1201BPS – ASSIGNMENT 2 – TERM 1 - 2014QUESTION 1 MARKING.docx

1201BPS – ASSIGNMENT 2 – TERM 1 - 2014
QUESTION 1 MARKING SCHEME –
Category
Criteria & marks
Criteria & marks
Criteria & marks
Definition of
Excellent explanation
Good explanation of
Errors in explanation
Functions
of definition
definition but some
or not done
7 – 9 marks
improvement is
0 marks
possible

1 – 6 marks
Definition of Domain
Good explanation of
of definition
definition but some
or not done
7 – 9 marks
improvement is
0 marks
possible
1 – 6 marks
Definition of Range
Good explanation of
of definition
definition but some

or not done
7 – 9 marks
improvement is
0 marks
possible
1 – 6 marks
Examples of
At least one example
Only 2 to 4 of the
quadratic,
of each of these
functions have been
or not done
polynomial,
functions has been
used in the
0 marks
exponential,
given as part of the
definitions above

logarithmic and at
explanations of
1 – 6 marks
least one periodic
definitions above – 5
function and all of
in total
their graphs
7 – 9 marks
Validation and
All websites used
Most websites used
citations
were validated and
were validated and
or not done

cited appropriately
cited appropriately
0 marks
5 marks
1 – 4 marks
Category
Criteria & marks
Criteria & marks
Criteria & marks
Explanation of a
Good explanation,
Insufficient
logarithmic scale
7 – 9 marks
but some
0 marks
improvement is

possible
1 – 6 marks
Identification of the
Good explanation,
Insufficient
purpose
7 – 9 marks
but some
0 marks
improvement is
possible
1 – 6 marks

Real world examples
Good explanation,
Insufficient
of real world
but some
0 marks
examples
improvement is
7 – 9 marks
possible
1 – 6 marks
Validation and
All websites used
Most websites used
Websites are not
citations if used but
were validated and
were validated and
cited properly
not needed

cited appropriately
cited appropriately
0 marks
5 marks
1 – 4 marks
Category
Criteria & marks
Criteria & marks
Criteria & marks
Explanation of
Good explanation but
Poor explanation or
inverses of sine,
10 – 13 marks
some improvement is
insufficient
cosine and tan
possible
0 marks

functions
1 – 9 marks
Real world examples
Excellent use of real
Good explanation of
Errors in use of
world examples to
real world examples
examples to back up
back up explanation
but some
explanation in detail.
in detail
improvement is
0 marks
10 – 13 marks
possible
1 – 9 marks
Validation and

All websites used
Most websites used
Websites are not
citations
were validated and
were validated and
cited properly
cited appropriately
cited appropriately
0 marks
5 marks
1 – 4 marks
1.
Your responses to each of these questions
· Grade 7 and grade 8 students benefit greatly when they a
comprehensive understanding of fractions and their respective
decimal and percent equivalences. With this in mind, which of
the fractions to decimal and percent equivalences would you
consider fit into the categories:
· Autofacts
· Stratofacts
· Clueless facts
You might think about autofacts as being those fractions to
decimals to percents that your students already know.
Stratofacts can be described as those facts that your students
can figure out slowly using an idiosyncratic strategy. This just

means a strategy your students can use to figure out the
conversion. Clueless facts are those facts that your students just
cannot recall at all. They are completely unknown.
· What are some strategies you can use with your students who
are clueless when it comes to identifying the fraction to
decimals for the eighths? sixths?
· How might you move your students from the Stratofacts to the
Autofacts category? Or, is it important to do so? Justify your
response.
· How might you move your students from the Clueless category
to the Stratofacts category? Or, is it important to do so? Justify
your reponse.
As we move into the 21st century we keep hearing that there are
basic facts that all students should know. These facts have
obviously changed over the past 50 years since cheap $2
calculators can do most of the simple computations that were
considered “basic facts” in the 1950s, 1960s, 1970s and 1980s.
More is expected of the children we teach than what we were
trained to teach…what is the more? Is it at the expense of what
used to be crucial? Have we changed what and how we do
things to accommodate the expectations that exist for the
future?
What are some mathematical facts that you believe are crucial
for all students to know and be able to do by grade 8 and…more
importantly…how are you going to help all students achieve
those expectations?
2
· Applications
Examine the following problem. It is designed for grade 7 or
grade 8 students. Since most of us teach in heterogeneous
classes we recognize that this may be a great challenge for some
of our students. That being said, the problem embraces the

