MTE 280

Numeration System357 ↑ Ones - The number system identifies the value of numbers by the 357 position the number that is in. ↑ Tenths357↑ Hundredths

Expanded Notation - Power of 10:Expanded Notation is writing a number to show the value of each digit. one important factor is understanding place value, and that zero still holds a place in your number. 207 This number would be identified as 2 hundred ↑ and seven. (The zero holds place for the tenths place). Examples of Expanded Notation - Power of 10 Example 1257 = 3 (Hundred) + 5 (tenths) + 7 (ones) = 300 + 50 +7 = (3 x 100) + (5 X 100) + (7x1) = (3 x 10^2) +(5 X10^1) + (7 x10^0)Example 2270 = 2 (Hundred) + 7(Tenths)+ 0 (Ones) = 200 + 70 + 0 = (2 x 100) + (7 x 10) +(0 x 10) = (2 x10^2) + (7 X 10^1) + (0 x 10 ^0)Base 5 - Expanded NotationExample 1211 (5)(2 x 5 ^2) + (1x 5^1) + (1x5^0)(2x 25) + (1x5) + (1x1)= (50) + (5) + (1) = 56

Base 10 Ones = 10^0Tenths = 10^1Hundredths = 10^2Thousandths = 10^3 Power of 10{0,1,2,3,4,5,6,7,8,9} In the base 10, the number system starts at 0 up to 9 and consistently repeats, creating the base 10 pattern. Base 5 ones = 5^0 Fives= 5^1 25 = 5^2 125 = 2^3Power of 5 {0.1.2.3.4} In the base 5, the number system starts at 0 to 4 and consistently repeats. In this no system no number can be larger than 5.

Base 2{0,1)ones = 2^0Twos= 2^1Fours= 2^2Eights= 2^3Example 1:10101 (6) step one - Use Expanded notation to solve.(1 x2^4) + (0x2^3) + (1 x2^2) + (0x2^1) + (0 x2^0) 16 + 0 + 4 + 0 + 1 = 21Example 2111 (2)step one - Use Expanded notation to solve.(1 x 2^3) + (1x2^1) + (1x2^0) 4 + 2 + 1 = 7

Bases(Examples of Bases two, three)Example 1:29 in base 3 xxxxxxxxxxxxxxxxxxxxxxxx xxxxx29=1002 (Base 3)base 3:ones threes nines twenty sevens Example 269 in Base 2xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx69=1000101 (Base 2)Base 2:ones twosfours sixteen'sthirty twos' sixty fours'

Addition Terms:Put togetherJoinCombine Sum properties: Property 1: Identity Property (a + 0= a) Examples(4 + 0 = 4)(1.12 + 0 = 1.12)Property 2: communicative Property (a+b=b+a)(4+3=3+4)(5+3=3+5)property 3: Associative Property ( a+b) +c=a+ (b+c)Examples(1+3) + 4= 1+(3+4)(9+1)+3= 9+(1+3)Terms Together Grouping

Subtraction Subtract means to take away. As a future educator I must be able to provide a variety of ways to teach students how to subtract. (Visually, or through representing pure knowing of placement value.) create a clear action.Example one:Zoey wants to make 8 cards. She already made 4 of them. How many more cards does Zoey need to make? Zoey . Card 1. Card 2. card 3. Card 4. Card 5. Card 6. Card 7. Card 8Clear action: How many more cardsI have 8 cards I need to make, and I already have 4, so I only need 4 more cards to make 8. 8-4=4

MultiplicationMultiplication is repeated addition. Terms.3 x 4 = 12↑ ↑ Factors 3 x 4 = 12Product ↑Multiplication is putting numbers in groups.Example3 groups of 2++ ++ ++++++++3x2=6