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Algebra Academy
a hands-on core solution for algebra readiness and algebra i
Algebra Academy contents Algebra Academy........................................1 Individualized Prescriptive Lessons™...........2 IPL Instructional Workflow..........................3 Culminating Group Activities.......................4 From Abstract to Real World.......................5 Blended Learning Model.............................6 Cooperative Learning..................................7 Hands-on, Project-Based Curriculum...........8 Diagnostic Days..........................................9 Homework............................................... 10 Culminating Group Activities................ 11-46 Integers................................................. 12 Introduction to Decimals....................... 13 Decimal Operations.............................. 14 Introduction to Fractions....................... 15 Operations with Fractions I................... 16 Operations with Fractions II.................. 17 Real Number System............................. 18 Properties of Real Numbers................... 19 Equations.............................................. 20 Ratios and Percents............................... 21 Linear Equations and Graphing.............. 22 Inequalities........................................... 23 Absolute Value..................................... 24 Functions.............................................. 25 Transformations..................................... 26 Exponents............................................. 27 Radicals................................................ 28
Special Equations.................................. 29 Systems of Equations............................. 30 Matrices............................................... 31 Polynomials.......................................... 32 Quadratics............................................ 33 Factoring.............................................. 34 Exponential Equations........................... 35 Probability............................................ 36 Data Graphs I....................................... 37 Data Graphs II...................................... 38 Logic and Sequences............................ 39 Angles.................................................. 40 Triangles............................................... 41 Polygons............................................... 42 Circles.................................................. 43 Prisms and Pyramids.............................44 Units.................................................... 45 Accuracy.............................................. 46 Algebra Readiness................................ 47-64 Algebra Readiness Curriculum Overview..48-49 Algebra Readiness Math Concepts............. 50 Algebra Readiness Curriculum Titles..... 51-64 Astronomy............................................ 51 BioEngineering...................................... 52 Confident Consumer............................. 53 Hotel Management............................... 54 Properties of Math................................ 55 Statistical Analysis................................. 56
Weights & Measures............................. 57 Chemical Math..................................... 58 Environmental Math.............................. 59 Forensic Math....................................... 60 Geometric Packing............................... 61 Home Makeover................................... 62 Laser Geometry.................................... 63 Water Management...............................64 Algebra I..............................................65-82 Algebra I Curriculum Overview............66-67 Algebra I Math Concepts........................... 68 Algebra I Curriculum Titles...................69-82 Gravity of Algebra................................. 69 Math Behind Your Meals....................... 70 Nuclear Energy..................................... 71 Sports Statistics..................................... 72 Supply & Demand................................ 73 Unsolved Mysteries............................... 74 Water Quality....................................... 75 Climate Change.................................... 76 Factoring & Polynomials........................ 77 Lenses & Optics.................................... 78 Population Perspectives......................... 79 Projectile Motion..................................80 The Universe........................................ 81 Where in the World.............................. 82
Algebra academy
Rigor. Relevance. Relationships.
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Algebra academy A HANDS-ON core Solution FOR ALGEBRA READINESS AND ALGEBRA I
Hands-on Core Curriculum for Algebra Readiness and Algebra I The Algebra Academy offers hands-on core courses for Algebra Readiness and Algebra I. Each course has been developed and written to meet state and national standards and provide students with rich, connected learning experiences in mathematics. This project-based, hands-on curriculum combines Individualized Prescriptive Lessons™, cooperative learning, Culminating Group Activities, and diagnostic assessments to build coherent mathematical literacy across Grades 7 through 10. These Pitsco Education courses effectively combine key learning components such as factual knowledge, procedural proficiency, and conceptual understanding with nontraditional, project-based activities. This powerful combination results in rigorous learning and relevant application and gives students meaningful opportunities to recognize and apply core math concepts beyond the walls of the classroom. • Builds mathematical literacy across Grades 7-10 • Individualized and team-based curriculum • Incorporates progressive delivery model • Includes small group activities • Promotes cooperative learning and teamwork • Project-based, hands-on curriculum • Includes diagnostic assessments • Provides homework reinforcement activities
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Algebra academy A HANDS-ON core Solution FOR ALGEBRA READINESS AND ALGEBRA I
Individualized Prescriptive Lessons™ (IPLs) Individualization in education is a critical component of any curriculum that successfully engages students and addresses their individual learning styles and needs. Individualized Prescriptive Lessons™ (IPLs) have been designed to first assess a student’s level of understanding of core math concepts using formative assessments. Based upon the results of each assessment, every student is prescribed lessons in math concepts for which they need targeted instruction. Each lesson begins with a practice test, and students then proceed with the lesson in preparation for successfully completing a mastery test at its conclusion. Students must pass each prescribed mastery test before moving on to their next assignment. The curriculum includes interactive checkpoints using text-entry, drag-and-drop, and multiple-choice actions, and students receive instant feedback for both correct and incorrect answers. Concept boxes are included throughout the curriculum, highlighting key concepts during each lesson. IPLs are computer based and used exclusively in combination with hands-on Culminating Group Activities (CGAs). The CGAs are designed specifically to provide real-world learning opportunities that culminate the math concepts taught in the IPLs.* • Includes diagnostic assessments • Incorporates targeted instruction • Has individualized, prescribed lesson plans • Provides practice and mastery tests • Incorporates interactive checkpoints • Provides a clickable vocabulary • Includes just-in-time feedback • Uses one-to-one, computer-based instruction
*Three IPL units of instruction – Orientation, Calculators, and Graphing Calculators – do not include associated CGAs.
Algebra academy A HANDS-ON core Solution FOR ALGEBRA READINESS AND ALGEBRA I
IPL Instructional Workflow Individualized Prescriptive Lessons™ (IPLs) are designed using a mastery learning model. Students begin each IPL with a diagnostic assessment to determine each student’s level of knowledge. The workflow illustrated below outlines the process students follow to master each concept delivered in the IPLs. The computer-based instruction targets each student to build mastery and gives teachers the opportunity for one-on-one intervention for those students who require additional practice. If a student fails the first mastery test, the student is prevented from continuing the lesson and our Synergy management system alerts teachers via computer and/or mobile device that intervention is needed. The process enables each student to learn and progress at their own pace and provides targeted student-teacher interaction at the moment of need.
Diagnostic Assessment
IPL Mastered
Pass
3 Minutes
Fail
Lesson
20 Minutes or Less
Next Lesson
Mastery Test 1 w/Question Remediation
Pass Pass
3 to 12 Minutes
Fail
Instructor Intervention 5 Minutes
Mastery Test 2 w/Question Remediation 3 to 12 Minutes
Fail
IPL Not Mastered
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Algebra academy A HANDS-ON core Solution FOR ALGEBRA READINESS AND ALGEBRA I
Culminating Group Activities (CGAs) Culminating Group Activities (CGAs) are small group, team-based activities that serve to reinforce students’ understanding of a series of math concepts delivered in their individualized instruction. Every CGA has been designed and written to provide students the opportunity to apply concepts learned in the IPLs to real-world activities and scenarios. Each CGA has been written as a culminating hands-on activity and aligned to a specific series of IPLs and math concepts. CGAs enable students to apply what they learn in the IPLs and reinforce for students how the math concepts they are learning impact the world around them. These CGAs provide students with a strong foundation in core mathematics. Each CGA includes both a student and a teacher guide; an instructional whole-class presentation; individual assessments; and engaging, hands-on activities and materials. • Combines whole-class and small group activities • Is written and aligned to core math concepts • Includes both teacher and student curriculum guides • Incorporates whole-class instructional presentations • Provides real-world, hands-on activities and related materials
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Algebra academy A HANDS-ON core Solution FOR ALGEBRA READINESS AND ALGEBRA I
from abstract to real world One of the biggest challenges educators face in teaching pre-algebra and
includes Culminating Group Activities (CGAs) developed specifically to
Algebra I concepts is providing students with real-world applications
incorporate real-world applications of algebraic concepts. Each CGA places
of the math concepts typically delivered in a traditional stand-and-
students in small groups where they are challenged to solve real-world
deliver classroom. Our Algebra Readiness and Algebra I courses shift the teaching from a traditional stand-and-deliver model to a student-directed approach, giving each student control over their own learning. The one-
problems using hands-on activities in a team environment. These activities not only culminate the math concepts they are learning but also build
to-one computing delivery of the IPLs enable students to be introduced to,
critical-thinking, communication, and problem-solving skills that benefit
and eventually master, pre-algebra and Algebra I concepts. To reinforce
them beyond the walls of a classroom. The charts below list the CGAs
the learning that occurs in the computer-based curriculum, each course
incorporated in both Algebra Readiness and Algebra I courses.
