1 K-12 MATH HIGH ACHIEVEMENT OUTCOMES Mission Statement: By working individually and cooperatively, students in math will apply mathematical concepts, demonstrate computational skills, and use technological resources to solve real-world problems. Kindergarten Math Focus Area: Grade Level Purpose Statement: Students will distinguish between basic geometric shapes. They will use numbers to compare, analyze, and solve problems, as well as to generate information. Students will be able to recognize and use numbers and shapes in their environment. High Achievement Outcomes: Outcome M.K.1: Students will develop an understanding of numbers and the relationships between them. K.1.1 Recognize, count and write numbers to 20 K.1.2 Count backwards from 10-0 K.1.3 Identify ordinal numbers K.1.4 Connect number words and numerals to the quantities they represent K.1.5 Use comparison vocabulary (more/less, equal, bigger/smaller) K.1.6 Count objects to demonstrate one-to-one correspondence Outcome M.K.2: Students will demonstrate the concepts of addition and subtraction. K.2.1. Demonstrate the value of basic facts using concrete objects. K.2.2. Recognize the symbols + and as representing operations of addition and subtraction K.2.3 Recognize the symbol = represents equal quantities K.2.4 Solve problems involving one-step solutions related to student experiences. Outcome M.K.3: Students will develop an understanding of measurement and basic measurement tools. K.3.1 Use simple standard and non-standard units of measure (ie: inch, paperclips, cubes, etc.) K.3.2 Identify and use various tools of measurement (ie: analog clock, balance scale, ruler, calendar, thermometer, etc.) Outcome M.K.4: Students will be able to collect, organize, display and analyze information. K.4.1 Sort and classify objects according to one or more attributes K.4.2 Use a graph to organize and summarize data K.4.3 Make appropriate conclusions from a graph
2 Outcome M.K.5: Students will develop an understanding of shapes and patterns. K.5.1 Identify, describe and create basic shapes K.5.2 Identify, describe and create a pattern sequence First Grade Math Focus Area: Grade Level Purpose Statement: Students will be able to use numbers to compare, analyze, record, solve problems and produce information. High Achievement Outcomes: Outcome M.1.1: Students will develop an understanding of numbers and the relationships between them. M Recognize, count, and write to 100 by 1s, 2s, 5s, and 10s M Count backwards from 10-0 M Identify and use ordinal numbers M Demonstrate place value (tens and ones) to 99 M Use comparison vocabulary and identify numbers that are: bigger/smaller, more/less, higher/lower, greater than/less than M Give and justify a realistic estimation M Identify and represent the fractions 1/2 and 1/4, and shapes with equal parts Outcome M.1.2: Students will develop an understanding of coins. M Identify and count quarters, dimes, nickels, and pennies to.99 Outcome M.1.3: Students will demonstrate addition and subtraction to 18. M Understand +, -, and = signs M Add and subtract to 18 M Add and subtract double digits without regrouping M Write a number sentence from a picture Outcome M.1.4: Students will develop an understanding of standard and non-standard measurement using a variety of tools. M Use a variety of non-standard units of measure (ie: paperclips, straws, etc.) M Use standard units of measure (ie: minutes, hours, pounds, kilograms, inch, cent., cups, pints, quarts, liters, degrees, days, weeks, months, year) M Identify and use various tools of measurement (ie: analog and digital clocks, balance scale, ruler, calendar, thermometer, etc.) M Identify and understand the terms past, present, and future Outcome M.1.5: Students will be able to collect, organize, display, and analyze information.
3 M Sort and classify objects according to one or more attributes M Make, interpret, and summarize data on a graph M Make appropriate conclusions from a graph Outcome M.1.6: Students develop an understanding of shapes. M Identify, describe, and create shapes (circles, triangles, squares, and rectangles) M Identify solids (cones, cubes, cylinder, and sphere) Outcome M.1.7: Students will develop an understanding of patterns. M Identify, describe, and create a pattern sequence M Identify patterns within the environment Second Grade Math Focus Area: Perform computations and problem solving skills. Grade Level Purpose Statement: Students will use numbers to compare, compute, analyze and record information. High Achievement Outcomes: Outcome M.2.1 The learner will understand numeration and number sense up to The learner will: M Identify number to 999 M Write numbers in words M Compare whole numbers M Identify place value to hundreds M Write numbers in standard form M Perform skip counting with 2 s, 5 s, 10 s M Identify fractional sets Outcome M.2.2 The learner will compute and estimate numbers up to The learner will: M Add up to 999 M Subtract up to 999 M Round numbers to tens and hundreds M Estimate M Understand fact families in addition and subtraction Outcome M.2.3 The learner will demonstrate an understanding of measurement. The learner will: M Measure mass in whole units M Measure temperature in whole units
4 M Measure weight in whole units M Measure volume in whole units M Measure length in whole units M Measure perimeter of a polygon in whole units M Understand calendar concepts M Measure time in 5 min. increments M Measure elapsed time M Count money (coins and dollars) Outcome M.2.4 The learner will analyze data by using patterns, graphs, tables and probability. The learner will: M Complete patterns M Read graphs/tables M Draw conclusions from graphs/tables M Predict outcomes through probability Outcome M.2.5 The learner will demonstrate an understanding of geometric and spacial concepts. The learner will: M Identify 2-dimensional shapes M Identify 3-dimensional shapes M Identify symmetrical shapes M Identify congruent shapes Outcome M.2.6 The learner will develop an understanding of beginning algebraic concepts used in addition and subtraction. The learner will: M Identify a missing variable in an addition problem M Identify a missing variable in a subtraction problem Third Grade Math Focus Area: Perform computations and problem solving skills. Grade Level Purpose Statement: Students will use numbers in all operations to compare, compute, analyze and record information. High Achievement Outcomes: Outcome M.3.1 The learner will understand numeration and number sense up to 100,000. The learner will: M Tell whether numbers are used to count, label, measure, or tell order M Identify place value to hundred thousand M Use fractions M Compare numbers
