The document provides examples of student work and analysis on a 7th grade math assessment task involving mixing paints. It includes:
1) Examples of four student solutions, with some students accurately tracking amounts and percentages while others lost track of whole amounts.
2) Analysis of common student errors like providing fractions instead of amounts in quarts or incorrectly thinking the percentage was 66% instead of 33%.
3) A summary of what students understood, such as finding fractional amounts of paint, and areas of difficulty like using fractions versus amounts and tracking part-whole relationships.
SECTION 1A. Journal Week 2Chapter 4 in Affirming Diversity pag.docxkenjordan97598
SECTION 1
A. Journal Week 2
Chapter 4 in Affirming Diversity pages 65-91.
1. How might you make a convincing argument that all students should have equal access and opportunity to algebra or its integrated counterpart in grade 8 and advanced placement courses in high school?
Reflect upon the following curriculum questions:
· In what ways is the mathematics curriculum limiting or detrimental?
· In what ways is the mathematics curriculum beneficial?
· Does the classroom teacher make his/her own mathematics curriculum and if so how is it evaluated in terms of student achievement?
· Have you and/or your colleagues been involved in developing the curriculum or do you rely on the textbooks?
Reflect upon the following pedagogy questions:
· What might you look for in order to identify the philosophical framework of a practitioner's pedagogy?
· How can pedagogical strategies reflect or promote anti-bias, equity, or social justice?
· What do you need to know in order to identify and claim your own pedagogy?
Read the Case Study: Linda Howard. Chapter 4, pages 91-101.
Answer the following questions in your journals:
1. If you were one of Linda's teachers, how might you show her that you affirm her identity? Provide specific examples.
2. What kind of teachers have most impressed Linda? Why? What can you learn from this in our own teaching?
3. What skills do you think teachers need if they are to face the concerns of race and identity effectively?
B. Journal Week 3—ANSWER QUESTIONS & REFLECT
A group of students were asked to compare the following ratios which represent the amount of orange concentrate mixed with the amount of water. The students needed to determine which of the mixes was the most 'orangey." The students were also told they could not convert the ratios to decimals or percents, nor could they use calculators.
Orange Mix
Water
a.
1
to
3
b.
2
to
5
c.
3
to
7
d.
4
to
11
One student responded as follows:
What does the evidence in this work tell you about the student's understanding of comparing ratios? How would you respond to the student?
C. Journal week 7---REFLECTION ON ARTICLE
D. JOURNAL WEEK 8
"Each student, regardless of disability, difference, or diversity, needs access to the curriculum that is meaningful and that allows the student to use his or her strengths."
Earlier in this course we examined templates for multiple representations and for vocabulary development. Examine the following graphic organizer:
From Math for All: Differentiation Instruction, Grades 3 - 5, pg. 143.
Complete this graphic organizer or one of your choosing for the Speeding Ticket problem.
How do you think using a graphic organizer will help your students? Would you require all students to use a graphic organizer or only certain students? Explain your thinking.
SECTION 2
A. REPLIES
ELIZABETH:You cannot take a smaller number from a larger number.
I’m thinking this must be a typo. It should read you couldn’t take a larger number from a.
An Investigation of Errors Related to Solving Problems on Percentagestheijes
In primary schools of Viet Nam, solving problems on percentages is a very important bit of knowledge because it not only provides a full range of knowledge of percentages but also a lot of practical applications and has a great effect in the development of thinking for students. However, it is a kind of new and difficult problem, so students often commit errors to solve problems on percentages. A survey of 149 primary school students was done. The students had to answer 7 questions about the problems on percentages. Results show that they suffer some errors such as: misunderstanding kinds of problems, doing wrong calculation, confusing the units of measurements. At the end of the paper, some suggestions in mathematics education are made to teachers to support students avoiding errors in solving problems on percentages
The Mistakes of Algebra made by the Prep-Year Students in Solving Inequalitiesiosrjce
This paper is based on student‘s performances and explores the mistakes done by the
Prepyearstudents taking College Algebra course in Mathematics when finding solutions sets for inequalities .
Purpose of this paper is to examine the prep year students of Jubail IndustrialCollege ,AlJubail who have taken
college algebra course. The prep year studentsresults are very poor in these basic concepts. They are not
successful in solving the problem of inequalities and graphs of the function. The most common mistake done by
the students is that they multiply both sides of the inequality
These are the unpacking documents to better help you understand the expectations for Kindergartenstudents under the Common Core State Standards for Math.
SECTION 1A. Journal Week 2Chapter 4 in Affirming Diversity pag.docxkenjordan97598
SECTION 1
A. Journal Week 2
Chapter 4 in Affirming Diversity pages 65-91.
1. How might you make a convincing argument that all students should have equal access and opportunity to algebra or its integrated counterpart in grade 8 and advanced placement courses in high school?
Reflect upon the following curriculum questions:
· In what ways is the mathematics curriculum limiting or detrimental?
· In what ways is the mathematics curriculum beneficial?
