Math 131

Spring 05

 

Homework (assigned 2/17)

 

Reflection

 

            Please email me your answers to (all of) these questions by Tues evening February 22.  I will respond to you via email and ask you to reply to my comments.  If you send your work earlier, I will try to send my comments earlier.

            You can simply type your answers in this document (and I’ll respond in another font).  However, I can only open word and wordpad files at home; if you don’t use one of these programs, please include your answers in the text of the message.

 

1.  A friend is doing her practicum in an elementary school.  She realizes that she doesn’t understand why multiplying by ten is the same as “adding a zero,” so she asks you.  What might you tell her?

 

2.  You are helping your ten-year-old cousin with his homework.  He is trying to learn the steps to solve multiplication problems such as 23 x 42, but right now he has them mixed up, and he really has no idea what he is doing; he’s just trying to remember rules for manipulating numbers.  How might you make this problem meaningful to him?  How can you use this meaning to help him compute the right answer?

 

3. a.  Write story problems to illustrate the sharing and the repeated subtraction model for division.  Use 12  3 to illustrate (note that you can use “insert symbol” in word to get a division sign).  Draw pictures (as best you can on the computer…)

 

b.  Explain the missing factor and array models of division (adapt from multiplication) with the same problem.

 

c.  Now, using the four models you have here, change the problem to 0  3.  How does each model adapt to this new problem?  What is the correct answer to this problem?  Which of the models best help you see that?

 

d.  Repeat with 12  0. 

 

Write-Up

 

            Work on all of the following problems, and then choose one to write up.  You can email me this write-up or turn it in class Wed.  It will be scored with a rubric similar to the one for the last write-up. 

 

a.    Take a three-digit natural number (example 567).  Write the six-digit number that is formed when two copies of the three-digit number are placed side by side (example: 567,567).  Now take out a calculator and first divide the six-digit number by 7.

Then divide the result by 11.   Then divide the result by 13.  What do you get?  Make a conjecture.  Does your conjecture seem to apply to all cases?  Can you explain why the trick works?

            b.  Find a shortcut for squaring natural number that end in 5.  Here are some examples: .  With your shortcut, you should be able to simply look at the natural number and announce its square.  Why does this shortcut work?

            c.  Here is a number trick.  Take the day of the month of your birthday and multiply it by 25.  Add 150.  Double.  Add 702.  Double.  If you’ve already had your birthday this year, add 1.  Subtract the year you were born in.  You should see your birthday day of the month, followed by your age.  Explain how this trick works.

 

Copyright 2005, Debra K. Borkovitz.  You may copy or edit this material for non-profit, educational use only.

 

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