iLikeMath K-12 Curriculum Overview by Jones Software Corp. Curriculum Development Team
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iLikeMath mag. Dear Friends, The ability to adapt as things change is not part of the education system in America, Katrina Stevens, director of learning science at the Chan Zuckerberg Initiative, and Matt Greenfield, managing partner of Rethink Education, wrote in a recent Ed Surge article. Yet many careers, from game design to engineering, require the ability to adjust plans as something is built and constructed.
REAL-WORLD EXPERIENCES ARE CRUCIAL FOR STUDENTS Lauren Barack
The Need Every Student Succeed Act (ESSA) is the law that guides schools’ requirements for
scholars’ success perimeters. The law requires: movement toward equity for disadvantaged and high need scholars, all scholars to be taught with high academic standards as preparation for college and career success, education and support communities receive important information from annual assessments that measure scholars’ progress toward high standards, assistance to support and grow local innovations developed by local leaders, and action for positive change and accountability in lowest performing school and students not making progress. https://www.ed.gov/essa
The iLikeMath System The reward system built in to the iLikeMath curriculum sets it apart from other learning software and builds skills students will need to succeed in the 21stCentury. Students who display growth and development through their exercise and assessment scores from the iLikeMath platform can earn points for rewards through the JSC Cares meritocracy program, which brings businesses and communities together to support and engage students.
Sincerely, Kevin Jones Co-Founder & CEO
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iLikeMath
CONTENTS 7 4.0 integrates geometric concepts
12 EXCERPT: 6.0 introducing students to statistical and probability Concepts
18 AUTHOR SPOTLIGHT: 8.0 intro into Algebra
2 Editor's Note 4 Grades K-2 Early Learning 6 3rd Grade Overview iLikeMath 3.0 focusing on number skills & numerical literacy 7 4th Grade Overview iLikeMath 4.0 focusing on number skills and numerical literacy 9 5th Grade Overview iLikeMath 5.0 focusing on number skills & mathematical literacy 12 6th Grade Overview iLikeMath 6.0 intro to number skills needed for algebra 13 7th Grade Overview iLikeMath 7.0 focusing on Strengthening the need in problem sovling 18 8th Grade Overview iLikeMath 8.0 intro to Algebra
4 Learn. Explore. Create. Early Learning Curriculum Solutions
3 JSC CURRICULUM MAGAZINE
23 Algebra I Overview Fundamentals 28 Algebra II Overview Fundamentals
iLikeMath K-2.0 COURSE OVERVIEW Early Learning Grades K-2 Curriculum Solutions Explore. Create. Learn about the world around them in Math creativity, and critical-thinking skills. Grade K. Numbers Students will memorize addition facts up through the number 10 and will be able to identify what numbers come before and after any number from 1 to 100. Students will also begin to learn about subtraction, complete one-step story problems with addition, and recognize the largest and smallest numbers from a set of numbers. 1.0 & 2.0 Overview Learning iLikeMath becomes “fun� with the variety of teaching techniques incorporated in the iLikeMath lesson plans! Rhymes, games, songs, handling objects, simulations, oral problems, and other techniques may make iLikeMath their favorite classroom instruction. And how they will learn! Thinking Cap sections and oral combination practice build mental skills and develop higher-level thinking.
Benefits Ease of use. This easy-to-use volume includes bold headings, charts, numbered steps, diagrams and illustrations, and a contents page. Find just what you need quickly.
Course overview.
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A “scope and sequence” chart gives you a sequential overview of concepts covered in the 170 lessons. You can know where you are headed! Clear, simple instructions. Even a first-year teacher can seem like an experienced one with these clear instructions for preparation, review, procedures, and application! Includes teaching tips, time allotted, and wording and specific examples to enable you to communicate new concepts effectively and efficiently. Features to make learning fun. Students love rhyme! Fun poems and songs make learning new concepts a breeze. And our 50+ practice/review games and activities incorporated into lessons make your students want to learn.
© 2015, 2017 iLikeMath, Inc.
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iLikeMath 3.0 COURSE OVERVIEW iLikeMath 3.0 is a full-year elementary math course focusing on number skills and numerical literacy. In it, students will gain solid experience with number theory and operations, learning how to apply these in measurement situations. This course also integrates geometric concepts and skills throughout the units, as well as introducing students to statistical concepts. By the end of the course, students will be expected to do the following: • • • • • • •
Understand place value and know how to compare and order numbers. Perform addition and subtraction, carrying and borrowing on whole numbers. Know basic multiplication facts. Understand representations in fraction and mixed number forms. Understand concepts of likelihood and basic probability. Understand concepts of shape, symmetry, and perimeter. Understand measurement concepts, including time and temperature. Understand representations using decimals and money.
