MATH 2 A (MASTER MAP)

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1 Page 1 of 6 Close Window Print Page Layout Show Standards View Paragraph Format View Course Description MATH 2 A (MASTER MAP) School: Binghamton High School Teacher: Master Map Course #: 206 Grade Level: 10,11 MONTH/YEAR ESSENTIAL QUESTIONS CONCEPTS/SKILLS/STANDARDS CONTENT September How do the Properties of Real Numbers Real Numbers numbers of the - Identify and apply the properties Real Number of real numbers Properties of Real System relate to Numbers - 2 each other and Scientific Notation Scientific Notation - how are they - Understand and use scientific 1 different? notation to compute products and Algebra Problems quotients of numbers How do you perform the four operations with rational numbers? How would you describe the order of operations? How does "Talking to the Text" allow better comprehension of mathematical problems? How are rational numbers applied in the business world? October 2006 What is the difference between an expression and an equation? What are the tools needed to Algebra Problems - Solve algebraic problems arising from situations that involve fractions, decimals, percents, and proportionality/ direct variation Exponents - Properties of exponents including zero, and negative - Multiplying, dividing, and power to power - Evaluating with exponents Operations with Monomials and Polynomials - Add, subtract, multiply and divide monomials and polynomials - Multiply and divide monomial expressions with a common base - Divide polynomials by a monomial or binomial, where the quotient has no remainder Translate between verbal sentences and mathematical expressions and equations - Translate a quantitative verbal phrase into an algebraic expression - Write a verbal expressions that matches a given mathematical Involving Fractions, Decimals, Percents and Proportions - 1 Exponents - 1 Polynomials - 10 Associative Property Base Binomial Closure Commutative Property Direct Variation Distributive Property Exponent Identity Property Integers Inverse Property Irrational Monomial Percent Polynomial Proportion Rate Ratio Rational Real numbers Scientific Notation Standard Notation Linear Equations Translate between verbal sentences and mathematical expressions and equations - - Solve all types of ASSESSMENT Project- Word Web for Real numbers including rational, irrational, fraction,etc. AREAS OF INTERACTION Problem solving and thinking skills (ATL) Designing a web of the Real number system (HF) Researching the history of numbers (HF) Researching the history of Algebra (HF) Recognizing concepts and applying skills (ATL)

2 Page 2 of 6 November 2006 solve linear equations and inequalities? When do you utilize these tools? Why do we reverse the inequality sign when multiplying or dividing by a negative number? How are the solutions of linear equations and linear inequalities different? Why does an inequality have an infinite number of solutions? How are terms and factors different? How do we know when we have completely factors and expression? expression - Distinguish the difference between an algebraic expression and an algebraic equation - Translate verbal sentences into mathematical equations or inequalities - Write algebraic equations that represent a situation Solving Linear Equations - Solve 1-step equations - Solve 2-step equations - Solve equations by using multisteps. - Use the Distributive Property to evaluate or simplify expressions. - Solve equations involving grouping symbols - Solve linear inequalities in one variable - Solve equations by combining like terms. - Solve equations with rational numbers - Solve literal equations for a given variable - Interpret simple word problems by paraphrasing mathematical language into signs, symbols, and mathematical sentences Linear Inequalities - Translate verbal sentences into mathematical inequalities - Write algebraic inequalities that represent a situation - Analyze and solve verbal problems whose solutions requires solving a linear inequality in one variable - Determine whether a given value is a solution to a given linear inequality in one variable Factoring and Fractional Equations - Identify and factor the difference of two perfect squares - Factor algebraic expressions completely, including trinomials with a lead coefficient of one (after factoring a GCF) a. Factor algebraic expressions using the GCF How are the roots b. Factoring a trinomial into two of a quadratic binomials, a=1 equation and c. Factoring a trinomial into two factors of a binomials, a>1 (optional) quadratic d. Factoring a trinomial into two expression binomials that involves factoring different and out a GCF first connected? e. Factoring a trinomial into two binomials that involves factoring out the negative of the GCF first Solving Quadratic Equations - Find the roots of a parabolic Linear Equations - Determine whether a value is a solution of a given equation - Literal equations - Proportions resulting in linear equations - Verbal Problems Linear Inequalities Translate verbal to mathematical - Linear Inequalities - Verbal problems Coefficient Constant Equation Expression Integral coefficient Linear equation Literal equation Terms Verbal expression Verbal sentence Factoring Factoring Solving Quadratic Equations Finding the roots - Verbal problems algebraic proportion coefficient composite number difference of two perfect squares factor Greatest Common Factor least/lowest common denominator linear equation linear inequality Flag project Developing problem-solving strategies (ATL)

