Helping students with homework can be easier with examples rather than rules.
10 times as much as vs. 1/10 of can be clarified by using better numbers:
so we chose 6 as our better number
6 is 10 times as much as 0.6 and 1/10 of 60
Now we know how to answer each column by comparing it to our easy example of 6!!
CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.
Once we see how 6 worked with 0.6 and 60, we can extend that idea to the harder decimal numbers given.
Notice that 5 has an exclamation point on it. This means factorial so that 5! = 5 x 4 x 3 x 2 x 1 = 120.
The more things change, the more they stay the same.
The new Common Core Algebra II Regents will be supplemented by the old Algebra 2/Trig Regents this June 2016. This new announcement comes on the heels of last week’s news of 2 more administrations of the Integrated Algebra in Feb and June 2016 for seniors. Info on Integrated Algebra Feb 2016 and June 2016.
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