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1 Liberal Arts Math

GENERAL INFORMATION Course Number: 1208300 Course Path: Section: Basic and Adult Education Grade Group: Secondary Grades 9-12 Subject: Mathematics SubSubject: Liberal Arts Mathematics Course Title: Liberal Arts Mathematics Abbreviated Title: Basic and Adult Education Course Section: Basic and Adult Education Number of Credits: One credit (1) Course Length: Year Course Type: Core Course Level: 2 Course Status: State Board Approved RELATED BENCHMARKS (35) : Scheme Descriptor Cognitive

Complexity LA.910.1.6.1 The student will use new vocabulary that is introduced and taught directly; LA.910.4.2.1 The student will write in a variety of informational/expository forms,

including a variety of technical documents (e.g., how-to-manuals, procedures, assembly directions);

MA.912.A.1.3 Simplify real number expressions using the laws of exponents. Low

MA.912.A.1.4 Perform operations on real numbers (including integer exponents, radicals, percents, scientific notation, absolute value, rational numbers, irrational numbers) using multi-step and real-world problems.

Moderate

MA.912.A.1.8 Use the zero product property of real numbers in a variety of contexts to identify solutions to equations.

Moderate

MA.912.A.2.1 Create a graph to represent a real-world situation. Moderate

MA.912.A.2.2 Interpret a graph representing a real-world situation. Moderate

MA.912.A.2.3 Describe the concept of a function, use function notation, determine whether a given relation is a function, and link equations to functions.

Moderate

MA.912.A.3.3 Solve literal equations for a specified variable. Moderate

MA.912.A.3.4 Solve and graph simple and compound inequalities in one variable and be able to justify each step in a solution.

Moderate

MA.912.A.3.5 Symbolically represent and solve multi-step and real-world applications that involve linear equations and inequalities.

Moderate

MA.912.A.3.7 Rewrite equations of a line into slope-intercept form and standard form. Low

MA.912.A.3.8 Graph a line given any of the following information: a table of values, the x- and y-intercepts, two points, the slope and a point, the equation of the line in slope-intercept form, standard form, or point-slope form .

Moderate

MA.912.A.3.9 Determine the slope, x-intercept, and y-intercept of a line given its graph, its equation, or two points on the line.

Moderate

MA.912.A.3.10 Write an equation of a line given any of the following information: two points on the line, its slope and one point on the line, or its graph. Also, find an equation of a new line parallel to a given line, or perpendicular to a given line, through a given point on the new line.

Moderate

MA.912.A.3.11 Write an equation of a line that models a data set, and use the equation or the graph to make predictions. Describe the slope of the line in terms of the data, recognizing that the slope is the rate of change.

High

MA.912.A.3.13 Use a graph to approximate the solution of a system of linear equations or inequalities in two variables with and without technology.

Moderate

MA.912.A.7.2 Solve quadratic equations over the real numbers by factoring and by using the quadratic formula.

Moderate

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MA.912.G.1.1 Find the lengths and midpoints of line segments in two-dimensional coordinate systems.

Moderate

MA.912.G.1.4 Use coordinate geometry to find slopes, parallel lines, perpendicular lines, and equations of lines.

Moderate

MA.912.G.2.3 Use properties of congruent and similar polygons to solve mathematical or real-world problems.

High

MA.912.G.2.5 Explain the derivation and apply formulas for perimeter and area of polygons (triangles, quadrilaterals, pentagons, etc.).

Moderate

MA.912.G.2.7 Determine how changes in dimensions affect the perimeter and area of common geometric figures.

Moderate

MA.912.G.3.1 Describe, classify, and compare relationships among quadrilaterals including the square, rectangle, rhombus, parallelogram, trapezoid, and kite.

Moderate

MA.912.G.4.4 Use properties of congruent and similar triangles to solve problems involving lengths and areas.

Moderate

MA.912.G.5.3 Use special right triangles (30° - 60° - 90° and 45° - 45° - 90°) to solve problems.

Moderate

MA.912.G.5.4 Solve real-world problems involving right triangles. High

MA.912.G.7.5 Explain and use formulas for lateral area, surface area, and volume of solids. Moderate

MA.912.G.7.7 Determine how changes in dimensions affect the surface area and volume of common geometric solids.