Required Resources Some assignments in this course require the use of resources that must be supplied by the user. These outside resources are listed by assignment. MATHEMATICS 3.0 Unit Assignment Title Supply List All Assignments Scratch paper © 2015, 2017 iLikeMath, Inc. 6
iLikeMath 4.0 COURSE OVERVIEW iLikeMath 4.0 is a full-year elementary math course focusing on number skills and numerical literacy. In it, students will gain solid experience with number theory and operations, including decimals and fractions. This course also integrates geometric concepts and skills throughout the units, teaches measurement skills, and introduces students to statistical concepts.
By the end of the course, students will be expected to do the following: • • •
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Perform all four operations on whole numbers. Compare and order numbers, using place value and rounding. Add and subtract fractions and decimals. Understand measurement concepts, including the metric system. Calculate perimeters and areas of regular plane shapes. Represent data on varied statistical charts.
Required Resources Some assignments in this course require the use of resources that must be supplied by the user. These outside resources are listed below by assignment.
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iLikeMath 4.0 Unit Assignment Title
Supply List
All Assignments
Scratch Paper
10. Project: Collecting Data
4 small paper bags, large glass jar assorted objects of 4 different colors.
10. Project: Predicting Data
4 small paper bags, One large glass jar assorted objects of 4 different colors.
Š 2015, 2017 iLikeMath, Inc.
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iLikeMath 5.0 COURSE OVERVIEW iLikeMath 5.0 is a full-year elementary math course focusing on number skills, mathematical literacy, and geometric concepts. Students will gain solid experience with number theory and operations, including whole numbers, decimals, and fractions. In addition, students will develop their understanding of measurement and two- and three- dimensional figures. This course also integrates mathematical practices throughout the units, as well as introducing students to algebraic, statistical, and probability concepts. In this course, students will be taught the following: Place Value, Addition, and Subtraction • • • • •
Adding and subtracting of decimals and fractions Comparing and ordering whole numbers Determining rules for number patterns Mental math Rounding and estimating
Multiplying Whole Numbers and Decimals • • • •
Estimating whole number products Multiplying decimals Multiplying whole numbers Properties of multiplication
Dividing Whole Numbers and Decimals • • • •
Dividing with money Dividing whole numbers and decimals Estimating quotients Interpreting remainders
Algebra and Graphing • Coordinate plane • Expressions 9
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Graphing functions Integers Numerical patterns in tables and graphs Order of operations Scatterplots
Measurement • • • • • • •
Capacity Density Length Mass Time and temperature The Metric System Weight
Factors and Fractions • • • • • • • • •
Comparing fractions and decimals Equivalent fractions Factors Fractions Greatest Common Factor/Least Common Multiple Improper fractions and mixed numbers Prime factorization Rounding fractions Simplifying fractions
Fraction Operations • • • • •
Adding and subtracting fractions Adding and subtracting mixed numbers Estimating sums and differences Multiplying mixed numbers Multiplying whole numbers and fractions
Data Analysis and Probability • • • • • • • • •
Bar/Line Graphs Choosing the right graph Collecting data and frequency tables Line plots Listing outcomes Making predictions Measures of central tendency Probability Stem-and-Leaf plots
Geometry • Angles • Circles 10
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Geometry terms Polygons Quadrilaterals Making predictions Similar and congruent figures Solid figures Symmetry Transformations Triangles
Perimeter, Area, and Volume • • • • • • • • • •
Perimeter, Area, and Volume Area Circumference Parallelograms Polygons Regular polygons Squares and rectangles Surface area Triangles Volume
Financial Literacy • Exploring your finances.
© 2015, 2017 iLikeMath, Inc.
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iLikeMath 6.0 COURSE OVERVIEW iLikeMath 6.0 is a full-year elementary math course focusing on number skills and numerical literacy, with an introduction to the number skills needed for algebra. In it, students will gain solid experience with number theory and operations, including decimals and fractions. This course also integrates geometric concepts and skills throughout the units, as well as introducing students to statistical and probability concepts. By the end of the course, students will be expected to do the following: • • • • • • •
Perform all four operations on whole numbers, decimals, and fractions. Factor numbers completely and find greatest common factors. Convert between fractions, decimals, and percentages. Represent numbers with exponents. Calculate perimeters and areas of regular plane shapes and measure angles. Plot ordered pairs on coordinate grids. Represent data on statistical charts, including picture, bar, line, and circle graphs.
Calculate probabilities and make predictions. Required Resources. Some assignments in this course require the use of resources that must be supplied by the user. These outside resources are listed below by assignment. iLikeMath 6.0 Unit
Assignment Title
All
All Assignments
© 2015,
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2017 iLikeMath, Inc.
