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Humboldt Community Schools Mathematics Core Curriculum Mathematics Standard 1: Use a variety of strategies in the problem solving process. ITP Indicator A4.Demonstrate ways of performing operations A8.Use variable expressions to model situations A4.Demonstrate ways of performing operations C3.Choose a method for Solving a problem CODE K.1.2 1.1.2 1.1.3 C2.Identify extraneous or Insufficient information in Problems C3.Choose a method for Solving a problem A4.Demonstrate ways of Performing operations A8.Use variable expressions To model situations Page 1 of 51 Local Indicator Analyze and solve problems using skills and strategies Uses models (e.g., pattern blocks, tiles, or other manipulative) to represent problems. Analyze and solve problems using skills and strategies K.1.1 1.1.1 A8.Use a variable expressions to model situations BENCHMARK Draws pictures to represent problems. 2.1.1 2.1.2 2.1.3 Restate problems in own words to demonstrate understanding Uses speaking, writing and drawing to represent problem situations (e.g., translate from pictures of objects to numerical expressions). Uses models (e.g., pattern blocks, tiles, or other manipulatives) to represent problems. Uses a variety of problem solving strategies (e.g., identifying a pattern, choosing an operation, using trial and error, manipulatives, evaluating methods of solution) Explain to others the process used to solve a problem. Uses speaking, writing and drawing forms to represent problem situations (e.g., translate from pictures of objects to numerical expressions). Teacher Observation Teacher Observation Independent practice Independent practice Uses touchpoints Uses counting up, counting back Uses doubles Uses 10 to add nine Explains the process used to solve a problem to another person Uses white boards to solve a problem Uses math journal Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum 3.1.1 C3.Choose a method for Solving a problem C1.Solve single-step and multiple-step math problems C2.Identify extraneous or Insufficient information in Problems C3.Choose a method for solving a problem C1.Solve single-step and multiple-step math problems C2.Identify extraneous or insufficient information in problems C3.Choose a method for solving a problem 3.1.2 4.1.1 4.1.2 5.1.1 5.1.2 5.1.3 6.1.1 Page 2 of 51 Knows information required to solve Make tally tables to collect data for graphs problems (e.g., make organized lists or tables of information necessary). Uses a variety of problem solving Uses trial and error when creating an strategies. (e.g., identifying a pattern, invention that solves a problem choosing an operation, using trial and error, manipulatives, and evaluating methods of solution). Represent problem situations in a Draw a picture to represent problems variety of forms (e.g., translate from a Guess and check and use estimation to test diagram to a number or symbolic reasonableness expression. Explain methods and reasoning behind Work together and talk about what it is that the problem solution to determine its you need to find out reasonableness. Does your answer made sense in the end Check labels Use a variety of problem-solving strategies Make an organized list Draw pictures and diagrams Use “guess and check” Work backwards Solves a simple problem Understand basic valid and invalid Using logical reasoning arguments Predict or estimate Justify answers in verbal and written form Understand that some ways of State problems in own works to increase representing a problem are more understanding helpful than others. Distinguish between pertinent and irrelevant information Use a calculator to compare amounts and larger numbers Convert fractions into decimals Use a variety of measuring processes to Exploring angles in a triangle model and to solve problems. Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum C1.Solve single-step and multiple-step math problems 6.1.2 Understand how to break a complex problem into single parts Finding area of irregular figures A9.Explore numerical patterns C3.Choose a method for solving a problem C2.Identify extraneous or insufficient information in problems 6.1.3 Uses multiple methods to solve mathematical problems Solving story problems 6.1.4 Construct informal logical arguments to justify reasoning processes Solving story problems 7.1.1 Uses a variety of strategies to understand problem solving situations 7.1.2 Use a variety of strategies to understand problem-solving situations and processes Solves real world problems by using estimation strategies Solves real world problems when given too much or too little information Solves real world problems by making a table Solves real world problems by finding a pattern Uses models to determine percents Solves real world problems using multiple strategies Solves real world problems by drawing a diagram Solves real world problems by using a “guess and test” strategy Solves real world problems by using estimation strategies Solves real world problems when given too much or too little information Solves real world problems by making a table Solves real world problems by finding a pattern Uses models to determine percents Solves real world problems using multiple C1.Solve single-step and multiple-step math probmens C2.Identify extraneous or insufficient information in problems C3.Choose a method for solving a problem Page 3 of 51 Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum A9.Explore numerical patterns 7.1.3 C3.Chooose a method for solving a problem 8.1.1 Generalize from a pattern of observations made in particular cases, make conjectures, and provide supporting arguments for these conjectures. Formulate a problem, determine information required to solve the problem, choose methods for obtaining this information, and set limits for acceptable solutions. strategies Solves real world problems by drawing a diagram Solves real world problems by using a “guess and test” strategy Solves real world problems by making a table Solves real world problems by finding a pattern Accurately identifies corresponding sides and angles in congruent triangles Solves real world problems by looking for a pattern Solves real world problems by drawing a diagram Writes and evaluates expressions with exponents Solves real world problems by using a “guess and test” strategy Uses exponents to simplify numbers in scientific notation Solves one and two step equations and inequalities using basic arithmetic operations including combining like terms Correctly simplifies variable expressions A9.Explore numerical patterns Understand the role of written symbols in representing mathematical ideas and the use of precise language in conjunction with the special symbols of mathematics. Understand how to break a complex problem into simpler parts or use a similar problem type to solve a problem [N]. Construct informal logical arguments Page 4 of 51 Mathematics Alignment Results – November 5, 2003 8.1.2 8.1.3 Decides on appropriate strategy or strategies to solve real world problems Solves equations with two variables Solves real world problems by using a Humboldt Community Schools Mathematics Core Curriculum C2.Identify extraneous or insufficient information in problems 8.1.4 to justify reasoning processes and methods of solutions to problems (i.e., use informal deductive methods). “guess and test” strategy Solves real world problems using logical reasoning 9-12.1.1 Understand, use, and construct a mathematical proof. [Geometry] IM2. Create a proof to show triangles or parts of triangles are congruent IM3. Write and/or compare coordinate and synthetic proofs IM3. Write indirect proofs using geometric situations IM3. Write and/or compare coordinate and synthetic proofs IM3. Write indirect proofs using geometric situations All. Translate real world problems into variable equations IM1. Interpret data in tables, graphs and concept maps IM1. Explore Im1. Use coordinate systems to solve realworld problems IM1. Explore and apply direct variation, slope and tangent IM2. Model real world situations in which one quantity is proportional to the square or cube of another quantity IM3. Write simple algorithms for mathematical and real-world problems IM3. Explore the relationships between ifthen and its converse, inverse and contrapositive IM3. Write simple algorithms for mathematical and real-world problems All: Uses inductive reasoning to make c.2. Reason quantitatively 9-12.1.2 9-12.1.3 Page 5 of 51 Apply the process of math modeling to open-ended real-world problem situations (i.e., problem formation, math modeling, solve, interpret, and justify use of technology when appropriate). [All} Construct logical arguments to test Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum conjectures and to justify solutions to problems. [All } 9-12.1.4 Page 6 of 51 9-12.1.4a Construct equations for simple problems. [All} conjectures IM1-3. Use a counter example to disprove a statement Trans-IM3. Verify or check for reasonableness of answers IM1. Investigate, write and graph equations for horizontal and vertical lines IM2. Calculate the odds of winning one of the Iowa lottery games and make a decision as to the intelligence of playing the game IM2. Use a calculator to calculate combinations, permutations and factorials IM2. Apply the meaning of the works and, or and not with a real life database IM2. Graph algebraic sentences that sue the words and and or IM2. Represent if-then statements and their converses with symbols and Venn diagrams IM2. Use rules of logic, symbols and Venn diagrams to reach conclusions and to decide if an argument is valid or invalid IM2. Write good definitions and make valid arguments using “if and only if” statements IM2. Recognize and write biconditionals All. Translate real world problems into variable equations, expressions or inequalities, expressions or inequalities IM1. Write rates and solve everyday problems with ratios IM1. Use proportions to model and solve problems IM1. Use direct variation models to make predictions and find the slop of a line Pass. Translate verbal phrase into algebraic Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum c.1. Solve math problems requiring multiple steps and operations 9-12-1.4b Construct equations for multi-step problems. [All} expressions Pass. Translate verbal sentences into algebraic equations Pass. Use the Triangle Inequality to estimate the length of the third side of a triangle APM. Read and write a formula APM. Translate a problem into an equation All. Translate real world problems into variable equations Standard 2: Understand and apply basic and advanced properties of the concepts of numbers. ITP Indicator CODE K.2.1 BENCHMARK Understand ordinal numbers (1st, 2nd, 3rd). Local Indicators Verbally identify positions Assemble pictures in order A16.Apply probability concepts and counting rules A1.Represent, compare and order numbers A5.Use place value and write numbers A9.Explore numerical patterns A1.Represent, compare and order numbers A2.Describe and apply properties of numbers K.2.2 Count objects to 20. 