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Mathematical Expression Editor
In this problem you are allowed to use the following symbols (and their
corresponding words): 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. (Note: There are no words such as
ten, eleven, twelve, thirteen, twenty, etc. allowed during this activity!)
Play with the sticks for a little while with the goal of counting them. Draw pictures
to represent your ideas and be prepared to show your pictures and discuss
your ideas with the class. Once you have some ideas, consider the following
questions.
(a)
In your system, how would you represent the following quantity of sticks with
the given symbols, and why?
(b)
In your system, how would you represent the following quantity of sticks with
the given symbols, and why?
In this problem we are still only using the following symbols: , , , , , , , , , . In
discussing problem 1 we defined what we mean by a “bundle”.
(a)
How would you draw and represent using the given symbols a quantity
of sticks that has bundles and sticks? How do you know your answer is
correct?
(b)
How would you draw and represent using the given symbols the next
quantity after bundles and sticks? How do you know your answer is
correct?
(c)
How would you draw and represent using the given symbols the largest
quantity we can make using only bundles and individual sticks? How do
you know your answer is correct?
(d)
How would you draw and represent using the given symbols the quantity
after the one in part (c), and why?
For all of the remaining problems, we will count using the symbols (zero), , and .
(Note that now we don’t have any symbols or words like , , , etc.)
Begin to count in this system. For each quantity you count, be sure to draw a picture
of the quantity using sticks and label your picture using the symbols of this system.
Count as high as you can – don’t stop until your instructor gives you the go ahead to
move to the next problem.
(a)
How would you draw and represent using the given symbols a quantity of
sticks that has bundles and sticks?
(b)
How would you draw and represent using the given symbols the next
quantity after bundles and sticks? How do you know your answer is
correct?
(c)
How would you draw and represent using the given symbols the largest
quantity you could draw using only bundles and individual sticks? How
do you know your answer is correct?
(d)
How would you draw and represent using the given symbols the next
quantity after the one in part (c)? How do you know your answer is correct?
(e)
Using the given symbols in this system, how many sticks are in a bundle?
How many sticks are in a superbundle? Describe your reasoning.
Remember, we are only using the symbols , , , , , , and for our counting.
(a)
Using sticks, draw a picture of the quantity in this system. Explain how
you know your answer is correct.
(b)
What quantity comes right before in this system? Be sure to use a picture
(or series of pictures) of sticks to find your answer, not a pattern involving
letters only. Explain your thinking.
(a)
Using sticks, draw a picture of the quantity in this system. Explain how
you know your answer is correct.
(b)
What quantity comes right before in this system? Be sure to use a
picture (or series of pictures) of sticks to find your answer, not a pattern
involving letters only. Explain your thinking. What does it mean to count
backwards?
Is there a highest number you could count in this system? Explain how you
know.