5 M Identify even and odd numbers M Use decimals Outcome M.3.2 The learner will compute and estimate numbers up to 100,000. The learner will: M Understand fact families M Round to the nearest hundred M Choose an operation to solve in a story problem M Multiply M Perform story problems M Estimate M Be able to carry and borrow when adding/subtracting M Be able to add and subtract problems Outcome M.3.3 The learner will demonstrate an understanding of measurement. The learner will: M Measure mass in whole units M Measure temperature in whole units M Measure weight in whole units M Measure volume in whole units M Measure length in whole units with standard and metric units M Measure perimeter of a polygon in whole units M Understand calendar concepts M Measure time M Count money (coins and dollars) Outcome M.3.4 The learner will analyze data by using patterns, graphs, tables and probability. The learner will: M Complete patterns M Read graphs/tables M Draw conclusions from graphs/tables Outcome M.3.5 The learner will demonstrate an understanding of geometric and spacial concepts. The learner will: M Find the area of a shape M Understand acute, obtuse, and right angles M Recognize congruent figures M Recognize lines of symmetry M Recognize geometric shapes up to 8 sides M Recognize the cube, sphere, rectangular prism, triangular prism, and pyramid Outcome M.3.6 The learner will demonstrate an understanding of algebraic concepts. The learner will: M Use variables in all operations of math
6 Fourth Grade Math Focus Area: Numeration, computation, measurement, and recall. Grade Level Purpose Statement: Students completing the 4 th grade math curriculum will apply their knowledge of numeration, computation and measurement while interpreting and analyzing data. High Achievement Outcomes: 4M 1. Place value of whole numbers through the millions and decimal to the hundredth place. 4M 2. Write and illustrate equivalences of whole numbers in expanded form, decimals, and fractions 4M 3. Describe and apply whole numbers, decimals, and fractions by order, comparison, and operation. 4M 4. Identify examples of positive and negative numbers and zero. 4M 5. Make and count out change up to $ M 6. Estimate, add, subtract, multiply, and divide whole numbers without and with calculators and solve word problems. 4M 7. Estimate, add, and subtract fractions with like denominators without calculators and solve word problems. 4M 8. Estimate, measure, and solve word problems using metric and standard units for linear measure, area, mass/weight, capacity, perimeter, and temperature. 4M 9. Tell and write correct time to the minute using analog clocks. 4M 10. Identify, describe, and create two-three-dimensional geometric shapes, Points, lines, line segments, rays, and angles. 4M 11. Identify, analyze and compare two-dimensional geometric figures using congruence, symmetry, similarity, and simple transformation. 4M 12. Collect, organize, record and interpret data and describe the findings. Fifth Grade Math Focus Area: Math Grade Level Purpose Statement: Students will be able to define, interpret, problem solve and use mathematical concepts to compute, compare, estimate, convert and order small and large numbers. High Achievement Outcomes: 1. Students will understand the concepts of numeration Identify place value through the billions Compare numbers Understand Fraction Concepts Write numbers in standard, written, and expanded form Use/understand multiples
7 2. Students will be able to use and identify multiple computation methods Compute Fractional numbers; add, subtract, multiply, divide Rounding numbers Division, Multiplication, addition, and subtraction of whole numbers Estimate using multiplication, division, addition, and subtraction 3. Students will use and Identify metric and customary measurements Measure length, weight, capacity and be able to convert in metric terms; Read and convert elapsed time both analog and digital; Make change and count back dollar amounts Measure length, weight, capacity and be able to convert in customary terms Identify and measure perimeter and area Identify and measure volume 4. Students will use and identify different forms of data Use line, bar, and pictographs Identify and use patterns in math 5. Students will use and identify geometric concepts Identify acute, obtuse and right angles Identify geometric solids and figures Begin to recognize and use transformations Identify quadrilaterals and polygons 6. Students will recognize and use basic algebraic terms Begin to recognize and use missing variables. Sixth Grade Math Focus area: Grade Level Purpose Statement: Students will apply number relationships and use these to solve problems involving all forms of mathematical operations. Outcome 1: The students will be able to apply different strategies of estimation skills to solve word problems. 6M 1.1 Students will be able to apply rounding skills 6M 1.2 Students will be able to demonstrate front-end estimates. 6M 1.3 Students will be able to evaluate expressions using order 6M 1.4 Students will be able to interpret simple algebraic expressions. Outcome 2: The students will be able to interpret tables, charts and graphs. The students will be able to construct various types of graphs and predict outcomes from the data. 6M 2.1 Students will be able to organize data into a table 6M 2.2 Students will be able to construct appropriate scales and intervals for data tables.
