# Math 165: Assignment 6

1. Make up three word problems with 56 divided by 6

In  each  problem , the remainder  should  be  handled  differently  as   we    talked about in the zoom session ( please watch the recording if you could not attend ).

2. We have established that division is a repeated subtraction

Do 784 divided by 13 by doing repeated Subtraction.It will take a while, take your time and but do it . The idea is to “feel “ it and then to “appreciate “ the algorithm for division which of course will be much faster right provided you know multiplication .

3. Now we also saw that we can do a division for example 24 divided by 8 by finding how many groups of 8 we have in 24 ? and you can certainly count them by drawing 24 things and counting how many of 8 you have.

Now if you have a bigger number like say 356 divided by 3 and you wanted to use that method It will be hard to draw all 356 but you could draw 3 blocks of 100, 5 blocks of 10 and 6

And then you can look at the groups of 3 by blocks. Doing this method of base 10 representation is a step to understand our standard algorithm of division.

4. Do 852 divided by 7 using the method of base 10 representation. You can draw the 100 and 10 blocks. Be creative and remember the idea is to separated in group, and if you don’t have enough you can break up blocks. An example is given in the lecture.

• Do the same operation 852 divide by 7 using our standard division algorithm ( that is our long division ).
• Reflect on this algorithm of division

This is a reflection, those questions are designed to help you think about it Do you remember how to do it ? Did you like it ? Was it hard when it came to two or three-digit numbers? Can you make sense of it now you can fundamentally understand what division it ? Is anyone from another country learned a different display of it?

5. I  posted  google  slides  on “Alternative  way  of  doing  divisions “ from “Math Matters “ Understanding the math you teach .”

“ Analyzing students thinking division “ .I also posted the response .Read it and write about the  three  different  ways  that  the  student  approached  it , sort  of  a  paragraph summarizing what you have understood about it.

Fill in the Out column tor the In-Out Table below where the rule is that the Out = ln2

Find a way to get the Out numbers when you know the In ones that does not require the full , long multiplication. Don’t look for a pattern between the Out numbers going down the column, but look for some way that you can tell exactly what the out number will be from knowing the In number {left to right). Describe your method. (Hint: You will need one pattern for the digit(s) on the right of the out number and another pattern for the digit(s) on the left ). Justify your rule from part b by using pictures and/or by algebra.

Below are Not optional  questions .You need to answer all of them to get the credit .

7) Write about a 20 lines paragraph about what   you sense you learned about  yourself  In  this class , as a person, a student and a future teacher .I am very aware that  this semester Is quite different as we were online and we missed the interactive group collaborations of the class. I do like to ask that question at the end of class to see if perhaps some of you, who did not like math or were afraid got something out of It or those who loved math got something as well also by going to fundamental . We did our best online. When you answered the question , try to  relate to  what you did learn  from  the content of the course Patterns, Ven diagram and the breaking down of each operation and its models .

How many discussions did you miss ? Please be honest as it seems like Ilearn has not been able to record all answers to grade as I was expecting  .Discussions are 20 % of your grade and you have about 16 of them so each of them 1.25 %

9) With the understanding of my grading policies, what grade do you expect In the class and while you don’t know how you did on this last hw, you probably have a good sense

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10) Do  you  feel  that  the  score  of  assignments  and  test  are  usually a reflection of one’s knowledge.

As for me , I was deeply honored to serve all of you,  amazing young people, future teachers .,I am so proud of all you have accomplished and express yourself  so freely and intelligently  and with compassion in the discussions.  All of you have such depth of awareness and kindness and it makes me so happy to know that the next generation of little ones coming up with be understood, be patients with and will enjoy playing with math thanks to all of you. Congrats for your work ,your presentations, and your participation.

I have  to  say  that  for  me l always  learn  so much  from my students ,zoom or live Connecting with all of you has been the highlight of my week .

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