Supply List • Scratch Paper • Calculator
iLikeMath 7.0 Fundamentals COURSE OVERVIEW iLikeMath 7.0 Fundamentals is designed to prepare junior-high students for Prealgebra. This course focuses on strengthening needed skills in problem solving, number sense, and proportional reasoning. It also introduces students to integers, equations, and geometric concepts. Students will begin to see the "big picture" of mathematics and learn how numeric, algebraic, and geometric concepts are woven together to build a foundation for higher mathematical thinking. •
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Integers: Students will learn how to locate, add, subtract, multiply, and divide integers to solve word problems, as well as compare integers using absolute value and the order of operation. Fractions: Students will understand how fractions can be written into other forms without changing their value, and how to add, subtract, multiply, and divide fractions. Decimals: Students will explore how to rewrite fractions as decimals, and how to use decimals to solve real-world problems. Patterns and Equations: Students will learn how to translate words into equations and use them to solve number patterns. Ratios and Proportions: Students will explore how to use ratios to compare numbers, solve proportions, and convert between percent, decimals, and fractions. Probability and Graphing: Students will be able to determine the probability of an event, and if they are independent or dependent events, as well as create a graph of an equation Data Analysis: Students will learn how to interpret statistics using stem-andleaf plots, histograms, and other graphical means. Geometry: Students will explore how points, lines, and planes interact and how to solve equations using their information. Measurement and Area: Students will learn about finding perimeters and areas of different polygons, and using the Pythagorean theorem to solve problems.
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Surface Area and Volume: Students will explore three-dimensional figures and how to find their surface area, volume of them. Curriculum Content and Skill Focus Unit 1: Integers
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Locate integers on the number line. Determine the absolute value of a number, and use it in an inequality statement. Add, subtract, multiply, and divide integers, both of same and different signs Identify the associative, commutative, and identity properties. Use the associative, commutative, distributive, and identity properties to simplify expressions. Use the order of operations, and exponents to simplify expressions.
Unit 2: Fractions •
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Convert between mixed numbers and improper fractions. Identify equivalent fractions, and mixed numbers. Identify fractions written in simplest form, and the reciprocal of a given fraction. Use a factor tree to find the prime factorization of a number. Find the GCF and LCM of a set of numbers. Add, subtract, multiply, and divide fractions with like and unlike denominators, and mixed numbers.
Unit 3: Decimals •
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Recognize the decimal place value and put groups of decimals in ascending and descending order. Round decimals to specified place values, and distinguish between terminating and repeating decimals. Add, subtract, multiply and divide decimals. Calculate the product of two decimal numbers, of a whole number and a decimal number, and the quotient of two decimal numbers. Interpret and write numbers in scientific notation.
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Identify and convert metric units using multiplication or division.
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Unit 4: Patterns and Equations • • • •
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Use a variable to represent an unknown number. Translate between word sentences and mathematical equations. Evaluate expressions for specific variables, and substitute values in for variables in an expression. Identify arithmetic and geometric sequences, and find the next term in the sequence. Translate a verbal phrase to a mathematical expression, and word problems into twostep equations and then solve. Solve equations using addition, subtraction, multiplication, division, and mental math. Solve two-step equations using the four basic operations. Unit 5: Ratios and Proportions Convert between customary units, and units in the metric system. Use proportions to find missing lengths. Convert fractions and decimals to percent, and percent to fractions and decimals. Find the percent of a number, and calculate a percent of change. Solve percent problems using a proportion or an equation. Compare ratios using unit rates. Write and solve proportions. Unit 6: Probability and Graphing
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Determine the theoretical and experimental probability of an event. Use the counting principle to find the sample space. Determine if events are independent or dependent, and determine the probability of independent and dependent events. Use a table to graph a linear equation. Given a graph of a linear function, write the equation, and determine the slope of the line. Determine if a function is a direct variation, and identify the slope of the direct variation.
Unit 7: Data Analysis • • •
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Determine the mean, median, mode and range of a set of data, and decide which measure of central tendency should be used in a situation. Determine the effect of outliers on an average, and on the range and the interquartile range. Interpret and construct a stem-and-leaf plot, or a box-and-whisker plot. Construct and interpret a histogram from a stem-and-leaf plot or a frequency table. Interpret and construct line, bar, and double bar graphs, and use them to make predictions about the data.
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Determine the percent and degree measures of sections on a circle graph. Construct and interpret circle graphs, and scatter plots. Unit 8: Geometry
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Measure angles using a protractor, and identify special pairs of angles. Use angle properties to determine missing angle measures. Determine the measure of an interior angle of a regular polygon. Inscribe regular polygons in circles using a protractor, compass, and straight edge. Identify and classify types of triangles and quadrilaterals, and find missing angle measures. Identify corresponding parts of similar and congruent figures, and use them to solve problems. Determine if a figure has line or rotational symmetry. Determine the coordinates of an image following a reflection, translation, or compound transformation. Unit 9: Measurement and Area
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Calculate the perimeter of a polygon, and use its perimeter to find a missing side length. Calculate the circumference of a circle, and use the circumference of a circle to find the radius or diameter. Calculate the perimeter of a composite figure, and use the area of a composite figure to find a missing measurement. Calculate the area of a triangle, trapezoid, circle, or composite figure. Determine the area of a figure after its dimensions have changed. Calculate the square of a number, and the square root of a number. Apply the Pythagorean theorem to solve for a missing length of a side of a right triangle, and solve word problems. Unit 10: Surface Area and Volume
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Classify and identify solid figures. Explain what surface area and volume mean, and find the surface area or volume of a solid figure. Use a formula to find the surface area or volume of a cylinder, rectangular prism, or triangular prism. Determine how the surface area or volume of a solid figure is affected by a change in the dimensions. Find the surface area or volume of a solid figure given a change in the dimensions.