1 to 1 correspondence K.2.3 Understands a variety of representations of whole numbers 0-20 (e.g., written numerals, objects in sets, number lines). Verbally recognize numbers represented in different settings K.2.4 Understands the order and relative values of whole numbers 0-20. Identify, compare, write and order numbers to 20 1.2.1 Understand ordinal numbers 1st to 10th 1.2.2 Count numbers 0-100 (e.g., count by 1’s, 2’s, 5’s, and 10’s) Teacher observation Unit test Teacher observation A9.Explore numerical problems Page 7 of 51 Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum A16.Apply probability concepts and counting rules A1.Represent, compare and order numbers A2.Describe and apply properties of numbers 1.2.3 1.2.4 A5.Use place value and write numbers 1.2.5 A1.Represent, compare and order numbers 2.2.1 2.2.2 2.2.3 A6.Use and interpret operational and relational symbols Page 8 of 51 2.2.4 Understands a variety of representations of whole numbers 0100 (e.g., written numerals, objects in sets, number lines) and the relationship among them. Understand the relationship of fractional parts, 1/3, 1/2, and 1/4 to a whole. Independent practice Chapter test Understand the concept of place value through the 10’s place (e.g., the relationship between a quantity of physical materials grouped by 10’s and 1’s and the corresponding written numeral) Count numbers 0-1000 (e.g., by 1’s, 2’s, 5’s, 10’s, 100’s). Every day counts - opening Understands a variety of representations of whole numbers 01000 and the relationship among them (e.g., relating written numerals to the corresponding word, relating objects in sets to the corresponding numeral). Read and write numerals 0-1000 (e.g., standard and expanded form). Spiral review Teacher observation ILS Chapter test Every Day counts Write numbers to 1000 Use variety of methods to compare and Spiral review order whole numbers (e.g. ordinal numbers, “first” through “twentieth”, symbols [<, >, =] and language, such as Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum A3.Classify numbers by dividibility 2.2.5 A5.Use place value; write numbers in standard, expanded and exponential form A5.Use place value; write numbers in standard and expanded form 2.2.6 3.2.1 3.2.2 3.2.3 A1.Represent, compare and order numbers A3.Classify numbers by divisibility A6.Use and interpret operational and relational symbols 3.2.4 3.2.5 A1.Represent, compare and order numbers A5.Use place value; write numbers in standard and expanded form B1.Use standard rounding to Page 9 of 51 4.2.1 4.2.2 “between”, “less than”, “greater than”, or “equal to”). Understand physical, verbal, and symbolic representations of the fractions of a whole number set. (e.g. halves, fourths, thirds, eighths Understand concept of place value for whole numbers through hundreds place (e.g., ones, tens, and hundreds). Understands the concept of place values of whole numbers through the ten thousand place (e.g., 1’s, 10’s, 100’s, 1000’s, 10,000’s). Understands the concept of odd and even numbers Understands decimals expressed through the hundredths place (e.g., in money) 3.2.4a Understands the comparison of whole numbers (e.g., to a 1000). 3.2.4b Understands the comparison of fractions (e.g., with denominators of 12 or less). 3.2.4c Understands the comparison of commonly used decimals (e.g., monetary amounts). Count, read, and write numbers from 1,000 to 999,999. Understand the concept of place values for whole numbers through the millions. Understand the concept of rounding Problem of the day Every Day counts Base ten blocks Board work Daily deposit Everyday counts Works with money Comp Dre and order numbers Everyday counts calendar (spring) Math 4 today Greater than and less than with money Practice on dry erase boards Use place value Write numbers in standard, expanded and written form through millions Play wipe out on calculators Use standard rounding to express numbers Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum estimate 4.2.3 4.2.4 5.2.1 A1.Represent, compare and order numbers A5.Use place values; write numbers in standard and expanded form A2.Describe and apply properties of numbers A3.Classify numbers by divisibility 5.2.2 A5.Use place value; write numbers in standard, expanded and exponential form 6.2.2 6.2.1 6.2.3 A1.Represent, compare and order numbers A6.Use and interpret operational and relational Page 10 of 51 6.2.4 numbers expressed through the thousands (e.g., nearest thousand). Compare fractions (e.g., for halves, thirds, fourths, eighths, tenths, sixteenths). through the thousands by estimating Understand the concept of proportion and the applications of proportional reasoning (e.g. scale, similarity, percentage, rate). Read, write, order, and compare whole numbers, fractions, decimals, percents (using concrete and pictorial models) Solving problems with proportions, rates and percents Represent, compare and order fractions using fraction strips to identify halves, thirds, fourths, eighths, tenths and sixteenths Identify fractions, decimals, mixed Recognize fractions, decimals, mixed numbers, and whole numbers. numbers and who numbers in math problems Understands equivalent forms of basic Compare percentages, fractions, and percents, fractions, and decimals (e.g. decimals 1/2 = 50% = .5) Use patterns to recognize and find equivalent fractions Understand the concept of place value Name, compare and order whole numbers for numbers from the thousandths place from the hundredths place to the one to the hundred millions place hundred millions Explain the relationship between decimals and whole numbers Understand the relationships among Identifies prime factors of whole numbers factors, multiples, divisors, and Use rules of divisibility products (e.g. prime factorization, GCF, LCM, rules of divisibility for 2,3,4,5,6,9,10) Understand base-ten place value for Uses place value to work with whole whole numbers and decimals. numbers and decimal numbers Compares and orders fractions Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum symbols A5.Use place values; write numbers in standard, expanded and exponential form 7.2.1 Understand the characteristics and applications of scientific notation and exponential notation Accurately solves expressions with exponents A1.Represent, compare and order numbers 7.2.2 Understand the relationships among fractions, decimals, and percents. A2.Describe and apply properties of numbers 7.2.3 Understand the concept of prime and composite numbers Accurately compares and orders decimals Correctly compares and orders fractions with like and unlike denominators Writes mixed numbers as improper fractions and improper fractions as mixed numbers Accurately converts fractions and decimals Converts percents to fractions and decimals and vice versa Uses prime factorization to find the greatest common factor or two numbers A1.Represent, compare and order numbers A3.Classify numbers by divisibility 8.2.1 Understand the relationships among equivalent number representations (e.g. whole numbers, positive and negative integers, fractions, ratios, decimals, percents, scientific notation, exponential) A5.Use place values; write numbers in standard, expanded and exponential form 8.2.2 9-12.2.1 Page 11 of 51 Solves real world problems by using a “guess and test” strategy Converts rational numbers from fractions to decimals and vice versa Decides appropriate units of measure to measure a variety of real world objects and situations Understand the basic laws of exponents Writes and evaluates expressions with exponents Use discrete structures (finite graphs, matrices, sequences) to represent and to solve problems. [Algebra II, PreCalculus, Geometry Trans. Construct and interpret bar graphs IM1. Use a sequence to generalize the pattern with a variable expression IM2-3. Use a matrix to represent a system of equations IM2. Use matrices to represent data sets and use matrix operations Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum 9-12.2.2 9-12.2.3 Page 12 of 51 IM2. Use matrices to represent changes in the size or position of a polygon IM2. Recognize when matrices can be multiplied and find the product of two matrices IM2. Use a graphing calculator to find the inverse of a matrix and use the inverse to solve a system of equations Understand the properties of the real Trans. Identify number as a whole number, number system and its subsystems or integer (irrational numbers, natural numbers, IM1. Identify number as whole, integers, integers, rational numbers) [Algebra I, rationals or irrationals II, Pre-Calculus, General Math, IM2. Identify real numbers and imaginary Geometry] number Pass. Model integers on a number line Pass. Find the absolute value of a number Pass. Use divisibility tests Pass. Factor natural numbers, integers, and algebraic expressions Pass. Classify natural numbers as prime or composite Pass. Find the greatest common factor of two numbers or expressions Pass. Find the least common multiple of two numbers or expressions Pass. Classify real numbers as rational or irrational Pass. Represent real numbers with a number line Understand the properties and basic All. Perform operations using basic roots theorems of roots and exponents. and exponents [Algebra I, II, Pre-Calculus, Geometry, IM2. Convert fractional