This presentation is based on CCSS.Math.Content.5.OA.A.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
CCSS.Math.Content.5.OA.A.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product
Teach Students about equivalent fractions
This free teaching resource is from Innovative Teaching Resources. You can access hundreds of their excellent resources here. https://www.teacherspayteachers.com/Store/Innovative-Teaching-Ideas
From Square Numbers to Square Roots (Lesson 2) jacob_lingley
Students will use their understanding of square numbers to evaluate square roots. Remember, square roots, quite literally mean going from square numbers, back to the root - the number which you multiplied in the first place to get the square number. Example: The square root of 49 is 7.
This presentation is based on CCSS.Math.Content.5.OA.A.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
CCSS.Math.Content.5.OA.A.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product
Teach Students about equivalent fractions
This free teaching resource is from Innovative Teaching Resources. You can access hundreds of their excellent resources here. https://www.teacherspayteachers.com/Store/Innovative-Teaching-Ideas
From Square Numbers to Square Roots (Lesson 2) jacob_lingley
Students will use their understanding of square numbers to evaluate square roots. Remember, square roots, quite literally mean going from square numbers, back to the root - the number which you multiplied in the first place to get the square number. Example: The square root of 49 is 7.
We know that a number that can be written as \frac{p}{q}, where p and q are integers and q \neq 0, is known as RATIONAL NUMBERS. Thus, the set of the rational numbers contains all integers and fractions. The set of rational numbers is denoted by Q. Therefore, N \subseteq W \subseteq Z \subseteq Q.
Professional air quality monitoring systems provide immediate, on-site data for analysis, compliance, and decision-making.
Monitor common gases, weather parameters, particulates.
This presentation explores a brief idea about the structural and functional attributes of nucleotides, the structure and function of genetic materials along with the impact of UV rays and pH upon them.
Cancer cell metabolism: special Reference to Lactate PathwayAADYARAJPANDEY1
Normal Cell Metabolism:
Cellular respiration describes the series of steps that cells use to break down sugar and other chemicals to get the energy we need to function.
Energy is stored in the bonds of glucose and when glucose is broken down, much of that energy is released.
Cell utilize energy in the form of ATP.
The first step of respiration is called glycolysis. In a series of steps, glycolysis breaks glucose into two smaller molecules - a chemical called pyruvate. A small amount of ATP is formed during this process.
Most healthy cells continue the breakdown in a second process, called the Kreb's cycle. The Kreb's cycle allows cells to “burn” the pyruvates made in glycolysis to get more ATP.
The last step in the breakdown of glucose is called oxidative phosphorylation (Ox-Phos).
It takes place in specialized cell structures called mitochondria. This process produces a large amount of ATP. Importantly, cells need oxygen to complete oxidative phosphorylation.
If a cell completes only glycolysis, only 2 molecules of ATP are made per glucose. However, if the cell completes the entire respiration process (glycolysis - Kreb's - oxidative phosphorylation), about 36 molecules of ATP are created, giving it much more energy to use.
IN CANCER CELL:
Unlike healthy cells that "burn" the entire molecule of sugar to capture a large amount of energy as ATP, cancer cells are wasteful.
Cancer cells only partially break down sugar molecules. They overuse the first step of respiration, glycolysis. They frequently do not complete the second step, oxidative phosphorylation.
This results in only 2 molecules of ATP per each glucose molecule instead of the 36 or so ATPs healthy cells gain. As a result, cancer cells need to use a lot more sugar molecules to get enough energy to survive.
Unlike healthy cells that "burn" the entire molecule of sugar to capture a large amount of energy as ATP, cancer cells are wasteful.
Cancer cells only partially break down sugar molecules. They overuse the first step of respiration, glycolysis. They frequently do not complete the second step, oxidative phosphorylation.
This results in only 2 molecules of ATP per each glucose molecule instead of the 36 or so ATPs healthy cells gain. As a result, cancer cells need to use a lot more sugar molecules to get enough energy to survive.
introduction to WARBERG PHENOMENA:
WARBURG EFFECT Usually, cancer cells are highly glycolytic (glucose addiction) and take up more glucose than do normal cells from outside.
Otto Heinrich Warburg (; 8 October 1883 – 1 August 1970) In 1931 was awarded the Nobel Prize in Physiology for his "discovery of the nature and mode of action of the respiratory enzyme.
