January 2016 Brain Teaser Solution

Q: A swindler showed an honest man a six sided die.  If the man rolled a ONE, he wins, and gets back twice the amount of his bet. If not, the swindler keeps the bet.   “But…my chances are only one out of six,” retorted the man.  “True,” grinned the swindler, “But I’ll give you three tries to get a one.”  The man considered if I have 3 tries, each try has a 1/6 chance of winning, so my  chances of winning are  3/6 or 1/2. Is the bet really fair? If not, what are the chances of the man winning?

A:  91/216
You cannot just add 1/6 + 1/6 +1/6 so 1/2 is incorrect. The probability of not getting a 1 is 5/6 (there are 6 sides and the other possible outcomes are 2, 3, 4, 5 or 6).  The probability of no 1s in 3 throws is 5/6 x 5/6 x 5/6 = 125/216 which is the probability of the swindler winning.  So the probability of the man winning is 1 – 125/216  =   216/216 – 125/216 = 91/216.

 

Should We Tell Them?

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“The rule for the square of a binomial”:  Spotted with a 12th grader Homework on Pearson’s My Math Lab

Should we tell students exactly what to do?
Categorization is one of the most important skills in Math and one of the most important takeaways for future Math classes and in  general.

The question above creates teaching and learning questions:
“Should we tell students what to do based on rules?”
“Can students (even) remember rules?”
“What would be the answer to this problem?”

 

 

Smart as a 5th grader using structure

Zoe 5th Grade 10 times

Helping students with homework can be easier with examples rather than rules.

10 times as much as  vs. 1/10 of  can be clarified by using better numbers:

so we chose 6 as our better number
6   is 10 times as much as 0.6 and 1/10 of 60

Now we know how to answer each column by comparing it to our easy example of 6!!

CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.
Once we see how 6 worked with 0.6 and 60, we can extend that idea to the harder decimal numbers given.

 

 

 

 

 

 

Two (2) Algebra II (2) June Regents

 

transitiontoccregentsalgebraII1215update

The more things change, the more they stay the same.

The new Common Core Algebra II Regents will be supplemented by the old Algebra 2/Trig Regents this June 2016.  This new announcement comes on the heels of last week’s news of 2 more administrations of the Integrated Algebra in Feb and June 2016 for seniors. Info on Integrated Algebra Feb 2016 and June 2016.

Algebra 2 122115 announcement

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