All posts by mathconfidence

October 2015 Brain Teaser Solution

Q: How many squares are on an 8 x 8 checkerboard?  10 x 10? How many rectangles?

8 x 8 There are:
64 1 x 1
49 2 x 2
36 3 x 3
25 4 x 4
16 5 x 5
9  6 x 6
4 7 x 7
1 8 x 8 for a total of 204 squares

For 10 x 10
100 1 x 1
81 2 x 2
64 3 x 3
49 4 x 4
36 5 x 5
25 6 x 6
16 7 x 7
9 8 x 8
4 9 x 9
1 10 x 10

for a total of 385 squares

The rectangle counting is significantly more challenging.
Click here for a beautiful explanation from Nigel Coldwell

Student work: How much is 12/0?

image

So how much is 12/0?  Go here to ask Google’s calculator: Google Calculator
G
oogle says Infinity

Now try the calculator from Web 2.0 Calculator
W
eb 2.0 says “Error: Divide by 0”

Desmos says “Infinity”

went through a lot of online calculators until I found this: http://www.calculator-tab.com/.  It says error and also says division by zero is not defined

Wolfram Alpha says “complex infinity”

Try your cell phone calculator(s) and post any other interesting answers here by leaving a comment…this student meant to write Undefined but wrote something super close 🙂

August 2015 Brain Teaser Solution

Q: You have 8 batteries but only 4 of them work and 2 are needed to power a flashlight.  What is the fewest number of pairs you need to test to guarantee you can get the flashlight on?
A: 7. If you break the batteries into 3 groups: Two groups of 3 and one group of 2. By doing this you guarantee that one of the groups has 2 working batteries. Both of the groups of 3 have 3 possible combinations of 2 batteries and the group of 2 only has 1 combination. So, 3 + 3 + 1 = 7 tries at most to find two working batteries.

SAT Weeks 3 and 4: My book looks loved

1438796197048My book is looking loved!  Check out the dog ear on the upper right hand corner of the blue College Board SAT book!

During weeks 3 and 4, I took the 4 non essay sections of each of the 4 exams in the SAT book.
This content is much more challenging than the old SAT.   I am not sure why the College Board is making the exam harder than it was.  It seems like many students will jump to the ACT.
Next steps:
Work on each of the 4 essays
Go through the Ivy Global SAT book ( arriving this week)
Get familiar with the Khan Academy offerings for SAT prep