WARNBURG EFFECT : cancer cells under aerobic (well-oxygenated) conditions to metabolize glucose to lactate (aerobic glycolysis) is known as the Warburg effect. Warburg made the observation that tumor slices consume glucose and secrete lactate at a higher rate than normal tissues.
Nutraceutical market, scope and growth: Herbal drug technologyLokesh Patil
As consumer awareness of health and wellness rises, the nutraceutical market—which includes goods like functional meals, drinks, and dietary supplements that provide health advantages beyond basic nutrition—is growing significantly. As healthcare expenses rise, the population ages, and people want natural and preventative health solutions more and more, this industry is increasing quickly. Further driving market expansion are product formulation innovations and the use of cutting-edge technology for customized nutrition. With its worldwide reach, the nutraceutical industry is expected to keep growing and provide significant chances for research and investment in a number of categories, including vitamins, minerals, probiotics, and herbal supplements.
Slide 1: Title Slide
Extrachromosomal Inheritance
Slide 2: Introduction to Extrachromosomal Inheritance
Definition: Extrachromosomal inheritance refers to the transmission of genetic material that is not found within the nucleus.
Key Components: Involves genes located in mitochondria, chloroplasts, and plasmids.
Slide 3: Mitochondrial Inheritance
Mitochondria: Organelles responsible for energy production.
Mitochondrial DNA (mtDNA): Circular DNA molecule found in mitochondria.
Inheritance Pattern: Maternally inherited, meaning it is passed from mothers to all their offspring.
Diseases: Examples include Leber’s hereditary optic neuropathy (LHON) and mitochondrial myopathy.
Slide 4: Chloroplast Inheritance
Chloroplasts: Organelles responsible for photosynthesis in plants.
Chloroplast DNA (cpDNA): Circular DNA molecule found in chloroplasts.
Inheritance Pattern: Often maternally inherited in most plants, but can vary in some species.
Examples: Variegation in plants, where leaf color patterns are determined by chloroplast DNA.
Slide 5: Plasmid Inheritance
Plasmids: Small, circular DNA molecules found in bacteria and some eukaryotes.
Features: Can carry antibiotic resistance genes and can be transferred between cells through processes like conjugation.
Significance: Important in biotechnology for gene cloning and genetic engineering.
Slide 6: Mechanisms of Extrachromosomal Inheritance
Non-Mendelian Patterns: Do not follow Mendel’s laws of inheritance.
Cytoplasmic Segregation: During cell division, organelles like mitochondria and chloroplasts are randomly distributed to daughter cells.
Heteroplasmy: Presence of more than one type of organellar genome within a cell, leading to variation in expression.
Slide 7: Examples of Extrachromosomal Inheritance
Four O’clock Plant (Mirabilis jalapa): Shows variegated leaves due to different cpDNA in leaf cells.
Petite Mutants in Yeast: Result from mutations in mitochondrial DNA affecting respiration.
Slide 8: Importance of Extrachromosomal Inheritance
Evolution: Provides insight into the evolution of eukaryotic cells.
Medicine: Understanding mitochondrial inheritance helps in diagnosing and treating mitochondrial diseases.
Agriculture: Chloroplast inheritance can be used in plant breeding and genetic modification.
Slide 9: Recent Research and Advances
Gene Editing: Techniques like CRISPR-Cas9 are being used to edit mitochondrial and chloroplast DNA.
Therapies: Development of mitochondrial replacement therapy (MRT) for preventing mitochondrial diseases.
Slide 10: Conclusion
Summary: Extrachromosomal inheritance involves the transmission of genetic material outside the nucleus and plays a crucial role in genetics, medicine, and biotechnology.
Future Directions: Continued research and technological advancements hold promise for new treatments and applications.
Slide 11: Questions and Discussion
Invite Audience: Open the floor for any questions or further discussion on the topic.
5. Of course we can also say 6 = 3 x 2
# #
# #
# #
But we'll agree that means the same thing because you are just
changing the order in which you multiply, which results in rotating
the rectangle.
8. “but this is a square not a rectangle!”
you'll say.
OK.
Here a square counts as a rectangle
because it is really just a rectangle
where both the rows and columns
are the same.
(glad we sorted that out!)
16. 11 = ?