3 Page 3 of 6 December 2006 function graphically (integral solution) - Analyze and solve verbal problems that involve quadratic equations - Solve algebraic proportions in one variable which result in quadratic equations - Understand and apply the multiplication property of zero to solve quadratic equations with integral coefficients and integral roots - Understand the difference and the connection between rootsof a quadratic equation and factors of a quadratic expression? Basics of Geometry - Find the connection between radius, diameter, circumference, and area - Warm-up Identify/find value of vertical angles. - Find value of complementary angles. - Reinforce the distance formula - Explore area and perimeter - Finding midpoint of segments Multiplication Property of Zero perfect square perfect square trinomial prime factorization prime numbers rational expression roots of a equation solution set undefined verbal expressions verbal sentence I. Basics of Geometry - 7 January 2007 Why is slope important? How do you create an equation of a line that misses certain quadrants? How are the graphs of a linear equation and a linear inequality similar and different? Why is the shaded region significant in reference to a linear inequality? Reasoning and Proof - Classifying right triangles - Identify converse, inverse, contrapositive Equations of Lines - Determine whether a given point is on a line, given the line - Given a point on a graph, solve for an unknown in the equation or for a coordinate (Given (3,2) is on the graph of x + 3y = k, find k) - Explain slope as a rate between dependent and independent variables - Determine the slope of a line, given the coordinates of two points on the line - Write the equation of line parallel to the x- or y-axis - Determine if two lines are parallel, given their equations in any form - Write the equation of a line given the slope and y-intercept - Investigate and generalize how changing the coefficients of a function affects its graph - Convert an equation into slopeintercept form and graph - Write the equation of a line, given its slope and the coordinates of a point on the line - Write the equation of a line, given the coordinates of two points on the line Inequalities II. Reasoning and Proof - 5 III. Graphing Linear Equations - 6 Equations of Lines IV. Inequalities - 6 Graphing Inequalities V. Congruent Triangles - 17 continue into February dependent variable domain function independent variable intercept method linear ordered pair parallel perpendicular point-slope form quadrant range relation slope slope- y-intercept form solutions x - axis Lab Activities - West Bay Crossing Activity - Playing Pool - Shakespeare and the Globe Theatre - Exploring Right Triangles - Aristarchus of Samos - Lesson opener, classifying trianlges using geometry - Yard service - Famous mathematician - Journal activity, chapter 4 - Birthday triangle Using a graphing calculator (ATL) Develop problem-solving strategies (ATL)

4 Page 4 of 6 - Graphing Linear inequalities - determine if reference line is dashed or solid - determine where to shade x - intercept y - axis y - intercept Congruent Triangles - Proving triangles congruent by ASA, SAS, SSS, AAS HL - Write a two-column proof February Right triangles and isosceles triangle proofs Continue with Triangle proofs and skills(atl) March 2007 Properties of Triangles -construct a perpendicular bisector through a point on a line -use properties of perpendicular bisectors - use properties of angle bisectors - use properties of medians of a triangle - use properties of altitudes of a triangle - identify the midsegments of a triangle - use properties of the midsegments of a triangle - use triangle measurements to decide which side is the longest or which angle is the largest Properties of Quadrilaterals - identify, name and describe polygons - use the sum of the measures of the interior angles of a quadrilateral - use properties of a parallelogram - use propeties of parallelograms in real-life situations - use coordinate geometry to prove a quadrilateral is a specified polygon - use properties of sides and angles of rhombii, rectangles, squares, and trapezoids V. Properties of Triangles - 7 Perpendicular Bisector Angle Bisector Median Altitude Midsegment VI.Properties of Quadrilateral - 10 Parallelogram Rhombus Rectangle Square Trapezoid VII. Transformations - 5 Reflection Translation Rotation Symmetry Glide Reflection Lab Activities: - Washington, D.C. - Egyptian Papyrus - Quilting - Review, midsegement, trapezoid, triangle inequality - Special Quadrilaterals - Bluebird houses - Crossword puzzle - Polygon chart - Rubber Stamp Lab - Transformation Skills and Application - Frieze Patterns Recognizing concepts and applying skills (ATL) Researching the history of Pythagoras (HF) Using and developing classification systems (ATL) Using drawing skills (ATL) Transformations - identify the three basic rigid transformations - identify and use reflection in a plane

5 Page 5 of 6 April identify relationships between reflections and line symmetry - identify rotations ina plane - use rotational symmetry in reallife situations - indentify and use translations in a plane - identify glide reflections in a plane Ratio and Proportion - find and simplify the ratio of two numbers - use proportions to solve real-life problems -use properties of proportions VIII.Ratio and Proportion - 4 Similar Triangles - 3 Dilations - 2 Similar Triangles - identify similar triangles - use proportionality theorems to calculate segment lengths to solve real-life problems Dilations -identify dilations - identify a scale factor Right Triangles - use the Pythagorean theorem to solve real-life situations - use the converse of the Pythagorean Theorem to solve problems - know and apply trig ratios May 2007 truth Circles - identify segments and lines related to circles - use properties of a tangent to a circle - use properties of arcs of circles - use properties of chorda of circles - use inscribed angles to solve probelms - use angles formed by lines that intersect a circle to solve problems -find the lengths of segments of chords - find the lengths of segments of tangents and secants -write the equation of a circle use the equation of a circle Locus - draw the locus of points that satisfy a given condition See supplements on Loci in Geometry section - strands 22, 23 IX. Right Triangles Pythagorean Theorem - Trigonometry Cosine Dilation Hypotenuse Leg Proportion Pythagorean Theorem Ratio Scale Factor Similar Triangles Sine Tangent Trigonometry X. Circles - 10 Arcs Angles Line Segments Locus - 10 Given one line Given parallel lines Given a point and distance Given two perpendicular lines Given two intersecting lines Arc Central angle Chord Circle Inscribed angle Locus Secant Segment Tangent Lab Activities: - Cooking - Architecture - Similar Triangles/Miniature Golf - Golden Ratio - Matreshkas Dolls - Baseball - Trig chart - Finding the height of difficult objects - Leaning Tower of Pisa - Roof truss - Hubble Space Telescope Lab Activity - Satellite Transmission - Apollo 13 - Circle Segments - Saturn Recognizing concepts and applying skills (ATL) Using the concepts of central tendency and spread (ATL) Using a graphing calculator (ATL) Prepare an economic analysis of the country (ATL. HS)

6 Page 6 of 6 pp , , , Vertex Solve problems using compound loci