# – 5Month High School, Day 19: charts, radicals, Khan. 12020HE (Holocene Era)

Making charts, working through complex lower mathematics, and writing about it in a journal all hone the skills of problem-solving and critical thinking, skills as essential for being a competent citizen in our modern society as they were in a changing 1838 Baltimore.  Many thanks again to Sal Khan for his free public service education site Khan Academy.

Lesson Plan, 6-9pm, Tuesday, March 5th, 12019 HE

In our Learning Toolbox: this thought:
Vocabulary:
Copy into your notes, and Mind Map each word:
Vocab.
Grammar
Vocabulary
Math Vocabulary Test-taking Skills
Multiple possible
interpretations of a
text/passage
Capitalization,
review, Essay
writing outline
introduction
to exponential and
Organizing your
information/choices/forms
of data or expression/pros
and cons (T-Charts…)
Various Common Nouns Radical as exponent substitution
Interpretations Proper nouns, I Fractional Exponent Different forms, same #
Express an idea, or
express a number
Brand name, Titles Negative Exponents Process of elimination
In terms of… Thesis & conclusion Fractional Exponents Listing varied possibilities
Quote/citation Pros and Cons of…
Rebuttal/To Rebut
Exponents
Most likely possibility
6pm: Spend one minute remembering a misunderstanding you had at some time in your life.
Write one or two sentences explaining: Write two sentences explaining various
possible interpretations of this song quote:
“…but I know what I am,
and I’m glad I’m a man,
and so is Lola…” (citation: the Rolling Stones)

7pm: Stand up & Stretch, if you wish…
7:07 to 7:15 Grammar lecture, using the passage below.
7:15 to 7:25 Math lecture, also using this same passage.
7:25-7:30 We do 1st question/problem from each online worksheet together, then you finish
the online activities from all lectures individually on the classroom computers.
Mathematics work online and/or in books from 7:45 until 8:45.
7:00-7:07: Reading Comp.: Capitalizing and Essay organizing
Today’s Passage: the dropping of the atomic bombs in japan marked the beginning
of the nuclear Age. in august 1949, the soviet union exploded its first atomic bomb. The
world’s two superpowers battled for supremacy and demanded that other nations take sides.
(Today’s reading comes from P. 289 in Peterson’s Master the HiSET, 2nd Edition…)
What are some possible interpretations of the phrase “battled for supremacy?”
Where are the Grammatical errors?
7:07 Grammar lecture part1/2: Capitalizing review
Rules: Capitalize These Words
1. Proper Nouns (and Brand Names)
2. Titles (except articles and prepositions)
3. First word in a sentence and the pronoun I
(source:
(Extra help on capitalizing:
Now let’s do a Grammar exercise question (using Chrome Browser…) from
Grammar lecture part2/2: Four main parts of an Essay
We’ve introduced the Thesis sentence, now we need to know that an essay should
have at least four paragraphs (¶):
Body paragraphs, with your pros and cons, and
Conclusion paragraph, summarizing your argument or topic.
(https://www.uvu.edu/writingcenter/docs/handouts/writing_process/basicessayformat.pdf
has a nice summary…)
Next week we will start writing an essay together.
7:15 Mathematics Topic: Exponents and Radicals, good friends that go together.
Why would we want to convert between forms of expression? Sometimes a problem
is easier to solve in an equivalent form…
Exponents rules and properties
Rule name Rule Example
Product rules
a
n
⋅ a
m
= a
n+m 2
3
⋅ 2
4
= 2
3+4 = 128
a
n
⋅ b
n
= (a ⋅ b)
n
3
2
⋅ 4
2
= (3⋅4)
2
= 144
Quotient rules
a
n
/ a
m
= a
n-m
2
5
/ 2
3
= 2
5-3
= 4
a
n
/ b
n
= (a / b)
n
4
3
/ 2
3
= (4/2)
3
= 8
Power rules
(b
n
)
m
= b
n⋅m
(2
3
)
2
= 2
3⋅
2
= 64
bn
m
= b(n
m
) 23
2
= 2(3
2
)= 512
m
√(b
n
) = b
n/m 2
√(2
6
) = 2
6/2 = 8
b
1/n
=
n
√b 8
1/3
=
3
√8 = 2
Negative exponents b
-n
= 1 / b
n
2
-3
= 1/2
3
= 0.125
Zero rules
b
0
= 1 5
0
= 1
0
n
= 0 , for n>0 0
5
= 0
One rules
b
1
= b 5
1
= 5
1
n
= 1 1
5
= 1
Minus one rule (-1)
5
= -1
(Source: https://www.rapidtables.com/math/number/exponent.html and
https://www.homeschoolmath.net/teaching/md/division-repeated-subtraction.php)
Notice that a negative exponent jumps the fraction bar, so b
-n
= 1 / b
n
Multiplication is repeated addition, so a
n
⋅ a
m
= a
n+m
Exponents are repeated multiplication, so (b
n
)
m
= b
n⋅m
Division is repeated subtraction, so a
n
/ a
m
= a
n-m
Let’s look at radicals, which are the flip-side of exponents:
m
√(b
n
) = b
n/m
b
1/n
=
n
√b
So, exponents really are just radicals in a different form!
Now, let’s do the first online math worksheet problem together:
s-of-decimals-and-fractions
7:30
1.) Please do the rest of our online grammar worksheet: (using Chrome Browser…)
and
2.) Please do the remainder of online math worksheet:
s-of-decimals-and-fractions
8:40 Exit Questions: 1. Please write one sentence explaining how you can use a chart to
show various forms of the same number.
2. What is a rebuttal?
3. What is the Distributive Property?
4. Show, using exponents, why the square root of five, multiplied by
itself, is equal to 5.
8:45 Turn in Exit Slip, Dismissal

Action Items in support of literacy that you can take right now:

1.) Search for two different resources for learning mathematics online (for free).

4.) Write a blog post or tweet that uses a math vocabulary word or story (like the Djinni’s gold offer), tells a fun story, and makes a difference. I’m working on that through my historical fantasy #WiP, #WhoByFireIWill. Once published, donate one or more copies to your local public library, as I intend to do.

Dear Readers, any additional ideas toward learning, especially multiple #LanguageLearning as part of on-going education and empathy-building, to #EndPoverty, #EndHomelessness,  #EndMoneyBail & achieve freedom for All HumanKind?

Support our key #PublicDomainInfrastructure  & #StopSmoking for CCOVID-19:
1. #PublicLibraries,
2. #ProBono legal aid and Education,
3. #UniversalHealthCare, and
4. good #publictransport
Read, Write, Ranked Choice Voting and Housing for ALL!!!!, Teach and Learn (Lesson Plans) !