Moderate

MA.912.G.8.2 Use a variety of problem-solving strategies, such as drawing a diagram, making a chart, guess-and-check, solving a simpler problem, writing an equation, and working backwards.

Moderate

MA.912.G.8.3 Determine whether a solution is reasonable in the context of the original situation.

Moderate

MA.912.S.3.1 Read and interpret data presented in various formats. Determine whether data is presented in appropriate format, and identify possible corrections. Formats to include:

bar graphs line graphs stem and leaf plots circle graphs histograms box and whiskers plots scatter plots cumulative frequency (ogive) graphs

Moderate

MA.912.S.3.2 Collect, organize, and analyze data sets, determine the best format for the data and present visual summaries from the following

bar graphs line graphs stem and leaf plots circle graphs histograms box and whiskers plots scatter plots cumulative frequency (ogive) graphs

High

MA.912.S.3.3 Calculate and interpret measures of the center of a set of data, including mean, median, and weighted mean, and use these measures to make comparisons among sets of data.

Moderate

MA.912.S.3.5 Calculate and interpret the range and quartiles of a set of data. Moderate

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RELATED GLOSSARY TERM DEFINITIONS (68) Absolute value A number's distance form zero on a number line. Distance is expressed as a positive value. Approximate A number or measurement that is close to or near its exact value. Area The number of square units needed to cover a surface. Axes The horizontal and vertical number lines used in a coordinate plane system. Benchmark A point of reference from which other measurements or values may be made or judged. Chart A data display that presents information in columns and rows. Cone A pyramid with a circular base. Congruent Figures or objects that are the same shape and size. Coordinate plane A two-dimensional network of horizontal and vertical lines that are parallel and evenly-

spaced; especially designed for locating points, displaying data, or drawing maps. Coordinate Numbers that correspond to points on a coordinate plane in the form (x, y), or a number that

corresponds to a point on a number line. Cylinder A three dimensional figure with two parallel congruent circular bases and a lateral surface

that connects the boundaries of the bases. More general definitions of cylinder may not require circular bases.

Diagonal A line segment that joins two non-adjacent vertices in a polygon. Diameter A line segment from any point on the circle (or sphere) passing through the center to

another point on the circle (or sphere). Dimension The number of coordinates used to express a position. Equal Having the same value (=). Equation A mathematical sentence stating that the two expressions have the same value. Also read

the definition of equality. Expression A mathematical phrase that contains variables, functions, numbers, and/or operations. An

expression does not contain equal or inequality signs. Formula A rule that shows the relationship between two or more quantities; involving numbers

and/or variables. Geometric solid A closed three-dimensional geometric figure. Geometry The branch of mathematics that explores the position, size, and shape of figures. Height A line segment extending from the vertex or apex of a figure to its base and forming a right

angle with the base or plane that contains the base. Histogram A bar graph that shows how many data values fall into a certain interval. The number of

data items in an interval is a frequency. The width of the bar represents the interval, while the height indicates the number of data items, or frequency, in that interval.

Hypotenuse The longest side of a right triangle; the side opposite the right angle. Integers The numbers in the set {…,-4, -3, -2, -1, 0, 1, 2, 3, 4, …}. Kite A quadrilateral with two distinct pairs of adjacent congruent sides. Length A one-dimensional measure that is the measurable property of line segments. Line A collection of an infinite number of points in a straight pathway with unlimited length and

having no width. Mass The amount of matter in an object. Mass of an object remains the same regardless of its

location; weight of an object changes depending on the gravitational pull at its location. Weight is determined by the pull of gravity on the mass of an object.

Mean There are several statistical quantities called means, e.g., harmonic mean, arithmetic mean, and geometric mean. However, “mean” commonly refers to the arithmetic mean that is also called arithmetic average. Arithmetic mean is a mathematical representation of the typical value of a series of numbers, computed as the sum of all the numbers in the series divided

4 Liberal Arts Math

by the count of all numbers in the series. Arithmetic mean is the balance point if the numbers are considered as weights on a beam.

