Sept. PREREQUISITE SKILLS: What basic skills are necessary for you to be successful in Pre-Algebra? Vocabulary Round, Estimate, Operations, Integer, Reciprocal, Percent, Place value, Evaluate, Solve, Estimation, Exponent, Grouping symbols, Mean, median, mode, range, Absolute value Variable, Square roots, Slope, Expression, Equation, Formula, Inequality, Property, Coordinate pair LCD, Rate All Gr 6 standards Gr 7: 7.RP.2a 7.RP.3 Gr 8: 8.NS.1 8.NS.2 8.EE. 7 8.G.1 8.G.9 High school: G-GMD.1 G-GMD.3 N-Q.1 Summer Work Review: Calculate multi-digit operations with real numbers Solve %- part-whole problems Solve % tax/total cost problems Evaluate algebraic expressions Simplify with order of operations Find measures of central tendency and range Evaluate absolute values Simplify square roots Find simple probabilities Find circumference of a circle and perimeter of a parallelogram Know properties of 3D figures Use similar triangles to find missing sides Find lines of symmetry given a figure Find missing angles by knowing sum of angles in a triangle and quadrilateral Find missing angles given parallel lines and transversals Calculate volume and surface area of prisms Plot in coordinate plane and use translations to create images Smartboard Gallery: Grade 6 folder AIM: Coordinate Plane Basics (Summer Work packet) Summer Work Packet
s Sept/ Oct UNIT 1- OVERVIEW OF REAL NUMBER SYSTEMS: What is the real number system and how do these numbers related to each other? Rational, Irrational, Radical, Integers, Whole numbers, Terminating decimal, Repeating decimal, Identities Commutative, Associative, Inverse Distributive 7.NS.1d 7.NS.2c 7.NS.2d 7.NS.3 8.NS.1 8.NS.2 7.EE.1 7.EE.3 8.EE.2 High School: A-REI.1 Identify domain/set a real number belongs to. Identify a rational number Identify an irrational number Simplify perfect square roots and identify if a radical is a rational or irrational number Order all real numbers on a number line, including integers, fractions, repeating and nonrepeating decimals Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers Apply the properties of real numbers: Commutative, associative, inverses, identities, multiplication property of zero, distributive Identify the property being applied to real numbers. Simplify numerical expressions by using the order of operations. Evaluate expressions by showing several algebraic steps, including the replacement of a variable with a value. Smartboard Gallery: Grade 7 Folder Algebra Algebraic Expressions, Properties of Algebra 5.2 Rational Numbers 9.2 The Real Number System 1.4 Properties 1.2 Numbers and Expressions 1.3 Variables and Expressions 3.1 The Distributive Property 9.1 Squares and Square Roots 3.2 Simplifying Algebraic Expressions Go Math! Chapter Unit 1 Common
Oct UNIT 2- SIMPLIFYING AND WORKING WITH REAL NUMBERS: How can we use real numbers in algebra and in the real world? Evaluate, numeric expression, algebric expression, integer, real number, estimate, value 7.NS.1a 7.NS.1b 7.NS.1c 7.NS.2a 7.NS.2b 7.NS.3 Simplify numerical expressions involving the addition, subtraction, mulitplication and division of integers, and use them in problem solving situations Simplify real numbers by finding the absolute value, evaluating exponents, simplifying radicals and by using the order of operations Estimate square roots, and find the reasonableness of answers Add, subtract, multiply and divide real numbers, including the negative values Evaluate and simplify algebraic expressions that include all types of real numbers (absolute values, radicals, exponents, fractions, decimals, etc.) Apply the real number calculations to realworld situations Utilize graphing calculator technology to simplify numerical expressions containing squares, square roots, absolute values and negatives Math button, square/square root, Math-Num- abs( command, negative button 2.1 Integers and Absolute Values 2.2 Adding Integers 2.3 Subtracting Integers 2.4 Multiplying Integers 2.5 Dividing Integers : Go Math! Chapter Unit 2 Common