8 6M 2.3 Students will be able to create bar and line graphs. 6M 2.4 Students will be able to analyze data by finding the mean, median, and mode. Outcome 3: The students will be able to order and compare decimals to the tenthousandths place. The students will be able to order and compare decimals to the tenthousandths place. The students will be able to demonstrate addition and subtraction of decimals. 6M 3.1 Students will be able to model, read and write decimals through the ten thousandth s place. 6M 3.2 Students will be able to rank decimals in order. 6M 3.3 Students will be able to round decimals. 6M 3.4 Students will be able to compute addition and subtraction of decimals. 6M 3.5 Students will be able to compute addition and subtraction of decimals. Outcome 4: The Students will be able to evaluate exponents in expressions. The Students will be able to multiply whole numbers and decimals and to apply this knowledge in finding perimeter of geometric figures and circumference of circle. 6M 4.1 Students will be able to use exponents in expressions. 6M 4.2 Students will be able to demonstrate the product of decimals. 6M 4.3 Students will be able to calculate circumference of circles. Outcome 5: The students will be able to divide decimals. The students will apply this knowledge in using inverse operations to solve equations with multiplication. The students will further use this knowledge by calculating conversion of metric units. 6M 5.1 Students will be able to compute division of whole numbers by decimals. 6M 5.2 Students will be able to compute division of decimals by decimals. 6M 5.3 Students will be able to distinguish metric units of mass and capacity. 6M 5.4 Students will be able to convert units within the metric system. 6M 5.5 Students will be able to demonstrate the use of inverse operations to solve multiplication equations. Outcome 6: The students will be able to apply principles of number theory to recognize the differences of prime and composite numbers. The students will be able to use this knowledge to determine greatest common factor, least common multiple, writing fractions in lowest terms and comparing and contrasting fractions. 6M 6.1 Students will be able to identify the prime factorization of composite numbers. 6M 6.2 Students will be able to show the greatest common factor of two or more numbers. 6M 6.3 Students will be able to model equivalent fractions. 6M 6.4 Students will be able to write fractions in simplest form. 6M 6.5 Students will be able to rank decimals. 6M 6.6 Students will be able to find the least common multiple of two or more numbers. Outcome 7: The students will be able to compute addition and subtraction of fractions. 6M 7.1 Students will be able to add and subtract fractions with like denominators.
9 6M 7.2 Students will be able to add and subtract fractions with different denominators. 6M 7.3 Students will be able to add and subtract mixed numbers. 6M 7.4 Students will be able to determine addition and subtraction of units of time. Outcome 8: The students will be able to multiply and divide fractions and demonstrate how this applies to changing units within the customary system of measurement. 6M 8.1 Students will be able to compute multiplication of fractions. 6M 8.2 Students will be able to calculate multiplication of mixed numbers. 6M 8.3 Students will be able to divide fractions. 6M 8.4 The students will be able to divide mixed numbers. 6M 8.5 Students will be able to convert units in the customary system measurements. Outcome 9: The students will be able to apply principles of Geometry to determine types of angles, comparison of two-dimensional figures, and defining congruence and lines of symmetry. 6M 9.1 Students will be able to classify angles. 6M 9.2 Students will be able to measure and diagram angles. 6M 9.3 Students will be able to distinguish and verify two-dimensional objects. 6M 9.4 Students will be able to show and demonstrate congruency and lines of symmetry. Outcome 10: The students will be able to compare the relationship of fractions, decimals and percents and apply this knowledge in using ratios and the creation of scale drawings. 6M 10.1 Students will be able to write ratios as fractions. 6M 10.2 Students will be able to determine actual length from scale drawings. 6M 10.3 Students will be able to show how ratios can be used to solve problems. 6M 10.4 Students will be able to demonstrate how ratios can be used to solve problems involving percents. Outcome 11: The students will be able to compute the area of geometric objects. The students will be able to identify and label 3 dimensional objects and find their surface area and volume. 6M 11.1 Students will be able to find the area of parallelograms, triangles, and circles. 6M 11.2 Students will be able to construct circle graphs. 6M 11.3 Students will be able to label 3 dimensional figures. 6M 11.4 Students will be able to draw 3 dimensional objects. 6M 11.5 Students will be able to find the surface area of rectangular prisms. 6M 11.6 Students will be able to calculate the value of rectangular prisms. Outcome 12: The students will be able to add, subtract, multiply and divide integers and to apply this knowledge to the coordinate system. 6M 12.1 Students will be able to diagram integers. 6M 12.2 Students will be able to add and subtract integers. 6M 12.3 Students will be able to multiply and divide integers. 6M 12.4 Students will be able to graph ordered pairs of integers on a coordinate grid.