exponents to General Math] radical form and vice versa IM3. Graph and use recursion with Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum 9-12.2.4 Understand appropriate use and corresponding notation of ratios, proportions decimals, and percents and scientific notation. [Algebra I, General Math, Pre-Calculus] exponential growth and decay functions IM3. Explore exponential functions with negative exponents IM3. Apply and explore the relationship between fractional exponents and radicals IM3. Solve exponential and log equations and use these in real-world applications IM3. Model real-world situations using exponential functions with base “e” IM3. Solve exponential and log equations and use these in real-world applications IM3. Apply and explore the relationship between fractional exponents and radicals IM1-2, App. Apply ratios and proportions to solve similar triangle problems Pass. Write proportions as percents Pass. Write percents as decimals Pass. Write decimals and percents Pass. Write fractions as percents Pass. Write percents as fractions Pass. Find a percent of a number IM2. Find the surface area and volume of spheres, and use the fact that all spheres are similar to solve problems Standard 3: Use basic and advanced procedures while performing the processes of computation ITP Indicator A6.Use and interpret operational and relational Page 13 of 51 CODE K.3.1 BENCHMARK K.3.1a Demonstrates addition problems with real objects Local Indicators Use manipulatives to represent addition or subtraction problems Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum symbols A7.Solve equations and inequalities A4.Demonstrate ways of performing operations A6.Use and interpret operational and relational symbols A4.Demonstrate ways of performing operations A6.Use and interpret operational and relational symbols K.3.1b Demonstrates subtraction problems with real objects K.3.2 Develop understanding of more, less, and same. Identify and compare groups of objects; equal, more, fewer, one more, one fewer 1.3.1 1.3.1a knows basic addition facts to 10. 1.3.1b knows basic subtraction facts to 10. Chapter test CBM Chapter test CBM 1.3.2 1.3.2a Add two digit numbers with no Independent practice regrouping 1.3.2b Subtract two digit numbers with no Independent practice regrouping 2.3.1 2.3.1a Knows addition facts through 20. 2.3.1b Knows subtractions facts through 20. 2.3.2a Solves two digit addition with and without regrouping 2.3.2b Solves two digit subtraction with and without regrouping Understand that addition and subtraction are inverse operations. Knows basic multiplication fats 0-9 Math timed tests 3.3.2 Use estimating strategies to the nearest 10 or 100 (e.g. rounding/front-end). Practice problems on board and dry erase boards 3.3.3 Solve multi-step problems (story Keeps a mental math journal C1.Solve single-step and multiple-step math problems 2.3.2 A2.Describe and apply properties of numbers A2.Describe and apply properties of numbers C1.Solve single-step and multiple-step math problems B1.Use standard rounding to estimate B3.Use number sense to estimate C2.Identify extraneous or 2.3.3 Page 14 of 51 3.3.1 Solves two digit problems with regrouping Solves two digit problems without regrouping Knows fact families Timed tests Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum insufficient information in problems A4.Demonstrate ways of performing operations C1.Solve single-step and multiple-step math problems A2.Describe and apply properties of numbers A4.Demonstrate ways of performing operations A2.Describe and apply properties of numbers A3.Classify numbers by divisibility problems, parentheses). 3.3.4 Solve addition and subtraction problems up to 4 digit. Practice problems on board and dry erase boards 4.3.1 Multiply 3 digit by a two-digit number. 4.3.2 Use all four operations with money. 4.3.3 4.3.3a Knows basic division facts 1-9. 4.3.3 Divides by a 1 digit divisor with or without a remainder A4.Demonstrate ways of performing operations 4.3.4 Understand the relationships and properties of the four operations. Demonstrate the process of how to multiply and three digit by a two digit number Describe and apply properties of the four operations with the use of money Demonstrates an understanding of basic multiplication and division facts of one through nine Understand the process of starting with a total and sharing or dividing by a one digit divisor with our without a remainder Timed tests Describe and apply properties of the four operations A7.Solve equations and inequalities B2.Use order of magnitude to estimate B3.Use number sense to estimate A14.Estimate measurements with appropriate precision B1.Use standard rounding to estimate B2.Use order of magnitude to estimate 4.3.5 Use estimation strategies (rounding/front end). Use different strategies of estimation (rounding and front end) to solve problems 5.3.1 Use a variety of estimation strategies (e.g. front-end, standard rounding, order of magnitude, compatible numbers, compensation) to solve and to check the reasonableness of results of computation problems involving whole numbers and Give high and low estimates of products Find greatest common factors of numbers Page 15 of 51 Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum B3.Use number sense to estimate decimals (e.g. money) A2.Describe and apply properties of numbers A3.Classify numbers by divisibility A4.Demonstrate ways of performing operations 5.3.2 5.3.2aAdd, subtract, multiple, and divide whole numbers. 5.3.2b Add, subtract, multiply and divide decimals A4.Demonstrate ways of performing operations 5.3.3 A7.Solve equations and inequalities 5.3.4 5.3.3a Add, subtract, and simplify fractions and mixed numbers with like denominators. 5.3.3b Add, subtract, and simplify fractions and mixed numbers with unlike denominators Use appropriate operation and method of calculation (e.g. mental math, paper and pencil, calculator, computer) to solve problems and to check the reasonableness of results 5.3.5 B1.Use standard rounding to estimate B2.Use order of magnitude to estimate B3.Use number sense to estimate Page 16 of 51 6.3.1 6.3.2 Define what division is and parts of a problem (divisor, dividend and quotient) Use a variety of estimation strategies (e.g. powers of ten, compatible numbers, breaking numbers apart, front-end estimation, rounding) to solve and to check the reasonableness or results of computation problems involving whole Demonstrate how to multiply a three digit by a two digit number Add and subtract decimals through the hundredths place Insert zeros in products with decimals Use multiples, prime numbers, factors and properties of multiplication Divide using two digit divisors Solve problems by choosing a calculation method Analyze word problems by interpreting remainders Solve problems by making decisions about whether an exact answer or an estimate is needed Identify divisors, dividends, quotients Uses estimation skills to find sums, differences, products and quantities with decimals Estimates sums and differences of mixed numbers Adds and subtracts using decimals Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum A4.Demonstrate ways of performing operations numbers, fractions, and decimals. 6.3.2a Add, subtract, multiply, and divide whole numbers. 6.3.2b Add, subtract, multiply, and divide, fractions and mixed numbers. 6.3.2c Add, subtract, multiply, and divide decimals. 6.3.3 Understand the correct order of operations for performing arithmetic computations. B1.Use standard rounding to estimate B2.Use order of magnitude to estimate B3.Use number sense to estimate 7.3.1 Use a variety of estimation strategies to solve and to check reasonableness of computation problems involving whole numbers, fractions, decimals, and percents A3.Classify numbers by divisibility A4.Demonstrate ways of performing operations A6.Use and interpret operational and relational symbols 7.3.2 Page 17 of 51 Multiplies and divides whole numbers Multiplies and divides whole numbers by decimals and decimals by decimals Solving problems using the four rules of order of operations Solves real world problems by using estimation strategies Uses estimation strategies to find the sum, difference, product or quotient of a fraction problem with proper fractions and mixed numbers Estimates lengths Understands computations with whole Correctly performs basic arithmetic numbers, fractions, decimals, and integers operations on decimals Accurately classifies decimals as terminating or repeating Uses order of operations to simplify whole number and decimal expressions Uses the distributive property to simplify expressions Performs basic arithmetic operations on integers Uses the order of operations to evaluate expressions Solves addition and subtraction problems Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum 7.3.3 involving proper fractions and mixed numbers Solves multiplication and division problems involving proper fractions and mixed numbers Uses basic conversions between fractions, Writes mixed numbers as improper percents, and decimals. fractions and improper fractions as mixed numbers Accurately converts fractions and decimals Converts percents to fractions and decimals and vice versa Use a variety of estimation strategies to Solves real world problems by working solve and to check reasonableness of backwards results of computation problems involving rational numbers. B1.Use standard rounding to estimate B2.Use order of magnitude to estimate B3.Use number sense to estimate A2.Describe and apply properties of numbers A4.Demonstrate ways of performing operations A6.Use and interpret operational and relational symbols 8.3.1 8.3.2 Perform operations on rational numbers (e.g. add, subtract, multiply, divide, raised to a power, extract roots, take opposites and reciprocals) A4.Demonstrate ways of performing operations 8.3.3 Understand how different algorithms work for arithmetic computations and operations. Page 18 of 51 Writes and simplifies variable expressions Correctly performs basic arithmetic operations on integers Uses exponents to represent products of factors Identify the relative size of rational numbers by comparing and ordering pairs and