Median When the numbers are arranged from least to greatest, the middle number of a set of numbers, or the mean of two middle numbers when the set has two middle numbers is called median. Half of the numbers are above the median and half are below it.

Model To represent a mathematical situation with manipulatives (objects), pictures, numbers or symbols.

Operation Any mathematical process, such as addition, subtraction, multiplication, division, raising to a power, or finding the square root.

Origin The point of intersection of the x- and y-axes in a rectangular coordinate system, where the x-coordinate and y-coordinate are both zero. On a number line, the origin is the 0 point. In three dimensions, the origin is the point (0, 0, 0).

Parallelogram A quadrilateral in which both pairs of opposite sides are parallel. Pentagon A polygon with five sides. Percent Per hundred; a special ratio in which the denominator is always 100. The language of

percent may change depending on the context. The most common use is in part-whole contexts, for example, where a subset is 40 percent of another set. A second use is change contexts, for example, a set increases or decreases in size by 40 percent to become 140% or 60% of its original size. A third use involves comparing two sets, for example set A is 40% of the size of set B, in other words, set B is 250 percent of set A.

Perimeter The distance around a two dimensional figure. Perpendicular Two lines, two line segments, or two planes are said to be perpendicular when they intersect

at a right angle. Plot To locate a point by means of coordinates, or a curve by plotted points, or to represent an

equation by means of a curve so constructed. Point A specific location in space that has no discernable length or width. Polygon A closed plane figure, having at least three side that are line segments and are connected at

their endpoints. Product The result of multiplying numbers together. Quadrilateral Any polygon with four sides, including parallelogram, rhombus, rectangle, square,

trapezoid, kite. Radius A line segment extending from the center of a circle or sphere to a point on the circle or

sphere. Plural radii. Rate A ratio that compares two quantities of different units. Real number The set of all rational and irrational numbers. Real-world problem

A problem that is an application of a mathematical concept in a real-life situation.

Rectangle A parallelogram with four right angles. Relation A relation from A to B is any subset of the cross product (Cartesian product) of A and B. Right triangle A triangle having an interior right angle. Set A set is a finite or infinite collection of distinct objects in which order has no significance. Side The edge of a polygon (e.g., a triangle has three sides), the face of a polyhedron, or one of

the rays that make up an angle. Simplify The process of converting a fraction or mixed number, to an equivalent fraction, or mixed

number, in which the greatest common factor of the numerator and the denominator of the fraction is one. Simplify also refers to using the rules of arithmetic and algebra to rewrite an expression as simply as possible.

5 Liberal Arts Math

Square A rectangle with four congruent sides; also, a rhombus with four right angles. Table A data display that organizes information about a topic into categories using rows and

columns. Triangle A polygon with three sides. Unit A determinate quantity (as of length, time, heat, or value) adopted as a standard of

measurement. Variable Any symbol, usually a letter, which could represent a number. A variable might vary as in

f(x)=2x+1, or a variable might be fixed as in 2x+1=5. Circle A closed plane figure with all points of the figure the same distance from the center. The

equation for a circle with center (h, k) and radius r is: (x - h)2 + (y - k)2 = r2 Exponent (exponential form)

The number of times the base occurs as a factor, for example 23 is the exponential form of 2 x 2 x 2. The number two (2) is called the base, and the number three (3) is called the exponent.

Function A relation in which each value of x is paired with a unique value of y. More formally, a function from A to B is a relation f such that every a A is uniquely associated with an object F(a) B.

Inequality A sentence that states one expression is greater than (>), greater than or equal to ( ≥), less than (<), less than or equal to (≤), another expression.

Rational Number A number that can be expressed as a ratio a/b, where a and b are integers and b ≠0. Scientific Notation

A shorthand method of writing very large or very small numbers using exponents in which a number is expressed as the product of a integer power of 10 and a number that is greater than or equal to one (1) and less that 10(e.g., 7.59.x 105 = 759,000).