The Unit Titles below are listed in the suggested order the students learn them. Integers
Ratios and Percents
Systems of Equations
Logic and Sequences
Introduction to Decimals
Linear Equations and Graphing
Matrices
Angles
Decimal Operations
Inequalities
Polynomials
Triangles
Introduction to Fractions
Absolute Value
Quadratics
Polygons
Operations with Fractions I
Functions
Factoring
Circles
Operations with Fractions II
Transformations
Exponential Equations
Prisms and Pyramids
Real Number System
Exponents
Probability
Units
Properties of Real Numbers
Radicals
Data Graphs I
Accuracy
Equations
Special Equations
Data Graphs II Page 5
Algebra academy A HANDS-ON core Solution FOR ALGEBRA READINESS AND ALGEBRA I
Blended Instruction model Algebra Academy combines three instructional methodologies: computer-based individualized instruction; hands-on, small group activities; and student-directed, cooperative learning. Our Individualized Prescriptive Lessons™ (IPLs) are seamlessly delivered within our Learning Content Management System, Synergy. To ensure students are not encountering consecutive weeks of software-only experiences, we have developed CGAs to use as “application checkpoints.” When a math unit is completed within the IPL software, the teacher gathers the entire class together to work in small groups on a hands-on application of the concepts they have experienced on the computer. These activities give students an opportunity to apply abstract math concepts within a small group, hands-on experience. Once students have completed their IPL instruction, they work in pairs and complete computer-delivered curriculum titles developed specifically to address pre-algebra and algebra concepts. Each title incorporates significant hands-on activities that take the math out of the abstract and into the real world. This unique approach to teaching algebra gives students ownership of their learning and provides real-world connections through the instruction that makes the math concepts meaningful and relevant.
Algebra academy A HANDS-ON core Solution FOR ALGEBRA READINESS AND ALGEBRA I
Cooperative Learning An overarching goal of Pitsco Education’s Algebra Academy projectbased curriculum is for students to become responsible learners and work cooperatively with others. The student-directed curriculum strengthens the students’ ability to think and reason, communicate and interpret the mathematical concepts they encounter, and develop more powerful ways of identifying and expressing insights. The hands-on projects they share in common ultimately promote positive communication, teamwork, inquiry, learning, and social skills and more effectively develop their ability to formulate ideas and solve complex problems. Moreover, every student’s unique learning style is accommodated in the project-based curriculum. The Algebra Academy courses ensure student success through a combination of text, graphics, video instruction, and experiential learning activities. Each curriculum title has been meticulously developed to meet individual state and Common Core State Standards with a heavy emphasis on depth over breadth, giving students highly interconnected learning experiences in core mathematical concepts. • Builds communications skills • Accommodates multiple learning styles • Promotes teamwork • Enables student-directed learning
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Algebra academy A HANDS-ON core Solution FOR ALGEBRA READINESS AND ALGEBRA I
Hands-on, Project-Based Curriculum The Pitsco Education Algebra Academy was developed to provide educators with a nontraditional alternative to teaching Algebra Readiness and Algebra I. The curriculum is a combination of individual, whole class, and cooperative learning instruction. Each course begins with a diagnostic assessment followed by Individualized Prescriptive Lessons™. The individualized instruction is designed to assess and increase each student’s level of knowledge of basic math concepts in preparation for the more advanced algebraic concepts encountered later in the coursework. When students move from the individualized instruction to the cooperative learning instruction, the separation between Pitsco Education courses and traditional methods of teaching algebra becomes evident. The emphasis shifts from conceptual learning to applied, project-based instruction. Students work in cooperative learning pairs and rotate through unique hands-on, project-based curriculum titles. Each title is computer based, student directed, and replete with hands-on activities developed to provide students with real-world applications of algebraic concepts. This approach effectively combines focused, coherent, highly interconnected core topical strands with project-based activities that make the math meaningful and relevant. • Individual, whole class, and cooperative pair learning • Project-based instruction • Hands-on activities • Conceptual, applied learning methodology • Innovative rotational delivery model
Algebra academy A HANDS-ON core Solution FOR ALGEBRA READINESS AND ALGEBRA I
Diagnostic Days As students progress through coursework, they complete unique hands-on, project-based curriculum titles. Each curriculum title is completed in a single rotation over nine class periods. During each rotation, the fifth and ninth class periods have been reserved for Diagnostic Days intentionally designed to assess student progress and provide an opportunity to measure whether a student fully understands the concepts being taught or is in need of remediation. Students in need of remediation are assigned Individualized Prescriptive Lessons™ aligned to the algebraic concepts being covered in each unit of instruction. Students who have mastered the concepts receive additional instruction in the form of enrichment activities. This enables the Algebra Academy facilitator to accurately evaluate each student’s progress and provide additional instruction where needed. • Student assessment • Targeted remediation • Enrichment activities • One-to-one computing
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Algebra academy A HANDS-ON core Solution FOR ALGEBRA READINESS AND ALGEBRA I
Homework Every student can tell you that math and homework go hand in hand. In a traditional math class, students typically experience teacher-led instruction designed around a textbook and complete a series of related homework assignments, quizzes, and tests. While some students do well in this learning environment, many struggle to retain what they are being taught and consequently lose ground as they are challenged by new and more complex algebraic concepts. In the Pitsco Education nontraditional Algebra program, students receive instruction in a unique and powerful way that provides meaningful and relevant projectbased learning experiences. Students work in pairs as they are engaged in our innovative, hands-on, project-based curriculum. Each curriculum title is delivered in nine sessions, providing computer-led instruction and hands-on activities to teach one algebraic concept. After students complete a session, they receive a homework assignment aligned to reinforce the concept taught in the session. Assignments are no more than two pages; are carefully designed to promote success; and include a brief overview of a math concept, an example, and a short series of problems.
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Culminating group activities
Unit titles Integers IPLs
MATH CONCEPTS
Speaking Math
• Define common math vocabulary. • Explore the four basic operations and their solutions. • Form equations and expressions.
Integers
• Define natural numbers, whole numbers, and integers. • Identify positive and negative integers and their relationship to zero.
CULMINATING GROUP ACTIVITY
• Order integers using a number line.
Students play up to 11 games to practice basic skills. The teacher determines which games are needed. Game 1 – Addition of integers – positive numbers Game 2 – Addition of integers – positive and negative numbers Game 3 – Addition of integers – increased difficulty of positive and negative numbers Game 4 – S ubtraction of integers
Adding Integers
• Calculate total yards by adding integers.
Subtracting Integers
• Subtract integers.
Multiplying and
• Multiply integers.
Dividing Integers
• Divide integers.
Game 5 – M ultiplication of integers Game 6 – Is one integer a factor of the other? Game 7 – Addition of two-digit integers – positive numbers Game 8 – Addition of two-digit integers – positive and negative numbers Game 9 – Subtraction of two-digit integers Game 10 – Multiplication of two-digit integers Game 11 – Division of a two-digit integer into a four-digit integer (use remainder)
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Curriculum titles Introduction to Decimals IPLs
MATH CONCEPTS
Decimal Numbers
• Learn about decimal numbers and their place values. • Find out how to correctly say decimal numbers. • Discover how decimal numbers can be visually represented.
Rounding Decimals
• Learn how to round decimal numbers.
CULMINATING GROUP ACTIVITY
• Learn how to round to a specific place value.
The teacher will lead a series of games through a
• Use rounding to estimate a sum.
PowerPoint. Students will practice recognizing, creating, saying, and rounding decimals using cards. Students will compare decimals and order them as if on a number line.
Ordering Decimals
• Plot decimals on a number line. • Order decimals. • Compare decimals.
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Unit titles Decimal Operations IPLs
MATH CONCEPTS
Adding Decimals
• Determine how to set up a decimal problem. • Add decimals to decimals. • Add decimals to whole numbers.
Subtracting Decimals
• Learn a procedure to subtract decimals. • Learn to subtract decimals by borrowing.
CULMINATING GROUP ACTIVITY
Multiplying Decimals
Students play a four-inning baseball game.
• Multiply decimals by whole numbers. • Multiply decimals by other decimal numbers.
Inning 1 – Addition of decimals Inning 2 – Subtraction of decimals Inning 3 – Multiplication of decimals
Dividing Decimals
• Divide decimals by whole numbers. • Divide decimals by decimals.
Inning 4 – Division of decimals
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Curriculum titles Introduction to Fractions IPLs
MATH CONCEPTS
Graphical Representation
• Learn the meaning of numerator and denominator.
of Fractions
• Convert a fraction from a graphical representation to a numerical representation. • Convert a fraction from a numerical representation to a graphical representation.
Interpretation of Fractions
• Learn to state fractions in words.
CULMINATING GROUP ACTIVITY
• Write a numerical form of a fraction from its word form.
Students create a unique bingo card. Then, they play
• Recognize and use special common fractions.
bingo by simplifying fractions that are given by the teacher as improper numbers, mixed numbers, or as an unsimplified fraction.
Improper Fractions and
• Recognize and define improper fractions.
Mixed Numbers
• Recognize and define mixed numbers. • Determine when to use an improper fraction or a mixed number.
Converting Between Mixed
• Convert improper fractions to mixed numbers.
Numbers & Improper Fractions
• Convert mixed numbers to improper fractions.
Representing Fractions
• Divide a number line into fractions.
on a Number Line
• Represent proper fractions on a number line. • Represent improper fractions on a number line. • Represent mixed numbers on a number line.
Factoring
• Define factors. • Find the factors of a number. • Find common factors.
Simplifying Fractions
• Find the greatest common factor (GCF). • Simplify fractions using division. • Compare fractions by simplifying. Page 15
Unit titles Operations with Fractions I IPLs
MATH CONCEPTS
Adding Fractions with
• Add fractions with like denominators.
Like Denominators
• Convert the number 1 into a fraction. • Add fractions to whole numbers.
Adding Multiple Fractions
• Add multiple fractions with like denominators.
with Like Denominators
• Add multiple fractions and whole numbers.
Adding Mixed Numbers
• Add fractions to mixed numbers. • Add mixed numbers by converting to improper fractions.
CULMINATING GROUP ACTIVITY
• Add mixed numbers by combining like terms.
