Activity 5:
Generating a sequence of all rational numbers greater than 1
Pat says: There must be more numbers between 1 and
infinity than between 0 and 1.
Is Pat
right? Explain.
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In Activity 4 we made fractions a/b where a is less than b. What kinds of numbers do we get if we had b/a instead?
Explain.
Train a robot named
Divides
1 that takes a number and gives a
bird 1 divided by that number. The pictorial instructions are at the end if you
need help.
Use the robots from Activity 4 to make all the proper fractions. Run
Divides
1 with the nest with all the fractions.
What
is the result?
Connect
Match
Maker with the result. Think about
what the robots are producing.
Sally says that something is fishy here. She says:
“There
must be the same number of rational numbers from 0 to 1 as there are from 1 to
2. And from 2 to 3. And 3 to 4. So there are an infinite number of intervals of the same size as 0 to 1. So
there must be an infinite times more rational numbers greater than 1 than
between 0 and 1.”
Do you agree or disagree with Sally? Why?
Activity 5, Task B: Training
Divides
1
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title | why | what | why toontalk | activities | rationale 1 | activity 1 | findings 1 | rationale 4/5 | activity 4 | activity 5 | findings 4/5 | rationale 8 | activity 8 | findings 8 | conclusions
