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# STRUCTURE OF MATH I MATH 365

Texas A&M

GPA 3.6

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This 11 page Study Guide was uploaded by Vivien Bradtke V on Wednesday October 21, 2015. The Study Guide belongs to MATH 365 at Texas A&M University taught by Staff in Fall. Since its upload, it has received 35 views. For similar materials see /class/226057/math-365-texas-a-m-university in Mathematics (M) at Texas A&M University.

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Date Created: 10/21/15

Scarborough adapted with thanks from Lynnette Cardenas 2005 Math 365 Study Guide Section 11 Explorations with Patterns Use inductive reasoning to determine a pattern Use inductive reasoning to lead to a conjecture hypothesis Use a counterexample to disprove a conjecture De ne a sequence Identify an arithmetic sequence and its difference Determine the nth term of an arithmetic sequence Identify a geometric sequence and its ratio Find the nth term of a geometric sequence Given some terms of an arithmetic or geometric sequence determine how many there are Determine the pattern of a given sequence not necessarily arithmetic or geometric and determine its nth term Section 12 Mathematics and Problem Solving Name each step in the fourstep problemsolving process Give examples ofdifferent strategies to use in order to devise a plan Use the fourstep problemsolving process to solve problems Section 13 Algebraic Thinking Identify variables in a word problem Write statements in algebraic form Apply the addition multiplication and cancellation properties of equality to solve equations Use substitution to solve equations Write mathematical models to solve application problems Section 14 Logic Identify statements Write the negation of a statement Identify quantifiers Write the negation of a statement with a quantifier Write statements and negations in symbolic form Scarborough adapted with thanks from Lynnette Cardenas 2005 Identify conjunctions and disjunctions and their symbols Write truth tables for conjunctions and disjunctions Determine whether statements are logically equivalent Recognize the symbol for logically equivalent Identify conditional statements implications including the hypothesis and conclusion and its symbolic notation Write a truth table for a conditional statement Be familiar with the 7 different ways conditional statements can be formed see pg 49 Identify and write the 3 statements related to the conditional converse inverse and contrapositive including their symbolic notation Understand that the conditional and the contrapositive are logically equivalent as are the converse and the inverse Identify a biconditional statement and its symbolic notation Write a truth table for a biconditional statement Understand what valid reasoning is Use Euler diagrams to help determine whether valid reasoning is being used in an argument Given a hypothesis use direct reasoning indirect reasoning and the chain rule to determine the conclusion Section 21 Describing Sets De ne a set and its elements members Determine if a set is welldefined Identify the set of natural numbers including its symbol N Write sets both by listing the elements and by using setbuilder notation Determine whether sets are equal Understand and use the definition of onetoone correspondence Understand and use the Fundamental Counting Principle Determine whether sets are equivalent Determine the cardinal number ofa set Determine whether a set is nite or infinite Identify the empty set and the universal set and their symbols De ne the complement ofa set a subset and a proper subset Identify the symbols used to represent the complement ofa set a subset and a proper subset Scarborough adapted with thanks from Lynnette Cardenas 2005 Draw Venn diagrams Determine the complement of a set Determine the subsets and proper subsets of a set Use the cardinal number of sets to show the ideas of less than and greater than Determine the number of subsets and proper subsets of a set Section 22 Other Set Operations and Their Properties Determine the intersection of sets and identify the symbol for intersection Determine the union of sets and identify the symbol for union Determine set difference the complement ofA relative to B and identify its symbolic notation Understand the commutative properties of set union and of set intersection Understand the distributive property of set intersection over set union Use a Venn diagram as a problemsolving tool Count and list the elements in a Cartesian product Section 23 Addition and Subtraction of Whole Numbers Identify the set ofwhole numbers including its symbol W Use a set model to illustrate addition of whole numbers State the de nition of addition of whole numbers using set notation Identify the addends and sum in an addition problem Use a numberline model to illustrate addition of whole numbers Understand the concepts of greaterthan lessthan greaterthanorequal to and lessthanorequalto State and use the de nition of lessthan Identify and use the properties of wholenumber addition closure commutative associative identity Identify the additive identity Identify basic addition facts State and use the three strategies of learning basic addition facts counting on doubles making 10 Identify the difference in a subtraction problem Use a takeaway model to illustrate subtraction of whole numbers Use a missingaddend model to illustrate subtraction ofwhole numbers Scarborough adapted with thanks from Lynnette Cardenas 2005 State the de nition of subtraction of whole numbers using addition Use a comparison model to illustrate subtraction ofwhole numbers Use a numberline model to illustrate subtraction of whole numbers Section 24 Multiplication and Division of Whole Numbers Use a repeatedaddition model to illustrate multiplication of whole numbers Use an array model to illustrate multiplication of whole numbers State the de nition of multiplication of whole numbers using addition Use a Cartesianproduct model to illustrate multiplication of whole numbers State the