Students play a game using dice to generate the numbers in the numerator and denominator for the fractions.
Least Common Multiples
Students add and subtract fractions with like and unlike denominators. Students also add and subtract improper fractions. Students simplify their answers.
• Determine common multiples. • Determine least common multiples for two or more numbers.
Adding Fractions with
• Use a least common multiple to find a least common denominator.
Unlike Denominators
• Add fractions and mixed numbers with unlike denominators.
Subtracting Fractions with
• Subtract fractions with like denominators.
Like Denominators
• Convert whole numbers to fractions. • Subtract fractions from whole numbers.
Subtracting Fractions with Unlike Denominators
• Use the least common multiple to find the least common denominator of two fractions. • Subtract fractions with unlike denominators. • Subtract fractions from whole numbers.
Subtracting Multiple Fractions
• Subtract more than two fractions with unlike denominators. • Convert whole numbers to fractions. • Subtract more than two fractions from a whole number.
Subtracting Mixed Numbers
• Subtract fractions from mixed numbers. • Subtract mixed numbers using like terms. • Subtract mixed numbers by converting to improper fractions. Page 16
Curriculum titles Operations with Fractions II IPLs
MATH CONCEPTS
Multiplying Fractions
• Multiply fractions with like denominators. • Multiply fractions with unlike denominators. • Multiply fractions by whole numbers.
Multiplying Mixed Numbers
• Multiply mixed numbers. • Multiply mixed numbers and whole numbers. • Multiply more than two mixed numbers.
CULMINATING GROUP ACTIVITY The teacher leads a series of activities through which
Dividing Fractions
students practice multiplying and dividing mixed numbers.
• Find the reciprocal of a fraction. • Divide two fractions.
Students create fractions through the use of fraction and
• Divide a whole number by a fraction.
number cubes. Dividing Mixed Numbers
• Create and use a reciprocal. • Divide mixed numbers.
Converting Between
• Convert decimals to fractions.
Decimals and Fractions
• Convert fractions to decimals. • Compare fractions and decimals.
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Unit titles Real Number System IPLs
MATH CONCEPTS
Real Number System
• Define set, subset, and superset. • Define the real number system and its subsets, which are rational, irrational, integer, whole, and natural. • Classify numbers according to their sets.
Ordering Numbers
• Order numbers using the number line. • Order numbers by converting to decimals.
CULMINATING GROUP ACTIVITY Students participate in several activities to work with the real number system. The teacher chooses to do all the
Order of Operations
• Apply the order of operations to solve simple and complex expressions.
Prime Factorization
• Learn about prime and composite numbers.
activities or has students complete only those that he or
• Find factors of natural numbers.
she feels the students need to practice most.
• Find prime factorizations of natural numbers.
Included Activities:
Scientific Notation 1
• Compare positive powers of 10.
• Create decimals and place them on a number line.
• Convert scientific notation to standard form.
• Solve equations using order of operations.
• Write large numbers in scientific notation.
• Create the factorization for given numbers. • Create prime factor trees for numbers. • Use scientific notation to show large and small
Scientific Notation 2
• Compare negative powers of 10. • Convert scientific notation to standard form. • Convert standard form to scientific notation.
numbers. • Create a standard number from scientific notation.
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Curriculum titles Properties of Real Numbers IPLs
MATH CONCEPTS
Properties of Equality 1
• Apply the Reflexive Property of Equality of real numbers. • Use the Symmetric Property of Equality of real numbers. • Explore the Transitive Property of Equality of real numbers.
Properties of Equality 2
• Apply the Addition Property of Equality. • Apply the Subtraction Property of Equality. • Apply the Multiplication Property of Equality.
CULMINATING GROUP ACTIVITY
• Apply the Division Property of Equality.
Students use cards and dice with math symbols to demonstrate examples of the properties of real numbers.
Substitution
• Use substitution to solve one-variable equations. • Use substitution to solve two-variable equations.
The students play a properties matching game.
• Substitute expressions in variables.
Commutative Properties
• Explore the Commutative Property of Addition. • Apply the Commutative Property of Multiplication.
Associative Properties
• Explore the Associative Properties of Addition and Multiplication to evaluate expressions. • Use the Associative Properties of Addition and Multiplication to solve expressions.
Identity and Inverse Properties • Apply the Additive and Multiplicative Identity Properties. • Explore the Additive and Multiplicative Inverse Properties. • Determine multiplication by zero.
Distributive Property
• Apply the Distributive Property over addition and subtraction. • Apply the Distributive Property using variables.
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Unit titles Equations IPLs
MATH CONCEPTS
Combining Like Terms
• Identify different parts of a term. • Locate like terms. • Combine like terms using addition and subtraction.
CULMINATING GROUP ACTIVITY
Solving One-Step Equations
• Solve for an unknown in one-step equations.
One-Step Equation
• Solve one-step equations from word problems.
Word Problems
• Solve one-step equations with decimals and fractions.
Multistep Equations
• Solve multistep equations.
Rate Equations
• Solve problems using the percentage formula.
Students use a hydraulic trainer to verify equations containing one or two variables.
• Solve problems using the distance formula.
Simplifying to Solve Equations • Simplify to solve equations. Variables and Variation
• Identify and solve direct variation equations. • Identify and solve inverse variation equations.
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Curriculum titles Ratios and Percents IPLs
MATH CONCEPTS
Percents
• Define percent. • Represent percents graphically. • Convert percents to decimals and decimals to percents. • Convert fractions to percents and percents to fractions.
Percent Change
• Determine if percent change is an increase or a decrease.
CULMINATING GROUP ACTIVITY Students use a car and roll ramp to obtain data for use with ratios and percentages.
• Calculate percent change.
Simple Interest
• Calculate simple interest.
Compound Interest
• Learn how to calculate compound interest.
Introduction to Ratios
• Explore concepts related to ratios. • Identify different types of ratios. • Determine if two ratios are equivalent.
Proportions and Unknowns
• Explore the concepts of proportions. • Identify the different parts of a proportion. • Apply knowledge of proportions to solve for unknowns.
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Unit titles Linear Equations and Graphing IPLs
MATH CONCEPTS
The Coordinate Plane
• Define and identify parts of the coordinate plane. • Identify the quadrants of the coordinate plane. • Plot ordered pairs.
Distance and Midpoint Formulas
• Calculate the distance between two points using the Distance Formula. • Determine the midpoint between two points using the Midpoint Formula.
CULMINATING GROUP ACTIVITY Students build and time LEGO ® cars on a ramp to
Linear and Nonlinear
• Determine if a graph is linear or nonlinear. • Determine if an equation will generate a linear or nonlinear graph.
determine speed. Students create linear equations. Students compare and contrast the relationships between the parts of the equations and their meanings
Slope
• Calculate the slope of a line using the slope equation.
in the experiments. They create graphs of the equations
• Classify slopes as positive, negative, zero, and undefined.
using a graph board.
• Determine the slope of a line given a graph of the line.
Slope-Intercept Form
• Write an equation in slope-intercept form. • Graph an equation in slope-intercept form. • Find an equation from a graph.
Standard Form
• Write an equation in standard form. • Graph an equation in standard form.
Point-Slope Form
• Write an equation in point-slope form. • Graph an equation in point-slope form. • Find an equation from a graph.
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Curriculum titles Inequalities IPLs
MATH CONCEPTS
Inequalities
• Set up inequalities from verbal sentences. • Graph inequalities on a number line.
Solving Inequalities
• Solve simple inequalities using algebra properties.
Solving Compound Inequalities
• Write a compound inequality. • Solve a compound inequality.
CULMINATING GROUP ACTIVITY Students use cards, dice, math symbols, Wikki Stix,
Linear Inequalities 1
• Convert inequalities into slope-intercept format.
and graph boards to solve and graph inequalities and
• Graph inequalities.
compound inequalities. Students use a number line or a coordinate grid to show solutions.
• Write inequalities.
Linear Inequalities 2
• Write linear inequalities using negative numbers. • Change the sign of linear inequalities. • Graph inequalities using a sign change.
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Unit titles Absolute Value IPLs
MATH CONCEPTS
Absolute Value
• Relate the absolute value of a number with distance from a starting point. • Use math to simplify the absolute value of numbers.
CULMINATING GROUP ACTIVITY
Solving Absolute
• Apply the rules of absolute value.
Value Equations
• Solve absolute value equations.
Graphing Absolute Value
• Find ordered pairs of absolute value equations and inequalities.
Students shoot straw rockets at a target and keep track of
• Graph absolute value equations.
the distance from the target – negative distance in front of
• Graph absolute value inequalities.
the target, positive distance beyond the target. Students create a table and then use absolute value to determine the total distance from the target. Students use their graph boards to plot absolute value equations.
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Curriculum titles Functions IPLs
MATH CONCEPTS
Functions
• Identify a function and its notation. • Determine the domain and range of a function. • Determine whether a relation is a function.
Special Functions
• Use and solve linear and quadratic functions. • Use and solve absolute value and step functions.
CULMINATING GROUP ACTIVITY
Graphing Functions
Students use dice to create domains for given functions
• Identify the graphs of linear, quadratic, and absolute value functions.
including linear, quadratic, absolute value, and step
• Identify the graph of a step function.
functions. Students graph the functions on a graph board.
• Use the vertical line test to determine if a graph is a function.