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Required Resources
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Some assignments in this course require the use of resources that must be supplied by the user. These outside resources are listed below by assignment.
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iLikeMath 7.0 Unit
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Assignment Title
Supply List
All Assignments
Scratch Paper Pencil Paper
8 Projects Inscribed Polygons Protractor
Compass Ruler
© 2015, 2017 iLikeMath, Inc.
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iLikeMath 8.0 Fundamentals COURSE OVERVIEW iLikeMath 8.0 Fundamentals is an introductory algebra course designed to prepare juniorhigh school students for Algebra I. The course focuses on strengthening needed skills in problem solving, integers, equations, and graphing. Students will begin to see the "big picture" of mathematics and learn how numeric, algebraic, and geometric concepts are woven together to build a foundation for higher mathematical thinking. • •
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The Real Number System: Student will explore different properties of numbers, and how to use them to simplify expressions and formulas to make computations easier. Modeling Problems in Integers: Student will translate and solve one-step equations, or two- step equations in context, and check solutions for reasonableness, using the order of operations, and by substituting values for variables. Modeling Problems with Rational Numbers: Student will add, subtract, multiply, and divide decimals, fractions, and mixed numbers with variables, likes, and unlike denominators to solve one and two-step word problems. Proportional Reasoning: Student will convert between fractions, decimals, and percent, and compare them, and identify similar and congruent figures and their corresponding parts, and solve for missing measures. More with Functions: Student will identify the parts of a line or quadratic equation and be able to graph it, and explore arithmetic and geometric sequences, as well asexponential growth and decay. Measurement: Student will explore relationships between sets of lines and the angles they create, understand and use the Pythagorean theorem, and identify characteristics of polygons. Plane Geometry: Student will determine how to calculate areas of common polygons, identify different transformations and how to determine the type and original image location. Measures of Solid Figures: Student will calculate surface area and volume of different objects, and solve for missing measures of 3 dimensional figures when given surface area or volume, and explain the relationship between surface area and
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volume. Data Analysis: Student will identify the mean, median, mode, range, lower quartile, and upper quartile of different data sets and construct the best display of the information. Probability: Student will identify all the possible outcomes of a given situation using combinations, permutations, probability, And determine if events are dependent or independent.
Curriculum Content and Skill Focus Unit 1: The Real Number System • • • • • •
Identify rational, irrational numbers, variables, terms or expressions. Use substitution, and order of operations to simplify expressions and formulas. Evaluate numerical expressions containing absolute value symbols, positive bases and positive or negative exponents. Use number properties to make computation easier. Write numbers given in standard form in scientific notation and given in scientific notation in standard form. Evaluate perfect square roots, determine if a square root is a rational or irrational number, and simplify square. Roots that are not perfect squares.
Unit 2: Modeling Problems in Integers •
Translate written statements into math symbols, expressions, and equations. Translate and solve one-step equations, or two-step equations in context, and check solutions for reasonableness. • Identify the inverse operation, or property of equality needed to solve a one-step equation. Recognize a function represented in various ways: rule, table, mapping, etc., and complete a t-chart for a function rule and graph the function • Use ordered pairs to graph a function, and answer questions based on a graph by reading and interpreting the graph. • Add, subtract, multiply, and divide integers within the context of a word problem. Evaluate expressions using the order of operations, and by substituting values for variables. Unit 3: Modeling Problems with Rational Numbers •
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Express the prime factorization of composite numbers and terms in exponential form. Determine the greatest common factor using prime factorization, and use it to solve problems. Reduce positive and negative fractions, with and without variables. Find the least common multiple (LCM), and the least common denominator (LCD) of two or more terms.
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Convert between improper fractions and mixed numbers. Add, subtract, multiply, and divide decimals, fractions, and mixed numbers with variables, likes, and unlike denominators to solve one and two-step word problems. Check solutions in equations and determine their reasonableness by estimating. Write and solve one-step and two-step inequalities and graph the solution set on a number line.
