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1. Group 6: Stephanie Crow, Millennia Franco, Christine Yang

   We analyzed multiplication.

   For Tabitha, she arranged the factors that they were multiplying along the top and side of the grid using the lattice method. For example: 1×1, 2×2, 1×3, 2×3. They then split their answers along the diagonal for the tens and ones for each answer. So for each answer, they’ll put a 0 in the space if there was only a ones column. Lastly they used the diagonal rows in the grid and wrote the sum of each diagonal along the row. So, they added 0+1+0 and got the 1. They added 3+0+2 and got 5. Therefore, the answer 156 for 12×13. For the second problem she did, they arranged the factors they were multiplying along the top and side of the grid, then they multiplied the number that meet in each space grid for example 4×6=24 3×6=18 4×2=8 3×2=6. they they split their answers along the diagonals for the tens and ones for each answer for example for 24 the 2 when in the tens place and the 4 in the ones place. lastly they used the diagonal rows in the grid and wrote the sum of each diagonal along the row. 2, 0+4+4=6, 8+0+8=6. Then they got 2666.

   For Sasha, she proceeded to answer the multiplication problems using the an algorithm very similar to the standard algorithm. For 12×13, she did 12 on the top and 13 on the bottom. She first did 2×3 which is 6. She added a 0 under the 6 as a place holder. She then multiplied 3×1 which is 3 which now becomes 30 under the 6. Under the 30, she adds another 0 and multiplied 1×2 which 2. This becomes a 20. So far, she as 6, 30 and 20 lined up underneath each other. After this, she adds two zeros and multiplies 1×1 which is 1, making it 100. She adds up 6+30+20+100 and gets 156. Her process was similar to the second multiplication problem as well. She used the standard algorithm to answer 43×62. She broke up her answers and making sure to add the place holder 0 to line up her answers which gives the correct answer, 2666. This student’s process works as it is an extended version of the standard algorithm. She multiplied top to bottom and then diagonally and while doing so, she added 0’s to be place holders. Her answers were correct. Something she also did was, instead of multiplying diagonally like in the standard algorithm, she kept adding the zeros to make it easier for her to add afterwards.

   For Emily, Emily broke up the problem into parts. The 12 she split into 10 then 2. Therefore she did 10x 13 and 2×13. Then added the answers up for those so 130+26. Same thing with the second problem she split 43 into 20,20, and 3. She did 20×62 then 20×62 and 3x 62. She add those answers 1240+1240+186 and got 2666.This process works because she was able to break down the numbers within their place values and it’s similar to the standard algorithm.

2. Janettza, Titiana, Justine

   The operation we analyzed was an addition.

   For the student named Kelly, she took her addition problem which was 567+259 and she first added 500 and 200 which gave her 700. After she added 60 and 50 which gave her 110. Finally, she added 7 and 9 which gave her 16. To get her final answer she added 700+110+16 and got 826.
   For the student named Rudy, they went about their problem by first adding 200 to 567 which gave them 767, then they added 50 to that and it gave them 817, and finally, they added 9 to get 826.
   Andy decided to solve the problem by making 567 into 600 by adding the 33 from 259 which makes that number become 226 (259-33+226). The final step is to add 600 and 226 which gave him 826.

   The way the students went about solving these problems work because they made sure to add up all the place values and used different steps to get their answers. This relates to the standard algorithm of addition because they followed a step-by-step procedure to get their total.

   • Thank you Janettza 🙂

3. GROUP1-Uzrah,Rashmit,Rabia,Muniba
   https://docs.google.com/document/d/12OgqIAugo13B0SQd56NGVUVJ7ybdIkzSWzbsxGr9Dqg/edit?usp=sharing

4. – Caralyn, Yaquelin, and Liufen- Group 3
   – Multiplication
   – Sasha–> Standard Algorithm: multiply the top number by the bottom number one digit at a time, working your way from right to left
   – Emily–> She broke up the problem (place value- leads to algorithm and partial addition)
   – Tabitha–> She drew a rectangle & drew 3 lines going vertically. Then, she drew the diagonal lines and wrote the 4 numbers and multiplied, then added the numbers vertically. In other words, Tabitha first put 12 and 13 on top and the side and multiplied each number. For example, 1 x1 is 1 and 2 x 3 is 6. She kept doing that and then did what is 2-1, 2+3, and 6 and got 156
   – the strategy that Sasha used worked because–> even though using long multiplication takes a long time, she still used this strategy to get to the correct answer– she used a repeated process while multiplying each number separately.
   – the strategy that Emily used worked because–> she broke up the problem into different pieces to make it easier to multiply, therefore allowing her to use this strategy to get to the right answer- she breaks the problem up and makes sure each part is equal.
   – the strategy Tabitha used worked because–> she broke down the multiplication in different parts. She multiplied the number on top of the box with the number to the right of the box and wrote the answer in that box. She then added the numbers in the box diagonally, carried to the next diagonal if necessary and was able to get her answers–> keeps the numbers and multiplication organized and helps when it comes to regrouping.

5. Group 4: Angela, Michelle, Ashley
   Operation Analyzed: Division
   Doug: Used place value to break down the numbers. Started with the hundreds place (100×5)=500. Then moved on to the tens place for three rows (10×5), 50 (3x). Last, he moved to the ones place and did (7×5).The students algorithm works because she used a new strategy that was able to give her the answer of 689/5.
   Nancy: Used long division to solve the problem. She started in the hundreds place and worked to the ones place. This method worked because it breaks the problem down into simpler steps. It allowed her to get the correct answer, 137 r 4.
   Madelaine: used simpler numbers that are divisible by 5 to break 689 into easier numbers to work with. Her algorithm works because she used a strategy easy for her to get to the answer of the problem.

6. Group 5 Division:

   https://docs.google.com/document/d/1bIIl8f3lBBNSqJyuLQ3IXw8s5K5zA1Fqs6OUrk4HiCM/edit

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