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Unit titles Transformations IPLs
MATH CONCEPTS
Points, Lines, and Shapes
• Plot ordered pairs. • Connect plotted points. • Create shapes from plotted points.
Translations
• Apply translation to plotted points. • Apply translation to plotted lines. • Apply translation to plotted shapes.
CULMINATING GROUP ACTIVITY Students use a geometry board with pegs and rubber bands,
Reflections
MIRAs, and graph boards to practice transformations.
• Understand the line of reflection. • Reflect points across the x- and y-axes. • Reflect shapes across the x- and y-axes. • Reflect shapes across a given line.
Rotations
• Determine an object’s rotational symmetry. • Identify the angle of rotation. • Rotate shapes on the coordinate plane.
Dilations
• Plot points for dilated shapes. • Identify the scale factor of a shape. • Plot shapes around the center of dilation.
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Curriculum titles Exponents IPLs
MATH CONCEPTS
Exponents
• Write repeated multiplications in exponential form. • Find the value of exponential expressions.
Properties of Exponents 1
• Explore the Product of Powers Property. • Explore the Power of a Power Property. • Explore the Power of a Product Property.
CULMINATING GROUP ACTIVITY Students have the opportunity to play up to 10 games to practice using exponents. The teacher decides which games will be played.
Properties of Exponents 2
• Explore zero exponents. • Explore negative exponents. • Explore and apply the Quotient of Powers Property. • Explore and apply the Power of a Quotient Property.
Game 1 – Create an exponential expression and the repeated multiplication problem expressed. Game 2 – Create an exponential expression and the numerical answer. Game 3 – Create a decimal number with an exponent and the numerical answer. Game 4 – Create a fraction with an exponent and the numerical answer. Game 5 – Create positive and negative numbers with exponents and the numerical answers. Game 6 – Product of Powers Property Game 7 – Power of a Power Property Game 8 – Power of a Product Property Game 9 – Negative exponents Game 10 – Quotient of Powers Property
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Unit titles Radicals IPLs
MATH CONCEPTS
Perfect Squares
• Identify perfect squares.
and Square Roots
• Find the square root of perfect squares. • Approximate the square root of whole numbers.
Cube Roots
• Find cube roots of numbers. • Solve cubic equations.
CULMINATING GROUP ACTIVITY
Simplifying Square Roots
Students use cards, math symbols, and graph boards to practice
• Find the principal and negative square root. • Simplify square roots to find the exact answer.
using and simplifying radicals and radical expressions. Radical Expressions
• Simplify radical expressions.
Radical Expressions
• Identify and solve direct variation equations.
– Operations
• Identify and solve inverse variation equations.
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Curriculum titles Special Equations IPLs
MATH CONCEPTS
Radical Equations
• Solve radical equations with x on one side.
Complex Fractions
• Define mixed expressions and complex fractions. • Simplify mixed expressions and complex fractions.
Rational Equations
• Solve for x in rational equations.
CULMINATING GROUP ACTIVITY Students solve rational expressions and equations and simplify complex fractions and mixed expressions using cards, math symbols, and graph boards.
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Unit titles Systems of Equations IPLs
MATH CONCEPTS
Systems of Equations
• Define system of linear equations.
– Graphs
• Find solutions to systems of linear equations by using graphs. • Determine the number of solutions to a system of linear equations.
Systems of Equations
• Isolate a variable in an equation.
– Substitution
• Solve systems of linear equations using substitution.
Students use cards, dice, math symbols, rulers, and graph boards
Systems of Equations
• Use elimination to solve systems of equations.
to solve systems of equations. Students graph some solutions.
– Elimination
• Use systems of equations to solve story problems.
Systems of Inequalities
• Solve systems of linear inequalities by graphing.
CULMINATING GROUP ACTIVITY
They use substitution and elimination to solve other systems of equations. Students also solve systems of inequalities.
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Curriculum titles Matrices IPLs
MATH CONCEPTS
Matrices – Data Collection
• Learn how to use matrix notation. • Use matrices to store and interpret data.
Matrices – Addition
• Add matrices.
and Subtraction
• Subtract matrices. • Learn about matrices of equal size.
CULMINATING GROUP ACTIVITY Students build and use a LEGO car to measure distance ®
traveled when only the hubs are used and again when
Matrices – Multiplication
• Learn how to multiply matrices by a scalar. • Learn how to multiply matrices together.
rubber tires are added. The two matrices are compared. Students are given the scenario of running a hobby shop that has several types of car kits for sale. They use matrices to keep track of inventory as sales and purchases are made. Then, they determine if they should build their own kit with raw materials or continue to purchase a premade kit. Students add and subtract matrices, multiply matrices by a scalar, and then multiply matrices together in order to run the hobby shop.
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Unit titles Polynomials IPLs
MATH CONCEPTS
Monomials
• Identify monomial expressions. • Multiply monomials. • Divide monomials.
Polynomials
• Identify different types of polynomials. • Find the degree of polynomials. • Order polynomials.
CULMINATING GROUP ACTIVITY The teacher leads students through the activity. Students use algebra tiles and graph boards to add, subtract, and multiply polynomials.
Adding & Subtracting
• Add polynomials.
Polynomials
• Subtract polynomials.
Multiplying Polynomials
• Multiply polynomials with the Distributive Property. • Multiply polynomials using the FOIL method.
Special Products
• Find the square of a sum.
of Polynomials
• Find the square of a difference. • Find the product of a sum and a difference.
Closure
• Apply closure to the Real Number System. • Apply closure to polynomials. • Determine a counterexample.
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Curriculum titles Quadratics IPLs
MATH CONCEPTS
Graphing Quadratics 1
• Identify quadratics. • Find the maximum or minimum on a graph. • Graph quadratics.
Graphing Quadratics 2
• Find the axis of symmetry of a parabola. • Graph a quadratic using the axis of symmetry. • Adjust the width of a parabola.
CULMINATING GROUP ACTIVITY
• Shift a parabola by changing the constant.
Students use straw rockets to view the shape of a quadratic equation. Students calculate the height of the arc based on the Quadratic Formula and their launch information. Students use a graph board to answer questions about quadratic equations. Students use cards and math symbols to solve equations, factor expressions, and use the discriminant. They write the solutions on a graph board.
Solving Quadratics
• Solve a quadratic by graphing.
by Graphing
• Identify the types of solutions a quadratic can have.
Quadratic Formula
• Solve quadratics using the Quadratic Formula.
The Discriminant
• Use the discriminant to find the number of real roots in a quadratic. • Find the discriminant to verify the roots of a quadratic.
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Unit titles Factoring IPLs
MATH CONCEPTS
Factoring Algebraic Terms • Factor to find the GCF. • Factor algebraic terms.
Factoring with the Distributive Property
• Factor simple algebraic expressions using the Distributive Property.
Factoring with FOIL 1
• Factor quadratics in the form x2 + bx + c using FOIL.
CULMINATING GROUP ACTIVITY
• Solve factored quadratics.
Students practice factoring integers; algebraic expressions; and polynomials using cards, math symbols, and graph
Factoring with FOIL 2
boards. Students use the Distributive Property, FOIL,
• Factor quadratics in the form ax2 + bx + c using FOIL. • Solve factored quadratics.
perfect squares, and completing the square methods along with simple prime factorization.
Factoring Perfect
• Identify perfect square trinomials.
Square Trinomials
• Factor perfect square trinomials. • Apply the Perfect Square Property.
Completing the Square
• Solve quadratic equations by completing the square.
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Curriculum titles Exponential Equations IPLs
MATH CONCEPTS
Exponential Functions
• Find ordered pairs of exponential functions. • Find the y-intercept of an exponential function. • Identify the graph of an exponential function.
Exponential Growth
• Review conversion of a percent to a decimal. • Identify and use the formula for exponential growth. • Calculate exponential growth and compound interest.
CULMINATING GROUP ACTIVITY Students will create a graph using circles to represent exponential growth and decay. They create the range from a given domain for an exponential function. Students then transfer the information to the graph board.
Exponential Decay
• Identify and use the formula for exponential decay. • Solve depreciation problems. • Identify and use the half-life formula.
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Unit titles Probability IPLs
MATH CONCEPTS
Fundamental
• Calculate the number of possible events using the Fundamental Counting Principle.
Counting Principle
• Determine if events are independent or dependent.
Probability
• Learn about probability and how likely an event is to occur. • Discover theoretical probability. • Discover experimental probability.
CULMINATING GROUP ACTIVITY Students use cards, dice, and graph boards to determine
Probabilities of Independent
• Decide if events are independent or dependent.
outcomes for independent and dependent events,
& Dependent Events
• Solve independent events.
combinations, and permutations.
• Solve dependent events.
Probability of
• Decide if events are exclusive or inclusive.
Compound Events
• Solve exclusive compound events. • Solve inclusive compound events.
Permutations
• Learn about factorials. • Solve repeating permutations. • Solve non-repeating permutations.
Combinations
• Learn the difference between permutations and combinations. • Solve repeating combinations. • Solve non-repeating combinations.
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Curriculum titles Data Graphs I IPLs
MATH CONCEPTS
Tree Diagrams,
• Learn about the different ways to organize data.
Tables, and Charts
• Use tree diagrams, tables, and circle graphs to organize data and find solutions.
Bar Graphs and Histograms
• Analyze data in bar graphs, double-bar graphs, and histograms. • Learn the steps to create a histogram.
