Math 1. Month Essential Questions Concepts/Skills/Standards Content Assessment Areas of Interaction

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1 Binghamton High School Rev.9/21/05 Math 1 September What is the unknown? Model relationships by using Fundamental skills of 2005 variables as a shorthand way Algebra Why do we use variables? What is a term? How can a variable transform itself? What does the exponent describe for the base? How do the numbers of the Real Number System relate to each other and how are they different? How do you perform the four operations with rational numbers? Write three examples of a term Demonstrate the idea of "combining like terms" Write terms using different degrees for variables Describe/Model what the exponent describes for the base Write mathematical expressions for verbal expressions. Design a web for The Real Number System variable term base, exponents, power expression equation inequality evaluate order of operations solve solution Real Numbers Project- Word Web for Real numbers including rational, irrational, fraction, etc. ATL -Problem solving and thinking skills Homo Faber -The web of the Real number system Can you find the absolute value of a rational number? How would you describe the order of operations? How does "Talking to the Text" allow better comprehension of mathematical problems? Evaluate numerical/algebraic expressions by using the order of operations Demonstrate the idea of the absolute value of a rational number Add, subtract, multiply and divide monomials and polynomials Multiply and divide monomial expressions with a common base Page 1 of 12

2 Divide polynomials by a monomial or binomial, where the quotient has no remainder October 2005 What are the tools needed to solve linear equations and inequalities? When do you utilize these tools? Distinguish the difference between an algebraic expression and an algebraic equation. Translate verbal sentences into equations/inequalities and vice versa Write algebraic equations/inequalities that represent a situation Solve equations and inequalities by using addition and subtraction. Solve equations and inequalities by using multiplication and division. Solve equations and inequalities by using multi-steps. Solving equations and inequalities using addition, subtraction, multiplication and division Solving multi-step equations and inequalities The Distributive Property Solving equations and inequalities with variables on both sides and by combining like terms Linear equations and inequalities and problem solving Solving rational number equations and inequalities Use the Distributive Property to evaluate or simplify expressions. Solve equations and inequalities involving grouping symbols Page 2 of 12

3 Solve equations and inequalities by combining like terms. Solve equations and inequalities with rational numbers Solve literal equations for a given variable Compare and interpret the solution(s) of equations to those of inequalities Interpret simple word problems by paraphrasing mathematical language into signs, symbols, and mathematical sentences November 2005 How do we graph using linear equations? How do we graph using linear inequalities? What are three forms of linear equations? How do you write a linear equation? How do you write an equation of a line compared to an existing line? Model the coordinate plane with appropriate attributes (i.e. labeling of parts) Define coordinates, ordered pairs, and intercepts Locate and graph points on a coordinate plane Define the four quadrants of the coordinate plane Determine when a relation is a Coordinate Plane - building a foundation Graphing linear equations and inequalities by table method, intercepts, or slope-intercept form Solving linear equations and inequalities Writing linear equations in slope-intercept form Standard form of a linear Applying skills and concepts of coordinate plane (ATL) Page 3 of 12

4 function, by examining ordered equation pairs Investigate and generalize how changing coefficients of a function affects its graph Explain slope as a rate of change between dependent and independent variables Determine the slope of a line, given its equation in any form Write an equation in slopeintercept form from an equation written in standard form Graph linear equations using table method, intercepts, and slope-intercept form Determine whether a given point is on a line, given the equation of a line Determine whether an equation is linear. Write the equation of a line, given its slope and the coordinates of a point on the line Determine the slope of a line, given the coordinates of two points on the line Write the equation of a line, given the coordinates of two Page 4 of 12

5 points on the line Determine if two lines are parallel, given their equations in any form Write the equation of line parallel to the x- or y-axis. December 2005 How do we analyze problems using linear equations? How do linear inequalities fit into real-world situations? Graph linear inequalities using table method, intercepts, and slope-intercept form with attributes of dotted/solid line and shading Create a scatter plot of bivariate data Determine the existence of a correlation Fitting a line to data Linear Models Comparison of guessed ages to real ages of stars on a scatter plot (ATL, H&S) Identify the relationship between the dependent and independent variables from a scatter plot Construct manually a reasonable line of best fit for a scatter plot and determine the equation of that line Use a reasonable line of best fit to make predictions involving interpolation or extrapolation Deciding when to use a linear model January 2006 What are the three different methods of solving systems Solving linear systems graphically System of linear equations Page 5 of 12

