND PROBABILITY 1.0: Students compute and analyze statistical measurement for data sets: STATISTICS, DATA ANALYSIS, AND PROBABILITY 2.0: Students use data sample of a population and describe the characteristics and limitations of the samples: STATISTICS, DATA ANALYSIS, AND PROBABILITY 3.0: Students Determine theoretical and experimental probabilities and use these to make predictions about events. MATHEMATICAL REASONING 1.0: Students make decisions about how to approach problems. MATHEMATICAL REASONING 2.0: Students use strategies, skills, and concepts in finding solutions. MATHEMATICAL REASONING 3.0: Students move beyond a particular problems by generalizing to other solutions.

Typical 6th Grade Equation

7th Grade: General Math Focus Standards to be addressed in 7th Grade Pre Algebra: Number Sense 1.0: Students know the properties of, and compute with rational numbers expressed in a variety of forms. Number Sense 2.0: Students use exponents, powers, and roots and use exponents in working with fractions. Algebra and Functions 1.0: Students express quantitative relationships by using algebraic terminology, expressions, equations, inequalities, and graphs. Algebra and Functions 2.0: Students interpret and evaluate expressions involving integer powers and simple roots. Algebra and Functions 3.0: Students graph and interpret linear and some nonlinear functions. Algebra and Functions 4.0: Students solve simple linear equations and inequalities over rational numbers Measurement an Geometry 1.0: Students choose appropriate units of measure and ratios to convert within and between measurement systems to solve problems. Measurement and Geometry 2.0: Students compute the perimeter, area, volume of common geometric objects and use the results to find measures of less common objects. They know how perimeter, area, and volume are affected by changes of scale. Measurement and Geometry 3.0: Students know the Pythagorean theorem and deepen their understanding of plane and solid geometric shapes by constructing figures that meet given conditions and by identifying attributes of figures. Statistics, Data Analysis, and Probability: Students collect, organize, and represent data sets that have one or more variables and identify relationships among variables within a data set by hand and through the use of an electronic spreadsheet software program. Mathematical Reasoning 1.0: Students make decisions about how to approach problems. Mathematical Reasoning 2.0: Students use strategies, skills, and concepts in finding solutions. Mathematical Reasoning 3.0: Students determine a solution is complete and move beyond a particular problem by generalizing to other situations.

Algebra Readiness • Number Sense 1.0: Students know the properties of, and compute with rational numbers expressed in a variety of forms. • Number Sense 2.0: Students use exponents, powers, and roots and use exponents in working with fractions. • Algebra and Functions 1.0: Students express quantitative relationships by using algebraic terminology, expressions, equations, inequalities, and graphs. • Algebra and Functions 2.0: Students interpret and evaluate expressions involving integer powers and simple roots. • Algebra and Functions 3.0: Students graph and interpret linear and some nonlinear functions. • Algebra and Functions 4.0: Students solve simple linear equations and inequalities over rational numbers. • Measurement an Geometry 1.0: Students choose appropriate units of measure and ratios to convert within and between measurement systems to solve problems. • Measurement and Geometry 2.0: Students compute the perimeter, area, volume of common geometric objects and use the results to find measures of less common objects. They Know how perimeter, area, and volume are affected by changes of scale. • Measurement and Geometry 3.0: Students know the Pythagorean theorem and deepen their understanding of plane and solid geometric shapes by constructing figures that meet given conditions and by identifying attributes of figures. • Statistics, Data Analysis, and Probability: Students collect, organize, and represent data sets that have one or more variables and identify relationships among variables within a data set by hand and through the use of an electronic spreadsheet software program. • Mathematical Reasoning 1.0: Students make decisions about how to approach problems. • Mathematical Reasoning 2.0:Students use strategies, skills, and concepts in finding solutions. • Mathematical Reasoning 3.0:Students determine a solution is complete and move beyond a particular problem by generalizing to other situations.

Typical 7th Grade Problem

Algebra 1AB ALGEBRA FOCUS STANDARDS: 1.0 Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable. 2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents. 3.0 Students solve equations and inequalities involving absolute values. 4.0 Students simplify expressions before solving linear equations and inequalities in one variable. 5.0 Students solve multi-step problems including word problems, involving linear equations and linear inequalities in one variable, and provide justification for each step. 6.0 Students graph a linear equation and compute the x and y intercepts. They are also able to sketch the region defined by a linear inequality. 7.0 Students verify that a point lies on a line , give an equation of the line, and are able to derive linear equations by using the point-slope formula. 8.0 Students understand the concepts of parallel and perpendicular lines and how their slopes are related. Students are also able to find the equation of a line perpendicular to a given line that passes through a given point. 9.0 Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution set. 10.0Students add, subtract, multiply, and divide monomials, and polynomials. Students solve multi-step problems, including word problems, by using these techniques. 11.0Students apply basic factoring techniques to second and third degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials. 12.0Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to lowest terms. 13.0 Students add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems. 14.0Students solve a quadratic equation by factoring or completing the square. 15.0Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems. 16.0Students understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information about given relations and functions. 17.0Students determine the domain of independent variables and the range of dependent variables defined by a graph, a set of ordered pairs, or a symbolic expression. 18.0Studnets determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion. 19.0Students know the quadratic formula and are familiar with it’s proof by completing the square. 20.0Students use the quadratic, formula to find the roots of a second-degree polynomial and to solve quadratic equations. 21.0Students graph quadratic functions and know that their roots are the x-intercepts. 22.0Students apply quadratic formula or factoring techniques or both to determine whether the graph of a quadratic function will intersect the x-axis in zero, one, or two points. 23.0 Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity. 24.0Students use and know simple aspects of a logical argument 25.0Students use properties of the number system to judge the validity of results, to justify each step of a procedure, and to prove or disprove statements.

Typical Algebra 1 Inequality

The sum of 2 consecutive odd integers is less than 137. What is the greatest possible pair?

Therefore, the two greatest consecutive odd integers less than 137 are 67 and 69! I Love my ALGEBRA !

Homework Policy • Homework is given 5 nights a week. • To receive credit, the following criteria will be used. 1. Must be in PENCIL 2. Must SHOW WORK 3. Must be LABELED 4. Must be IN JOURNAL/NOTEBOOK 5. Must be NEAT • Please check your child’s journal periodically that they are keeping their work in order, and that homework is being done.

Homework Help • Notes • www.HotMath.com • Friend • Book • Millikan Drop in Tutoring • Support as a Team

Algebra Placement Criteria • Algebra Readiness Test • Teacher Recommendation

Higher Level Mathematics 7th8th9th10th11th12th Pre- Algebra Algebra 1 Algebra II Geometry Trig. Calculus Algebra Readiness Algebra 1 Algebra II Geometry Trig. Recommendation Pre-requisite Passing Algebra Readiness Algebra 1 Teacher Recommendation Algebra Readiness All others

Minimum Requirement for a 4-year College • 3 years of high School Math • 4 years is recommended

California High School Exit Exam (CAHSEE) • Every student must • Pass to receive diploma • 4 - 6 hour exam • Two Parts: ELA (100 questions) Math (100 questions) • Math Content: 6th grade standards 7th grade standards 70 % Algebra standards • Begin taking it in 10th grade. May take it up to 3 times per year.

Thank YouFor Coming!

Millikan’s Mathematics Department