CULMINATING GROUP ACTIVITY Students will complete up to five activities. Some activities
Organizing Data
• Evaluate data to create stem-and-leaf plots.
include using two LEGO ® cars for comparison of distance
• Use back-to-back stem-and-leaf plots.
traveled. Students will create a back-to-back stem-and-
• Create a line plot.
leaf plot. They will also use cards and dice to create information for use in averages. Students will use colored circles, algebra tiles, and other manipulatives to create data for bar graphs and box-and-whisker plots.
Averages
• Calculate mean, median, mode, and range.
Box-and-Whisker Plots
• Understand quartiles. • Identify the parts of a box-and-whisker plot. • Learn how to show data in box-and-whisker plots.
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Unit titles Data Graphs II IPLs
MATH CONCEPTS
Population and Sampling
• Determine a population, sample, and sample size. • Learn about sampling techniques.
Scatter Plots
• Create scatter plots. • Analyze scatter plots to determine relationships.
CULMINATING GROUP ACTIVITY Students create simple, stratified, and systematic samples using cards and dice. They plot coordinate pairs on a scatter plot and draw a line of best fit on a graph board.
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Curriculum titles Logic and Sequences IPLs
MATH CONCEPTS
Inductive and
• Learn the difference between inductive and deductive reasoning.
Deductive Reasoning
• Identify examples of each type of reasoning. • Determine if a statement is true or false based on logical reasoning.
Introduction to Sequences
• View various types of sequences.
CULMINATING GROUP ACTIVITY
• Identify terms and the order of terms.
Students use straw rockets to create data for arithmetic
• Find the next term in a sequence.
sequences. Information about the components are used to
• Find the missing term in a sequence.
create geometric sequences. Arithmetic Sequences
• Recognize an arithmetic sequence. • Determine the common difference. • Find the nth term in a sequence.
Geometric Sequences
• Use geometric sequences. • Determine the common ratio. • Find the nth term in a sequence.
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Unit titles Angles IPLs
MATH CONCEPTS
Introduction to Geometry • Define and name points. • Define and name lines, rays, and segments. • Define and name planes.
Parallel, Perpendicular,
• Define and label parallel lines.
and Skew Lines
• Define and label perpendicular lines. • Define and label skew lines.
CULMINATING GROUP ACTIVITY Students use a geometry board with pegs and rubber bands and graph boards to create lines, angles, and transversals.
Angles
• Name the parts of an angle. • Name angles using the vertex. • Name angles using three points.
Measuring Angles
• Use a protractor to measure angles. • Name angles by their measures.
Angle Relationships
• Define and identify congruent angles. • Define and identify an angle bisector. • Define and identify complementary and supplementary angles.
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Curriculum titles Triangles IPLs
MATH CONCEPTS
The Transversal
• Define and identify a transversal. • Define and identify corresponding angles. • Define and identify alternate-interior, alternate-exterior, and same-side angles.
Introduction to Triangles
• Define and label the parts of a triangle. • Name triangles.
CULMINATING GROUP ACTIVITY Students identify, measure, and create a variety of triangles and congruent triangles. They determine ratios in a given
• Calculate missing angle measures.
Congruent Triangles
• Prove congruency with the Side-Angle-Side Theorem.
triangle including sine, cosine, and tangent. Students use
• Prove congruency with the Angle-Side-Angle Theorem.
geometry boards, pegs, rubber bands, protractors, rulers, and graph boards during the activity.
• Prove congruency with the Side-Side-Side Theorem.
Classifying Triangles
• Identify and classify triangles by their angle measures. • Identify and classify triangles by their side lengths.
Similar Triangles
• Write proportions for similar triangles. • Prove two triangles similar using SSS and SAS Similarity. • Prove two triangles similar using AA Similarity.
Sine, Cosine, and Tangent
• Write and identify sine, cosine, and tangent ratios. • Solve for the missing side of a right triangle using sine, cosine, and tangent ratios.
Trigonometric Ratios
• Find the missing angles of right triangles using sine, cosine, and tangent.
Inequality, Right Triangles,
• Use the Triangle Inequality Theorem to determine whether you can draw a triangle.
& the Pythagorean Theorem
• Identify the parts of a right triangle. • Solve for the missing side of a right triangle using the Pythagorean Theorem.
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Unit titles Polygons IPLs
MATH CONCEPTS
Introduction to Polygons
• Identify polygons. • Name polygons by their sides. • Classify polygons as regular or irregular.
CULMINATING GROUP ACTIVITY Students use polygon shapes, paper, rulers, and graph
Missing Angles
• Calculate the total degrees of all the angles of a polygon.
of Polygons
• Find missing angle measures in polygons.
Quadrilaterals,
• Learn and identify the properties of quadrilaterals.
Rectangles, and Squares
• Identify rectangles and their properties. • Identify squares and their properties.
boards to work with polygons. Students compare, measure, and create polygons.
The Parallelogram
• Identify a parallelogram and its properties.
& the Rhombus
• Identify a rhombus and its properties.
Trapezoids & Kites
• Identify a trapezoid and its properties. • Identify a kite and its properties.
Perimeter
• Find the perimeter of quadrilaterals. • Find the perimeter of regular polygons. • Find the perimeter of irregular polygons.
Area
• Find the area of a rectangle. • Find the area of a triangle. • Find the area of a trapezoid.
Area of Irregular Shapes
• Break irregular shapes into polygons. • Calculate the area of irregular shapes. • Find the area of shaded portions of circles.
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Curriculum titles Circles IPLs
MATH CONCEPTS
Circles
• Identify the diameter and radius of a circle. • Identify chords in a circle. • Identify arcs in a circle.
Circumference and Area
• Evaluate expressions with pi. • Find the circumference of a circle. • Find the area of a circle.
CULMINATING GROUP ACTIVITY Students calculate the area of circles; use circumference to determine radius; and calculate the volume and surface
Cylinders
• Find the surface area of a cylinder.
area of cones, cylinders, and spheres. Students use card
• Find the volume of a cylinder.
stock to create a package and then create a scaled version of the package.
• Define a cylinder and its parts.
Cones
• Identify a cone and its parts. • Calculate the surface area of a cone. • Calculate the volume of a cone.
Spheres
• Identify spheres and their parts. • Find the surface area of a sphere. • Find the volume of a sphere.
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Unit titles Prisms and Pyramids IPLs
MATH CONCEPTS
Cubes
• Identify a cube and its parts. • Calculate the surface area of a cube. • Calculate the volume of a cube.
Rectangular Prisms
• Identify rectangular prisms and their properties. • Find the surface area of a rectangular prism. • Find the volume of a rectangular prism.
CULMINATING GROUP ACTIVITY Students identify and construct prisms and pyramids using straws and pipe cleaners. Students calculate the area and
Triangular Prisms
• Identify the base and height of a triangular prism. • Find the surface area of a triangular prism.
volume of prisms and pyramids and identify their nets.
• Find the volume of a triangular prism.
Rectangular Pyramids
• Identify the height of a rectangular pyramid. • Find the surface area of a rectangular pyramid. • Find the volume of a rectangular pyramid.
Triangular Pyramids
• Identify the parts of a triangular pyramid. • Find the surface area of a triangular pyramid. • Find the volume of a triangular pyramid.
Nets
• Identify the nets of prisms. • Identify the nets of pyramids. • Identify the nets of cylinders and cones.
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Curriculum titles Units IPLs
MATH CONCEPTS
Standard Units
• Recognize the standard base units. • Identify the property each standard base unit measures. • Choose the correct unit to measure an object.
Metric Units
• Identify the common units of the metric system. • Use the basic prefixes of the metric system.
CULMINATING GROUP ACTIVITY Students determine and convert standard and metric
Dimensional Analysis
• Evaluate the arrangement of variables in a problem. • Convert a single unit to a different unit within a system and between systems.
measurement for length and temperature. Students measure several objects in the room and use graph boards to gather
• Convert derived units.
data and solve problems. Converting Fahrenheit
• Convert from Celsius to Fahrenheit.
and Celsius
• Convert from Fahrenheit to Celsius.
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Unit titles Accuracy IPLs
MATH CONCEPTS
Significant Digits
• Explore the rules of identifying significant digits. • Determine the significant digits in a number.
Operations with Significant Digits
• Round answers to the correct number of significant digits for addition and subtraction problems. • Round answers to the correct number of significant digits for multiplication and division problems.
CULMINATING GROUP ACTIVITY Students use accuracy and precision to measure the
Accuracy and Precision
• Define accuracy and precision.
distance from their rocket to the target. They use
• Distinguish between accuracy and precision.
significant digits in addition, subtraction, multiplication,
• Describe accuracy using the ± symbol.
and division.
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Algebra readiness
Algebra readiness Algebra Readiness Curriculum Overview The Pitsco Education Algebra Readiness curriculum is specifically designed to provide students with a deeper and more refined understanding of fundamental mathematics in preparation for achieving success when they encounter the more abstract algebraic concepts in Algebra I. Its design and delivery methodology successfully provide students with a coherent focus on core mathematical concepts while providing relevant connections and hands-on opportunities to apply what they learn and successfully develop skill proficiency.
