Week 1
Before the first day of class:
READ
. . . about famous, unsolved problems on page 197. IN THE NEWS!!!! Yitang
Zhang has made some progress on the twin prime conjecture. Watch this
explanation: https://www.youtube.com/watch?v=vkMXdShDdtY
And then Primes and Divisibility Tests: 199 – 207
Prime numbers are useful in nature as well. Read about the cicada and primes
here: http://www.newyorker.com/tech/elements/the-cicadas-love-affair-withprime-numbers
Divisibility tests: Be prepared to explain each of the divisibility tests, (and we will
justify the tests for 3, 9 and 11 work in class). If the book’s justification for any of
the tests does not make complete sense to you, at least you will be prepared to
work these justifications out in class.
The Prime Factor Test is useful in what way? ____________________________
__________________________________________________________________
WATCH
The primes are infinite, here is the proof (and it is in your book too!)
https://www.youtube.com/watch?v=ctC33JAV4FI
Mathematicians used to think that 1 was prime, but why not now.
https://www.youtube.com/watch?v=IQofiPqhJ_s
Why is 1 not a prime? ____________________________________________
Create your own Sieve of Erastothenes after you watch this video using the
hundred tables on the back of this page. You will have to cross-out, rather than
zap, the numbers: https://www.youtube.com/watch?v=9m2cdWorIq8
After you have the sieve, can you see what is going on with this video?
https://www.youtube.com/watch?v=R8zqqLlrnQM
Divisibility test for 3 explained using base ten blocks:
https://www.youtube.com/watch?v=V1tMZ8vsbk4
Divisibility test for 11: https://www.youtube.com/watch?v=CzghDI_6Gqs
PLAY
All A problems in 5.1 are assigned. Please e-mail questions before class.
Play with this using the show, animate and practice settings at the bottom of the
hundred chart. The patterns are very fun for students:
http://nlvm.usu.edu/en/nav/frames_asid_337_g_1_t_1.html?from=grade_g_1.
html
Use the method of Erastothenes to identify the prime numbers on each of these
hundreds tables. Do these separately. Which one is easier?
In class problems (due next Monday): 5.1B #1, 5, 27, 28, 29, 46
Monday
READ
(1) Section 5.2, pages 213 to 214: Counting Factors: Notice how interesting
“counting” is! Pay careful attention to the exponents on the primes, and figure out
this pattern! Be prepared to “count” factors in class.
(2) Section 5.2, pages 214 to 217: Greatest Common Factors: Practice using the set
intersection and prime factorization method below. Find the GCF of 84 and 120.
Set Intersection:
Prime Factorization:
WATCH
The ladder method is probably used most often now to
find the GCF and the LCM. Watch this video and then
use the ladder method to find the GCF today. (You
study the LCM tomorrow):
https://www.youtube.com/watch?v=3W8SeYgZcMo
Find GCF(40,56) here using the
ladder method. I’ll start:
2 40 56
20 28
Notice that this method fits
our definition of algorithm.
PLAY
All A problems in 5.1 that deal with GCF are assigned. Please e-mail questions
before class.
Select “two trees” from the buttons at the bottom of this interactive, then find the
factors and GCF for the two numbers you are given:
http://nlvm.usu.edu/en/nav/frames_asid_202_g_3_t_1.html?from=search.html?qt=
gcf
When you are getting the gcf correct, and you want to increase your speed, try this:
http://www.sheppardsoftware.com/mathgames/fractions/GreatestCommonFactor.htm
In class problems (due next Monday): 5.2 B #5, 6 (use the ladder), 14, 22, 25.
Tuesday
READ
Pages 217 to 221.
I your own words, what is the least common multiple? ____________________
________________________________________________________________
The ladder method can be used to find the LCM, and because the book does not
use this method, you may want to watch this video again:
https://www.youtube.com/watch?v=3W8SeYgZcMo
Make sure you do understand how the “Set Intersection” and “Prime Factorization”
methods work.
The last two theorems in this section are very interesting and important. Be
prepared to discuss.
WATCH
Venn diagrams for GCF and LCM: Notice that this teacher does not use the
language of intersection and union. Would that make this easier?
http://www.schooltube.com/video/e8e94b386e89480ba118/Using%20Venn%20Di
agrams%20to%20Find%20the%20GCF%20and%20the%20LCM.
Using Venn diagrams, perhaps I can provide you with a good justification for the
the fact that GCF(𝑎, 𝑏) × 𝐿𝐶𝑀(𝑎, 𝑏) = 𝑎𝑏. Let me know in class if this “proved”
this idea for you: http://screencast.com/t/9KXLKB47
PLAY
All A problems in 5.1 that deal with GCF are assigned. Please e-mail questions
before class.
What do you think about these games? GCF, LCM, Factor & Multiple Jeopardy,
GCF application problem interactive
Perhaps one of you would like to write an Excel game for the ladder method. Here
is the NLVM factor tree interactive .
In class problems (due next Monday): 5.2 B #7(use the ladder though), 10 online,
21, 24, 27.
Wednesday
READ
Your first computer lab for this quarter: http://go.roguecc.edu/user/chutt/math-212computer-labs
WATCH
E-mail any online resources that help as you play with formulas. For example
here is one for the GCD formula.
PLAY
Play with the Excel formulas before class.
See the first tab on the Excel lab workbook above link.