Elementary Mathematics

642,538.192 PLACE VS. VALUE:6 : hundred thousands PLACE vs. 600,000 VALUE4 : ten thousands PLACE vs. 40,000 VALUE2 : one thousands PLACE vs. 2,000 VALUE5 : hundreds PLACE vs. 500 VALUE3 : tens PLACE vs. 30 VALUE8 : ones PLACE vs. 8 VALUE1 : tenths PLACE vs. 1/10 VALUE9 : hundredths PLACE vs. 9/100 VALUE2 : thousandths PLACE vs. 2/1,000 VALUE

EXPANDED FORM:642,538.179(6 x 10ˆ5) + (4 x 10ˆ4) + (2 x 10ˆ3) + (5 x 10ˆ2) + (3 x 10ˆ1) + (8 x 10ˆ0) + (1 x 10ˆ-1) + (7 x 10ˆ-2) + (9 x 10ˆ-3)WORD FORM:642,538.179Six hundred fourty two thousand, five hundred thirty-eight AND one hundred seventy nine thousandths

ARRAY: 9 X 3 NUMBER LINE: 2 X 8+2 +2 +2 +2 +2 +2 +2 +2______________________________________________________1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16REPEATED ADDITON:5 X 8 5+5+5+5+5+5+5+5SKIP COUNTING: 7 X 67, 14, 21, 28, 35, 42

Typically we count in base 10, but we learned how to count in other bases this week. For example: if you are counting in base 4, you will not have a number 4or over in your number. - - - - - - - - - - (10 in base 10)These are 12 base 10 dots, but if I wanted to count these in base 4, it would be: __0__ __2__ __2__4ˆ2 4ˆ1 4ˆ0 So are there any groups of 16 in the number 10? No, therefore there would be a 0 in the 4ˆ2 column. There are 2 groups of 4, so there would be a 2 in the 4ˆ1 column, and there are 2 left over after that, therefore there would be a 2 in the 4ˆ0 column

543 + 279EXPANDED FORM:500 + 40 + 3200 + 70 + 9 _______________700 + 110 + 12 = 822TRADITIONAL ALGORITHM:11543+279________822NUMBER LINE: +100+100 +10+10+10+10+10+10+10+1+1+1+1+1+1+1+1______________________________________________ 543 743 813 822BASE TEN BLOCKS: Since there are 12 ones blocks, you cross out 10 of them and bring over and add another tens block. There are then 12 tens blocks, so you cross out 10 of them to equal another hundreds block.

570-278EXPANDED FORM:400 160 10500 + 70 + 0-200 + 70 + 8_________________200 + 90 + 2 TRADITIONAL ALGORITHM:4 16 105 7 0 - 2 7 8 __________292NUMBER LINE:-100-100-10-10-10-10-10-10-10-1-1-1-1-1-1-1-1________________________________________________________________570 370 300 292BASE TEN BLOCKS: You start with 5 hundreds blocks, 7 tens, and 0 ones. You borrow a tens block to the ones place, which then makes it 10 ones, to be able to take away 8 which leaves you with 2. You borrow a hundreds block to the tens to be able to take away 7 which then leaves you with 9. And you take away 2 hundreds blocks.

AREA MODEL: 312 X 92 (300x90) + (300x2) + (12x90) + (12x2) 300 + 12 90 27,000 + 1,080 + 2 600 + 24 27,000+1,080+600+24 _____________28,704 PARTIAL PRODUCTS:7,182X 153_____________6 (3X2)240 (80X3) 300 (100X3)21,000 (7,000X3)100 (50X2)4,000 (50X80)5,000 (50X100)350,000 (50X7,000)200 (100X2)8,000 (100X80)10,000 (100X100)700,000 (7,000X1000)____________________________1,098,846TRADITIONAL:5,361X 425_____________268051072202144400_____________2,278,425

FACTOR NINJAS:Factors of 12: 1, 2, 3, 4, 6, 12MULTIPLE MONSTERS:Multiples of 12: 12, 24, 36, 48, 60, 72, ...FACTORS OF 72: 1 X 722 X 363 X 244 X 186 X 128 X 9PRIME NUMBERS: Numbers that are only divisible by 2 natural numbers (themself and 1) 2, 3, 5 ,7, 11, 13, 17, 19, 23, 29, 31 ,37, 41, 43, 47, 53, 59, 61, 67, 71 73, 79, 83, 89, 97, ...For example, you can only divide 53 by 53 and 1 to get a natural numberPRIME FACTORIZATION: 75: 3 X 5 X 5The reason this is prime factorization is because these three numbers are prime numbers, meaning they can't be broken down any further. If they were able to be broken down further than that wouldn't be prime factorization. For example: 75 is multipliable by 15 and 5, but 15 is also multipliable by 5 and 3, therefore it turns into 5 X 5 X 3 instead of 5 X 15.