10 Outcome 13: The students will be able to distinguish algebraic equations in order to solve equations and inequalities by graphing them. 6M 13.1 Students will be able to solve addition and subtraction equations. 6M 13.2 Students will be able to solve multiplication and division equations. 6M 13.3 Students will be able to solve two-step equations. 6M 13.4 Students will be able to graph functions. Outcome 14: The students will be able to use laws of probability and apply them to make predictions. 6M 14.1 Students will be able to determine the probability of an event. 6M 14.2 Students will be able to demonstrate experimental probability. 6M 14.3 Students will be able to hypothesize the occurrence of an event. Seventh Grade Math Focus Area: Problem solving in simple math areas, pre-algebra concepts and geometrical concepts using all operational skills with positive and negative numbers. Grade Level Purpose Statement: Students will interpret, evaluate and apply basic math operations in order to solve pre-algebraic equations, calculate geometric measurements and estimation involving both negative and positive numbers. High Achievement Outcomes: Outcome 1: Students will demonstrate problem-solving strategies. 7M 1.1 Estimate sums and differences using rounding 7M 1.2 Estimate products and quotients using patterns 7M 1.3 Evaluate expressions using the order of operations 7M 1.4 Evaluate numerical and simple algebraic expressions 7M 1.5 Evaluate powers and exponents in expressions Outcome 2: Students will convert, order, compare and apply decimal applications. 7M 2.1 Compare and order decimals 7M 2.2 Multiply decimals 7M 2.3 Multiply decimals mentally by powers of ten 7M 2.4 Express numbers greater than 100 in scientific notation and vice versa 7M 2.5 Divide decimals 7M 2.6 Convert metric units of length, capacity, and mass Outcome 3: Students will collect, organize, plot, and interpret data 7M 3.1 Interpret bar graphs, line graphs, and circle graphs 7M 3.2 Organize data in a table 7M 3.3 Find the mean, median, and mode of a set of data 7M 3.4 Identify mode, median, and mean to make predictions
11 Outcome 4: Students will demonstrate number theory skills with prime and composite numbers. 7M 4.1 Test divisibility rules 7M 4.2 Find the prime factorization of a composite number 7M 4.3 Recognize and extend sequences 7M 4.4 Find the greatest common factor of two or more numbers 7M 4.5 Express fractions in simplest form 7M 4.6 Find the probability of a simple event 7M 4.7 Find the least common multiple of two or more numbers Outcome 5: Students will perform operations and applications with fractions. 7M 5.1 Convert mixed numbers to improper fractions and vise versa 7M 5.2 Add and subtract fractions 7M 5.3 Multiply fractions and mixed numbers 7M 5.4 Find the circumference of circles 7M 5.5 Divide fractions and mixed numbers 7M 5.6 Identify unit price Outcome 6: Students will solve simple equations. Student will: 7M 6.1 Solve equations using inverse operations 7m 6.2 Solve equations using the addition and subtraction properties of equality 7M 6.3 Solve equations using the multiplication and division of properties of equality 7M 6.4 Write simple algebraic expressions from verbal phrases 7M 6.5 Convert units in the customary system 7M 6.6 Find the area of rectangles and parallelograms Outcome 7: Students will demonstrate relationships among fractions, decimals, percents, and proportion. 7M 7.1 Read and write integers. Find the opposite and absolute value of an integer 7M 7.2 Compare and order integers 7M 7.3 Graph points on a coordinate plane 7M 7.4 Add integers 7M 7.5 Subtract integers 7M 7.6 Multiply integers 7M 7.7 Divide integers Outcome 8: Students will identify angles, polygons, and simple geometric concepts. 7M 8.1 Measure angles by using a protractor 7M 8.2 Classify angles 7M 8.3 Construct a line perpendicular to another line 7M 8.4 Identify polygons 7M 8.5 Discover the sum of the angle measures of any polygon 7M 8.6 Classify triangles and quadrilaterals 7M 8.7 Identify regular polygons
12 7M 8.8 Create Escher-like drawings by using translations 7M 8.9 Create Escher-like drawings by using reflections Outcome 9: Students will identify squares and square roots, and apply the Pythagorean Theorem 7M 9.1 Find square roots of perfect squares 7M 9.2 Find the relationship among the sides of a right triangle 7M 9.3 Solve problems using the Pythagorean Theorem 7M 9.4 Calculate the area of a trapezoid 7M 9.5 Compute the area of triangles and trapezoids 7M 9.6 Compute the area of circles Outcome 10: Students will determine surface area and volume of 3-dimensional figures. 7M 10.1 Calculate the surface area of rectangular prisms 7M 10.2 Compute the volume of rectangular prisms 7M 10.3 Calculate the volume of cylinders Outcome 11: Students will demonstrate relationships among fractions, decimals, percents, and proportion. 7M 11.1 Explore the meaning of ration and proportion 7M 11.2 Calculate unit rates 7M 11.3 Solve proportions 7M 11.4 Solve problems involving scale drawings 7M 11.5 Convert fractions to percents and vice versa 7M 11.6 State decimals as percents and vice versa Outcome 12: Students will calculate percents, simple interest, and solve percentage equations 7M 12.1 Find the percent of a number 7M 12.2 Solve problems using the percent proportion 7M 12.3 Solve problems using the percent equation 7M 12.4 Construct a circle graph 7M 12.5 Solve problems involving simple interest Outcome 13: Students will examine and predict outcomes and calculate probability. 7M 13.1 Construct tree diagrams to count outcomes 7M 13.2 Count outcomes by multiplying 7M 13.3 Find and compare experimental and theoretical probabilities Outcome 14: Students will solve two step equations and graph linear equations. 7M 14.1 Solve problems by working backward 7M 14.2 Solve two-step equations with integers using models 7M 14.3 Solve two-step equations