Unit 4: Proportional Reasoning •
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Use proportional reasoning to solve problems, and determine unit rate or unit price. Recognize a relationship as a direct variation, calculate the constant of variation, and use the constant of variation to determine the equation of a direct variation. Calculate a missing value in a direct variation problem, and a percent problem. Convert between fractions, decimals, and percent, and compare them. Write and solve a multi-step word problem involving percent. Solve problems that require unit conversions of measurements. Identify similar and congruent figures and their corresponding parts, and solve for missing measures.
Unit 5: More with Functions • • •
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Rewrite formulas to solve for a specific variable, and solve for a missing value. Identify and combine like terms in an algebraic expression, and use the distributive property to simplify algebraic expressions and solve equations. Find the slope of a line on a graph, identify the x-intercept and the y-intercept of a line, graph a line from its intercepts and identify the type of slope from a graph. Identify equations in slope-intercept form, identify the slope and the y-intercept, and graph the line. Identify a quadratic equation and an absolute value equation from graphs, and graph quadratic and absolute value functions from t-charts. Determine if a sequence is arithmetic, or geometric, find the common difference in an arithmetic sequence, or the common ratio in a geometric sequence, extend the sequence, and use a formula to calculate the nth term of the sequence. Identify exponential growth and decay from both an equation and a graph, and graph exponential functions.
Unit 6: Measurement •
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Identify angles by their measure, classify pairs of angles, and find the measure of an angle. Identify a transversal, the angles it creates, and find the measure of those angles.
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Identify the relationships between, and find the measures of, angles created by a transversal across parallel lines. Classify and find the measures of angles and arcs of circles. Identify which figures are polygons, classify them as regular, irregular, concave or convex, and name them based on their properties. Identify the different parts of polygons (sides, vertexes, diagonals, interior angles, and exterior angles), and the name of the quadrilateral by its properties. Find the interior and exterior angle measures of polygons, and recognize the relationship that exists between the number of sides of a polygon and the sum of the measures of its interior angles. Classify a triangle by its sides or by its angles, and solve a contextual problem using the Pythagorean theorem.
Unit 7: Plane Geometry • • • • • • • •
Find the circumference or perimeter of a figure, and find unknown dimensions of a figure by solving algebraic equations. Calculate the area of a parallelogram, triangle, or trapezoid, and find a missing measure in a parallelogram, triangle, trapezoid, or circle. Recognize the common shapes that make up a composite figure, and determine the area of a composite figure using common area formulas. Identify lines of symmetry in shapes, and write equations of lines of symmetry for shapes in a coordinate plane. Find the distance, and midpoint between two points, and solve word problems using distance and midpoint. Identify a transformation as a reflection, translation, or rotation, and determine the coordinates of an image or pre-image. Identify a tessellation, and know which regular polygons will tessellate. Identify the scale factor for a dilation, determine whether a dilation is an enlargement or a reduction, and find the coordinates of an image or pre-image point in a dilation.
Unit 8: Measures of Solid Figures • • • • • • 21
Classify a three-dimensional figure by its characteristics. Identify the relationship that exists among the number of faces, edges, and vertices of a solid figure. Calculate the surface area and volume of rectangular prisms, triangular prisms, pyramid, cone, sphere, and cylinder using a net, and its formula. Solve for a missing measure when given the surface area or volume and other dimensions of 3-dimensional objects. Calculate the surface area and volume of a composite figure. Define the relationship that exists between the volume of a cone and the
volume of a cylinder with the same dimensions. Unit 9: Data Analysis • • • • •
Interpret a tally chart to identify trends and make predictions about the general population. Identify the mean, median, mode, and range for a set of data. Construct and interpret a bar graph, circle graph or line graph from a set of data. Construct and interpret box-and-whisker plots, stem-and-leaf plots, scatter plots, frequency tables, and histograms from sets of data. Identify the lower quartile, upper quartile, and the median from sets of data. Identify a line of best fit for a scatter plot. Identify how a graph is misleading and changes needed to correct a misleading graph. Choose the correct graph to display information.
Unit 10: Probability • • •
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Identify all the possible outcomes for a given situation. Use tree diagrams, permutations, combinations to identify probabilities. Define theoretical probability, fairness, and odds. Use the theoretical probability to predict experimental probability. Find the probability of a disjointed or an overlapping event. Identify if events are independent or dependent, and find the probability of dependent and independent events.
Required Resources Some assignments in this course require the use of resources that must be supplied by the user. These outside resources are listed by assignment. Modeling Problems in Integers: Student will translate and solve one-step equations, or two- step equations. iLikeMath 8.0 Unit Assignment Title Supply List All Assignments
Scratch Paper
© 2015, 2017 iLikeMath, Inc.