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Algebra academy
Phase I
Phase II
Curriculum components
Curriculum components
Curriculum components
• Orientation • Diagnostic Assessment • Individualized Prescriptive Lessons™ • Culminating Group Activities
• Orientation • Project-based Curriculum • Targeted Remediation or Enrichments • Homework Assignments • Diagnostic Days • Individualized Prescriptive Lessons™ • Culminating Group Activities
• Project-based Curriculum • Targeted Remediation or Enrichments • Homework Assignments • Diagnostic Days • Individualized Prescriptive Lessons™
Math Concepts • Integers • Decimals • Fractions • Converting between Decimals and Fractions
Math Concepts • Absolute Value • Area, Volume, and Geometric Shapes • Coordinate Geometry • Exponents and Scientific Notation • Percents, Ratios, Proportions, and Scaling • Probability • Subsets of Real Numbers • Systems of Measurement • Theory of Numbers • Operations on Real Numbers • Properties of Real Numbers • Statistics and Data Representation
Phase III
• Culminating Group Activities
Math Concepts • Angles and Triangles • Area and Volume of Geometric Shapes and Polygons • Functions and Relations • Inequalities • Slope • Solving and Graphing Linear Equations • Solving Single-step and Multistep Equations • Square Roots and the Pythagorean Theorem • Translations, Rotations, Reflections, and Tessellations
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Home Makeover
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Exponents and Scientific Notation
Geometric Packing
Forensic Math
Environmental Math
Chemical Math
Weights & Measures
Statistical Analysis
Properties of Math
Hotel Management
Confident Consumer
Math Concepts
BioEngineering
Algebra Readiness
Astronomy
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Curriculum titles Astronomy
Phase II
MATH concepts • Area, Volume, and Geometric Shapes • Exponents and Scientific Notation • Operations on Real Numbers • Percents, Ratios, Proportions, and Scaling • Properties of Real Numbers • Systems of Measurement
Overview In Astronomy, students investigate the Sun-Moon-Earth system
MATH objectives • Determine arcs and circumference • Create a scale model
and their relationship to it. They use models to demonstrate day-night cycles, time zones, eclipses, seasons, tides, and Moon phases. They consider planetary motion, including elliptical orbits, gravity, and Kepler’s laws. In addition,
• Estimate using scientific notation
they explore the solar system, categorizing the planets
• Multiply decimals
by size, type, and general characteristics and creating
• Measure angles • Order and round decimals
a scale model of planetary distances. They assemble and use a small refracting telescope and calculate magnification based on focal length. Also, they learn methods for expressing the vast distances in space using scientific notation.
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Curriculum titles BioEngineering
Phase II
MATH concepts • Absolute Value • Angles and Triangles • Properties of Real Numbers
MATH objectives • P ractice absolute value, number lines, and positive and negative numbers • Identify characteristics and types of angles and measure angles with a protractor • Learn and demonstrate the characteristics of projectile motion • Measure and classify angles using a digital camera and imaging software
Overview In BioEngineering, students explore topics related to kinesiology and sports performance. They measure the body angles and range of motion (ROM) of selected joints to explore the mathematics behind projectile motion. Students cover mathematical concepts including identifying and measuring angles; averaging positive and negative integers; data collection; graphing; and
• Relate types of angles to body movement and athletic performance
converting fractions, decimals, and percentages.
• Gather, graph, and interpret ROM data to determine personal flexibility
images of the tests, and use the computer to
Then, they perform flexibility tests, take digital analyze student flexibility.
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Curriculum titles Confident Consumer
Phase II
MATH concepts • Area, Volume, and Geometric Shapes • Operations on Real Numbers • Percents, Ratios, Proportions, and Scaling • Properties of Real Numbers • Subsets of Real Numbers
MATH objectives • Use ratios to solve problems
Overview In Confident Consumer, students use problem-solving techniques to complete activities related to consumer education. Students
• Compute percentage rates
calculate unit prices, evaluate sales and discounts provided by
• Calculate area
vendors, calculate the most economical way to
• Compare total cost
purchase food and drinks for a party of 25, evaluate
• Calculate unit price • Calculate the better buy
products based on strength and absorbency, and much more. Percents, ratios, and proportions are used extensively throughout this curriculum title.
• Multiply and divide decimals
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Curriculum titles Hotel Management
Phase II
MATH concepts • Operations on Real Numbers • Percents, Ratios, Proportions, and Scaling • Properties of Real Numbers • Solving Single-step and Multistep Equations
MATH objectives • Use and simplify ratios of costs • Solve proportions related to room rates within a hotel
Overview In Hotel Management, students trace the earliest types of lodging establishments in America. They explore the day-to-day responsibilities of running a hotel and examine the following hotel
• Determine unit rate of rooms
areas: front desk, hotel accounting, housekeeping,
• Convert decimals, fractions, and percentages
engineering and maintenance, and hotel security.
• Determine the discount price on room charges
They learn that each component is necessary to successfully run a hotel. Students utilize math skills by calculating occupancy rates, RevPAR, ADR, room rates, and room discounts. Students use percentages, decimals, ratios, and proportions.
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Curriculum titles Properties of Math
Phase II
MATH concepts • Absolute Value • Coordinate Geometry • Exponents and Scientific Notation • Operations on Real Numbers • Properties of Real Numbers • Solving Single-step and Multistep Equations
Overview
• Subsets of Real Numbers
In Properties of Math, students first build the number system from
• Theory of Numbers
MATH objectives • Classify each subset of the complex numbers using sets and set notation • Order integers and rational numbers and explore the density of the real numbers
the ground up by exploring set theory and using tiles to explore the density of the real numbers. They are then introduced to the order of operations and properties and ordering of rational numbers through a series of explorations using activities on mathematical software. Students learn relationships between prime factorizations and quotients of integers while relating all ideas to the rational number system. Finally, all concepts
• Discover operations using real numbers
are brought together by solving problems using
• Use the greatest common divisor and the least common multiple
multistep operations.
• Explore prime factorizations • Use the order of operations to solve single- and multistep problems
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Curriculum titles Statistical Analysis
Phase II
MATH concepts • Probability • Properties of Real Numbers • Statistics and Data Representation
MATH objectives • Create bar graphs • Work with line and circle graphs • Determine independent and dependent events • Calculate the mean, median, and mode • Calculate experimental and theoretical probability • Create a histogram • Create a stem-and-leaf plot
Overview While engaged in Statistical Analysis, students create and conduct a survey and graph their data. They learn to calculate measures of central tendency and range. Students explore histograms, box-andwhisker plots, stem-and-leaf plots, bar graphs, circle graphs, and line graphs and use them to display statistical information. Students also complete probability activities ranging from tossing twocolor counters and rolling dice to generating and using Pascal’s Triangle to calculate experimental and theoretical probabilities. Students use their knowledge of probability to create a fair game.
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Curriculum titles Weights & Measures
Phase II
MATH concepts • Operations on Real Numbers • Percents, Ratios, Proportions, and Scaling • Properties of Real Numbers • Solving Single-step and Multistep Equations • Statistics and Data Representation • Systems of Measurement
MATH objectives
Overview In Weights & Measures, students get a variety of hands-on experiences measuring and weighing items using customary and
• Measure items using standard and metric measurement
metric measurement. They practice converting measurement
• Weigh items using standard and metric measurement
analysis to convert from one measurement system
• Convert standard and metric units
temperature from one system to another.
within a system and then learn to use dimensional to another. Using a formula, they learn to convert
• Use dimensional analysis to convert metric units to customary units and vice versa
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Curriculum titles Chemical Math
Phase III
MATH concepts • Functions and Relations • Inequalities • Percents, Ratios, Proportions, and Scaling • Properties of Real Numbers • Solving and Graphing Linear Equations • Solving Single-step and Multistep Equations
MATH objectives
Overview Chemical Math covers basic chemical concepts such as properties of matter, structure of atoms and molecules, bonding, chemical
• Translate algebraic expressions from words to symbols
equations, and the mole concept, all from a mathematical point
• Define expressions
expressions, how to translate word descriptions
• Solve multistep equations • Use inverse operations • Solve inequalities
of view. Students learn types of mathematical of a process into an equation, and how to solve both single-step and multistep equations. They balance chemical equations and learn to recognize and graph inequalities.
• Locate freezing and boiling points for given substances using a number line • Calculate density using a simple equation
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Curriculum titles Environmental Math
Phase III
MATH concepts • Angles and Triangles
• Area, Volume, and Geometric Shapes • Equivalency and Congruency • Operations on Real Numbers • Properties of Real Numbers • Slope • Solving Single-step and Multistep Equations • Square Roots and Pythagorean Theorem • Subsets of Real Numbers
MATH objectives
• Estimate and calculate square roots • Identify rational and irrational numbers • Identify angle type and measure angles • Identify triangles and measure the angles
Overview In Environmental Math, students explore the many uses of geometry in the study and measurement of the environment. They use squares and square roots as they determine dimensions and areas of study plots and natural areas. They learn to use triangulation to measure distances, heights, and depths while exploring concepts such as types of triangles, the Pythagorean Theorem, and the Distance Formula. Students relate linear functions and slope to environmental factors such as rates of runoff and erosion.
• Use the Pythagorean Theorem to determine the hypotenuse • Determine the length of a side of special right triangles • Find the distance between two points on a coordinate plane
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Curriculum titles Forensic Math
Phase III
MATH concepts • Coordinate Geometry • Functions and Relations • Operations on Real Numbers • Percents, Ratios, Proportions, and Scaling • Properties of Real Numbers • Slope
Overview
• Solving and Graphing Linear Equations
In Forensic Math, students discover the “numbers” behind
• Solving Single-step and Multistep Equations • Statistics and Data Representation • Systems of Measurement
MATH objectives
crime scene investigation. They use algebra in determining the approximate height of both suspects and victims, in calculating the turning diameter of a vehicle, and in computing the velocity of a car. Students use the concepts of slope, y-intercept, functions, and equations to complete a crime scene data analysis.