13 Pre-Algebra Focus Area: Basic Math and Beginning Course Purpose Statement: Students will apply basic algebraic concepts in solving a variety of different types of equations. High Achievement Outcomes: Outcome 1: Students will learn to solve problems, to evaluate expressions, and to use variables and expressions when solving real-world problems. PA 1.1 Use the order of operations to evaluate expressions. PA 1.2 Translate verbal phrases into algebraic expressions. PA 1.3 Identify and use properties of addition and multiplication. PA 1.4 Use ordered pairs to locate points. Outcome 2: Students will learn to compare and order integers, find the absolute value of an expression and find the average of a set of data. PA 2.1 Apply the rules for adding, subtracting, multiplying, and dividing integers PA 2.2 Evaluate algebraic expressions PA 2.3 Use the Cartesian coordinate system to graph points in all four quadrants of the coordinate grid Outcome 3: Students will use the Distributive Property to combine like terms in order to simplify algebraic expressions. PA 3.1 Solve equations using properties of equality PA 3.2 Learn how to write and solve two-step equations PA 3.3 Use formulas to solve real-world problems such as finding the area and perimeter of rectangles Outcome 4: Students will examine factors and monomials. PA 4.1 Evaluate expressions containing powers and exponents PA 4.2 Use greatest common factor to simplify expressions and algebraic fractions PA 4.3 Multiply and divide monomials PA 4.4 Express numbers using positive and negative exponents and scientific notation Outcome 5: Students will explore rational numbers. PA 5.1 Multiply and divide fractions PA 5.2 Add and subtract like and unlike fractions PA 5.3 Convert fractions to decimals PA 5.4 Factor numbers PA 5.5 Find the least common multiple (LCM) and examine measures of central tendency PA 5.6 Solve equations PA 5.7 Identify sequences
14 Outcome 6: Students will study ratios, rates, and proportions. PA 6.1 Solve problems, including scale drawings and models PA 6.2 Convert fractions to decimals to percents PA 6.3 Find simple probability Outcome 7: Students will solve equations with variables on each side. PA 7.1 Use the Distributive Property PA 7.2 Write and graph inequalities PA 7.3 Solve inequalities by using properties of inequality Outcome 8: Students will define function as a special type of relation and graph a linear equation. Outcome 9: Students will define squares and square roots, classify angles and triangles, and find missing angle measurements in triangles. PA 8.1 Use the Pythagorean Theorem to explore right triangles PA 8.2 Use Distance and Midpoint Formulas PA 8.3 Identify and use properties of similar figures PA 8.4 Use trigonometric ratios to solve problems Outcome 10: Students will identify the relationships of parallel and intersecting lines, and the properties of congruent triangles. PA 9.1 Identify and draw transformations PA 9.2 Classify and find angle measures of polygons PA 9.3 Find the area of polygons and irregular figures PA 9.4 Find the circumference and area of circles Outcome 11: Students will identify three-dimensional figures PA 10.1 Find the surface area of prisms, cylinders, pyramids, and cones PA 10.2 Find the volume of prisms, cylinders, pyramids and cones Outcome 12: Students will identify polynomials to include expressions with more than one term, such as binomials and trinomials. PA 11.1 Add, subtract, and multiply polynomials Outcome 14: Students will solve two step equations and graph linear equations. PA 12.1 Graph equations by plotting points Algebra I Focus Area:
15 Course Purpose Statement: High Achievement Outcomes: Outcome 1: The student will use variables and algebraic expressions. They will use the order of operations and work with open sentences and they will understand and use the algebraic properties. A1 1.1 Convert mathematical expressions to verbal expressions A1 1.2 Convert verbal expressions to mathematical expressions A1 1.3 Evaluate numerical expressions by using the order of operations A1 1.4 Evaluate algebraic expressions by using the order of operations A1 1.5 Solve open sentence equations A1 1.6 Solve open sentence inequalities A1 1.7 Recognize the properties of identity and equality A1 1.8 Use the properties of identity and equality A1 1.9 Use the Distributive Property to evaluate expressions A Use the Distributive Property to simplify expressions A Recognize the Commutative and Associative Properties A Use the Commutative and Associative Properties to simplify expressions Outcome 2: The students will correctly place of decimals on a number line. They will do the four basic operations with rational numbers and use square roots and real numbers. A1 2.1 Graph rational numbers on a number line A1 2.2 Find absolute values of rational numbers A1 2.3 Add integers and rational numbers A1 2.4 Subtract integers and rational numbers A1 2.5 Multiply integers A1 2.6 Multiply rational numbers A1 2.7 Divide integers A1 2.8 Divide rational numbers A1 2.9 Find square roots A Classify and order real numbers Outcome 3: The students will write equations and they will solve them using the four basic algebraic operations and they will solve multi-step equations. They also will use ratios and proportions. A1 3.1 Translate verbal sentence into equations A1 3.2 Translate equations into verbal sentences A1 3.3 Solve equations by using addition A1 3.4 Solve equations by using subtraction A1 3.5 Solve equations by using multiplication A1 3.6 Solve equations by using division A1 3.7 Solve problems by working backward A1 3.8 Solve equation involving more than one operation A1 3.9 Solve equations with the variable on each side A Solve equations involving grouping symbols A Determine whether two rations form a proportion
16 A Solve proportion A Find percents of increase and decrease A Solve problems involving percents of change A Solve equations for given variables A Use formulas to solve real-world problems Outcome 4: The students will use the coordinate plane to do transformations. The students will use relations and graph functions and work with arithmetic sequences. A1 4.1 Locate points on the coordinate plane. A1 4.2 Graph points on a coordinate plane. A1 4.3 Transform figures by using reflections, translations, dilation, and rotations. A1 4.4 Transforms figures on a coordinate plane by using reflections, dilations, and rotations. A1 4.5 Represents relations as sets of ordered pairs, tables, mapping, and graphs A1 4.6 Find the inverse of a relation A1 4.7 Use an equation to determine the range for a given domain A1 4.8 Graph the solution set a given domain A1 4.9 Determine whether an equations is linear A Graph linear equations A Determine whether a relations is a function A Find function values A Recognize arithmetic sequences A Extend and write formulas for arithmetic sequences Outcome 5: The students will use slope and use slope related equations. A1 5.1 Find the slope of a line A1 5.2 Use rate of change to solve problems A1 5.3 Write and graph direct variation equations A1 5.4 Solve problems involving direct variation A1 5.5 Write and graph linear equations in slope-intercept form A1 5.6 Model real-world data with an equation in slope intercept form A1 5.7 Write an equation of a line given the slope and one point on a line A1 5.8 Write and equation of a line given two points on the line A1 5.9 Write the equation of a line in point-slope form A Write linear equations in different forms Outcome 6: The students will solve inequalities using the four basic algebraic operations. They will also solve multi-steps inequalities and compound inequalities. The students will graph inequalities in two variables. A1 6.1 Solve linear inequalities by using addition A1 6.2 Solve linear inequalities by using subtraction A1 6.3 Solve linear inequalities involving more then one operation A1 6.4 Solve linear inequalities involving the Distributive Property A1 6.5 Solve compound inequalities containing the word and and graph their solution sets A1 6.6 Solve compound inequalities containing the word or and graph their solution sets