Slope The ratio of change in the vertical axis (y-axis) to each unit change in the horizontal axis (x-axis) in the form rise/run or ∆y/∆x. Also the constant, m, in the linear equation for the slope-

intercept form y =mx + b, where 21

21

xxyym

−−

=

Volume The amount of space occupied in three dimensions and expressed in cubic units. x-intercept The value of x at the point where a line or a curve intersects the x-axis. The value of y is

zero at this point. y-intercept The value of y at the point where a line or a curve intersects the y-axis. The value of x is

zero at this point.

6 Liberal Arts Math

LIBERAL ARTS MATHEMATICS (Revised June 2011) Algebra 1 Saxon

Liberal Arts Mathematics - First Nine Weeks – Revised June 2011 In response to input from Liberal Arts Mathematics teachers, the following lessons have been re-sequenced and grouped by each 9-weeks. The amount of time spent on each lesson will vary according to skills of the students. The lessons are sequenced in a logical order suggested by the teachers. It is important that at the end of each 9-weeks, those lessons have been addressed.

NGSSS MA.912.A.1.4 Perform operations on real numbers (including integer exponents, radicals, percents, scientific

notation, absolute value, rational numbers, irrational numbers) using multi-step and real-world problems.

MA.912.G.2.3 Use properties of congruent and similar polygons to solve mathematical or real-world problems. MA.912.G.2.7 Determine how changes in dimensions affect the perimeter and area of common geometric

figures. MA.912.G.4.4 Use properties of congruent and similar triangles to solve problems involving lengths and areas. MA.912.G.7.7 Determine how changes in dimensions affect the surface area and volume of common

geometric solids.

Lesson NGSSS Benchmarks 1 Classifying Real Numbers Previously taught skills 10 Adding and Subtracting Real Numbers Previously Taught Skill 6 Subtracting Real Numbers MA.912.A.1.3 11 Multiplying and Diving Real Numbers Previously Taught Skill 3 Simplifying Expressions Using the Product Rule of Exponents

MA.912.A.1.3

17 Translating Between Words and Algebraic Equations MA.912.A.3.5 2 Understanding Variables and Expressions Previously Taught Skills 18 Combine Like Terms MA.912.A.3.5 4 Using Order of Operations MA.912.A.1.4 7 Simplifying and Comparing Expressions with Symbols of Inclusions MA.912.A.1.4

16 Simplifying and Evaluating Variable Expressions MA.912.A.1.4 9 Evaluating and Comparing Algebraic Expressions MA.912.A.1.4 12 Using the Properties of Real Numbers to Simplify Expressions

MA.912.A.1.4

31 Using Rates, Ratios and Proportions Previously Taught Skills 36 Writing and Solving Proportions MA.912.G.2.3, MA.912.G.2.7, MA.912.G.4.4,

MA.912.G.7.7 42 Solving Percent Problems Previously taught skills 5 Finding Absolute Value and Adding Real Numbers Ma.912.A.1.4

Liberal Arts Mathematics - First Nine Weeks (continued) – Revised June 2011

7 Liberal Arts Math

NGSSS MA.912.A.1.4 Perform operations on real numbers (including integer exponents, radicals, percents, scientific

notation, absolute value, rational numbers, irrational numbers) using multi-step and real-world problems.

MA.912.A.3.3 Solve literal equations for a specified variable. MA.912.A.3.5 Symbolically represent and solve multi-step and real-world applications that involve linear

equations and inequalities. MA.912.A.3.4 Solve and graph simple and compound inequalities in one variable and be able to justify each

step in a solution. MA.912.A.3.5 Symbolically represent and solve multi-step and real-world applications that involve linear

equations and inequalities.

Lesson NGSSS Benchmarks 15 Using Distributive Property to Simplify Expressions MA.912.A.1.4 19 Solving One Step Equations by Adding and Subtracting Previously Taught Skills 21 Solving One Step Equations by Multiplying and Dividing

Previously Taught Skills

23 Solving Two-Step Equations MA.912.A.3.5 24 Solving Decimal Equations MA.912.A.3.5 26 Solving Multi-Step Equations MA.912.A.3.5 28 Solving Equations with Variables on Both Sides MA.912.A.3.5 29 Solving Literal Equations MA.912.A.3.3 50 Graphing Inequalities MA.912.A.3.4 66 Solving Inequalities by Adding and Subtracting MA.912.A.3.4 70 Solving Inequalities by Multiplying and Dividing MA.912.A.3.4 73 Solving Compound Inequalities MA.912.A.3.4 77 Solving Two-Step and Multi-Step Inequalities MA.912.A.3.5 81 Solving Inequalities with Variables on Both Sides MA.912.A.3.5

