1. American-Standard (not really the best)  R ---> L No mention of place value By natural instict students will think or want to start from Left to Right 2. Partial Sums 3. with emphasis on Place Value   Asking students to do the steps need to talk about place value for student to understand One of the best algorithms 4. Left to Right  More natural for the student to start from left to right mentions place value 5. Expanded Notation  we want to strive for students to understand each step, place value, and why instead of just memorizing the addition and just needing to carry a number 6. Lattice 

 no reference of place value Right to left Last step after learning other methods 2. European-Mexican  instead of 1 less from the value take from the top it changes to 1 more for the bottom value 3. Reverse Indian  Borrow from the bottom instead 4. Left to Right 

Base 2: 0,1 Ones=2^0 Two's= 2^1 Four's= 2^2 Eight's= 2^3 Examples: 101011 base 2 = (1x2^5)+(0x2^4)+(1x2^3)+(0x2^2)+(1x2^1)+(1x2^0) = 32+0+8+0+2+1 = 43 101011.11 base 2= 43+(1x1/2)+(1x1/4) = 43+1/2+1/4 = 43+ 2/4+1/4 = 43 3/4

Base 3 & 5 Notes Drawn Example

1. Give the Base-10 numeral for each given number. Use expanded notation to explain your answer: 10^0=1 10^1= 10 10^2=100 10^3=1000 10^4=10,000 10^5= 100,000 a) 41.58= (4x8^1)+(1x8^0)+(5x1/8) = (4x8)+(1x1)+(5/8) = 32+1+5/8 = 33 5/8 b) 13415= (1x5^3)+(3x5^2)+(4x5^1)+(1x5^0) = (1x125)+(3x25)+(4x5)+(1x1) = 125+75+20+1 =221 2. Write the number 12 in each given base: a) Base 9  b) Base 8  c) Base 7 

Homework #3

Addition putting things together Identity Order Property a+0=a 4+0=4 -2+0=0 0.25+0=0.25 3/4+0=3/4 Commutative Property a+b=b+a Associative Grouping Property (a+b)+c= a+ (b+c) (3+4)+1=3+(4+1) Subtraction - different meanings Take away (no difficulty remembering) (makes most sense to students) Comparison? - Katie has 2 markers, Marks has 5 markers, How many more does Mark have? Missing addends - no properties; subtracting 3 is like adding -3 Multiplication "Groups of..." & repeated addition Identity Property ax1=a 7x1=7 (identity doesn't change) Commutative Property axb=bxa Associative Property (axb)xc= ax(bxc) Zero Property ax0=0 (anything times 0 = 0 always)

Ones= 10^0 Tens= 10^1 Hundreds= 10^2 Thousands 10^3 375= 300 +70+5 = (3x100)+(7x10)+(5x1) = (3x10^2)+(7x10^1)+(5x10^0) Base 10= 0,1,2,3,4,5,6,7,8,9 Base 5= 0, 1,2,3,4 Ones= 5^0 Fives= 5^1 Twenty-fives= 5^2 One-Hundred Twenty Fives= 5^3 121 base 5 = (1x5^2)+(2x5^1)+(1x5^0) = (1x25)+(2x5)+(1x1) = 25+ 10+ 1 =36 think about values of the digits depending on what base your in 375.32 = (3x10^2)+(7x10^1)+(5x10^)+(3x1/10)+(2x1/100) 121.5 base 5 = (1x5^2)+(2x5^1)+(1x5^0)+(3x1/5) = (1x25)+(2x5)+(1x1)+(3/5) = 25+10+1+3/5 = 36 3/5

(a) 1,075.31 = 1,000+70+5+3/10+1/100 = (1x1,000)+(7x10)+(5x1)+(3x1/10)+(1x1/100) = (1x10^3)+(7x10^1)+(5x10^0)+(3x1/10)+(1x1/100) (b) 79.003= 70+9+3/1000 = (7x10)+(9x1)+(0x1/10)+(0x1/100)+(3x1/1000) = (7x10^1)+(9x10^0)+(3x1/1000) (c) 1212 base 5= (1x5^3)+(2x5^2)+(1x5^1)+(2x5^0) = (1x125)+(2x25)+(1x5)+(2x1) = 125+50+5+2 (d) 32.12 base 5= (3x5^1)+(2x5^0)+(1x1/5)+(2x1/25) = (3x5)+(2x1)+(1/5)+(2/25) =17 7/25 (e) 2123.34 base 5= (2x5^3)+(1x5^2)+(2x5^1)+(3x5^0)+(3x1/5)+(4x1/25) = (2x125)+(1x25)+(2x5)+(3x1)+(3/5)+(4/25) =250+25+10+3+3/5+4/25 =275+13+15/25+4/25 =288 19/25

Base 3: 0,1,2 Ones=3^0 Threes+3^1 Nines= 3^2 Twenty sevens= 3^3 2122.12 base 3= (2x3^3)+(1x3^2)+(2x3^1)+(2x3^0)+(1x1/3)+(2x1/9) = (2x27)+(1x9)+(2x3)+(2x1)+(1/3)+(2/9) =60+11+3/9+2/9 = 71 5/9 Base 8: 0,1,2,3,4,5,6,7 Ones= 8^0 Eights=8^1 Sixty-fours= 8^2 512s= 8^3

 Using pants and shirts as a demonstration you can see the different combinations that you can do with the orange and purple pants to the white, red, and blue shirts. Each pant can be paired with one of the different shirts meaning you have 3 different combos for each pair of pants. You can draw out each combo or use math. 3 orange pant combos + 3 purple pant combos = 6 combinations or 2 pants x 3 shirts = 6 combinations Multiplication can be done since it shows how much of each pant or shirt you have and multiplying 3 and 2 together you are trying to get the amount of times each clothing piece can be combined to make a different combinations.

 Base 10 is the values of the 10s in different place values. No matter the place the 10 base each digit in one of the different place values shows a different quanitity Ones = 10 of the one's single unit Tens= a unit of 10 units together Hundreds= 10 units of 10 ten's Thousands= 1000 units of 10 of the 100's

Number Base 10 Example

Decimals

Examples

4 Steps to Solving Problems Understand the problem Know what is being asked from you to do or show Can you say what the problem is asking in your own words? 2. Devise a plan plan what strategy you are going to use in order to solve the problem 3. Carry out the plan Trial and Error, if one strategy doesn't work try another one Charts, diagrams, drawing, tables, etc. 4. Reflect/ Look Back Does the answer make sense to the question? What did you learn from doing the problem? Are all the questions answered?

Student Methods

Writing Out

Drawing Pictures

Acting Out

1. There are 12 basketball teams in a league. If each of the teams plays each of the other teams once and only once, how many games take place?  2. I have four 3-cent stamps and three 7-cent stamps. Using one or more of these stamps, how many different amounts of postage can I make?