All posts by mathconfidence

June 2018 Brain Puzzler Solution

Q: Sabina’s car has 50% better fuel efficiency (miles per gallon) than her old car.  The new car uses diesel which is 20% more costly than the gas in her old car.  On a percent basis, how much will she save on a long trip?

A:  20%
For this problem, we made up numbers to make the Math easier 🙂
We can use 10 miles per gallon for Sabina’s old car which would make the new one 15 mpg.
We can pick an easy number that plays nice with 10 and 15 like 30.
If she goes 30 miles on a trip, she will need 3 gallons with the old car but only 2 gallons with the new car.
Now we need a price for gas so we assumed $4.
If gas is $4/gallon but diesel is 20% more at $4.80 per gallon, she would have spent 3 x $4 = $12 with the old car but now spends only $9.60 for the new car (2 x $4.80).
She saved $2.40 on $12 which is a 20% savings.

Equity and Access: Empowering Students for the Common Core Alg I Regents

Shout out to New York the Empire State aka the Regents State!  The Regents is coming!
CC Algebra I is the most important Regents as s’s need at least 1 Math Regents to graduate and Alg I is so much more accessible than Geo or Alg II.
The best prep: Do Regents questions!!

There are certain questions that all and I mean ALL students should be able to answer correctly and get 2 points!  Too often, students have not seen all the content and/or are not adept at the TI-83/4 calculator.

Make sure that you and your student(s), teacher(s) feel empowered to take the exam and learn Math in the process 🙂

Here is a link to the Bible of Algebra I (thanks to the jmap folks!)
If you prefer, you can call it an OED of Algebra I or the Primer of Algebra I.
http://www.jmap.org/JMAPArchives/CurrentVersion/JMAPAI_REGENTS_BOOK_BY_PI_TOPIC.pdf

 

 

May 2018 Brain Puzzler Solution

Q: Two coins are flipped and you cannot see the outcome but are told that at least one is a head.  What is the probability that the other coin also landed on heads?
A: 1/3
This is a classic probability question.  Once you know that one coin is a head, there are 3 possible outcomes for the two coins with at least one head.
HH
HT
TH
Since you know that one is a heads, and there are 3 possible outcomes, the probability is 1/3.

April 2018 Brain Puzzler Solution

Q: How many 6 digit numbers are there whose digits sum to 51?

A: 56.

There are 3 possible sets of 6 numbers: 999996 where the 6 can be the 1st, 2nd, 3rd, 4th, 5th, 6th place values making 6 6 digit numbers

3 9s and 3 8s which is the same probability as 3 boys and 3 girls with 6 children 3C6 = 20 6 digit numbers

and 4 9s with an 8 and a 7 with 30 possibilities
789999
798999
799899
799989
799998
879999
897999
899799
899979
899997
978999
979899
979989
979998
987999
989799
989979
989997
997899
997989
997998
998799
998979
998997
999789
999798
999879
999897
999978
999987

 

 

 

credit to Julia Robinson Mathematics Festival