# # # #
# # # #
# # # (no)
# # # # # #
# # # # # (no)
Again, it looks like however you divide it
11 can't be a rectangle
17. Of course we could say that a row of #s is really a
rectangle:
7 = # # # # # # #
11 = # # # # # # # # # # #
But this spoils it because it's too easy, so we say that a
rectangle with only one row doesn't count!
18. So what can we see? A number can be a
rectangle if there are a whole number of rows and
columns in the shape.
This is the same as saying that we can find two
numbers that we can multiply together to make
the number we are testing.
19. But with numbers like 7 and 11 it seems that there
aren't any numbers that we can use to multiply
together to make the right result.
When you multiply two numbers and get the
answer the numbers you multiplied are called
factors
20. So we can say that the only factors of 7
are 1 and 7
Or with eleven the same
11= 1 x 11
There's no other way to divide up the number
21. So for that reason we call these numbers that
can't be rectangles
PRIME NUMBERS
22. And we call the other numbers that have factors
other than 1 and themselves
COMPOSITE NUMBERS
23. A prime number is a whole number that
is only divisible by itself and 1
All the other whole numbers are
composite
(there's no way to be both...)
28. But if 12 = 3 x 4
then we can say that,
since 4 = 2 x 2,
Then actually
12 = 3 x 2 x 2
29. In the same way, if 12 = 2 x 6
And 6 = 2 x 3
Then again
12 = 3 x 2 x 2
30. So if a number has a factor that is composite
We can express that factor as a result of
multiplication of its factors.
12 = 2 x 6 = 3 x 4 = 2 x 2 x 3
31. If we carry on doing this until
all the factors in the list are prime
then that list consists of the
PRIME FACTORS
of the number
32. And every composite number
only has one set of prime factors
(that's called
The Fundamental Theorem of Arithmetic
by the way...)
34. How many ways can we
write 90 as the result
of a multiplication?
90 = 9 x 10
90 = 6 x 15
90 = 5 x 18
90 = 3 x 30
90 = 2 x 45
35. But once we take the factors we
just found and try to reduce them all
into prime factors we only get
one way of making 90
And that is
90 = 2 x 3 x 3 x 5
36. So this explains how some numbers can be the answer to
more than one multiplication
If a number has 3 or more different prime factors in its
factorisation then there will be more than one way of
combining them
37. Here's an example
30 = 5 x 6
30 = 2 x 15
30 = 3 x 10
So we can explain this by showing
That if the prime factors of 30 are 2, 3 and 5
(Meaning that 30 = 2 x 3 x 5)
Then
30 = (2 x 3) x 5
30 = 2 x (3 x 5)
30 = 3 x (2 x 5)
38. So, really, prime factorisation is
a way of breaking a number down
into its smallest constituents
Such that they can't be broken
down any further
44. If it was false then there would be
only a finite number of primes…
a number such that when you
counted them you would
eventually reach the end and
have counted them all
45. If you can reach the end of counting them,
then you can put them all in a list…
...and that list will not go on forever.
(yes?)
46. So lets imagine the list
and say that, although we don't
know how many there are
(how long the list is) then
at least we do know that
this length is a normal number
Like 127, 5 or 1 Million.. whatever
(just not infinite)
51. This will mean that w has as its factors every
single prime, which is the same as every single
number in our list
52. Now let's go further and say
“what about w + 1 ?”
What would we know for sure
about this number?
53. To help us we quickly need to see
that when you multiply any two or
more primes and add 1
then the result is never divisible by any of the
factors you used
Lets try an example
(2 x 5) + 1 = 11
11 is not divisible by 2 or 5
54. Is this always true?
Yes because no matter how many numbers you
multiply, if you try and divide the product plus 1 by
any of them you'll always have a remainder of 1
always…
55. So with our number w + 1…
We now ask:
is w + 1 prime?
56. If w + 1 is prime then
(since it is not in the list)
we must have made
a way to add a new prime which
was not in the list of r(n)
In which case our list is not complete
57. What if w + 1 is composite?
If it is composite it must have a prime
factorisation. Yet we know that none of r(n)
can be its factors, from what we demonstrated
So there must be another prime that is a factor of
w + 1 that is not in the list
So again the list is not complete
58. So whatever we do, saying that there can be a
finite list of primes leads to a contradiction
59. If it is not the case that we can make a finite list
then the only remaining choice is that that the
collection of all primes is in fact neverending.
There are an infinite number of primes
This is Euclid's Proof