• Define a function • Learn about polar and Cartesian coordinates • Use the vertical line test to determine if the relation is a function • Solve linear equations with two variables • Graph linear equations • Define slope and be able to find the slope of a line • Define y-intercept
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Curriculum titles Geometric Packing
Phase III
MATH concepts • Angles and Triangles
• Area, Volume, and Geometric Shapes • Coordinate Geometry • Consumer Applications • Equivalency and Congruency • Operations on Real Numbers • Percents, Ratios, Proportions, and Scaling
Overview
• Properties of Real Numbers
In Geometric Packing, students explore surface areas and volumes
• Slope • Solving Single-step and Multistep Equations • Square Roots and Pythagorean Theorem • Theory of Numbers • Translations, Rotations, Reflections, and Tessellations
MATH objectives
• Discover surface areas and volumes of three-dimensional objects • Create tessellations by the use of rotations, reflections, and translations
of various objects by packing materials. They explore spatial relationships and tessellations by transformations and the use of mathematical software. Students are introduced to the concept of slope, have tactile explorations of spherical packing, and find applications of Pascal’s Triangle. They use the Fibonacci sequence to understand the greatest common divisor and the least common multiple. Finally, they investigate mathematical history by using ancient Egyptian algebra to find the golden ratio and explore the Pythagorean Theorem by building a scale replica of the Pyramid of Giza.
• Investigate spherical packing and the applications of Pascal’s Triangle in packing • Use the golden ratio, greatest common divisor, and least common multiple to understand architecture and designs • Utilize ancient Egyptian mathematics to explore the golden ratio and the Pythagorean Theorem Page 61
Curriculum titles Home Makeover
Phase III
MATH concepts • Area, Volume, Geometric Shapes • Operations on Real Numbers • Percents, Ratios, Proportions, and Scaling • Properties of Real Numbers • Square Roots and Pythagorean Theorem
MATH objectives • Determine the area of a rectangle, triangle, and circle
Overview When students complete Home Makeover, they will have an understanding of how to preplan for remodeling a home. Students design an addition to a home by calculating area, selecting
• Determine circumference, diameter, and radius
materials, and computing overall costs. Students
• Determine the surface area of a rectangular prism and a cylinder
volume of a cylinder as they relate to homes and
• Use the Distributive Property
students to study many of the concepts used by
• Create scale drawings
determine square feet, square yards, and the home remodeling. This curriculum title enables those who remodel professionally.
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Curriculum titles Laser Geometry
Phase III
MATH concepts • Angles and Triangles
• Area, Volume, and Geometric Shapes • Coordinate Geometry • Equivalency and Congruency • Exponents and Scientific Notation • Operations on Real Numbers • Percents, Ratios, Proportions, and Scaling • Properties of Real Numbers • Slope • Solving and Graphing Linear Equations • Solving Single-step and Multistep Equations • Square Roots and Pythagorean Theorem • Theory of Numbers • Translations, Rotations, Reflections, and Tessellations
MATH objectives
• Investigate types and properties of angles and triangles
Overview In Laser Geometry, students use algebra and geometry to explore different mathematical concepts including exponents, scientific notation, angles, and waves. Students conduct experiments to investigate interior and exterior angles; Heisenberg’s Uncertainty Principle; and transverse, longitudinal, and surface waves. Finally, they explore degrees of angles by using a game controller to create an inexpensive, interactive whiteboard and by manipulating the direction of laser beams to piggyback a radio signal to a receiver.
• Relate angle properties to parallel and perpendicular lines • Use exponents and scientific notation to represent numbers • Use and solve proportions in order to discover similar and congruent polygons • Use a compass and straightedge to create parallel and perpendicular lines, create triangles, and bisect angles
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Curriculum titles Water Management
Phase III
MATH concepts
• Area, Volume, and Geometric Shapes • Operations on Real Numbers • Properties of Real Numbers • Solving Single-step and Multistep Equations • Statistics and Data Representation
MATH objectives
Overview
• Identify polygons and polyhedrons
In Water Management, students explore the hydrologic cycle, uses
• Determine surface area
of water, types of water pollution, and the design and function of
• Calculate volume
water treatment plants. They use a River Tank to estimate surface
• Solve equations using formulas • Create a scatter plot and bar, circle, and line graphs
area and volume of water in a water body and to calculate flow rate. They use a watershed model to simulate runoff, groundwater activity, and pollution. Students calculate a water budget for a family and use a variety of graphs. They also consider methods of water conservation.
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Algebra I
Algebra I Algebra I Curriculum Overview The Pitsco Algebra I curriculum builds upon skills learned in the Algebra Readiness course. Like Algebra Readiness, Algebra I combines project-based learning with critical core content while giving students real-world opportunities to think analytically, formulate ideas, and solve increasingly complex problems using algebraic expressions. Upon completing the Algebra I core curriculum, students will have successfully reached the necessary level of mathematical literacy to earn full credit in “the gateway course.”
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Algebra I
Phase I
Phase II
Phase III
Curriculum components
Curriculum components
Curriculum components
• Orientation • Diagnostic Assessment • Individualized Prescriptive Lessons™
• Orientation • Project-based Curriculum • Targeted Remediation or Enrichments • Homework Assignments • Diagnostic Days • Individualized Prescriptive Lessons™ • Culminating Group Activities
• Project-based Curriculum • Targeted Remediation or Enrichments • Homework Assignments • Diagnostic Days • Individualized Prescriptive Lessons™ • Culminating Group Activities
• Culminating Group Activities
Math Concepts • Real Number System • Properties of Real Numbers • Scientific Notation • Simplifying and Solving Equations • Linear Equations and Graphing • Statistics and Data Representation
Math Concepts • Combinations and Permutations • Direct and Inverse Variations • Graphing Technology • Inequalities • Matrices • Percents, Ratios, and Proportions • Rational Expressions and Equations • Statistical Analysis • Systems of Equations • Writing, Graphing, and Solving Linear Equations
Math Concepts • Exponential Expressions and Equations • Factoring • Functions and Relations • Graphing and Solving Quadratic Equations • Properties of Real Numbers • Radicals • Simplifying Polynomials • Solving Single-step and Multistep Equations
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The Universe
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Factoring
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Functions and Relations
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Graphing and Solving Quadratic Equations •
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Inequalities
Percents, Ratios, and Proportions
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Properties of Real Numbers
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Matrices
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Radicals •
Rational Expressions and Equations
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Solving Single-step and Multistep Equations
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Statistical Analysis
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Systems of Equations
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Simplifying Polynomials
Writing, Graphing, and Solving Linear Equations
Where in the World
Projectile Motion
Lenses & Optics
Factoring & Polynomials
Climate Change
Water Quality
Unsolved Mysteries
Supply & Demand
Population Perspectives
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Exponential Expressions and Equations
Graphing Technology
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Combinations and Permutations Direct and Inverse Variations
Sports Statistics
Nuclear Energy
Math Concepts
Math Behind Your Meals
Algebra I
Gravity of Algebra
Algebra I
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Curriculum titles Gravity of Algebra
Phase II
MATH concepts • Direct and Inverse Variations • Graphing Technology • Solving Single-step and Multistep Equations • Statistical Analysis • Writing, Graphing, and Solving Linear Equations
MATH objectives • Explore direct and inverse variations
Overview In Gravity of Algebra, students will interpret data from a free-fall experiment by applying mathematical concepts such as direct and inverse variations, scatter plots, and slope. They will use the
• Create scatter plots and determine types of correlations
point-slope and y-intercept forms of a line to create a
• Explore slope as well as x- and y-intercepts
the acceleration due to gravity. Students will also use
• Write linear equations in slope-intercept and point-slope form
graphing skills to learn the relationship between the
• Graph linear equations
mathematical representation of the data and calculate
kinetic and the potential energy of a falling object and explore the Law of Conservation of Energy.
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Curriculum titles Math Behind Your Meals
Phase II
MATH concepts • Percents, Ratios, and Proportions
• Properties of Real Numbers • Solving Single-step and Multistep Equations
MATH objectives • Use properties to solve single operation equations • Use properties to solve multistep equations with and without exponents • U se properties to solve multistep equations with variables on both sides • Solve proportions • Solve percent of change problems
Overview In Math Behind Your Meals, students will relate algebraic terms and algorithms to tangible examples – in this case, the foods they consume. They will use basic operations and properties to evaluate expressions as they analyze meals from the production to the ingestion phases. They will substitute values for variables to determine how they can get the most nutritional value for their food dollars. They will calculate percent of change to find how much fast food costs today compared to past prices. They will learn how food advertising and marketing relate to portion sizes. They will solve proportions relating to portion sizes and calorie and fat content. They will also calculate the price of food over-consumption as it relates to health care costs and obesity.