Nov./ Dec. UNIT 3- SIMPLIFYING AND SOLVING ALGEBRAIC EXPRESSIONS AND EQUATIONS: How can you solve for unknowns in real world situations? Equivalent expressions, coefficient, constant, null or empty set, identity, inequality, literal equation 7.EE.3 7.EE.4a 7.EE.4b 7.EE.4c 8.EE.7a High School: A-CED.1 A-CED.2 A-CED.4 A-REI.3 Translate verbal phrases and sentences from real world situations into one-step numerical and algebraic expressions/equations/inequalities Combine like terms using real number properties, including positive and negative values and irrationals. Apply the distributive property in real life situations with like algebraic terms, including doughnut areas. Apply inverse properties to solve one step equations and inequalities that include both positive and negative numbers Manipulate literal equations with inverse operations to solve problems in application Apply inverse properties to solve two- step equations and inequalities that include both positive and negative numbers Apply inverse and distributive properties to solve equations and inequalities with variables on both sides that include both positive and negative numbers Identify null set solutions and all real number(infinite) solutions, and apply this to problem solving situations Math button, square/square root, Math-Num- abs( command, negative button 1.2 Numbers and Expressions 1.3 Variables and Expressions 3.1 Distributive Property 3.2 Simplifying Algebraic Expressions 3.3 Solving Equations by Adding and Subtracting 3.4 Solving Equations by Multiplying or Dividing 3.5 Solving Two-step Equations 3.6 Writing Two-step Equations 7.1 Solving Equations with Variables on Each Side 7.2 Solving Equations with Grouping Symbols 7.3 Inequalities 7.4-7.6 Solving Inequalities : Go Math! Chapter Unit 3 Common
Jan. UNIT 4- APPLYING ALGEBRA: How do we analyze proportional relationships, and use them to solve real-world and mathematical problems? Ratio, rate, proportion, unit rate, rational expressions, algebraic fraction, proportional relationship, equivalent ratios, origin, discount, tax, increase, decrease, profit, mark-up, commision 6.RP.3c 7.RP.1 7.RP.2a 7.RP.2b 7.RP.2c 7.RP.2d 7.RP.3 7.EE.2 7.EE.3 Solve equations containing rational expressions and rational numbers Change real numbers to different forms by converting fractions, decimals, percents, or mixed numbers Translate mathematical situations into algebra that involves fractions, decimals and percents. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. Recognize and represent proportional relationships between quantities Decide whether two quantities are in a proportional relationship by testing for equivalent ratios in a table, graphing on a coordinate plane, or observing whether a graph is a straight line through the origin. Represent proportional relationships by equations involving discount, interest, tax, tip, commision, mark-up/profit, total cost, percent of increase/decrease, etc. Explain what a coordinate point on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0,0) and (1, r), where r is a unit rate. Use proportional relationships to solve multistep ratio and percent problems Math-Fraction command, Y=, Graph, Table buttons 5.9 Solving Equations with Rational Numbers 6.1 Ratios and rates 6.2 Using Proportions 6.4 Fraction, Decimals and Percents 6.5 Using the Percent Proportion 6.7 Using Percent Equations 6.8 Percent of Change Other Materials: Go Math! 4.8 CC Edition, Ch 5: Proportional relationship on a coordinate plane Applications with proportionsmulti-step Unit 4 Common
Feb. UNIT 5- GRAPHICAL AND NUMERICAL RELATIONSHIPS WITH ALGEBRA AND NUMBERS: What does a linear algebraic relationship look like? Sequence, arithmetic sequence, common difference, term, geometric sequence, common ratio, quadrants, function, linear equation, slope, rate of change, relation, domain, range, x- intercept, y-intercept, direct variation, constant of variation, positive/negative correlation, scatterplot 7.EE.MA.4c 8.F.1 8.F.2 8.F.4 8.F.5 Demonstrate how sequences can be used to make predictions given a list, table or algebraic expression Identify and extend Geometric sequences Write sequences as algebraic statements Review