17 A1 6.7 A1 6.8 Graph inequalities on the coordinate plane Solve real-world problems involving linear inequalities. Outcome 7: The students will graph system of equations and they will solve equations in two variables using substitution and elimination. The students will graph systems of inequalities. A1 7.1 Determine whether a system of linear equations has 0, 1, or infinitely many solutions. A1 7.2 Solve system of equations by graphing. A1 7.3 Solve system of equations by using substitution. A1 7.4 Solve real-world problems involving systems of equations. A1 7.5 Solve systems of equations by using elimination with addition. A1 7.6 Solve systems of equations by using elimination with subtraction. A1 7.7 Solve systems of equations by using elimination with multiplication. A1 7.8 Determine the best method for solving systems of equations. A1 7.9 Solve system of inequalities by graphing. A Solve real-world problem involving system of inequalities. Outcome 8: The students will multiply and divide monomials and they will do the basic operations with polynomials. A1 8.1 Multiply monomials. A1 8.2 Simplify expressions involving the quotients of monomials. A1 8.3 Simplify expressions involving the quotient of monomials. A1 8.4 Simplify expressions containing negative exponents. A1 8.5 Express numbers in scientific notation and standard notation. A1 8.6 Find products and quotients of numbers expressed in scientific notation. A1 8.7 Find the degree of a polynomial. A1 8.8 Arrange the terms of a polynomial in ascending or descending order. A1 8.9 Add polynomials. A Subtract polynomials. A Find the product of a monomial and a polynomial. A Multiply two binomials by using the FOIL method. A Multiply two polynomials by using the Distributive Property. A Find squares of sums and differences. A Find the product of a sum and difference. Outcome 9: The students will do all the basic types of factoring and they will solve using factoring. A1 9.1 Find prime factorizations of integers and monomials. A1 9.2 Find the greatest common factors of integers and monomials. A1 9.3 Factor polynomials by using Distributive Property. A1 9.4 Solve quadratic equations of the form ax2 + bx= 0 A1 9.5 Factor trinomials of the form x2+bx+c A1 9.6 Solve equations of the form x2+bx+c=0 A1 9.7 Factor trinomials of the form x2+bx+c=0 A1 9.8 Solve equations of the form ax2+bx+c=0 A1 9.9 Factor binomials that are the differences of squares
18 A Solve equations involving the differences of squares A Factor perfect squares trinomials A Solve equations involving perfect squares Outcome 10: The students will graph and solve quadratic equation using completing the square and the quadratic formula. A Graph quadratic functions. A Find the equations of the axis of symmetry and the coordinates of the vertex of a parabola A Solve quadratic equations by finding the square root A Solve quadratic equations by completing the square A Solve quadratic equations by using the Quadratic formula A Use the discriminate to determine the number of solutions for a quadratic equation A Graph exponential functions A Identify data the displays exponential behavior A Recognize and extend geometric sequences A Find geometric means Outcome 11: The students will do the basic radical operations. They will use the Pythagorean Theorem and the distance formula. Student will: A Simplify radical expressions using the Product Property of Square Roots A Simplify radical expressions using the Quotient Property of Square Roots A Add and subtract radicals A Multiply radical expressions A Solve radical equations A Solve radical equations with extraneous solutions A Solve problems by using the Pythagorean A Determine whether a triangle is a right triangle A Find the distance between two points on the coordinate plane A Find a point that is a given distance from a second point in a plane A Determine whether two triangles are similar A Find the unknown measures of sides of two similar triangles Outcome 12: The students will use inverse variation and they will do the four operations with rational expressions. They will divide polynomials. A Graph inverse variations A Solve problems involving inverse variations A Identify values excluded form the domain of a rational expression A Simplify rational expressions A Multiply rational expressions A Use dimensional analysis with division A Divide rational expressions A Use dimensional analysis with division A Divide a polynomial by a monomial A Divide a polynomial by a binomial
19 A Add rational expressions with like denominators A Subtract rational expressions with like denominators A Add rational expressions with unlike denominators A Subtract rational expressions with unlike denominators A Simplify mixed expressions A Simplify complex fractions A Solve rational equations A Eliminate extraneous solutions Outcome 13: The students will do work with measures of variation and box and whisker plots. A Interpret data display in histograms A Display data in histograms A Find the range of a set of data A Find the quartiles and interquartile range of a set of data A Organize and use data in box-and whisker plots A Organize and use data in parallel box-and-whisker plots Outcome 14: The students will correctly do work with probability and probability distributions A Count outcomes using a tree diagram A Count outcomes using the Fundamental Counting Principle A Determine probabilities using permutation A Determine probabilities using combination A Find the probability of two independent events or dependent events A Find the probability of two mutually exclusive or inclusive events. A Use random variables to compute probability A Use probability distributions to solve real-world problems Geometry Focus area: Course Purpose Statement: Students will use definitions and properties of geometric figures to logically solve problems. High Achievement Outcomes: OUTCOME 1: Students will be introduced to and use inductive reasoning which then provides the foundation for the rest of the Geometry course. G1.1 Define inductive reasoning and familiarize students with patterns. G1.2 Use inductive reasoning to find the next term in number patterns. G1.3 Generalize basic number patterns to find the nth term of a given number sequence. G1.4 Generalize figurate number patterns to find the nth term in a number sequence. G1.5 Apply inductive reasoning to find patterns and to use mathematical modeling in problem solving.