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Curriculum titles Nuclear Energy
Phase II
MATH concepts • Direct and Inverse Variations • Exponential Expressions and Equations • Graphing Technology • Inequalities • Rational Expressions and Equations • Statistical Analysis
Overview
• Writing, Graphing, and Solving Linear Equations
In Nuclear Energy, students learn about the basics of energy, atomic structure, the periodic table, binding energy, fission, nuclear reactors, and radioactivity. Students graph equations related to
MATH objectives
energy, rational functions related to Coulomb’s Law,
• Use a graphing calculator to graph an equation related to energy
equations containing powers and roots, and rational equations relating to radioactivity. Also, using the
• Use a graphing calculator to graph a function related to Coulomb’s Law
graphing calculator, students analyze inequalities,
• Use a graphing calculator to graph equations and analyze inequalities • Use a graphing calculator to produce a graph and evaluate data in table form
evaluate data in a table form, and calculate various aspects of radioactivity using rational equations. Finally, students use the simulation software Nuclear Power Plant to attempt to successfully operate a nuclear power plant.
• Use a graphing calculator to graph equations containing powers and roots • Use a graphing calculator to graph a rational equation
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Curriculum titles Sports Statistics
Phase II
MATH concepts • Combinations and Permutations • Matrices • Statistical Analysis
MATH objectives • Learn the definition of and the parts that make up a matrix • Learn to add, subtract, and multiply matrices • Create a scatter plot and determine the line of best fit
Overview In Sports Statistics, students explore the role of mathematics in sports statistics. Students will use actual professional sports data to find trends and make decisions. Students will also collect data from their own tabletop sports and complete
• C reate frequency tables and histograms and then use the histograms to interpret statistical information
analyses on the data. They will explore many
• C reate a box-and-whisker plot by calculating the range, quartiles, median, and outliers
combinations.
different mathematical concepts including matrices, graphing, factorials, permutations, and
• E xplore factorials, permutations, and combinations and how they relate to sports statistics
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Curriculum titles Supply & Demand
Phase II
MATH concepts • Graphing Technology • Systems of Equations • Writing, Graphing, and Solving Linear Equations
MATH objectives • Solve linear equations for one variable • Graph linear equations • Solve a system of linear equations by graphing
Overview In Supply & Demand, students will learn about the Law of Supply and Demand and how it affects their lives. They will use graphing skills and learn multiple methods of solving systems of equations to determine the equilibrium price and
• Use substitution to solve a system of equations
quantity of a given product. Finally, students will use
• Use elimination to solve a system of equations
a simulated business.
their ability to solve systems of equations to manage
• Explore solving a system of equations with a graphing calculator
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Curriculum titles Unsolved Mysteries
Phase II
MATH concepts • Graphing Technology • Functions and Relations • Percents, Ratios, and Proportions • Writing, Graphing, and Solving Linear Equations
MATH objectives • Use scaling and proportional reasoning to calculate the actual distances between objects • G raph points on a coordinate graph and then use coordinate graphing to identify locations on a graph • Learn about relationships and functions and how to identify functions using the vertical line test
Overview In Unsolved Mysteries, students will use functions and coordinate graphing in determining who committed a fictional crime. Using cell phone records and coordinate graphing, students will identify an area in which a stolen cell phone was last operated. Students will also use functions to estimate the time of the robbery as well as the approximate height of the suspect. Students will link algebra skills to a real-world career in forensic science.
• Use a graphing calculator to create a graph and determine the function that describes the graph • Identify the x- and y-intercepts of a function
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Curriculum titles Water Quality
Phase II
MATH concepts • Graphing Technology • Inequalities • Solving Single-step and Multistep Equations • Systems of Equations • Writing, Graphing, and Solving Linear Equations
MATH objectives • Identify inequalities and double inequalities
Overview In Water Quality, students complete an internship with Scientific Laboratory Services. As part of their internship, students will analyze various standards and regulations relating to water quality
• Match graphs for inequalities
and use. Through laboratory testing and activities,
• Solve simple inequalities
students will experience real-world applications of
• Solve inequalities with two variables • Create a T-chart and graph inequalities on a coordinate plane
inequalities and learn to solve and graph simple, multistep, and compound inequalities using both paper and pencil and a graphing calculator.
• Graph a linear system of inequalities on a graphing calculator • Define and graph absolute value inequalities
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Curriculum titles Climate Change
Phase III
MATH concepts • Matrices • Solving Single-step and Multistep Equations • Statistical Analysis
MATH objectives • Evaluate an expression by substituting a value for the variable • Analyze a scatter plot to make predictions • Solve literal equations for a specified variable
Overview In Climate Change, students will explore recent IPCC data on climate change, concentrating on how it will affect people and environments in the near future. They will look at patterns of
• Represent applied problems by using matrices
melting ice and rising sea levels, changes in
• U se dimensional analysis to convert units of measure within a system
precipitation, increases in severity of storms, and northward movement of plants and animals. They will use a variety of monomial and polynomial equations and will use the InspireData software to calculate and graph rates of change of various climatic functions, based on the most recent data.
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Curriculum titles Factoring & Polynomials
Phase III
MATH concepts • Factoring • Graphing and Solving Quadratic Equations • Properties of Real Numbers • Simplifying Polynomials
MATH objectives • Identify types of polynomials • Examine prime and composite numbers
Overview In Factoring & Polynomials, students will learn about different types of polynomials and how to identify and write monomials,
• Factor terms
binomials, and trinomials. Students examine prime and composite
• Use the Distributive Property in factoring
numbers and polynomials. Students will learn to factor
• Use the FOIL method to solve quadratic equations • Graph quadratic equations
and solve quadratic equations using the Distributive Property and the FOIL method. Students will learn to graph polynomials, use factors in graphing, and graph quadratic and special equations.
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Curriculum titles Lenses & Optics
Phase III
MATH concepts • Direct and Inverse Variations • Factoring • Rational Expressions and Equations • Solving Single-step and Multistep Equations
MATH objectives • Learn about inverse variation • Solve simple rational equations
Overview In Lenses & Optics, students will use the focal length of a lens to solve rational equations. Students will gather information by
• Solve rational equations with more than one term
performing an activity to determine lens optic measurements
• Reduce rational equations by factoring
will perform an experiment to discover the
• Solve complex rational equations • Use cross multiplication to solve formulas
and then graph the measurements. Students relationship between the object height and the image height, which is used to define the magnification ratio. Students create a slide projector and discover how lenses are made to correct vision problems.
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Curriculum titles Population Perspectives
Phase III
MATH concepts • Exponential Expressions and Equations • Functions and Relations • Graphing and Solving Quadratic Equations • Percents, Ratios, and Proportions • Simplifying Polynomials
MATH objectives • A nalyze the graph of a function to determine its domain and range
Overview In Population Perspectives, students will explore the field of demography, or the study of human populations, learning how demographers use algebra to analyze the growth and changing
• Apply proportional reasoning to solve problems
composition of populations. They will analyze
• Carry out a procedure to simplify polynomial expressions
census taking with population sampling, compare
• Define and graph quadratic equations
polynomials related to age cohorts of populations,
• Define and graph exponential equations
and solve population growth equations, compare population sizes at different growth rates, construct and compare populations in more developed and less developed countries. They will use the graphing calculator to graph and solve exponential and quadratic equations.
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Curriculum titles Projectile Motion
Phase III
MATH concepts • Exponential Expressions and Equations • Functions and Relations • Graphing and Solving Quadratic Equations • Graphing Technology • Radicals
MATH objectives • Graph simple quadratic functions
Overview In Projectile Motion, students build and launch straw rockets in order to observe how flying objects follow a curved path called a
• Solve quadratic functions by graphing
parabolic path. Students predict the launch angle that will make
• Solve quadratic functions using a graphing calculator
the straw rocket travel the greatest horizontal
• Use square root to find roots of quadratic functions • Solve quadratic functions using different methods • Define and graph exponential functions
distance and test the predictions. Students learn the general form of a quadratic equation, identify the coefficients in a quadratic equation, and use the coefficients in a quadratic equation to predict the shape of a parabola. Students predict where the straw rocket will land using a quadratic equation that describes the straw rocket’s path.
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Curriculum titles The Universe
Phase III
MATH concepts • Exponential Expressions and Equations • Properties of Real Numbers • Radicals • Solving Single-step and Multistep Equations
MATH objectives • Carry out a procedure to solve literal equations for a specified variable • Apply the laws of exponents and roots to solve problems
Overview In The Universe, students will cover astronomical concepts from the solar system outward, including stars, nebulas, and galaxies, and will explore evidence for the origin and expansion of the universe. They will calculate magnification of a telescope,
• Carry out a procedure to perform operations with numbers written in scientific notation
measure the speed of light, develop and interpret a
• Carry out a procedure to evaluate an expression by substituting a value for the variable
concentrate on size and distance in the universe,
• Use dimensional analysis to convert units of measure within a system
multistep polynomial equations.
scatter plot to categorize stars, and analyze different types of light using a spectroscope. They will applying algebra concepts such as exponents, powers and roots, scientific notation, and
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Curriculum titles Where in the World
Phase III
MATH concepts • Percents, Ratios, and Proportions • Radicals • Solving Single-step and Multistep Equations
MATH objectives • Solve radical expressions using addition and subtraction • Determine distance using the Pythagorean Theorem • Calculate the distance between two points using the Distance Formula • Complete angle measurements and compute calculations in degrees • Change the scale of a map and see the impact
Overview In Where in the World, students explore from Eratosthenes to GPS to see how mathematics is used in mapping the world in which we live. Students complete activities that utilize algebraic concepts such as solving radical expressions, the Pythagorean Theorem, and the Distance Formula while exploring the history of mapmaking from ancient tools to global positioning. Students will create a Mercator projection, use trilateration to determine distances, and use a GPS unit to calculate distances between locations.
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