When putting the answer choices into the TI-84 we can see that the only match is II.
Analyzing a graph can teach students about the zeros or solutions of a function. This function passes through the x-axis 3 times: at x = -2, x = 1 and x =3. We can also use this question to talk about factoring, y-intercepts, end behavior and other cool Math ideas. The process of elimination is very rewarding as compare/contrast is a great way to learn content and metacognition.
I am in favor of students knowing the Math part of this for sure but with the TI-84 , they can get the Math and get points. The 2 points on this type of question may make the difference between Pass and Fail and perhaps even high school graduation. The problem below comes from the June 2015 Algebra I Regents.
Option I is a NO GO so answers (1) and (3) are OUT.
Option II looking good — it’s a keeper!!
Option III is a NO GO
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
Some people may want to add why this works (or doesn’t work) but this is an anchor to help students remember where the zero cannot go!
Thank you to the teacher who shared this at a workshop.
This can be supplemented with other examples like 12 cookies divided by no people or count by zeros and you will never get to 12.
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 :)
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
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 :)
Q: Find positive integers A, B and C such that 3^A + 5^B + 7^C (3 to the A power + 5 to the B power + 7 to the C) is a perfect square. What is the smallest perfect square possible?
A: 81 is the smallest perfect square possible
List the powers of 3 5 and 7
3 9 27
5 25 125
7 49 343
If we combine 9 + 25 + 49 = 81