End of the First Term

Liberal Arts Mathematics - Second Nine Weeks – Revised June 2011

8 Liberal Arts Math

NGSSS MA.912.A.1.3 Simplify real number expressions using the laws of exponents. MA.912.A.1.4 Perform operations on real numbers (including integer exponents, radicals, percents, scientific

notation, absolute value, rational numbers, irrational numbers) using multi-step and real-world problems.

MA.912.A.1.3 Simplify real number expressions using the laws of exponents. MA.912.A.1.4 Perform operations on real numbers (including integer exponents, radicals, percents, scientific

notation, absolute value, rational numbers, irrational numbers) using multi-step and real-world problems.

MA.912.A.7.2 Solve quadratic equations over the real numbers by factoring, and by using the quadratic formula.

Lesson NGSSS Benchmarks

32 Simplifying and Evaluating Expressions with Integers and Zero Exponents MA.912.A.1.3

40 Simplifying and Evaluating Expressions Using The Power of Rule for Exponents MA.912.A.1.3, MA.912.A.1.4

13 Calculating and Comparing Square Roots MA.912.A.1.3 46 Simplifying Expressions with Square Roots and Higher Order Roots

MA.912.A.1.3, MA.912.A.1.4

61 Simplifying Radical Expressions MA.912.A.1.4 69 Adding and Subtracting Radical Expressions MA.912.A.1.4 76 Multiplying Radical Expressions MA.912.A.1.4 58 Multiplying Polynomials Previously Taught Skill 60 Finding Special Products of Binomials Previously Taught Skill 53 Adding and Subtracting Polynomials Previously Taught Skill 38 Simplifying Expressions Using GCF Previously Taught Skill 43 Simplifying Rational Expressions MA.912.A.1.4 39 Using the Distributive Property to Simplify Rational Expressions

MA.912.A.1.3, MA.912.A.1.4

Liberal Arts Mathematics - Second Nine Weeks (continued) – Revised June 2011

Lesson NGSSS Benchmark

51 Simplifying Rational Expressions with Like Denominators Previously Taught Skills 57 Finding the Least Common Multiple Previously Taught Skills 72 Factoring Trinomials x^2 + bx =c MA.912.A.7.2 75 Factoring Trinomials ax^2 + bx = c MA.912.A.7.2 83 Factoring Special Products MA.912.A.7.2 98 Solving Quadratic Equations by Factoring MA.912.A.7.2 110 Using Quadratic Formula MA.912.A.7.2

End of the Second Term -Course Midpoint-

Liberal Arts Mathematics - Third Nine Weeks– Revised June 2011

9 Liberal Arts Math

NGSSS MA.912.S.3.1 Read and interpret data presented in various formats. Determine whether data is presented in

appropriate format, and identify possible corrections. Formats to include: • bar graphs • line graphs • stem and leaf plots • circle graphs • histograms • box and whiskers plots • scatter plots • cumulative frequency (ogive) graphs

MA.912.S.3.2 Collect, organize, and analyze data sets, determine the best format for the data and present visual summaries from the following:

• bar graphs • line graphs • stem and leaf plots • circle graphs • histograms • box and whiskers plots • scatter plots • cumulative frequency (ogive) graphs

Lesson NGSSS Benchmarks

20 Graphing Coordinate Plane MA.912.A.2.1, MA.912.A.2.2

22 Analyzing and Comparing Statistical Graphs MA.912.A.2.1, MA.912.A.2.2, MA.912.S.3.1, MA.912.S.3.2

25 Differentiating Between Relations and Functions MA.912.A.2.3 48 Analyzing Measures of Central Tendency MA.912.A.3.3 54 Displaying Data in Box-and-Whisker Plot MA.912.S.3.1, MA.912.S.3.2, MA.912.S.3.5 62 Displaying Data in Stem-and-Leaf Plots and Histograms MA.912.S.3.1, MA.912.S.3.2 71 Making and Analyzing Scatter Plots MA.912.A.3.11, MA.912.S.3.1,

