MATHEMATICS Common Core and STEM Give Meaning to Mathematics When the math wars began in the 1990s on one side were those who argued for a new focus on concepts and reasoning rather than drilling students on their times-tables On the other were the traditionalists who said the progressive approach allowed students to become unmoored from the building blocks of the subject leaving them unprepared for more advanced mathematics The writers of the Common Core math standards have sought a middle ground By the early 2000s every state had developed and adopted its own learning standards that outlined what students in grades 3-8 and high school should be able to do Every state also had its own definition of proficiency which is the level at which a student is determined to be sufficiently educated at each grade level and upon graduation This lack of standardization was one reason why states decided to develop the Common Core State Standards in 2009 The creation of the math standards was in large part an editing process So the Common Core math standards tackle fewer topics and also move students more slowly through arithmetic subtraction multiplication and the other operations that build up to more complex math particularly algebra Applying mathematics during engineering design challenges can help children develop critical thinking problem solving and communication skills Understanding involves making connections Challenging students with important mathematics prepares them to solve problems in class and at home NCTM’s Principles and Standards for School Mathematics 2000 outlines five Process Standards that are essential for developing deep understanding of mathematics 1 Problem Solving 2 Reasoning and Proof 3 Communication 4 Connections 5 Representation Integrated engineering units of study allow for the application of mathematics skills in real-world contexts removing barriers and enhancing the development of NCTM’s five Process Standards and the Common Core’s eight Standards for Mathematical Practice The purpose for learning is evident with a coherent integrated curriculum freeing students to reason about complex problems analyze multiple solutions and communicate ideas and results They develop habits of mind along with the necessary mathematics skills M A T H E M A T I C S W H A T I S 7
A hairstylist uses math to measure the chemicals to color hair Businesses use mathematics when dealing with money Stores add up our bills using math Math is also the basic tool used by scientists and engineers They use it to describe the universe and everything within it Math isn’t just for school Math is everywhere and we use it every day Number Systems Humans have used numbers for a very long time Throughout the history of man every culture used some form of mathematics The numbers that we use today have been around for thousands of years The Base Ten System Today we use a base ten number system The digits used in base ten are 0 1 2 3 4 5 6 7 8 9 Using those 10 digits we can make any number in the system The base ten system was probably created because we have ten fingers to count on There are other bases as well Some bases use more than ten numbers Some use fewer What numbers can you make with these digits S C I T A M E H T A M S I T A H W 8 MATHEMATICS Digits Whole Numbers 5 7 57 75 1 3 9 139 193 319 391 913 931 In the base two system only two The Base Two System Binary Numbers digits are used They are 0 and 1 Most computers use the binary system Binary numbers are base two because all numbers can be made using zero or one Let’s look at how the base ten numbers look in binary Can you figure out the pattern The Base In Base Two There Would Be Ten Digits 0 1 2 3 4 5 6 7 8 9 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001
MATHEMATICS W H A T I S M A T H E M A T I C S 9 Base two is difficult for humans to use Larger numbers get very large The number 100 in base two is 1100100 Roman Numerals In ancient Rome people wrote numbers differently They used Roman numerals Roman numerals that look interesting but they are hard to use in mathematics Arabic Numerals Today we use Arabic numerals The digits 0 1 2 3 4 5 6 7 8 9 are all Arabic numerals These numerals were developed in the Middle East thousands of years ago This clock shows that it is seven minutes to one Roman Numerals Arabic Numerals I1 II 2 III 3 IV 4 V5 VI 6 VII 7 VIII 8 IX 9 X 10 L 50 C 100 D 500 M 1000 The Biggest Number is Infinity Infinity is used to describe a number that goes on forever You can never reach infinity no matter how high or low you count In 1665 mathematician John Wallis 1616 1703 created a symbol for infinity and we still use his symbol today The symbol for infinity looks like a sideways 8 8 digit DIJ-it any Arabic numerals from 1 to 9 and sometimes 0 number NUHM-bur a word or symbol used for counting and for adding and subtracting numeral NOO-mur-uhl the symbol that represents a number such as 4 or IV
Numbers Numbers are everywhere We use numbers to tell time They help us count money We measure food with them We use numbers in everything we do Numbers are an important form of communication Every language on the planet has some form of number system Look around and see all the numbers in your world S R E B M U N We use numbers in recipes MATHEMATICS The Federal Reserve prints a serial number on each bill printed There are a maximum of 832 bills with the same serial number Serial numbers help prevent counterfeiting There are many different types of numbers The most common are whole numbers Whole numbers are the ones we use for counting They are numbers like 1 4 15 27 and 42 They are also called natural or positive numbers A positive number is greater than zero Sometimes numbers are negative This means that they are less than zero A negative number looks like a whole number with a minus sign in front of it the negative numbers and zero combined Integers are all the natural numbers Digital clocks display the time using numbers NEGATIVE NUMBERS POSITIVE NUMBERS 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 10
