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# MATH FOR ELEM TEACHERS MA 201

UK

GPA 3.54

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This 8 page Class Notes was uploaded by Kennith Herman on Friday October 23, 2015. The Class Notes belongs to MA 201 at University of Kentucky taught by Megan Dailey in Fall. Since its upload, it has received 33 views. For similar materials see /class/228136/ma-201-university-of-kentucky in Mathematics (M) at University of Kentucky.

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Date Created: 10/23/15

MA 201 Agenda Tuesday 9809 981 Multiplication as Repeated Addition 0 Example Misha has an afterschool job at a local bike factory Each day he has a 3mile roundtrip walk to the factory At his job he assembles 4 hubs and wheels How many hubs and wheels does he assemble in 5 afternoon How many miles does he walk to and from his job each week 0 De nition Let a and b be any two whole numbers Then the product of a and 1 written a b is de nedby abbbbwhena0 aaddends and 0bb 0 Notation abagtltbababab 982 Models of Addition 0 Set Model 0 Array Model 7 Example Lida planted 5 rows of bean seeds and each row contains 8 seeds How many seeds did she plant in her rectangular plant 0 Rectangular Area Model 7 Example Janet wants to order ceramic tiles to cover the oor of her 4 ft by 6 ft hallway If the tiles are each 1 sq ft how many tiles will she need to order 0 Skip Count Model 0 Multiplication Tree Model 7 Example Melissa has a box of 4 ags7 colored red7 yellow7 green7 and blue How many ways can she display 2 of the ags on the agpole o Cartesian Product Model 7 Example At Sonya s Ice Cream Shop7 a customer can order either a sugar or a wa le cone and one of four avors of ice cream vanilla7 chocolate7 mint7 or raspberry Represent the total set of ice cream orders using a rectangular array 7 De nition The Cartesian product of sets A and B7 written A X B7 is the set of all ordered pairs whoe rst component is an element of set A and whose second component is an element of set E 7 Alternate De nition Let a and b be whole numbers and let A and B be any sets for which a nA and b Then a b nA X B 983 Properties of Whole Number Multiplication 0 Closure Property If a and b are any two whole numbers7 then a b is a unique whole number 0 Commutative Property If a and b are any two whole numbers7 then a b b a o Associative Property If a b and c are any three whole numbers7 then a b c a b c o Multiplication Identity Property of One number 1 is the unique whole number for which I l l b 12 holds for all whole numbers I o MultiplicationbyZero Property 1 whole numbers I 0 b b 0 0 o Distributive Property of Multiplication over Addition 1 If ab and c are any three Whole numbers7 then a b c a b a c and abc acbc 984 After this lecture7 you should be able to understand multiplication of Whole numbers represent multiplication With various models understand the properties of multiplication illustrate the properties of multiplication With the models and manipulatives 985 Before the next lecture7 you should 0 read section 24 in the textbook 0 begin the third homework assignment MA 201 Agenda Thursday 82709 8271 Sets 0 What is a set How are sets useful 0 What are some everyday and mathematical examples of sets 0 How do we describe sets 0 When is a set wellde ned 8272 Venn Diagrams o What is a Venn diagram 0 What is the complement of a set and how do we nd it 8273 Relationships and Operations on Sets 0 De nitions to know subset7 empty set7 intersection of sets7 disjoint sets7 union of sets 0 Use Venn diagrams to illustrate these terms 0 ls there a difference between a subset and proper subset 8274 Properties of Set Operations and Relations 0 ls inclusion transitive 0 Unions and intersections of sets are commutative and associative What does this mean 0 What are the properties of the empty set 0 Are there distributive properties for the union and intersection of sets 8275 After this lecture7 you should be able to o understand the concept of sets and how they are de ned and represented 0 construct a venn diagram to represent a given set 0 understand the set operations and their properties 8276 Before the next lecture7 you should 0 read sections 21 and 22 in the textbook 0 complete the rst homework assignment section 21 37 57 7 107 127 18b7 207 29 0 visit the course website Examples Shade the portion of the Venn diagram that represents the given set 1A B 2 AUB 3 BUC U B C 4 C Z U 5 BUC A U B C MA 201 7 Tuesday 9109 911 Types of Numbers 0 A nominal number is a sequence of digits used as a name or