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iLikeMath Algebra I Fundamentals COURSE OVERVIEW iLikeMath Algebra I Fundamentals is a full year, high school credit course that is intended for the student who has successfully mastered the core algebraic concepts covered in the prerequisite course, iLikeMath 8.0 Fundamentals. Within the Algebra I Fundamentals course, the student will explore basic algebraic fundamentals such as evaluating, creating, solving and graphing linear, quadratic, and polynomial functions. • •
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Foundations of Algebra: Student will identify different real number properties, and how to use them to solve algebraic expressions. Linear Equations: Student will translate word problems into algebraic equations, and solve them using real number properties, converting between fractions, decimals, and percent. Functions: Student will understand the characteristics of functions, how to plot them, how to derive their equations, and determine what type of function a graph represents. Inequalities: Student will write, graph, and solve inequalities using real number properties. Linear Systems: Student will determine the solution of a pair of linear equations, using the addition method, substitution method and matrices. Polynomials: Student will add, subtract, multiply, and divide monomials and polynomials, as well as factor polynomials, using several different methods. Exponential and Radical Functions: Student will simplify powers of products, a power raised to a power, and quotients of powers, using the rule of exponents, and add, subtract, multiply, and divide radical expressions to solve equations. Quadratics: Student will identify, write, and graph various triangle, circle and quadratic equations and inequalities using the Pythagorean theorem, and by factoring, completing the square, and using the square root method. Rational Expressions: Student will add and subtract fractions with like and unlike denominators, solve proportions, equations and inequalities containing rational expressions, and solve different word problems using rational equations.
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Probability and Statistics: Student will determine the central tendencies of a given data set, as well as evaluate probability of possible outcomes using multiple methods.
Curriculum Content and Skill Focus Unit 1: Foundations of Algebra •
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Identify a variable expression and its components: variable, coefficient, constant. Translate expressions written as English phrases into algebraic expressions, and interpret algebraic expressions. Convert terminating, or repeating decimals to fractions. Identify the additive identity and multiplicative inverse of a number.
Add, subtract, multiply, or divide signed numbers. • Identify the commutative and associative properties of addition and multiplication, and the distributive property. • Simplify algebraic expressions by using real number properties, absolute value symbols, order of operations, removing parentheses and combining like terms. Unit 2: Linear Equations • • •
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Translate sentences into algebraic equations. Use the addition and multiplication properties of equality to solve equations. Solve two-step equations by using both the addition and multiplication properties of equality. Solve multi-step equations by combining like terms on one or both sides of the equation first. Solve a word problem by writing and solving a related equation. Solve word problems with more than two unknowns using an equation. Convert between fractions, decimals, and percent. Calculate percent increase and decrease. Solve investment word problems, and mixture word problems.
Unit 3: Functions • •
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Write an equation to express a relationship between coordinates in the plane, and find the domain and range of a relation. Identify and evaluate a function for a value of the dependent variable using a function rule, graph, or table, and find the value of the independent variable of a function given the dependent variable. Identify the graph of a function, and graph a function from its equation. Identify an arithmetic sequence, find the common difference, extend an arithmetic sequence, and find the nth term Identify a function as being a direct variation, determine the constant of variation, and
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write the equation of a direct variation. Write a linear equation in general form, in slope-intercept form, and graph it by finding solutions of the equation. Identify the graph of an absolute value function in the form y = |x| + c, and y = |x + c|. Find the slope of, and write an equation for, a line parallel, or perpendicular, to a given line.
Unit 4: Inequalities • • •
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Use set builder notation to express a set. Graph a set of numbers on the number line, and write the set that is represented by a graph. Solve an inequality, and graph the solution set of an inequality. Determine if a value is a solution of an inequality. Translate phrases into inequality statements, and solve an inequality using the multiplication property of inequality. Write a compound inequality as a union or intersection, graph it, and solve it. Solve and graph the solution sets of absolute value equations, and inequalities.
Unit 5: Linear Systems • • •
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Identify, and determine, a solution of a linear system graphically, and determine the number of solutions of a linear system. Identify if a linear system is consistent, inconsistent, or equivalent. Determine if a point, or ordered pair lies in the solution set of a system of linear inequalities. Solve a system of two linear equations by the addition method, and substitution method. Find the system determinant, x determinant, and y determinant for a system of two linear equations. Solve a system of two linear equations algebraically using determinants, and containing fractional coefficients. Write a system of linear equations to represent and solve a word problem, and coin and pricing problems. Unit 6: Polynomials Recognize a polynomial and the number of terms it has, and write a polynomial in descending order. Add or subtract polynomials using a horizontal or vertical format. Find products of binomials using the FOIL method, and Use shortcuts for squaring a binomial and finding the difference of two squares. Divide monomials by monomials. Multiply and divide polynomials with more than one term by a monomial, and using long division. Find the greatest common factor of two or more monomials, or a polynomial, using prime factorization, and factor out the GCF of a polynomial.
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Factor four-term polynomials by grouping, and trinomials into a product of binomials. Factor perfect square trinomials, the difference of two perfect squares, and a polynomial into prime factors.