· Does the classroom teacher make his/her own mathematics curriculum and if so how is it evaluated in terms of student achievement?
· Have you and/or your colleagues been involved in developing the curriculum or do you rely on the textbooks?
Reflect upon the following pedagogy questions:
· What might you look for in order to identify the philosophical framework of a practitioner's pedagogy?
· How can pedagogical strategies reflect or promote anti-bias, equity, or social justice?
· What do you need to know in order to identify and claim your own pedagogy?
Read the Case Study: Linda Howard. Chapter 4, pages 91-101.
Answer the following questions in your journals:
1. If you were one of Linda's teachers, how might you show her that you affirm her identity? Provide specific examples.
2. What kind of teachers have most impressed Linda? Why? What can you learn from this in our own teaching?
3. What skills do you think teachers need if they are to face the concerns of race and identity effectively?
B. Journal Week 3—ANSWER QUESTIONS & REFLECT
A group of students were asked to compare the following ratios which represent the amount of orange concentrate mixed with the amount of water. The students needed to determine which of the mixes was the most 'orangey." The students were also told they could not convert the ratios to decimals or percents, nor could they use calculators.
Orange Mix
Water
a.
1
to
3
b.
2
to
5
c.
3
to
7
d.
4
to
11
One student responded as follows:
What does the evidence in this work tell you about the student's understanding of comparing ratios? How would you respond to the student?
C. Journal week 7---REFLECTION ON ARTICLE
D. JOURNAL WEEK 8
"Each student, regardless of disability, difference, or diversity, needs access to the curriculum that is meaningful and that allows the student to use his or her strengths."
Earlier in this course we examined templates for multiple representations and for vocabulary development. Examine the following graphic organizer:
From Math for All: Differentiation Instruction, Grades 3 - 5, pg. 143.
Complete this graphic organizer or one of your choosing for the Speeding Ticket problem.
How do you think using a graphic organizer will help your students? Would you require all students to use a graphic organizer or only certain students? Explain your thinking.
SECTION 2
A. REPLIES
ELIZABETH:You cannot take a smaller number from a larger number.
I’m thinking this must be a typo. It should read you couldn’t take a larger number from a.
An Investigation of Errors Related to Solving Problems on Percentagestheijes
In primary schools of Viet Nam, solving problems on percentages is a very important bit of knowledge because it not only provides a full range of knowledge of percentages but also a lot of practical applications and has a great effect in the development of thinking for students. However, it is a kind of new and difficult problem, so students often commit errors to solve problems on percentages. A survey of 149 primary school students was done. The students had to answer 7 questions about the problems on percentages. Results show that they suffer some errors such as: misunderstanding kinds of problems, doing wrong calculation, confusing the units of measurements. At the end of the paper, some suggestions in mathematics education are made to teachers to support students avoiding errors in solving problems on percentages
The Mistakes of Algebra made by the Prep-Year Students in Solving Inequalitiesiosrjce
This paper is based on student‘s performances and explores the mistakes done by the
Prepyearstudents taking College Algebra course in Mathematics when finding solutions sets for inequalities .
Purpose of this paper is to examine the prep year students of Jubail IndustrialCollege ,AlJubail who have taken
college algebra course. The prep year studentsresults are very poor in these basic concepts. They are not
successful in solving the problem of inequalities and graphs of the function. The most common mistake done by
the students is that they multiply both sides of the inequality
These are the unpacking documents to better help you understand the expectations for Kindergartenstudents under the Common Core State Standards for Math.
Professional air quality monitoring systems provide immediate, on-site data for analysis, compliance, and decision-making.
Monitor common gases, weather parameters, particulates.
Richard's aventures in two entangled wonderlandsRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
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.
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.
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.
Richard's entangled aventures in wonderlandRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
Multi-source connectivity as the driver of solar wind variability in the heli...Sérgio Sacani
The ambient solar wind that flls the heliosphere originates from multiple
sources in the solar corona and is highly structured. It is often described
as high-speed, relatively homogeneous, plasma streams from coronal
holes and slow-speed, highly variable, streams whose source regions are
under debate. A key goal of ESA/NASA’s Solar Orbiter mission is to identify
solar wind sources and understand what drives the complexity seen in the
heliosphere. By combining magnetic feld modelling and spectroscopic
techniques with high-resolution observations and measurements, we show
that the solar wind variability detected in situ by Solar Orbiter in March
2022 is driven by spatio-temporal changes in the magnetic connectivity to
multiple sources in the solar atmosphere. The magnetic feld footpoints
connected to the spacecraft moved from the boundaries of a coronal hole
to one active region (12961) and then across to another region (12957). This
is refected in the in situ measurements, which show the transition from fast
to highly Alfvénic then to slow solar wind that is disrupted by the arrival of
a coronal mass ejection. Our results describe solar wind variability at 0.5 au
but are applicable to near-Earth observatories.
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.