MA.912.S.3.2 35 Locating X and Y Intercepts MA.912.A.3.9 41 Finding Rate of Change and Slope MA.912.A.3.9 44 Finding Slope Using the Slope Formula MA.912.A.3.9 49 Writing Equations in Slope-Intercept Form MA.912.A.3.7 52 Determine the Equation of a line Given Two Points MA.912.A.3.10 65 Writing Equations of Parallel and Perpendicular Lines MA.912.A.3.10 55 Solving Systems of Equations by Graphing MA.912.A.3.13 63 Solving Systems of Equations by Elimination Previously Taught Skill

End of the Third Term

Liberal Arts Mathematics - Fourth Nine Weeks– Revised June 2011

10 Liberal Arts Math

NGSSS MA.912.G.1.1 Find the lengths and midpoints of line segments in two-dimensional coordinate systems. MA.912.G.5.4 Solve real-world problems involving right triangles.

Lesson NGSSS Benchmarks 37 Using Scientific Notation MA.912.A.1.4 85 Solving Problems Using the Pythagorean Theorem MA.912.G.5.4 86 Calculating the Midpoint and Length of a Segment MA.912.G.1.1

Geometry This Geometry unit addresses required benchmarks not covered in the Saxon Algebra 1 textbook. The following instructional materials are suggested resources for each topic/benchmark: Saxon Algebra 1 Skills Bank Lessons (SB) Saxon Algebra 1 Prerequisite Skills Intervention (PSI) Prentice Hall Geometry 2011 Text and/or Workbook (PH)

NGSSS MA.912.G.2.3 Use properties of congruent and similar polygons to solve mathematical or real-world problems. MA.912.G.2.5 Explain the derivation and apply formulas for perimeter and area of polygons

(triangles, quadrilaterals, pentagons, etc.). MA.912.G.3.1 Describe, classify, and compare relationships among quadrilaterals including the

square, rectangle, rhombus, parallelogram, trapezoid, and kite. MA.912.G.7.5 Explain and use formulas for lateral area, surface area, and volume of solids. MA.912.G.7.7 Determine how changes in dimensions affect the surface area and volume of common

geometric solids.

Liberal Arts Mathematics - Fourth Nine Weeks (continued– Revised June 2011

Lesson NGSSS Benchmarks

Geometry SB Lesson 14: Classifying Quadrilaterals MA.912.G.3.1 PH Lesson 6-6: Trapezoids and Kites MA.912.G.3.1 SB Lesson 16: Congruence MA.912.G.2.3 PSI Skill 33: Congruent Figures MA.912.G.2.3 PSI Skill 34: Identify Similar Figures MA.912.G.2.3 PSI Skill 35: Find Missing Measures in Similar Figures

MA.912.G.2.3

PSI Skill 31: Pythagorean Theorem MA.912.G.2.3 PSI Skill 32: Special Right Triangles MA.912.G.2.3 PSI Skill 36: Find Perimeter MA.912.G.2.5 PSI Skill 37: Area of Polygons MA.912.G.2.5 PSI Skill 39: Circumference and Area of Circles Previously taught skills

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PH Lesson 11-2: Surface Areas of Prisms and Cylinders MA.912.G.7.5 PH Lesson 11-3: Surface Areas of Pyramids and Cones MA.912.G.7.5 SB Lesson 21: Surface Area of Prisms and Pyramids MA.912.G.7.5 PH Lesson 11-4: Volumes of Prisms and Cylinders MA.912.G.7.5 SB Lesson 26: Volumes of Prisms and Cylinders MA.912.G.7.5 PH Lesson 11-5: Volumes of Pyramids and Cones MA.912.G.7.5 PH Lesson 11-6: Surface Areas and Volumes of Spheres

MA.912.G.7.5

PH Lesson 11-7: Areas and Volumes of Similar Solids MA.912.G.7.7

End of the Fourth Term -Course Endpoint-