standard_description: Interpret multiplication as scaling (resizing), by:
- Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
- Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
problem_activity: Task
Imagine Scott stood at zero on a life-sized number line.  His friend flipped a coin 50 times.  When the coin came up heads, he moved one unit to the right. When the coin came up tails, he moved one unit to the left. After each flip of the coin, Scott's friend recorded his position on the number line. Let $f$ assign to the whole number $n$, when $1 \leq n \leq 50$,
Scott's position on the number line after the $n^{\rm th}$ coin flip.
If $f(6) = 6$ what can you conclude about the outcomes of the first $6$ coin
tosses?  Explain.  What if $f(6) = -4$?
Is it possible that $f(7) = 2$?  Explain.
Find all integers $m$ so that the probability that $f(50) = m$ is zero.


aligns: no