Unit 6: Exponential and Radical Functions •
Evaluate and simplify expressions with zero, negative, and integer exponents. Convert between numbers in standard form and scientific notation. • Simplify powers of products, a power raised to a power, and quotients of powers, using the rule of exponents. • Identify, find the common ratio, and extend to the nth term a geometric sequence. Simplify square roots that have a perfect square factor, and radicals with fractional. Rationalize a fraction. • Add, subtract, multiply, and divide radical expressions. Solve equations with irrational solutions. Unit 7: Quadratics • • •
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Determine if the given sides form a right triangle, and use the Pythagorean theorem to find the missing length of a side of a right triangle. Find the distance between two points, and find the coordinates of the midpoint of a line segment given the endpoints. Write the equation of a circle whose center is at the origin, determine if a point lies on a circle with center at the origin, and Find the center of a circle given the endpoints of a diameter. Identify a quadratic equation, and write a quadratic equation in general form. Find ordered pairs on the graph of a quadratic function, and identify the solutions of a quadratic equation from the related parabola. Write the vertex form of a quadratic equation from the given graph, and identify the vertex of a parabola from the equation. Identify and graph the solution set of a quadratic inequality, and determine if a point is a solution of a quadratic inequality. Solve quadratic equations having rational or irrational roots by factoring, completing the square, and using the square root method.
Unit 8: Rational Expressions • •
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Reduce, multiply, and divide rational expressions. Add and subtract fractions that have a common denominator. Determine the lowest common denominator of rational expressions. Add rational expressions with unlike denominators. Solve proportions, and complex fractions.
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Solve equations containing rational expressions by clearing fractions. Solve inequalities containing rational expressions with variables in the numerators. Solve time, distance, mixture, and rate problems using rational equations. Solve work and pipe flow problems.
Unit 9: Probability and Statistics •
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Find the mean, median, mode, the range and inter-quartile range of a given set of data. Calculate quartiles of a data set, identify outliers of a data set and determine how they affect a measure of central tendency. Interpret data presented in a histogram, a frequency table, a stem-and-leaf plot, box-and- whisker plot, or a graph. Collect, organize, and analyze data, and make predictions based on data. Determine the number of outcomes, or sample space, of an event using a table, a tree diagram, or using the multiplication principle. Evaluate numeric expressions containing factorial notation. Evaluate and apply the permutation formula, and combination formula. Determine the theoretical probability of a single event, or compound events.
Required Resources Some assignments in this course require the use of resources that must be supplied by the user. These outside resources are listed below by assignment. Online Scientific Calculator. (https://calculatorpi.com/) ALGEBRA I Unit
Assignment Title
All
Assignments Supply List Scratch Paper/Notebook 3,5 Various Assignments Graph Paper 4,5,9 Various Assignments Printer
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iLikeMath ALGEBRA II FUNDAMENTALS COURSE OVERVIEW iLikeMath Algebra II Fundamentals is a full-year, high school math course intended for the student who has successfully completed the prerequisite course Algebra I. This course focuses on algebraic techniques and methods in order to develop student understanding of advanced number theory, concepts involving linear, quadratic and polynomial functions, and pre-calculus theories. This course also integrates geometric concepts and skills throughout the units, as well as introducing students to basic trigonometric identities and problem solving.
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Set, Structure, and Function: Student will review the properties of sets and functions, determine the domains, ranges and inverses of functions, and simplifying expressions by combining like terms, exponent rules for multiplication and division and exponents. Numbers, Sentences, and Problems: Student will solve linear equations and inequalities using multiplication, addition, and distributive properties, graph absolute value, and compound equations and inequalities, and problems involving rate, distance, and time. Linear Equations and Inequalities: Student will determine the slope of a line and use that information to write an equation, compare lines, and solve a system of equations using the addition property of equality, the substitution property of equality, and graphical methods. Polynomials: Student will factor trinomials using the difference of two squares, the product of the sum of two perfect cubes, perfect square trinomials, and the difference of two cubes, and solve problems involving direct variation, inverse variation and joint or combination variation. Algebraic Fractions: Student will reduce fractions, add and subtract fractions, and change mixed numbers and complex fractions to simple algebraic fractions, and solve equations that contain algebraic fractions, variables in the denominator of a fraction, and mixture problems. Real Numbers: Student will evaluate and simplify radical expressions and fractional exponent expressions, and solve quadratic equations by the
factoring method, and by completing the square. • •
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Quadratic Relations and Systems: Student will determine the major components of different conic sections, write their equations, solve and graph them. Exponential Functions: Student will evaluate and simplify equations in logarithmic form, exponential form, graph them, and use matrices to solve a system of equations.