3. Seventh Grade – 2003 pg. 6
Looking at Student Work – Mixing Paints
Mixing Paints was a difficult task for students. A little more than half the students in
the sample scored no points on this task, even though 85% of the zeros attempted the
task. Therefore it is important to look carefully at strategies that helped successful
students and ways they clarified their explanations. Student A makes an area model
diagram to keep track of the parts and whole. It makes it easy to see the relative sizes
of the different components of the paint.
Student A
(c) Noyce Foundation 2012
4. Seventh Grade – 2003 pg. 7
Student B does a very thorough job of showing all the calculations necessary for each
step of the process, including the portioning of brown into yellow and violet. The
student shows an understanding operations and calculations with fractions.
Student B
(c) Noyce Foundation 2012
5. Seventh Grade – 2003 pg. 8
Student C has a good grasp of the problem, explaining the whole and which part is
blue. The student explains the process for calculating a percentage and rounding off.
Many students had difficulty keeping track of the whole. Student D loses the amount
of paint for blue in part 2. However the student seems to know the overall
relationships and has an interesting, but unusual way, of finding the percentage in part
3. Student D knows that blue is 2/3 of half the paint. To simplify this calculation the
student finds or knows 2/3 of 100 and divides that answer by 2.
(c) Noyce Foundation 2012
6. Seventh Grade – 2003 pg. 9
The most common error is to lose track of the total amount of paint. Student E
correctly finds the amount of red and blue paint, but forgets that the total amount of
paint is 6 quarts instead of two quarts.
Student E
Teacher Notes:
(c) Noyce Foundation 2012
7. Seventh Grade – 2003 pg. 10
Frequency Distribution for each Task – Grade 7
Grade 7 – Mixing Paints
Score: 0 1 2 3 4 5
% < = 50.7% 56.0% 73.5% 77.7% 81.3% 100.0%
% > = 100.0% 49.3% 44.0% 26.5% 22.3% 18.7%
The maximum score available on this task is 5 points.
The cut score for a level 3 response is 2 points.
A little less than half the students could find the amount of red or blue paint needed.
Less than 20% could find the amount of red and blue paint and calculate the
percentage of total paint that represented. A little more than 50% of the students
scored zero points on this task. About 7% of all the students did not attempt this task,
even though it was the first problem in the test. 43% of the students attempted the
task with no success.
Mixing Paints
Mean: 1.61, S.D.: 1.95
0
1000
2000
3000
4000
5000
6000
7000
Score
Frequency
Frequency 5940 616 2054 492 428 2185
0 1 2 3 4 5
(c) Noyce Foundation 2012
8. Seventh Grade – 2003 pg. 11
Mixing Paints
Points Understandings Misunderstandings
0 85% of the students with this
score attempted the task.
The most common error was to give
a fraction rather than convert to
quarts. About 1/5 of the students
gave the response 1/3 and 2/3. A
less frequent error was to put 2
quarts of red and 4 quarts of blue.
1 Students with this score could
either find the amount of red or
blue paint.
2 Students could find both the
amount for red or blue paint.
They had difficulty finding the
percent of blue paint. Students did
not recognize that the violet paint
was only half of the total paints.
Therefore most students thought the
percentage was 66% instead of
33%.
5 Students could keep track of
part/whole relationships,
calculate the amount of red and
blue paint needed, and find the
percentage of blue paint. Some
students were able to make
good use of diagrams. Other
students demonstrated a facility
with operations with fractions.
Based on teacher observations, this is what seventh grade students knew and were
able to do:
• Find the fractional amount of red or blue paint and use that to find the number
of quarts
Areas of difficulty for seventh graders, seventh grade students struggled with:
• Understanding the whole in a multi-step problem
• Calculating percentages
• Tracking part/whole relationships
• Using fractions instead of taking a fractional part of the whole
(c) Noyce Foundation 2012
9. Seventh Grade – 2003 pg. 12
Questions for Reflection on Mixing Paints:
• Did your students seem to know the difference between a fraction of a whole
and the quantity the fractional part represented? (Could they find the amount
of red and blue paint?)
• Did students seem comfortable working with fractions? Did they use
multiplication or diagrams to help make sense of the problem?
• Do students seem to know landmark percents or did they calculate the
percentage of blue paint?
• Would their procedure for finding percents have been correct if they had
started with the correct fraction?
Teacher Notes:
Instructional Implications:
Students need strategies to help them make sense of problem situations. Being able to
draw a picture or make a model helps them see part/whole relationships. Until the
student can see how the parts fit together, the student cannot calculate with fractions
or find percentages for the different components. Students need more experiences
working with problems in which “the whole” changes. Students need more
experience using information from problems to get the answer instead of repeating
numerical information that has been given in the problem. Too many students
thought the numbers in the text of the problem were the solutions. Students at this
grade level should be able to convert mentally between common fractions and
percents. At this grade level, students should “just know” the relationship between
common fractions and the equivalent percents.
Teacher Notes:
(c) Noyce Foundation 2012