MTE 280

George Rolya has a 4 set processes when it comes to the problem-solving process:Step 1. Read the problem Step 2. Plan- ( using problem-solving strategies) This is the longer step and takes the most amount of time Step 3. Implement the plan- ( due to prior work in step 2 this step is a lot easier) Step 4. Look back and look to see if the answer is reasonable*It is important to remember what the problem is asking you!

There is more than just one number system, with that being said one thing could have different meanings are you shift between each new design. As you say the number you read is the value of each symbolExpanded notation is where we write the number as common parts Example:347 is the same as 300+50+7 and this is also the same as (3x100)+ (5x50)+ (7x1) and this is also the same as (3x10 to the 2n power)+ (5x10 to the 1st power)+ ( 7 x10 to the zero power)*All these result in the same thing and have the same value

In America, we use the base ten number systems but there are many more systems used around the world In base 10 we use the number 0,1,2,3,4,5,6,7,8,9 We don't include the number 10 because we can't have more ones than the base we are in. When we write the number 10 in base ten this means was have 1 10 and 0 ones this rule applies to every base you are using More examples of this are when we are using base 5 the numbers we use are 0,1,2,3,4, If we have the number 124 in base 5 there is a way to convert this into our base 10 value The first step we would take would be to break down each part we would first we would take the 1 and in base 5 this 1 is 25 because it is the 25's place then we would look at the 2 and this is really 2 5's and that we would lastly take the 4 ones and we would all them all together. it would be like this =(1x5to the 2nd power) + ( 2x 5 to the 1st power) + (4x 5 to the zero power) =25+10+4=39 so the number 124 in base 4 is 39 in base 10Another example:153 in base 5 If you notice that there is a 5 in the 5's place this is important because we are unable to do anything since it isn't possible to have a 5 in base 5 this rule applies to all bases not just 5 you can't have a number higher than the base your in For example:the number 123 in base 2 doesn't work because in base 2 we can only use 0,1 we can also take numbers in base 10 and covert them into different basesFor example:if we had the number 12 the number 12 in base 9 would be 13 How we would do this is by taking the number 12 and figuring out how it would be written in base 9. Since we can take 1 9 out of 12 we would pit a 1 in the 9's place and since would only have 3 left which isn't enough to make another 9 we would put the remaining 3 ones in the ones place making 12 in base 10, 13 in base9

1. Identity: A+0=a With the identity operation, the identity of the number never changes when you add 0 to any # the dignity will never change2. Communicative property: A+B= B+A The order you add numbers doesn't matter they are all the same and you will get the same order no matter what order you write the number in 1. Assocative property: ( A+B) + C= A + (B+C) Groups of 3 can be written in any order and mean the same thing Subtraction 1. Take away: 5-2=3 2. Compansion: Anna has 5 books and Ted has 3 how many more books does Anna have? Is it not an addition or subtraction problem just looking and comparing 3.Missing addend: 3+ ?=7 Not a takeaway problem/trial and error Multiplication 3 Different types of counting Count as a wholeskip counting 2,4,6group counting 1. Identity property: Ax1=Amultiplying by 1 the identity of the number doesn't change 2. Zero property: Ax0=0 when multiplying by o the product is always zero 3. Commuative proppant: AxB=BxAorder when multiplying doesn't matter the answer is the same no matter what. 4. Assostive property: (AxB) x C= Ax (BxC)Groups of 3 can be written in any order and mean the same thingDivision 3 parts to a division problem: the quotient, division, and dividend