All posts by mathconfidence

brain teaser

November 2015 Brain Teaser Solution

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Which is greater, 2^1100 or 3^700?
Bonus: Approximately how many times greater is it (to the nearest 10)?
Both of these are too large to do on a calculator and will force the calculator into overflow.  So we have to come up  with another way to compare them rather than getting both actual values.
We can write them as:
(2^11)^100   and (3^7)^100 and just compare the
2^11   vs 3^7
2048 vs 2187
so 3^700 is the winner!!
Here is a link to the answer to the bonus
Thanks for solving
test prep

Now and Later: Get/Give 2 Copies of a Review Sheet

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Now and Later

A review sheet is a gift and usually a preview of the exam!

if your teacher gives you a review sheet, do not write on it so you will be more likely to REDO the problems.
If you are a teacher, hand out 2 copies and/or post a copy on line so students can redo rather than just reading them over.

Study skills are different for Math than for other content areas…please practice now and then again later :)

brain teaser

October 2015 Brain Teaser Solution

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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

Student work: How much is 12/0?

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image

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

Now try the calculator from Web 2.0 Calculator
Web 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 :)