Counting Principles: Student will differentiate between a finite and an infinite series, and between an arithmetic and a geometric series, calculate the number of permutations or combinations of elements from a set of n elements, and use the counting principle, conditional probability, and multiplication principle to calculate the probability of complex events Curriculum Content and Skill Focus
Unit 1: Set, Structure, and Function • • • • • • •
Count the number of elements in a set, find the subsets of a set, and find the intersection or union of two sets. Review the axioms and properties of Algebra, the mathematical operations. (+, -, • , /), the distributive property, and order of operations. Identify functions and relations, and tell the difference between them. Find the domain and range of a function, and determine whether or not a given graph represents a function. Evaluate a function at any point, and find the inverse of a function or set of ordered pairs. Evaluate expressions, including negative and zero exponents, and simplify them, combining like terms. Review exponent rules for multiplication and division of like bases, and exponentiation of powers.
Unit 2: Numbers, Sentences, and Problems • • • • • •
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Review addition and multiplication of signed numbers. Solve linear equations and inequalities using multiplication, addition, and distributive properties. Differentiate between the multiplication property of inequality and the multiplication property of equality. Express the solutions of single variable inequalities using a line graph. Solve and graph absolute value, and compound equations and inequalities. Solve problems involving rate, distance, and time.
Unit 3: Linear Equations and Inequalities • • • • • • •
Identify linear and nonlinear equations. Determine if two lines are parallel or perpendicular, or if a line is horizontal or vertical. Write the point-slope form of parallel lines, perpendicular lines, a line given the slope and a point on the line, and a line that passes through two given points. Write equations of a line in general form, point-slope, and slope-intercept form. Find the x and y intercepts by inspecting the general form of a line. Solve a system of two equations by using the addition property of equality, the substitution property of equality, and graphical methods. Graph the solution sets for linear equations or inequalities.
Unit 4: Polynomials • • • • • •
Multiply binomials and trinomials. Find special products such as the perfect square trinomial. Factor trinomials using the difference of two squares, the product of the sum of two perfect cubes, perfect square trinomials, and the difference of two cubes. Add and subtract polynomials, and perform long division of polynomials. Use shorthand 'synthetic' division to divide two polynomials. Solve word problems that involve direct variation of two quantities, inverse variation of two quantities, and joint or combination variation of three quantities.
Unit 5: Algebraic Fractions • • • • • •
Simplify and evaluate algebraic expressions Reduce fractions, add and subtract fractions, and change mixed numbers and complex fractions to simple algebraic fractions. Add, subtract, multiply and divide algebraic expressions. Find the common denominator of algebraic fractions. Solve equations that contain algebraic fractions, variables in the denominator of a fraction, and mixture problems. Solve proportions of algebraic equations that have one variable.
Unit 6: Real Numbers • • • 30
Write the fractional equivalent of a rational decimal number. Change a radical expression to the equivalent expression with fractional exponents. Evaluate and simplify radical expressions and fractional exponent expressions.
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Use conjugates to rationalize the denominator of an algebraic expression. Solve quadratic equations by the factoring method, and by completing the square. Determine the sum and product of the roots of a quadratic equation. Find the discriminant of a quadratic equation, and use it to determine what kinds of solutions a quadratic equation has.
Unit 7: Quadratic Relations and Systems • • • • •
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Use the distance formula to find the distance between two points. Find the radius and center of a circle from its equation, and write the equation of a circle, given its center and radius. Find the length of the major axis, length of the minor axis, foci, and equation of an ellipse, and graph an ellipse given an equation. Find the directrix, and focus of a given parabola, and graph it. Write the equation of a hyperbola, and graph it. Identify a quadratic equation as a circle, parabola, hyperbola, or ellipse. Solve and graph a system of equations or inequalities. Find the conic section, and its equation, that represents a physical situation.
Unit 8: Exponential Functions • • • • • • •
Evaluate and simplify exponential functions, and expressions with fractional exponents. Express an exponential equation in logarithmic form, and a logarithmic function in exponential form. Evaluate logarithmic functions. Express decimal numbers in scientific notation. Use change of base formula to evaluate common logarithms, solve exponential equations and graph them. Identify entries in a matrix by row and column, and use the matrix method to solve a system of equations. Perform addition or subtraction of matrices.
Unit 9: Counting Principles • • • • • • 31
Indicate the general term of a sequence, and find the nth term. Differentiate between a finite and an infinite series, and between an arithmetic and a geometric series. Use summation notation, and evaluate factorial expressions. Calculate the number of permutations or combinations of r elements from a set of n elements. Demonstrate knowledge of the pattern of Pascal's triangle, and use it to find powers of binomials. Use the counting principle, conditional probability, and multiplication
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principle to calculate the probability of complex events. Define independent and dependent events.
Required Resources Some assignments in this course require the use of resources that must be supplied by the user. These outside resources are listed by assignment. ALGEBRA II Unit Assignment Title All
All Assignments
Supply List Scratch Paper/Notebook Scientific or Graphing Calculator
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