alternate de nition of multiplication of whole numbers using Cartesian product Identify the factors and product in a multiplication problem Identify and use the properties of wholenumber multiplication closure commutative associative identity zero multiplication Identify and use the distributive property of multiplication over addition for whole numbers Determine the order of operations for addition and multiplication Use a set partition model to illustrate division of whole numbers Use a missingfactor model to illustrate division of whole numbers State the de nition of division of whole numbers using multiplication Identify the dividend divisor and quotient in a division problem Use a repeatedsubtraction model to illustrate division of whole numbers Identify the remainder in a division problem State and use the division algorithm See pg 105 Explain and determine the value of each ofthe following 9 andfor 71 any nonzero whole number n Section 25 Functions Guess the rule given the input and output ofa game Understand and use the notation for a function State the de nition ofa function Identify the domain and range ofa function Determine whether sets ordered pairs and graphs represent functions Scarborough adapted with thanks from Lynnette Cardenas 2005 Sketch and read graphs of functions Determine the equation of the function for a given rule or sequence Determine the composition of two functions Section 31 Numeration Systems Understand what a numeral is De ne a numeration system Identify the properties ofand numerals used in the HinduArabic numeration system Identify the face value and place value ofa numeral in the HinduArabic numeration system Write a number in expanded form Understand the values of the pieces used in baseten blocks unit long flat block Recognize the additive property ofa numeration system Identify the properties ofand numerals used in the Roman numeration system Recognize the subtractive property of a numeration system Recognize the multiplicative property ofa numeration system Convert numbers in the HinduArabic system to the Roman system and vice versa Identify the digits used in other bases including basetwelve Count in other bases including basetwelve Convert numbers in other bases including basetwelve to baseten and vice versa Section 32 Algorithms for WholeNumber Addition and Subtraction De ne an algorithm Use several different algorithms to illustrate addition of whole numbers lefttoright lattice scratch standard Use the equaladdends algorithm and the standard algorithm to illustrate subtraction of whole numbers Add and subtract in other bases Scarborough adapted with thanks from Lynnette Cardenas 2005 Section 33 Algorithms for WholeNumber Multiplication and Division Understand how to use partial products in a multiplication problem Explain how to multiply by 10quot Multiply like bases Use the lattice multiplication algorithm and the standard algorithm to illustrate multiplication of factors with more than one digit each Use repeated subtraction to develop the standard division algorithm Use short division Identify the four steps used in elementary texts to teach division estimate multiply subtract compare Divide by a twodigit divisor Multiply and divide in other bases Section 34 Mental Mathematics and Estimation for WholeNumber Operations Understand and explain the difference between mental mathematics and computational estimation Explain and use the mental math addition techniques adding from left breaking up and bridging trading off using compatible numbers making compatible numbers Explain and use the mental math subtraction techniques breaking up and bridging trading off drop the zeros Explain and use the mental math multiplication techniques frontend multiplying using compatible numbers thinking money Explain and use the mental math division techniques breaking up the dividend using compatible numbers Explain and use the computational estimation techniques for addition frontend grouping to nice numbers clustering rounding using the range Explain and use the computational estimation techniques for multiplication frontend and division compatible numbers Section 41 Integers and the Operations of Addition and Subtraction Identify the set of integers including its symbol Z Determine the opposite of a given integer Use chip charged eld pattern and numberline models to illustrate addition of integers State and use the de nition of lessthan Scarborough adapted with thanks from Lynnette Cardenas 2005 De ne absolute value Solve problems involving absolute value Identify and use the properties of integer addition closure commutative associative identity Identify the additive inverse State the Uniqueness Property ofthe additive inverse Use other properties of integers listed on page 193 Use chip charged eld pattern and numberline models to illustrate subtraction of integers De ne subtraction of integers Restate an integer subtraction problem as an equivalent addition problem Understand the order of operations for integer addition and subtraction Section 42 Multiplication and Division of Integers Use pattern chip and charged eld models to illustrate multiplication of integers Understand the properties of multiplying by negatives see page 204 Identify and use the properties of integer multiplication closure commutative associative identity distributive property over addition zero multiplication Identify and use the distributive property of multiplication over subtraction for integers Understand and use the formula for the difference of squares De ne integer division Understand the order of operations on integers when no grouping symbols are used De ne less than for integers Put integers in order from least to greatest or vice versa Section 43 Divisibility Understand what is meant by one number being divisible by another Understand the different ways of stating that one number is divisible by another Understand what is meant by quotb divides aquot and the notation used Understand and use Theorems 41 and 42 on pages 215 and 216 State and use the divisibility tests for 2 3 4 5 6 8 9 10 