label 0 A ordinal number is used to communicate location in an ordered set 0 The cardinal number of a set is the number of objects in the set 0 What are some examples of these three types of numbers 912 11 u r and 1 Sets 0 A oneitoione correspondence between sets A and B is an assignment for each element of A of exactly one element of B in such a way that all elements of B are used 0 Sets A and B are equivalent if there is a onertorone correspondence between A and B andwewriteA N B o Is the set of seats equivalent to the set of students in our classroom 0 Is DT 17 2 Is 12 17 2 913 Whole Numbers 0 A set is called nite if it is either the empty set or it is equivalent to a set 17 2 3 n for some natural number n Otherwise it is called infinite o The whole numbers let us classify any set according to how many elements the set contains 0 Example For each set below nd the whole number that gives the number of elements in the set Let M is a month of the year A abcz B n E N n is a square number smaller than 200 Z n E N n is a square number between 70 and 80 S 0 914 Representations of Whole Numbers 0 Tiles 0 Cubes c Number Strips and Rods c Number Line 915 Ordering the Whole Numbers 0 Let a nA and b nB be whole numbers where A and B are nite sets If A matches a proper subset of B we say that a is less than b and write a lt b o How can we use the representations of whole numbers to illustrate the order of whole numbers 916 Problem Solving with Venn diagrams 0 Example pg 103 26 At a school with 100 students 35 students were taking Arabic 32 Bulgarian and 30 Chinese Twenty students take only Arabic 20 take only Bulgarian and 14 take only Chinese In addition 7 students are taking both Arabic and Bulgarian some of whom also take Chinese How many students are taking all three languages How many students are taking none of these languages 917 After this lecture you should be able to o understand the concept of equivalent sets 0 understand whole numbers including representation and ordering 0 problem solve with Venn diagrams 918 Before the next lecture you should 0 read section 23 in the textbook 0 begin homework assignment 2 Section 22 2 6 9 l4 22ab 38 4O Section 23 3 4bdf 5 6 9 10 19 27 MA 201 Agenda Thursday7 91009 9101 Division of Whole Numbers RepeatedSubtraction Model of Division 7 Example Ms Rislov has 28 students in her class whom she wishes to divide into cooperative learning groups of 4 students per group If each group requires a set of manipulatives7 how many set of manipulatives must Ms Rislov have available Partition Model of Division 7 Example When Ms Rislov checked her supply cupboard7 she discovered she had only 4 sets of manipulatives to use with the 28 students in her class How many students must she assign to each set of manipulatives MissingFactor Model of Division De nition Let a and b be whole numbers with I f 0 Then a 7 b c if and only if a b c for a unique whole number 6 Example Suppose you have 78 number tiles Describ how to illustrate 78 7 13 wit the tiles using each of the three basic models for division Terminology 7 adividend 7 bdivisor 7 cquotient 9102 Division by Zero Why is division by zero unde ned Useful relationships Eiaforalla b Zilforallb7 0 17 9103 Division with Remainders The set of whole numbers is not closed under division So7 what happens when we have problems such as 27 7 6 The Division Algorithm Let a and b be whole numbers with I f 0 Then there is a unique whole number q called the quotient and a unique whole number 7 called the remainder such that aqb39r Ogrgb 9104 Exponents and the Power Operation De nition Let a and m be whole numbers7 where m f 0 Then a to the mth power7 written am is de ned by a11ifm1 and amaaa ifmgtl W x m terms Terminology 7 abase 7 mexponent or power 7 aMexponential expression Multiplication Rules of Exponentials Let a 12721 and n be whole numbers where m f 0 and n f 0 1 am n 7 am n 2 am V a by lt3 aw 0 De nition Let a be any Whole number7 a f 0 Then 00 is de ned to be 1 0 Why is 00 unde ned 0 Rules for Division of Exponentials Let abm and n be Whole numbers7 Where m 2 n gt 012 f 07 and a b is de ned Then lt1gt W a a m 2 Tm 984 After this lecture7 you should be able to o understand diVision of Whole numbers and exponential expression 0 represent diVision With various mode s o understand the properties of exponential expressions 1 0 illustrate the properties of diVision and A 39 With 39r 985 Before the next lecture7 you should 0 read section 32 in the textbook 0 complte the third homework assignment

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