1. Week 3
1.1. Addition
1.1.1. - Addition is to JOIN - The numbers being added are the addents and the outcome is the sum - Identity Property: When you add any number with zero the identity of that number does not change - Commutative Property (ORDER): The order in which you add two numbers does not impact the sum - Associative Property (GROUPING): The way in which you group the numbers does not matter Algorithms: - Standard American (How we learn addition in the U.S.) - Partial Sums (Draw lines through each number to make it easy) - Partial Sums with emphasis on place value (Same as previous algorithm, but it focuses on each numbers place value) - Left to Right (Solve problem from left to right) - Expanded Notation (Write out each value of each number in the problem and then solve) - Lattice Algorithm (Create box under the problem, split it 3 ways, draw diagonal lines, solve)
1.2. Subtraction
1.2.1. - Subtraction is to take away (comparison, missing addent) - Top number is minuend - Bottom number is subtrahend - The answer is the difference Algorithms: - American Standard (The way we are taught in the U.S.) - European- Mexican (Add to subtrahend instead of taking from the minuend) - Reverse Indian (Goes from left to right with no emphasis on place value) - Left to Right (Solve the problem from left to right with emphasis on place value) - Expanded Notation ( Write out the problem before solving from right to left) - Integer Subtraction (Solve from right to left)
2. Week 4
2.1. Multiplication
2.1.1. Multiplication = repeated addition - In class we looked at examples using blocks, arrays, skip counting, and number lines - In a multiplication problem the numbers being multiplied together are the factors and the answer is the product Properties: - Identity: Multiplying any number by one does not change the number (A x 1 = A) - Commutative: The order in which we multiply the numbers does not matter (A x B = B x A) - Zero: Multiplying and number by zero gives you zero ( A x 0 = 0) - Associative: The way in which you group the numbers does not matter (A x B x C = B x A x C) - Distributive: Allows students to redistribute numbers to make the problem easier A x (B+C) = (A x B) + (A x C) Algorithms: - Standard: The way in which children in the U.S. learned multiplication (should be taught last) - Expanded Notation: Breaks down the problem and shows place value - Place Value: Multiply each individual set of numbers to emphasis the importance of place value - Lattice: Box with diagonal lines that maps out the problem for the student to see
2.2. Division
2.2.1. 3 different division signs (line with 2 dots on top and bottom, fraction bar, and vinculum) - Number being divided is the divident - Number going into the other number is the divisor - The answer is the quotient - The leftover number is the remainder - Can use long division or boxes to practice
2.3. https://www.youtube.com/watch?v=PsKPMg11qFk
3. Week 1
3.1. Problem Solving
3.1.1. - Teaches students strategies that they can remember because they found them on their own - Wooden sticks activity (turn 4 boxes into 3 by moving 2 sticks) - Colorful block activity - Sandwich problem (my group used blocks to solve this problem by having each color block represent a part of the sandwich) - Handshake problem (solved this problem by using letters to represent each person and grouping them together)
3.1.2. 4 Steps in Solving Problems
4. Week 2
4.1. Base Numbers
4.1.1. - 2,375.32 ( thousands, hundreds, tens, ones, tenths, hundreths) - Anything to the zero power is ONE - Depending on what base you are in will depend on what numbers you can use Base Five: 0,1,2,3,4 - STOPS AT 4 (one to five relationship) - You can't have a number higher than 4 in base 5 Base 2 is also known as Binary which means it is used for computers - In base 2 the only numbers we can have are 0 and 1 Base Ten: 0,1,2,3,4,5,6,7,8,9 - Stops at 9 - One to ten relationship