and 11 Scarborough adapted with thanks from Lynnette Cardenas 2005 Section 44 Prime and Composite Numbers De ne prime and composite numbers Find the prime factorization ofa number State the Fundamental Theorem of Arithmetic Determine the number ofdivisors for a given number Determine the divisors ofa given number Determine the largest prime that would be a possible divisor ofa given number Once you39ve determined the largest prime that would be a possible divisor list all other primes that could be a factor of the given number Determine whether a given number is composite or prime Section 45 Greatest Common Divisor and Least Common Multiple De ne the greatest common divisor and recognize its abbreviations GOD and GCF Use intersectionof sets primefactorization and EuclideanAlgorithm methods to determine the GOD De ne relatively prime numbers Identify numbers that are relatively prime De ne the least common multiple and recognize its abbreviation LCM Use intersectionof sets primefactorization EuclideanAlgorithm and divisionbyprimes methods to determine the LCM Section 46 Clock and Modular Arithmetic Be able to add subtract multiply and divide in modular arithmetic Section 51 The Set of Rational Numbers Identify the set ofrational numbers including its symbol Q Recognize the different forms of writing a rational number Identify proper and improper fractions Use the Fundamental Law of Fractions to write equivalent rational numbers and to simplify rational numbers De ne simplest form ofa rational number Determine whether rational numbers are equivalent equal using one of the strategies listed on pages 271 272 Put rational numbers in order from least to greatest or vice versa Scarborough adapted with thanks from Lynnette Cardenas 2005 State the denseness property for rational numbers Given two rational numbers find other rational numbers between these two Section 52 Addition and Subtraction of Rational Numbers De ne addition for rational numbers Use area and numberline models to represent addition of rational numbers with like denominators Add rational numbers both with a common denominator and without De ne and identify mixed numbers Convert mixed numbers to improper fractions and vice versa Identify and use the properties of rational number addition closure commutative associative identity inverse Identify the additive inverse ofa rational number State and use the de nition of lessthan De ne subtraction of rational numbers Subtract rational numbers Use common fractions or integers to estimate the values of rational numbers Section 53 Multiplication and Division of Rational Numbers Use repeatedaddition and an area model or use a numberline model to illustrate a whole number multiplied by a rational number Use an area model to illustrate multiplication oftwo rational numbers less than one De ne multiplication of rational numbers Identify the reciprocal ofa nonzero rational number Identify and use the properties of rational number multiplication closure commutative associative identity inverse distributive over addition equality zero multiplication Multiply mixed numbers Use an area model to illustrate division by rational numbers De ne division ofrational numbers State and use the division algorithm for division of fractions Use mental math to find the exact answer in a problem involving rational numbers Scarborough adapted with thanks from Lynnette Cardenas 2005 10 Use estimation to nd an approximate answer in a problem involving rational numbers De ne a quot Understand and use the properties of exponents page 301 Section 54 Proportional Reasoning Understand and compute ratios De ne and use proportions Use ratios and proportions to solve word problems Understand and use the properties of proportions Section 61 Introduction to Decimals Understand how to use baseten blocks to represent decimal numbers Write decimal numbers in expanded form Identify terminating decimals Convert rational numbers to terminating decimal numbers Put terminating decimal numbers in order from least to greatest and vice versa Find decimals numbers between two given terminating decimal numbers Section 62 Operations on Decimals Show a student how to add subtract multiply and divide decimal numbers Convert a number in standard form to scienti c notation and vice versa Use mental math to find the exact answer of problems involving decimal numbers Round decimal numbers to a given place Use estimation to nd approximate values of problems involving decimal numbers Section 63 Nonterminating Decimals Recognize the difference between terminating and repeating decimal numbers Identify the repetend ofa repeating decimal number Use division to convert rational numbers to repeating decimal numbers Scarborough adapted with thanks from Lynnette Cardenas 2005 11 Identify the greatest number ofdigits the repetend of a repeating decimal number may have Convert a repeating decimal number to a rational number Put repeating decimal numbers in order from least to greatest and vice versa Find decimals numbers between two given repeating decimal numbers Section 64 Percents Convert percents to rational numbers and decimal numbers Convert decimal numbers and rational numbers to percents Solve word problems involving percents Use mental math to find the exact answer in a percent problem Use estimation to nd an approximation in a percent problem Section 65 Computing Interest This material was covered in Math 141 and so is not covered in here Section 66 Real Numbers Identify the irrational numbers and their symbol R Q Write examples of irrational numbers including their decimal forms Identify the principal square root ofa number Use the Pythagorean Theorem Use the squeezing process to estimate square roots to the nearest tenth Identify the real numbers and their symbol R State and use the de nition of lessthan Identify the relationships of the number systems we39ve studied N W Z Q R Q R Identify and use the properties of the real numbers Understand and use the properties of radicals and rational exponents

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