groups of rational numbers, accurately performs arithmetic operations (add, subtract, multiply and divide) with rational numbers Recognizes square numbers, and find square roots Uses the Pythagorean theorem formulas to find lengths of sides of right triangles Solves one and two step equations and inequalities using basic arithmetic operations including combining like terms Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum 9-12.3.1 a.1. Understand and apply number properties and operations Page 19 of 51 9-12.3.2 8.3.4 Find percents and percent of a number. Add, subtract, multiply, and divide rational expressions. [All] Use a variety of operations on expressions containing real numbers (e. g., adding, subtracting, multiplying, dividing, finding a reciprocal, raising to a power, taking a root, taking opposites and reciprocals, determining absolute value). [Algebra II, I] Solves real world problems using area and perimeter formulas Writes ratios and rates in a multiple of ways All. Add, subtract, multiply and divide fractions IM1. Add, subtract, multiply and divide fractions with units and scientific notation IM1-3, Add, subtract, multiply and divide variable expressions Pass. Add and subtract like fractions Pass. Add and subtract unlike fractions Pass. Combine fractions by writing the fractions as decimals Pass. Multiply rational numbers Pass. Divide rational numbers All. Compute opposites, reciprocals and absolute values of numbers All. Compute exponents and basic roots All. Add, subtract, multiply and divide real numbers Pass. Evaluate expressions using the four basic number operations Pass. Evaluate powers and square roots Pass. Evaluate numerical expressions using the order of operations Pass. Evaluate variable expressions using the order of operations Pass. Apply the distributive property Pass. Add two or more integers Pass. Subtract integers Pass. Multiply integers Pass. Divide integers IM1. Explore, simplify and multiply square Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum 9-12.3.3 9-12.3.4 b.1. Understand and apply concepts and procedures of standard rounding, order of magnitude and number sense b.2. Evaluate reasonableness of solutions Page 20 of 51 9-12.3.5 roots IM1. Factor and multiply algebraic equations All. Use the distributive property and order of operations Solve problems using proportional App, Trans. Find percent of a number reasoning (e.g., Finding percent and App, Trans. Find percent of increase or percents of a number, finding percent decrease increase/decrease, using data from tables App, IM1. Use scales and proportions to and graphs, use of scale). [General Math, solve problems Algebra I] Pass. Solve proportions Pass. Find what percent one number is of another Pass. Solve a percent equation Pass. Find a percent of increase or decrease Pass. Find a percent of a number Pass. Simplify and compare fractions Pass. Show that a number is rational Pass. Write a decimal as a fraction Add, subtract, multiply, divide, and IM1. Simplify radical expressions simplify radical expressions containing containing whole numbers positive rational numbers. [Algebra II] IM2. Simplify radical expressions containing fractions APM. Add, subtract, and simplify expressions containing radicals Use a variety of approximation and All. Check reasonableness of answers, estimation strategies to solve and to check verify answers reasonableness and results of a variety of IM1. Estimate measurements problems Pass. Round decimals while solving equations Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum Standard 4: Understand and apply basic and advanced properties of the concepts of measurement ITP Indicator A12.Apply the concepts of volume A13. Measure weight and volume A12.Apply the concepts of perimeter A13.Measure length, distance, and weight A15.Identify and use appropriate units of measurement A13.Measure length/distance, time, temperature, weight, mass and volume A13.Measure length/distance, Page 21 of 51 CODE K.4.1 BENCHMARK Recognizes value of coins and their names. Local Indicators Identify and count using pennies, nickels and dimes K.4.2 Read and write time to the hour. Identify, compare and tell time K.4.3 Use and recognize parts of the calendar K.4.4 Read a calendar to recognize days of week, sequence of days, months, and seasons. Compares objects by size and weight. 1.4.1 Read and write time to the hour-half-hour 1.4.2 Count money by pennies, nickels, and dimes Chapter test ILS Independent practice 1.4.3 Demonstrate measurement using familiar objects (weight and length). Demonstrate measurement using familiar objects 2.4.1 Understands time by 5 minute intervals. Every Day counts Uses clocks 2.4.2 Counting money using quarters and half dollars Every Day counts 2.4.3 Understanding temperature and how it is Every Day counts Explore weight and size (includes comparing and ordering) Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum time, temperature, weight, mass and volume A13.Measure length/distance, time, temperature, weight, mass and volume A15.Identify and use appropriate units of measurement A13.Measure length/distance, time, temperature, weight, mass and volume A15.Identify and use appropriate units of measurement A12.Apply the concepts of perimeter, area and volume A13.Measure length/distance, time, temperature, weight, mass and volume A14.Estimate measurements with appropriate precision A15.Identify and use appropriate units of measurement A13.Measure length/distance, time, temperature, weight, mass and volume Page 22 of 51 measured. 2.4.4 Can measure and compare length, height, and weight. Uses rulers Uses balances 3.4.1 Can tell time to the nearest minute, a.m., and p.m. Work with clocks to compute the time 3.4.2 Counts, writes, and computes money up to Work with play money $5.00. 3.4.3 Measure (perimeter) length, weight, and volume to the nearest whole unit. Math 4 Today activities 4.4.1 Able to figure elapsed time. 4.4.2 4.2.2a Count correct change 4.2.2b Make correct change Choose the correct method to discover the difference between the starting and stopping time and whether it is AM or PM Demonstrate an understanding of counting and giving correct amount of change Demonstrate an understanding of counting on in order to make correct change Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum A12.Apply the concepts of perimeter, area and volume A13.Measure length/distance, time, temperature, weight, mass and volume A14.Estimate measurements with appropriate precision A15.Identify and use appropriate units of measurement A13.Measure length/distance, time, temperature, weight, mass and volume A15.Identify and use appropriate units of measurement A12.Apply the concepts of perimeter, area and volume 4.4.3 4.4.3 a Uses appropriate units of measurement of length, weight, volume, temp. in the standard system to problem solve (ex. perimeter, area). 4.4.3b Uses appropriate units of measurement of length,. Weight, volume, temp. in the metric system to problem solve (ex. Perimeter, area) Choose correct unit of measurement to solve a problem (time, length, weight, volume, perimeter and area) Use labels in the answer Identify and use the appropriate unit of measurement 5.4.1 Uses appropriate units of measure and basic conversions within the same system (dimensional analysis) Chooses between customary or metric systems of measurement Can choose appropriate size of measurement 5.4.2 Understands and applies the basic measures of perimeter, area, volume Find perimeter, area and volume of shapes and solids A13.Measure length/distance, time, temperature, weight, mass and volume A13.Measure length/distance, time, temperature, weight, mass and volume A14.Estimate measurements with appropriate precision A15.Identify and use appropriate units of measurement A12.Apply the concepts of perimeter, area and volume 5.4.3 Understands and manipulates the concept of time (add, subtract, convert) 6.4.1 Selects and uses appropriate tools for given measurement situations Measures angles using a protractor 6.4.2 Understands and applies measures of perimeter, area, volume, and circumference Solves problems involving perimeter Page 23 of 51 Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum A12.Apply the concepts of perimeter, area and volume A13.Measure volume 7.4.1 Understands and applies measures of surface area and volume of rectangular prisms, perimeter and area of polygons. A15.Identify and use appropriate units of measurement A13.Measure length/distance, time, temperature, weight, mass and volume A14.Estimate measurements with appropriate precision A15.Identify and use appropriate units of measurement A12.Apply the concepts of perimeter, area and volume 7.4.2 Selects and uses appropriate tools for given measurement situations 8.4.1 Uses multi-step dimensional analysis when converting within a system of measurement Converts measurements to different units in both customary and metric systems 8.4.2 Understands and applies measures of perimeter, area, volume, and circumference. 