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October 13th

By Saturday, October 16th, please respond to the post with:

Your name and the name of your group members.

What operation that you all analyzed.

Your notes on what each student did to answer the question.

An explanation of why the student’s process works and how it relates to the standard algorithm.


4 Comments

  1. Group 4 Analyzing Students Thinking: Each member of my group picked one persons to analyze. My answer is for Doug: Dough utilized Partial Quotients Strategy to solve his answer along with long division. He must’ve been more comfortable with multiplication which is okay because it’s the inverse of division. The first thing he asked himself was what number he could make to get him closest to 689. He started off by using simple numbers like 100 that are easy to multiply. So he knew that 100 times 5 gave him 500 and subtracted it from 689 to give him another friendly number to work with. He repeated the same thing with the new sum 189. He thought once again what easy number he can use to get close to 189 which was 10 to give him 50 and this continued twice more. Lastly when he reaches 39 he asks himself how many times does 5 go into that number and he knows 7 times to give him 35. He adds up all of his estimates (100+10+10+10+7) to get the answer 137 with a remainder of 4. He is correct.

  2. Group 3 – Eric, Jasmine, Kiara
    We analyzed multiplication.

    Sasha multipled by breaking down both numbers by place value and using the distributive property. (10+2)x(10+3) -> (10×10)+(10×3)+(2×10)+(2×3)

    Emily multipled by rewriting the problem using the distributive property. i.e. (12X13) -> (10+2)X13 -> (10X13)+(2X13) = 156

    Tabitha multiplied using lattice multiplication, breaking down both numbers into their place values.
    The student’s process works because each student solved the problem in categories or in parts.
    Sasha and Emily’s methods work because both of them are simply breaking down the multiplication of the numbers into parts. The numbers are essentially broken down by place value using expanded forms of the numbers and then the distributive property tells us that multiplying the sum of two or more addends provide the same result as when each attend are individually multiplied then added together.

    This relates to the standard algorithm because instead of having to multiply and regroup, using the distribute proprty allows students to write everything out.

    The student’s work relates to the algorithm method because all three used a step- by-step process which is called the Lattice Method, in-order to align and problem solve. The studuents also used a series of facts and transformed them into parts.

  3. Subtraction
    Nayoung Choi, Lacey Deans, Ha Young Jung

    Caitlin: Caitlin is breaking 18 into 10+8 which is correct. Then she subtracted 10 from 63 (63-10=53). From there she counted 8 backwards by writing down the numbers (52, 51, 50, 49, 48, 47, 46, and 45), which meant 53-8=45. She has an correct answer and this algorithm is working. This relates to the standard algorithm because she is doing step by step to solve the question by breaking the number into a familiar number and counting backwards.

    Louis: Louis used the regrouping method. Since he cannot subtract 8 from 3, he gave a set of 10 to both 63 and 18, which is not 60&13 and 28, respectively. Then he subtracted 8 from 13 (for ones place) and 2 from 6 (for tens place) → 5 ones and 4 tens = 45. Louis’ method works because he is adding 10 to the first number and also adding 10 to the second number.

    Kenley: Kenley started from 18 and worked up to get 63. He counted up four 10s from 18 to 58(18→28→38→48→58) and then counted up 5 more from 58 to 63 which was (58+5=63). (40+5=45). This algorithm works because he shows that he can count backwards and it was easy to count by 10 and it was done in order.

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