the graphing of coordinate pairs on a coordinate plane Graph algebraic relationships given a table Describe input values as a domain, and output values as a range Understand the meaning of a function Generate a table of values given an algebraic two-variable equation. Graph the relationship. Apply relations to real-word situations Create scatterplots given real-world data, and determine if the have a positive, negative or no correlation. Find slope of graphed relationships by applying rise/run Identify intercepts of a linear graph Find rates of change given problem-solving situations. Y=, Graph, Table, Trace AIM: Coordinate Plane Basics 5.10 Arithmetic and Geometric Sequences 2.6 The Coordinate System 8.1 Functions 8.2 Linear Equations in Two Variables 8.3 Graphing Linear Equations Using Intercepts 8.4 Slope 8.5 Rate of Change 1.6 Ordered Pairs and Relations 1.7 Scatterplots Unit 5 Common
Mar/ April UNIT 6- FACTORS, MONOMIALS AND BINOMIALS: How do we simplify factors and differences in algebra? Factor, divisibility, monomials, binomials, trinomials, polynomials, base, power, exponent, prime, composite, factor tree, GCF, algebraic fraction, negative exponent, standard form, scientific notation 8.EE.4 8.EE.1 8.EE.3 7.EE.4a 7.EE.MA.4c 7.EE.3 List factors of a multi-digit number by applying the divisibility rules for 2, 3, 4, 5, 6, 9, and 10 Identify monomials, binomials, trinomials and polynomials given algebraic expressions containing variables, exponents and terms Change numerical and algebraic expressions in expanded form into exponential form, and visaversa. Determine if numbers are prime or composite. Generate a prime factorization with a factor tree. Evaluate algebraic expressions containing exponents with real numbers Utilize a Venn diagram, list of factors and/or factor tree to determine GCF of a set of numbers or monomials. Solve problem solving situations by utilizing the GCF Simplify monomial algebraic fractions by using the GCF and expanded form Apply algebraic techniques to solve real-world situations. Multiply and divide monomials by examining monomials in expanded form first. Make a conjecture about a rule to determine the exponent of a product or fraction with monomials Apply the laws of exponents to simplify monomial products and quotients. Write expressions with negative exponents. Extend patterns to show negative exponent rules Rewrite and simplify expressions containing negative exponents Write, compare and order numbers written in standard form and scientific notation ^ for exponents, negative (-) exponents AIM: Greatest Integer 4.1 Factors and Monomials 13.1 Polynomials 4.2 Powers and Exponents 4.3 Prime Factorization 4.4 Greatest Common Factor 4.5 Simplify Algebraic Fractions 4.6 Multiplying and Dividing Monomials 4.7 Negative Exponents 4.8 Scientific Notation Summer Work Packet Unit 6 Common assessment
May/ June UNIT 7- PROBABILITY: How do we find the probability of an event or events? Probability, tree diagram, Fundamental Counting Principal, quartiles, range, measure of variation, interquartile range, permutation, factorial, combination, compound event, independent event, dependent event, mutually exclusive event 7.SP.4 7.SP.5 7.SP.6 7.SP.7a,b 7.SP.8a,b,c Review mean, median, mode, range, quartiles and interquartile range Review simple probability Use tree diagrams or the Fundamental Counting Principal to count outcomes Use the Fundamental Counting Principal to find the probability of an event Calculate factorials, permutations and combinations, and use them to appropriately find possible outcomes and probabilities Find the probability of independent and dependent events Find the probability of mutually exclusive events Stat, factorial, Math 12-2 Measures of Variation 12-6 Counting Outcomes 12-7 Permutations and Combinations 12-9 Probability of a Compound Event Summer Work Packet Unit 7 Common assessment LE-II, V TC- 2, 7 *Note: Courses 270 and 271 will move at different paces. Time allotments may change as the year continues. All assessments may not be given. Administration of these are based on the needs of the students.