9-12.4.1 Solve real world problems involving 2and 3-dimensional measures (e.g. area, volume, perimeter). [Geometry] Selects and uses formulas to find areas of geometric figures Selects appropriate formula and use to find surface areas and volumes of threedimensional figures (prisms, pyramids, cylinders and cones) Decides on appropriate strategy or strategies to solve real world problems IM2. Calculate volume and surface area of a sphere All. Calculate area and perimeter of two dimensional figures Pass. Build and describe polyhedrons Pass. Identify and draw 3D solids Pass. Find the surface area of a prism and a cylinder Page 24 of 51 Selects and uses formulas to find areas of plane geometric figures (parallelograms, triangles, trapezoids, and circles) Uses formulas to find circumferences of circles Uses formulas to find surface area and volume of prisms and cylinders Estimates lengths Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum 9-12.4.2 9-12.4.3 9-12.4.4 9-13.4.5 Solve problems involving rate as a measure (e.g., velocity). [Algebra and Pre-Calculus] Determine precision and accuracy of measurement. [Algebra I] Use the appropriate tools or units to determine measurement. [General Math] Uses multi-step dimensional analysis to convert within and between systems of measurement Pass. Find the volume of a prism Pass. Find the volume of a cylinder Pass. Find the volume of a pyramid and a cone Pass. Find volumes of 2 solids put together Pass. Find the volume of a sphere IM1. Find surface areas of prisms, cylinders, and pyramids IM1. Find volumes of pyramids and cones IM1. Solve problems using d=rt Pass. Find rate and ratios App. Students can measure to a set accuracy level App. Use scales, rulers, protractors, micrometers and meter sticks to measure All. Convert within a system of measurement IM1. Solve a problem by finding the point of intersection of two lines Standard 5: Understand and apply basic and advanced properties of the concepts of geometry. ITP Indicator A10.Identiify, classify, and compare geometric figures CODE K.5.1 K.5.2 Page 25 of 51 BENCHMARK Understand geometric patterns and relationships (similarities/differences among basic plane figures: circles, square, rectangle, and triangle). Understand the common language of spatial sense (e.g., “inside”, “outside”, “between”, “above”, “below”, and “behind”. Local Indicator Identify 2 and 3 dimensional figures; circle, triangle, square, rectangle, rectangular prism, pyramid, sphere, and cube Identify and use positional words: top, middle, bottom, in front, behind, over, under, on, inside, outside, left and right Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum A11.Describe geometric properties, patterns, and relationships K.5.3 Understands that patterns can be made by putting different shapes together or taking them apart. A10.Identiify, classify, and compare geometric figures A11.Describe geometric properties and patterns A10.Identiify, classify, and compare geometric figures A11.Describe geometric properties, patterns and relationships 1.5.1 Knows basic characteristics and properties Chapter test of basic plane figures (e.g., a square has ILS four equal sides, closed vs. open figures). Performance task 2.5.1 Understand properties of and similarities and differences among basic solid figures (e.g., spheres, cubes, rectangular prisms, cylinders, pyramids, and cones) and basic geometric terms (e.g., sides, edges, and corners) associated with these figures. Understand what makes a figure symmetric. Identifies plane figures and space figures: parallelogram, trapezoid, sphere, and cube. Identifies space relationships (symmetry, congruence). Problem of the day Understand characteristics of line (e.g., parallel, perpendicular, intersecting) and angles (e.g., right, acute, obtuse). Understand basic properties of figures (e.g., two or three- dimensionality, symmetry, number of faces, type of angle). Know basic geometric language for Identify the different angles by understanding the characteristics of lines 2.5.2 A10.Identiify, classify, and compare geometric figures 3.5.1 A11.Describe geometric properties, patterns, and relationships A10.Identiify, classify, and compare geometric figures 3.5.2 A11.Describe geometric properties, patterns, and relationships 4.5.2 4.5.1 4.5.3 Page 26 of 51 Use a variety of manipulatives Problem of the day Every Day counts calendar Make faces out of paper, fold and cut to show symmetry, sides, flips and turns Describe geometric properties, patterns and relationships Use geoboardes Identify, classify and compare shapes by Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum 4.5.4 describing and naming shapes (e.g., trapezoid, parallelogram, cube, sphere, and polygon). Understand basic geometric transformations in a plane and the relationships among transformed figures (e.g., symmetry, congruency, similarity, slide flip and turn). Understands the characteristics of (classification) and relationships among (symmetry, congruence) points, lines, line segments, rays, planes, and polygons. A10.Identiify, classify, and compare geometric figures A11.Describe geometric properties, patterns and relationships 5.5.1 A10.Identiify, classify, and compare geometric figures A11.Describe geometric properties, patterns and relationships A10.Identiify, classify, and compare geometric figures A11.Describe geometric properties, patterns and relationships 6.5.1 Understands the characteristics of (classification) and relationships among (parallel, perpendicular, congruence) lines, angles, polygons and circles. 7.5.1 Understands the characteristics of (classification) and relationships among (parallel, perpendicular, congruence) lines, angles, polygons, circles, trapezoids, parallelograms, triangles A10.Identiify, classify, and 8.5.1 Understands the characteristics of Page 27 of 51 using appropriate geometric language Flips, sides and turns Use geoboards Explain the difference between congruence and symmetry Recognize and classify quadrilaterals and triangles Count edges and faces on geometric shapes and solids Measure angles using a protractor Identifies right, obtuse and acute angles Classifies lines and angles Identifies types of quadrilaterals and polygons Correctly classifies and measures angles Correctly classifies triangles by their sides and angles Accurately identifies corresponding sides and angles in congruent triangles Correctly classifies polygons and quadrilaterals Accurately identifies parts of a circle (chords, radii, diameter) Selects and uses formulas to find areas of plane geometric figures (parallelograms, triangles, trapezoids and circles) Identifies geometric figures and their parts Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum compare geometric figures A11.Describe geometric properties, patterns and relationships (classification) and relationships among quadrilaterals, triangles, and circles. (types of triangles, quadrilaterals and other polygons) Page 28 of 51 Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum a.3. Understand and apply concepts of geometry and measurement Page 29 of 51 9-12.5.1 Understand and use inductive and deductive reasoning to make observations about and to verify properties of and relationships among figures (e.g., the relationship among interior angles of parallel lines cut by a transversal). [Geometry] All. Use inductive reasoning to make conjectures about polygons IM2. Use deductive reasoning to probe angle and triangle relationships IM1. Use inductive and deductive reasoning to investigate the relationships among the length of the sides of right triangles IM2. Write proofs using properties of algebra IM2. Use postulates, definitions, given information, and proven theorems to write proofs about angles IM2. Write proofs for properties of parallel lines IM2. Apply converses of parallel lines theorems in proofs IM2. Explore angles related to triangles and quadrilaterals and apply this information to numerical problems IM2. Use SSS, SAS, AAS, and ASA to prove triangles are congruent IM2. Apply properties of isosceles and equilateral triangles IM3. Find the interior and exterior angles of polygons IM3. Explore polygons inscribed in a circle (central angles, arcs, chords) IM3. Investigate and apply the relationships between inscribed angles and arcs of circles IM3. Explore the relationships between circumscribed polygons and inscribed circles Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum 9-12.5.2 9-12.5.2a Know and use the Pythagorean Theorem and its converse to solve mathematical and real-world problems. [Geometry, Algebra] 9-12.5.2b Know and use the properties of special right triangles (e.g., 30-60-90 degree right triangles) to solve mathematical and real-world problems (Geometry and Algebra) 9-12.5.3 Use properties of figures to solve mathematical and real-world problems (e.g., use understanding of arc and properties of circles to interpret information in circle graphs). [Geometry] 9-12.5.4 Use geometric constructions (e.g., the parallel to a line through a given point not on the line, line segment congruent to a given line segment) to complete simple proofs, to model, and to solve mathematical and real-world problems. [Geometry] Understand that objects and relations in geometry correspond directly to objects and relations in algebra (e.g., a line in 9-12.5.5 Page 30 of 51 IM2. Review Pythagorean theorem APM. Understand and know how to use the Pythagorean Theorem All. Use Pythagorean theorem and its converse to solve real world problems IM2. Use properties of special right triangles to solve real world problems Pass. Use the Pythagorean theorem IM2. Identify similar right triangles and apply right triangle theorems IM2. Find the geometric mean between two numbers IM2. Use trigonometry and properties of special right triangles to find angle measures and segment lengths IM1. Use properties of circles to interpret information in circle graphs IM1. Apply angle relationships found by intersecting lines, in circles and triangles IM1. Investigate, write and graph equations for horizontal and vertical lines IM1. Graph linear inequalities IM2. Apply the properties of similar triangles IM1-3. Translate between tables, equations and graphs IM1. Write expressions for measures of Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum geometry corresponds to a set of ordered pairs satisfying an equation of the form ax+by =c) [Geometry, Algebra II] Page 31 of 51 9-12.5.6 To understand and use geometric transformations and their properties to solve problems. [Geometry, Pre-Calculus] 9-12.5.7 Understand the basic concepts of right triangle trigonometry (e.g., basic trig ratios, such a sine, cosine, and tangent) and use trigonometric ratio methods to solve mathematical and real-world problems. [Pre-Calculus] geometric figures IM2. Explain and use the relationships between the slopes of parallel and perpendicular lines IM2. Describe characteristics of quadrilaterals and develop classification skills IM2. Use the formula for slope and distance to explore quadrilaterals and their properties on the coordinate plane IM2. Use the formula for midpoint of a segment in a variety of situations IM1. Identify transformations and symmetry IM2-3. Use transformations to solve real world problems IM1. Translate figures in a coordinate plane IM1. Rotate figures in a coordinate plane and on polar