20 OUTCOME 2: Students are introduced to the basic geometric terms and will use these and the symbols of geometry to write definitions. G2.1 Define and use the terms associated with points, segments, lines, planes, and angles. G2.2 Use tools of measurement, learn how to express the measure of angles and segments, and learn the definition of congruence as related to segments/angles. G2.3 Practice writing definitions and explore many geometric definitions. G2.4 Define special line and angle relationships and to use these to develop critical thinking. G2.5 Define, classify, and work with polygons and related terms. G2.6 Define, classify, and work with triangles and their related parts. G2.7 Define, classify, and describe quadrilaterals. G2.8 Visualize and practice drawing objects in the second and third dimensions. G2.9 Translate descriptions into diagrams and use these to solve word problems. OUTCOME 3: Students will discover basic geometric constructions using a compass/straightedge and learn how to make discoveries on their own. G3.1 Use appropriate methods and practice constructing congruent segments and angles. G3.2 Discover and use a method of constructing perpendicular bisectors of segments. G3.3 Discover and use a method of constructing perpendiculars from a point on and not on a line. G3.4 Discover and use a method of constructing an angle bisector and make conjectures related to this construction. G3.5 Discover and use a method of constructing parallel lines. G3.6 Explore through construction whether or not a triangle can be determined given certain parts. G3.7 Discover and use a method of construction to find a triangle s incenter, circumcenter, orthocenter, and centroid. OUTCOME 4: Students will use all major processes from earlier chapters to perform investigations and make conjectures about line and angle relationships/properties. G4.1 Discover relationships between special pairs of angles and practice performing investigations and writing conjectures. G4.2 Explore relationships of parallel lines cut by a transversal and to further develop inductive reasoning and problem-solving skills. G4.3 Discover a formula for finding the midpoint of a segment and to define the slope of a line in the coordinate plane. G4.4 Discover the relationships between the slopes of parallel and perpendicular lines. G4.5 Discover and use the slope-intercept form of the equation of a line. G4.6 Find the intersection of lines both graphically and algebraically and to solve problems by finding intersection of lines. OUTCOME 5: Students will explore and discover the properties of triangles and congruent triangles. Students will also follow the reasoning in flow-chart proofs and create proofs of their own. G5.1 Discover the relationship between the three angles of any triangle. G5.2 Discover the relationship between the base angles of any isosceles triangle.
21 G5.3 Discover inequalities among the sides and angles of any triangle. G5.4 Explore shortcut methods in determining whether triangles are congruent and use the methods that are valid to prove triangles congruent. G5.5 Use the definition of congruent triangles to show that corresponding parts of congruent triangles are congruent and create proofs using the methods developed in 5.4. G5.6 Investigate and use all properties of isosceles triangles. OUTCOME 6: Students will create and use the properties related to polygons, specifically properties related to the special quadrilateral. G6.1 Discover and use the sum of the angle measures in a polygon conjecture to solve problems. G6.2 Discover the sum of the measures of one set of exterior angles of any convex polygon. G6.3 Discover properties related to kites and trapezoids and use new vocabulary related to these special quadrilaterals. G6,4 Define and discover properties of mid-segments in triangles and trapezoids. G6.5 Discover and use properties of all types of parallelograms to solve problems. G6.6 Use properties and definitions of rectangles, rhombi, and squares to create these figures using the geometer s sketchpad. OUTCOME 7: Students will develop and use properties related to circles, including the circumference, area, and arc-length conjectures. G7.1 Identify the parts of a circle and use these to help create definitions related to circles. G7.2 Discover the properties of chords and use these to solve related problems. G7.3 Discover and explore properties of tangents and common tangents to a circle. G7.4 Discover and use relationships between inscribed angles of a circle and their intercepted arcs. G7.5 Discover and use the number π to solve problems related to the circumference of a circle. G7.6 Apply the circumference formula of a circle to solve real world problems. G7.7 Discover and use the formula for finding the length of an arc of a circle. OUTCOME 8: Students will discover formulas and other conjectures which will allow them to solve problems related to calculating the area of polygons, circles, and threedimensional solids. G8.1 Develop the concept of area and derive formulas for area of rectangles and parallelograms. G8.2 Derive and apply formulas for the area of triangles, trapezoids, and kites. G8.3 Solve various types of area problems related to real world applications. G8.4 Derive and apply the formula for the area of regular polygons. G8.5 Derive the formula for the area of a circle and apply it in solving area of a circle problems. G8.6 Discover and apply methods for calculating areas of annuli, sectors, and segments of circles. G8.7 Review terminology for solids and apply methods for finding the surface area of solids. G8.8 Develop comprehensive problem-solving skills which will be used in area applications.
