Q: A group of 100 students play various instruments: 70 play trombone, 75 play accordion, 85 play violin and 80 play guitar. What is the minimum number of students who must play all 4?
A: 10 students is the minimum number that must play all 4 instruments
Here we need to look for the overlap since there must be some students who play more than one instrument. The best way to do this is with a Venn diagram (which was really popular during the New Math of the ’70’s when I was in school!).
The Math below is done to find the minimum number of students who must play all 4:
So if 70 play trombone and 75 play accordion (which add up to 145) there must be at least a 45 overlap that play both.
We will now consider those 45 (that play 2 instruments) with the 85 who play violin (which add up to 130) so there must be a 30 overlap that play 3.
We will now consider those 30 with the 80 who play guitar (which add up to 110) so there must be a 10 overlap that play all 4 instruments.
When can you add 2 to eleven and get 1?
on a clock
you can add 2 to 11 and get 1
except if you have a clock like this for military/overseas time:
90% interest IS huge!
0 .90%, um, not so much
In the bond market, a basis point (or bp or bipp) is 1/100 of 1%. 0.90% (or 90 bp) is less than 1% — it would take over 75 years to double your money at this rate — not so huge!
This 4th grade student did know how to get the answer but fell for the good wrong answer because she forgot about the first number in Jill’s pattern. This is a Fencepost mistake (for example, for a 100 foot fence with posts every 10 feet, you need 11 fence posts!).
We can improve Math scores and enjoyment of Math by helping people to notice details.
My son, a high school senior, shared that Simon Sinek, leadership expert and author of Start with Why, will be presenting a talk today at assembly. First thought, I wish I could go. Second thought, let my fingers do the walking so I go to www.startwithwhy.com and got hit with “Imagine a world where people wake up inspired to go to work”… would love this to say
“Imagine a world where students and teachers wake up inspired to go to school”.
This is why (haha!) I have a talk called “When Are We Ever Going to Use This Math?” to answer this question of “Why?” although upon deeper reflection, maybe I have been answering the wrong question. So what could the question be? Here are some ideas:
Why does every country have their students study Math?
Why study Math?
Why do people think people who study STEM (Science Technology Engineering Math) are smart?
Why do people who study STEM usually make more money?
Please comment to add your own Why questions that will inspire and motivate students…thanks!