graph paper IM1. Explore properties of similar polygons IM1. Enlarge or reduce a figure IM1. Draw a mirror image of object, explore reflections IM2. Use right triangle trigonometry IM1. Investigate right triangle ratios IM2. Use trigonometry and properties of special right triangles to find angle measures and segment lengths IM3. Use the law of cosines to solve realworld problems IM3. Use the law of sines to solve realworld problems Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum Page 32 of 51 9-12.5.8 Describe and use relationships among figures to solve mathematical and realworld problems (e.g., congruent and similar polygons, parallel and perpendicular lines). [Geometry] 9-12.5.9 Understand the characteristics and uses of vectors (e.g., representations of velocity ad force) and basic operations on vectors (e.g., vector addition, scalar multiplication). [Pre-Calculus] IM3. Use the law of sines to solve real world problems IM3. Use the law of cosines to solve real world problems APM. Use ratios for the sine, cosine and tangent to solve right triangle problems IM1. Recognize graphs and everyday relationships that represent functions IM1. Explore area formulas using manipulatives IM1. Find and compare corresponding lengths, areas, and volumes of similar figures using ratios IM2. Find the surface area and volume of spheres, and use the fact that all spheres are similar to solve problems IM2. Model real world situations in which one quantity is proportional to the square or cube of another quantity IM3. Convert polar coordinates to rectangular coordinates and vise verse, and find the sin,cos and tan of any angle IM3. Solve real-world problems using graphic representations of vectors IM3. Solve real-world problems using vectors in rectangular form IM3. Solve real-world problems by using pairs of equations in parametric form IM3. Locate points in a plane using polar coordinates and bearing IM3. Convert polar coordinates to rectangular coordinates and vise verse, and find the sin, cos and tan of any angle IM3. Solve real-world problems using Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum 9-12. 5.10 Compare, describe, and analyze two-and three-dimensional figures and their intersections with a plane. [Geometry, Pre-Calculus] graphic representations of vectors IM3. Solve real-world problems using vectors in rectangular form IM3. Solve real-world problems by using pairs of equations in parametric form IM3. Investigate properties of 3-D figures Standard 6: Understand and apply basic and advanced concepts of statistics and data analysis ITP Indicator CODE K.6.1 D1.Read amounts on scales of bar and line graphs D2.Locate amounts in specific cells of a table D3.Compate quantities D4.Use tables and graphs to generalize and draw conclusions D1.Read amounts on scales of bar and line graphs D2.Locate amounts in specific cells of a table D3.Compate quantities D4.Use tables and graphs to generalize and draw conclusions K.6.2 Page 33 of 51 1.6.1 BENCHMARK Collects and displays data using charts and graphs. Interprets graphs (bar and pictograph). Local Indicator Demonstrate the use of graphing; line, bar, tally, picture Demonstrate the use of graphing; line, bar, tally, picture Collect, organize, interpret data, and make predictions using simple charts, tables, and graphs. Chapter test ILS Performance task Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum D2.Locate amounts in specific cells of a table D3.Compare quantities to determine ranks, sums, or differences D1.Read amounts on scales of bar and line graphs D4.Use tables and graphs to determine rates or identify trends, understand underlying or functional relationships, and generalize or draw conclusions D1.Read amounts on scales of bar and line graphs 2.6.1 Collects and organizes data on tables, graphs, and charts. Class graphs 2.6.2 Reads and interprets tables, graphs, and charts. Class graphs 3.6.1 D1.Read amounts on scales of bar and line graphs D2.Locate amounts in specific cells of a table D3.Compate quantities to determine ranks, sums, or differences D4.Use tables and graphs to determine rates or identify trends, understand underlying or functional relationships, and generalize or draw conclusions D1.Read amounts on scales of bar and line graphs D2.Locate amounts in specific cells of a table D1.Read amounts on scales of bar and line graphs D3.Compate quantities to 3.6.2 Collect and organize data into graphs Graph temperature in journals (daily) (bar, line, pictographs, circle), tables, and charts. Read and make simple inferences from Make decisions about temperature using the data displayed in diagrams, charts, bar temperature graph from the journal graphs, and tables (e.g., generalize or draw simple conclusions). Page 34 of 51 4.6.1 Read and interpret simple tables, graphs (e.g., simple bar, line, and charts (e.g. pie) Constructs or interprets simple bar, line and picto graphs 4.6.2 Use line, circle, and bar graphs with various scale increments to display information. Recognize that data represents specific pieces of information, may have different scale increments to display this information Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum determine ranks, sums, or differences D4.Use tables and graphs to determine rates or identify trends, understand underlying or functional relationships, and generalize or draw conclusions Halloween and birthday graphs 4.6.3 D1.Read amounts on scales of bar and line graphs D2.Locate amounts in specific cells of a table D3.Compate quantities to determine ranks, sums, or differences and to find ratios 5.6.1 5.6.2 A17.Understand and apply measures of central tendency and variability D1.Read amounts on scales of bar and line graphs D2.Locate amounts in specific cells of a table D3.Compate quantities to determine ranks, sums, or differences and to find ratios D4.Use tables and graphs to determine rates or identify trends, understand underlying or functional relationships, and generalize or draw conclusions A17.Understand and apply Page 35 of 51 6.6.1 7.6.1 Understands appropriate measures of central tendency Use graphs and plots to display information Find mean, median and mode Find range Draw conclusions and make predictions from information on a graph Use a bar graph to compare information Use coordinates to make a line graph Read a pictograph for information Understands appropriate measures of central tendency (mean, median, mode) Read and interpret tables, graphs, and charts Can find mean, median and mode Reads graphs of four types: bar, pictograph, line and circle Uses appropriate scales and intervals in making bar graphs Understand appropriate measures of Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum measures of central tendency and variability D1.Read amounts on scales of bar and line graphs D2.Locate amounts in specific cells of a table D3.Compate quantities to determine ranks, sums, or differences and to find ratios D4.Use tables and graphs to determine rates or identify trends, understand underlying or functional relationships, and generalize or draw conclusions A17.Understand and apply measures of central tendency and variability D1.Read amounts on scales of bar and line graphs D2.Locate amounts in specific cells of a table D3.Compate quantities to determine ranks, sums, or differences and to find ratios D4.Use tables and graphs to determine rates or identify trends, understand underlying or functional relationships, and generalize or draw conclusions d.2. Interpret data from a variety of sources Page 36 of 51 statistics, (e.g. mean, median, mode, and range) 7.6.2 Make comparisons, predictions and inferences from data in a variety of formats Solves real world problems by making a table Solves real world problems by finding a pattern Solves real world problems by using a “guess and test” strategy 8.6.1 8.6.2 9-12.6.1 Use appropriate format for organizing and displaying statistical data Understand faulty arguments, common errors, and misleading presentations of data 9-12.6.1.a Understands and applies basic concepts of data collection, data analysis, and distribution. [Pre-Calculus and Algebra II] 9-12.6.1b Understands and applies advanced concepts of data collection, data analysis, and distribution (PreCalculus and Algebra II) Organizes and displays data graphically Determines central tendency values from a set of data (mean, median and mode) Displays data in a variety of plots and graphs Determines appropriate ways to display information from real world data Finds solutions to real world questions by reading and analyzing graphs IM1. Makes appropriate predictions based on tendencies indicated by real world data displayed in scatter plots, circle and bar graphs IM1. Determines appropriate way to display information from real world data IM1. Recognize when data displays give misleading impressions APM. Apply logical reasoning to interpreting graphs and tables in reasoning Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum IM2. Use a survey of part of a population to predict results for the entire population IM2. Recognize different ways to select a sample IM2. Recognize factors that influence statistics and survey results IM2. Model real life situations with equations IM2. Classify expressions IM2. Use rules of exponents to simplify expressions d.1. Make inferences based on data presented in a variety of ways 9-12.6.2 Understands appropriate methods for using data to make predictions (trends, surveys, samples). [Algebra I, II, and Pre-Calculus] a.4. Understand and apply concepts in probability and 9-12.6.3 Selects and uses the best method of representing and describing a set of data Page 37 of 51 IM3. Explore and analyze types of frequency distributions IM3. Explore the effect of adding a constant to a data set IM3. Explore the effect of multiplying each data value by a constant IM3. Find the expected average gain or less in a real-world situation IM3. Find the expected average gain or loss in a real-world situation IM3. Use standardized values and the normal distribution of compare real-world data IM1. Collect real world data and analyze it IM1. Investigate and model sampling techniques Pass. Use tables and graphs to