22 OUTCOME 9: The students will discover the Pythagorean theorem and gain experience in solving many types of word problems. G9.1 Discover and apply the Pythagorean theorem to basic right triangle problems. G9.2 Discover the converse of the Pythagorean theorem and use it to determine if a given triangle is a right triangle. G9.3 Apply the Pythagorean theorem and its converse in solving various types of word problems. G9.4 Practice simplifying square roots and use these properties to discover relationships between the special types of right triangles. G9.5 Discover and apply relationships of multiples of Pythagorean triples. G9.6 Apply the Pythagorean theorem to solve word problems involving radicals. G9.7 Discover and apply the Pythagorean theorem as it is related to the distance formula in the coordinate plane. OUTCOME 10: The students will discover the formulas needed to find the volume of prisms, pyramids, cylinders, cones, and spheres. They will also use other conjectures to solve word problems and density problems. G10.1 Explore and use new vocabulary related to polyhedra, spheres, cylinders, and cones. G10.2 Discover and apply the formulas for volume of prisms and cylinders. G10.3 Discover and apply the formula for volume of pyramids and cones. G10.4 Apply the volume formulas to word problems and to develop problem-solving skills. G10.5 Discover and apply the concepts of density in solving various types of displacement problems. G10.6 Derive and use formulas to calculate the volume and surface area of spheres. OUTCOME 11: The students will discover and use the properties related to similarity of triangles and polygons. G11.1 Use and apply properties of ratios and proportions to solve problems. G11.2 Define similar polygons and use the definition to solve problems involving similarity. G11.3 Discover shortcut methods for determining similar triangles and use proportions to find measurements in similar figures. G11.4 Use similar triangles to solve problems involving indirect measurement. G11.5 Discover a relationship between corresponding parts of similar triangles and use it to solve problems involving angle bisectors, medians, and altitudes of similar triangles. G11.6 Discover the relationship between the area and volume of similar figures. G11.7 Discover and apply the relationship between the ratios of the parts into which parallel lines cut the sides of a triangle. OUTCOME 12: The students will be introduced to some of the properties related to right triangle trigonometry. G12.1 Introduce trigonometry and discover the sine, cosine, and tangent ratios. G12.2 Apply trigonometry to various types of word problems. G12.3 Apply the concept of angle of elevation/depression to solve word problems. Algebra 2
23 Focus Area: Course Purpose Statement: High Achievement Outcomes: Outcome 1: The students will use expressions and formulas. They will use properties of real numbers to solve equations and inequalities. A2 1.1 Use the order of operation to evaluate expressions and use formulas A2 1.2 Classify real numbers and use the properties pf real numbers to evaluate expressions A2 1.3 Translate verbal expressions into algebraic expressions and equations, and vice versa A2 1.4 Solve equations using the properties of equality A2 1.5 Evaluate expressions involving absolute values and solve absolute value equations A2 1.6 Solve inequalities A2 1.7 Solve compound inequalities and absolute value inequalities Outcome 2: The students will use relations and functions; They will work with and graph linear equations. A2 2.1 Analyze and graph relations and find functional values A2 2.2 Identify linear equations and functions and write linear equations in standard form and graph them A2 2.3 Find and use the slope of a line A2 2.4 Graph parallel and perpendicular lines A2 2.5 Write and equation of a line given the slope and a point on the line and write an equation of a line parallel or perpendicular to a given line A2 2.6 Draw scatter plots A2 2.7 Identify and graph step, constant, and identify functions A2 2.8 Identify and graph absolute value and piecewise functions A2 2.9 Graph linear inequalities and graph absolute value inequalities Outcome 3: The students will graph and solve systems of equations and inequalities in two and three variables. A2 3.1 Solve systems of linear equations by graphing A2 3.2 Determine whether a system of linear equations is consistent and independent consistent and dependent, or inconsistent A2 3.3 Solve system of linear equations by using substitution and elimination A2 3.4 Solve systems of inequalities by graphing A2 3.5 Determine the coordination of the vertices of a region formed by the graph of a system of inequalities A2 3.6 Find the maximum and minimum values of a function over a region A2 3.7 Solve systems of linear equations in three variables Outcome 4: The students will do all the basic operations involving matrices.