6 of equations? Solve linear systems System of linear inequalities When do you use a particular method? algebraically by substitution method and elimination Applications of Linear Systems method Are you able to solve a linear inequality by graphing? What is the best method to solve a system of equations and inequalities in problem solving? Applying the techniques of solving linear systems to mathematical problems Solve a system of linear inequalities by graphing Solving and graphing quadratic Functions System of linear and quadratic equations How does the solution of a system of linear equations compare to the solution of a system of linear inequalities? How do you graph a quadratic equation? Determine whether a given point is in the solution set of a system of linear inequalities Graph a representation of a quadratic function Find the roots of a parabolic function graphically (integral solutions) Determine the vertex and axis of symmetry of a parabola, given its graph Determine the vertex and axis of symmetry of a parabola, given its equation Solve systems if linear and quadratic equations graphically Page 6 of 12

7 February 2006 How do we factor different forms of quadratic equations? Solve systems of two linear equations in two variables algebraically Factor by finding the product of "c" and the sum of "b" M and M Lab to Demonstrate Exponential Growth or Decay (ATL, Homo Faber) When do we solve for a variable and when do we leave it in factored form? What does "GCF" stand for? How do you factor using the GCF method? What are the benefits of using scientific notation than standard form of numbers? What makes a fraction undefined? How does performing the basic operations of algebraic fractions compare to performing the basic operations of numerical fractions? Understand and apply the multiplication property of zero to solve quadratic equations with integral coefficients and integral roots Understand the difference and connection between roots of a quadratic equation and factors of a quadratic expression 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) Solve s system of one linear and one quadratic equation in two variables, where only factoring is required Analyze and solve verbal problems that involve quadratic equations Find the values of a variable for which an algebraic fraction is undefined Add or subtract fractional expressions with monomial or like binomial denominators Factoring special products using difference of two perfect squares and perfect square trinomial pattern Factoring trinomials using the GCF method Real-World Applications Algebraic Fractions Scientific Notation Exponential Growth and Decay Page 7 of 12

8 Multiply and divide algebraic fractions and express the product or quotient in simplest form Simplify fractions with polynomials in the numerator and denominator by factoring both and renaming them to lowest terms Understand and use scientific notation to compute products and quotients of numbers Analyze and solve verbal problems the involve exponential growth and decay March 2006 How can you evaluate and approximate square roots? When is a radical in simplest form? Rewriting radicals in simplest form. Add, subtract, multiply and divide radicals Square Roots Simplify Radicals Pythagorean Thm. How do you perform the Pythagorean Thm. using a right triangle? How do you perform the correct trig. function? How do you know when to use the Pythagorean Thm. or Determine the measure of a third side of a right triangle using the Pythagorean Thm., given the lengths of any two sides Determine the measure of an angle of a right triangle, given the length of any two sides of the triangle Right Triangle Trig. Area and Perimeter Formulas of volume and surface area Relative Error Page 8 of 12

9 Right Triangle Trig.? Find the sine, cosine, and tangent Conversions of Measurement What is the difference between the measurements of perimeter, area, and volume? ratios of an angle of a right triangle, given the lengths of the sides What are the exponential units of measurement for perimeter, area, and volume? How can relative error exist in measuring? Find the measure of a side of a right triangle, given an acute angle and the length of another side Find the area and/or perimeter of figures composed of polygons and circles, or sectors of circles Use formulas to calculate volume and surface area of rectangular solids and cylinders Calculate the relative error in measuring square and cubic units when there is an error in linear measure Solve problems involving conversions within measurement systems, given the relationship between the units April 2006 Solve algebraic proportions in one variable which result in linear or quadratic equations Solve algebraic problems arising from situations that involve Rates and Proportions Real-World Applications Counting Principle Page 9 of 12

10 fractions, decimals, percents (decrease, increase, and discount), and proportionality/direct variation Permutation Probability Calculate rates using appropriate units Determine the number of possible events, using counting techniques or the Fundamental Principle of Counting Determine the number of possible arrangements using permutations Know the definition of conditional probability and use it to solve for probabilities in finite sample spaces Determine the number of elements in a sample space and the number of favorable events Calculate the probability of an event and its complement Determine empirical probabilities based on a specific sample data Determine probability of a set of events Calculate the probability Page 10 of 12

11 May 2006 Evaluate published reports and graphs that are based on data Identify and describe sources of bias and its effect, draw conclusions Categorize data; Qualitative vs. Quantative; Univariate or Bivariate; Bias or Unbias Compare and contrast the central tendencies for given data Recognize how linear transformations of one-variable data affect the data's central tendencies Construct, analyze, and interpret a histogram and cumulative frequency histogram for a given set of data Find the percentile rank and quartiles for a data set Construct, analyze, and interpret a box-and-whisker plot for a given set of data Understand how the five statistical summary (min., max., and the three quartiles) is used to construct a box-andwhisker plot Page 11 of 12

12 June 2006 Prepare for exam!! Page 12 of 12