organize data Pass. Use tables and graphs to solve problems APM. Be able to make conjectures and form conclusions given a set of data IM1. Display and interpret data using histograms, frequency tables and stem and Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum statistics (e.g., scatter plot, line graph, two-way table). [Algebra I, II, Geometry, General Math, and Pre-Calculus] 9-12.6.4 Page 38 of 51 Understands measures of central tendency and variability (e.g., standard deviation, range, quartile deviation) and their applications to specific situations. [Pre-Calculus, Algebra II, General Math] leaf plots IM1. Model situations and solve simple equations spreadsheets, tables, graphs, equations and technology Pass. Apply the distributive property Pass. Simplify expressions by adding like terms Pass. Check that a number is a solution of an equation Pass. Use addition or subtractions to solve an equation Pass. Use multiplication or division to solve an equation Pass. Translate verbal phrase into algebraic expressions Pass. Use a table of values to sketch and graph of a linear equation IM3. Use systematic lists to organize data IM3. Use statistics to reach conclusions via line graphs, scatter plots, etc. IM3. Use statistics to reach conclusions via line graphs, scatter plots, etc. APM. Know the parts of a right triangle IM3. Use technology and compute the mean and standard deviation of a data set IM3. Explore and apply properties of normal distributions IM3. Use technology to find least-squares line and median-median lines IM3. Use standardized values and the normal distribution to compare real-world data and find percentiles IM3. Use technology to compute the mean and standard deviation of a data set Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum IM3. Use technology to find least-squares line and median-median lines APM. Calculate mean, median and mode from a set of data Standard 7: Understand and apply basic and advanced concepts of probability. ITP Indicators A16.Apply probability concepts and counting rules A14.Estimate measurements with appropriate precision A16.Apply probability concepts and counting rules A17.Understand and apply measure of central tendency and variability CODE 1.7.1 2.7.1 2.7.2 3.7.1 A1.Represent, compare and order numbers A16.Apply probability concepts and counting rules A16.Apply probability concepts and counting rules Page 39 of 51 3.7.2 4.7.1 BENCHMARK Understands that some events are certain and others are impossible. Understands the basic concepts of likely and unlikely outcomes. Local Indicators Teacher Observaiton Understands that some events can be predicted fairly well, but others cannot because we do not always know everything that may affect an event. Understands that some events are sure to happen, some events are sure not to happen, and some events may or may not happen. Understands that the word “chance” refers to the likelihood of an event. Predicts outcome of simple experiments Determine the probability of simple events using basic experiments or Make predictions based on situations presented Can estimate Every Day counts exploration of patterns Make a table of likely and unlikely events Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum 4.7.2 A16.Apply probability concepts and counting rules D4.Use tables and graphs to determine rates or identify trends, understand underlying or functional relationships, and generalize or draw conclusions A16.Apply probability concepts and counting rules 5.7.1 6.7.1 6.7.2 A16.Apply probability concepts and counting rules Page 40 of 51 7.7.1 simulations (e.g., using coins, spinners, and dice). Use basic sample groups (e.g., all possible outcomes) to describe events. Use a variety of simple models (tree diagrams, sample spaces, grids, tables) to represent the possible outcomes for probability situations. Draw conclusions and make predictions from simple probability situations Determine probability using simulations or experiments Determine probability using math/theoretical models 7.7.2 Understand the concepts of combinations and permutations 7.7.3 Understand how predictions are based on data and probabilities Predicts results of probability situations Uses simulations to find experimental probability Solves real world problems by using simulations Solves to find the theoretical probability of an event Uses a sample space to list the set of all possible outcomes Uses the counting principle to find the number of outcomes Solves to find the probability of independent and dependent events Uses permutations to find all the arrangements of items in a group Uses combinations to find the number of arrangements when order does not matter Estimates the size of a population using the capture/recapture method Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum A16.Apply probability concepts and counting rules 8.7.1 A16.Apply probability concepts and counting rules 8.7.2 a.4. Understand and apply concepts of probability and statistics 9-12.7.1 Understands the basic concepts of probability and applies them to real-world situations. [Algebra II, I, Pre-Calculus, General Math] 9-12.7.2 Understands the differences among experimental, simulation, and theoretical probability techniques and uses the appropriate method to determine probabilities. [Pre-Calculus, Algebra I, II, General Math] 9-12.7.3 Determines the probability and understands the concepts of independent Page 41 of 51 Understand that the measure of certainty in a given situation depends on a number of factors (sample size, method of data collection, what is known about the situation, how current data are) Understand the difference between theoretical and experimental probability Makes appropriate assessments of surveys using real world sampling situations Evaluates and assesses real world situations to determine if there is too much or too little information IM1. Theoretically and experimentally explore probability IM2. Find the probability of an event and/or of mutually exclusive events IM2. Relate probability to odds IMJ3. Perform experiments using random numbers IM3. Perform experiments using random numbers Understands the differences between experimental and theoretical probability techniques and uses the appropriate method to determine probabilities. IM1. Recognize direct variation graphs IM2. Use an experiment to simulate the results of a survey and to estimate probabilities IM2. Calculate the odds of winning one of the Iowa lottery games and make a decision as to the intelligence of playing the game IM3. Find the probability of either of two events happening IM3. Find the probability of either of two events happening IM2. Find the probability of independent and/or dependent events Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum and dependent events. [Algebra I, II, PreCalculus, General Math] Counting techniques 9-12.7.4 Page 42 of 51 IM3. Draw a tree diagram to find the probability under restricted conditions APM. Find the probability of a single event, mutually exclusive events, dependent and independent events IM3. Explore probabilities in a binomial experiment IM2. Use tree diagrams, tables or systematic lists to count outcomes, choices and possibilities IM2. Use the multiplication counting principle to find the number of different arrangements of a group of items IM2. Find the number of ways to select some items from a group IM2. Use a calculator to calculate combinations, permutations and factorials Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum Standard 8: Understand and apply basic and advanced properties of functions and algebra. ITP Indicators C1.Solve single-step and multiple-step math problems CODE K.8.1 BENCHMARK Extend and create simple repeating patterns (e.g., with physical objects, geometric shapes). Local Indicators Identify, extend and create patterns A7.Solve equations and inequalities 1.8.1 Understand simple repeating and growing patterns. Performance task Teacher observation 1.8.2 Solve simple open sentences involving addition and subtraction to 12. 1.8.3 Understand that regularities exist in a variety of contexts (e.g., events, designs, shapes, sets of numbers). Understand and extend a wide variety of patterns (linear and non-linear). Chapter test ILS Independent practice Independent practice Teacher observation A9.Explore numerical patterns 2.8.1 C1.Solve single-step and multiple-step math problems C2.Identify extraneous or insufficient information in problems C3.Chose a method for solving a problem 2.8.2 Understand basic number patterns (skip counting). Skip counts 2.8.3 Use variables (e.g., letters, boxes, or other symbols) and number sentences to represent solutions to problems (e.g. 7+N=23). Solve simple number sentences involving addition and subtraction (e.g., sentences involving one or both operations). Solve number sentences involving basic Solves story problems A7.Solve equations and inequalities 2.8.4 A3.Classify numbers by 3.8.1 Page 43 of 51 Every Day counts Solves number sentences Use manipulatives to create multiplication Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum divisibility C1.Solve single-step and multiple-step math problems A9.Explore numerical patterns A8.Use variable expressions to model situations A7.Solve equations and inequalities 3.8.2 3.8.3 3.8.4 4.8.1 4.8.2 A8.Use variable expressions to model situations A9.Explore numerical patterns 4.8.3 4.8.4 multiplication and division facts. and divisions sentences Understand the concepts “elements” and “repetitions” in a pattern (e.g. ABB, ABB has three elements and two repetitions). Use a variety of methods and tools to represent patterns and relationships. Understand the concept of an equation (e.g., a number sentence that shows two quantities that are equal). Solve open sentences involving multiplication and division (N+17=23). Use symbols of equality (=) and inequality (<, >). Every Day counts calendar Understand that the same pattern can be represented in different ways (e.g., using words, pictures, and numbers). Understand the characteristics and features of coordinates and the coordinate plane (e.g. the horizontal axis and vertical axis). Identify patterns and explain the rule that the pattern is generated from. A9.Explore numerical patterns 5.8.1 A7.Solve equations and inequalities A8.Use variable expressions to model situations A7.Solve equations and inequalities 6.8.1 Solve simple (addition, subtraction) equations with one variable using informal or formal methods. 