learning objectives and expectations for grade 8 students in the
NAEP frameworks. How might you differentiate this problem so
that all students have opportunity to access the situation and
work on a grade 7 or grade 8 level mathematically? Be sure to
justify your thinking and post your “redo” of the problem.
You are given the total cost of $2,589.96 for one iPad and three
IPad2’s and a total cost of $2,659.95 for two iPad 2’s and three
IPad’s.
a. What is the price of one IPad?
b. What is the price of one iPad 2?
Be sure to explain your answers.
As we noted earlier, differentiating instruction means providing
rigorous mathematics, presented in ways that include all
students in grade appropriate mathematics. Based upon the fact
that all students will be asked to solve this problem in one form
or another take some time to develop a rubric on a scale from 1
– 4 that is inclusive of both the original problem and the revised
problem. As you develop the rubric consider the different
representations that are appropriate for this problem. Think
about the evidence of understanding you will be looking for as
you analyze what each student knows and is able to do. Be sure
to post your rubric.
Discuss with your peers, the rubric you developed, the rubrics
they developed and how you can all come to consensus and
provide one rubric that is appropriate for the problem situation
and all students.
3.
· Reflect on the Following Accomodations and Article

“It is a wise man who once said that there is no greater
inequality than the equal treatment of unequals.” -Felix
Frankfurter, Supreme Court Justice
Read and reflect on the following accommodations that are
sometimes used for all students in a mathematics classroom.
Indicate on a scale of 1 – 5 with 5 being “I strongly agree” how
you feel about their implementation in a heterogeneous
classroom. Include a brief justification of how you rated each
accommodation.
· Read the attached Article: Write your thoughts on this.
1. All students should be allowed extended time to complete
quizzes and tests. Strongly disagree / disagree / agree / strongly
agree
2. I provide all my students the opportunity to retake a quiz or
test and count the corrections towards the quiz or test grade.
Strongly disagree / disagree / agree / strongly agree
3. I provide multiple-model assessments for all students.
4. I build into my classroom teaching and assessing routines
that are always followed.
5. I count my student’s homework for no more than 5% of their
term grade.
6. I use mathematics strategy notebooks developed in class and
used for class problem solving for part of the term grade.
7. I allow my students some control over the difficulty level of
their classwork and homework.
The presentation of your answers matters a lot – you must
explain what youare doing and you must use proper

mathematical notation (as used in texts, notes etc). Just writing
an answer without working is not enough.
Guidelines for submitted work
This is an academic assignment so it must be referenced.
Include a Reference list at the end of your assignment. You
must cite all the different authors from different sources (books,
journals, electronic). Please do not use Wikipedia or other such
non-refereed sources.
Start each new question on a new page.
Conduct a spell check yourself and ensure you have a critical
friend read and comment on your English usage, grammar,
punctuation and other technical issues.
Please use Microsoft Word Equation to express any
mathematical formulas needed, and Microsoft Word to write the
assignment.
You may use graphical or drawing software to show your
graphs.
Please use size 12 font for any written work.
Leave a wide margin on the left for feedback comments from
your teachers.
What is plagiarism
Plagiarism is when you copy someone else’s answers. Even if
you make slight changes in symbols it is still plagiarism.
Plagiarism is cheating and is wrong. If it is detected all the
people whose answers are extremely similar will get zero marks
for the questions involved.
It is a good idea to discuss problems with other people. It is
often helpful to work in study groups, but you must write up
your answers by yourself and your examples must be unique.
Any similarities identified with TURNITIN will be investigated
and penalties will be applied.
FUNCTIONS ASSIGNMENT

QUESTION 1 –
Based on the definitions discussed in the course material and
other references, explain in your own words what makes a
function, the domain of a function and the range of a function.
Give an example and draw a proper graph of each of the
following: quadratic, polynomial, exponential, logarithmic and
at least one periodic function in your examples.
QUESTION 2 –
Investigate logarithmic scaling. What is it? How does it work?
What is it useful for? Make sure that your explanation shows
the mathematics behind logarithmic scaling through at least one
example.
QUESTION 3 –
Investigate and explain in your own words and using your own
examples how the inverses of sine, cosine and tan functions are
defined, how are they calculated and how they are used in real
life applications.
Performance Objectives: Know:
Most common types of functions their domain, range and
graphical representation.
Inverses of functions.
Do:
Analyze and describe functions
Use functions to solve real-world problems
Browse and search the Internet
Create electronic documents using graphics

Cite sources within documents appropriately

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1201BPS – ASSIGNMENT 2 – TERM 1 - 2014QUESTION 1 MARKING.docx