7.8.1 Understands basic algebraic terms and symbols (e.g. equation, inequality, Page 44 of 51 Every Day counts calendar Math 4 Today activities Demonstrate knowledge of fact families and inverse properties Demonstrate ways to interpret operational and relational symbolism problems with <, >, or + Show that patterns can be displayed differently (draw a picture, explain in words) Show location of specific coordinates on horizontal and vertical axis Use division patterns to find quotients Use patterns in multiplying decimals Create a pattern and present the pattern to a group Writes and solves equations Evaluates and writes variable expressions Correctly writes equations Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum variable, exponent) D4.Use tables and graphs to determine rates or identify trends, understand underlying or functional relationships, and generalize or draw conclusions A7.Solve equations and inequalities A7.Solve equations and inequalities A8.Use variable expressions to model situations C1.Solve single-step and multiple-step math problems Page 45 of 51 7.8.2 8.8.1 Solves expressions using variables Use a coordinate grid for a variety of representations (e.g., number, figures, points, lines) 8.8.2 Solve simple inequalities with rational number solutions, using concrete and informal methods. 8.8.3 Solve two-step equations of one variable using informal and formal methods. Accurately solves expressions with exponents Evaluates and writes variable expressions Graphs points in a coordinate plane Solves one and two step equations and inequalities using basic arithmetic operations including combining like terms Writes and graphically displays inequalities on number lines Uses a variety of strategies to plot solutions to linear equations (plotting ordered pairs, using slope-intercept) Solves one and two step equations and inequalities using basic arithmetic operations including combining like terms Solves real world problems by writing and solving equations Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum a.2. Understand and apply concepts and procedures of algebra Page 46 of 51 9-12.8.1 9-12.8.1bUnderstand properties of linear graphs and the relationships between a graph and its corresponding expression (e.g., maximum and minimum points, slopes, intercepts). [Algebra I, II, Geometry, Pre-Calculus] 9-12.8.1b Understand properties of nonlinear graphs and the relationships between a graph and its corresponding expression (e.g., maximum and minimum points, slopes, intercepts). (Algebra I,II, Geometry, Pre-Calculus) IM1. Explore and apply direct variation, slope and tangent IM1. Use direct variation models to make predictions and find the slope of a line IM1. Find circumference of circles and arc lengths IM1. Recognize direct variation graphs Pass. Recognize graphs of horizontal and vertical lines Pass. Find slope of a line from a graph Pass. Find the slope and y-intercept form to sketch a quick graph IM2. Recognize and interpret graphs of functions, including growth and decay of graphs IM2. Find the domain and range of a function IM2. Review linear functions, slope of a line, and direct variation IM2, Solve systems of linear equations by graphing and graph systems of linear inequalities IM3. Locate the maximum and/or minimum using formulas, graphs and network diagrams IM3. Model and solve real-world problems using linear programming IM3. Graph equations used to model realworld problems IM3. Solve systems of linear and real-world problems using algebra, graphs, and matrices IM3. Model and solve real-world problems using linear programming Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum 9-12.8.2 Page 47 of 51 Understand the general properties and characteristics of many types of basic functions and their corresponding graphs (e.g., notation and terminology of linear, quadratic, step, absolute value). [Algebra I, II] Pass. Find intercepts of lines Pass. Find the distance between two points Pass. Find the midpoint of a line segment IM1. Investigate, write and graph equations for horizontal and vertical lines IM2. Explore hyperbolas and model real world situations involving constant products IM2. Graph quadratic functions using technology IM2. Find the vertex, line of symmetry and intercepts of a parabola IM2. Explore translations of parabolas IM2. Solve simple quadratic equations by graphing and undoing IM2. Solve the assigned homework problems relating graph analysis to a career IM2. Use a graphing calculator to graph functions IM2. Graph quadratic functions using graphing calculators IM2. Use graphing calculators to observe how changes in an equation affect the graph of a parabola APM. Find the slope of a graphed line APM. Find the intercepts of a graphed line IM1. Explore ways to represent functions IM1. Explore, multiply and simplify square roots IM2. Model exponential growth and decay using tables, graphs and equations IM3. Represent functions using graphs, tables and equations IM3. Find the domain, range and equation of a linear function Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum IM3. Write, graph and apply piecewise and absolute value functions IM3. Graph quadratic functions involving real-world problems IM3. Write, evaluate and apply direct variation functions and polynomials IM3. Explore, solve and apply functions involving radicals IM3. Evaluate, graph and apply rational functions IM3. Explore and apply functions formed by combining two functions IM3. Graph quadratic functions involving real-world problems IM3. Write, evaluate and apply direct variation functions and polynomials IM3 Explore, solve and apply functions involving radicals IM3. Evaluate, graph and apply rational functions IM3. Use technology and matrices to find quadratic models for data IM3. Use technology and matrices to find quadratic models for data 9-12.8.3 9-12.8.4 Page 48 of 51 Understand the general properties and characteristics of many types of trigonometric functions and their corresponding graphs (e.g., sine, cosine). [Pre-Calculus Understand the general properties and characteristics of many types of advanced functions and their corresponding graphs (e.g., exponential, logarithmic). [PreCalculus] IM2. Model exponential growth and decay using tables, graphs and equations IM3. Model real-world situations using exponential functions with base “e” IM3. Recognize when a function has an Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum inverse, and if it does, fin and graph it IM3. Explore the relationship between exponential functions and log functions IM3. Simplify and evaluate log expressions IM3. Recognize when a function has an inverse, and if it does, find and graph it Page 49 of 51 Mathematics Alignment Results – November 5, 2003 Humboldt Community Schools Mathematics Core Curriculum 9-12.8.5 Page 50 of 51 IM1. Simplify variable expressions and solve simple equations IM1. Use algebra tiles to solve equations with the variable on both sides IM1. Rewrite algebraic and geometric equations in simplest form IM1. Solve equations using reciprocals Pass. Find solutions of a linear equation with two variables IM2. Solve systems of linear equations by graphing and graph systems of linear inequalities IM2. Solve systems of linear equations by substitution IM2. Solve systems of equations by addition and choose a method for solving a specific system of inequalities IM2. Solve simple quadratic equations by graphing and undoing IM2. Solve quadratic equations by factoring IM2. Use the quadratic formula to solve quadratic equations and real world problems IM2. Use the discriminant to find the number of real solutions of a quadratic equation IM2. Apply systems to solve real world problems to decide the best economic plan IM2. Use a graphic calculator to find the inverse of a matrix and use this to solve a system IM3. Graph equations used to model realworld equations IM3. Solve systems of linear and real-world problems using algebra, graphs and matrices IM3. Graph equations used to model realworld problems APM. Solve linear systems by graphing Mathematics Alignment Results – November 5, 2003 Use a variety of methods (e.g. with graphs, algebraic methods, and matrices) to solve linear and quadratic equations [Algebra I, II, Pre-Calculus Uses a variety of methods(e.g., with graphs, algebraic methods, and matrices) to solve linear inequalities (Algebra I, II, Pre-Calculus) Uses a variety of methods (e.g., with graphs, algebraic methods, and matrices) to solve systems of equations and inequalities (Algebra I, II, Pre-Calculus) Humboldt Community Schools Mathematics Core Curriculum 9-12.8.6 9-12.8.7 Page 51 of 51 Understand the basic concept of complex numbers (e.g. conjugate) [Algebra II, PreCalculus] Understand various applications (compound interest) of formal notation (e.g., sigma notation, factorial representation). [Pre-Calculus] IM1. Rewrite and solve simple inequalities IM1. Find area of circles and sectors Pass. Graph an inequality Pass. Write equivalent inequalities Pass. Use multiplication and division to solve inequalities Pass. Solve multi-step inequalities IM1. Solve pairs of two-variable equations using substitution IM1. Use dimensional analysis to solve everyday problems IM2. Add, subtract, and multiply complex numbers IM3. Write and apply formulas for sequences in which each term is found by using the preceding term(s) IM3. Write and apply explicit and recursive formulas for sequences IM3. Find the sum of a finite arithmetic series IM3. Find the sum of a finite geometric series IM3. Recognize when an infinite series has a sum and if it does, find it IM3. Write and apply formulas for sequences related to algebraic, geometric, and everyday situations IM3. Write and apply explicit and recursive formulas for sequences IM3. Recognize when an infinite series has a sum and it if does, find it Mathematics Alignment Results – November 5, 2003