CPA PRESENTATION
I.
II.
III.
IV.
V.
VI.
VII.
Overview of CA Common Core Standards
a. Major Organizational Changes –
i. Six Conceptual Categories
1. Number & Quantity
2. Geometry
3. Algebra
4. Functions
5. Modeling
6. Statistics & Probability
ii. Justified by real world applications of math
b. Statistics
c. Mathematical Modeling
i. Seeing mathematics as a creative process
ii. EXCEL makes the abstract more concrete.
d. Functions – Focus on inputs and outputs
Overview of Financial Literacy Standards
Statistics Examples of Excel
a. Probability: Discrete Probability
b. Probability: Normal Curve Questions
Mathematical Modeling
a. Stock Price
b. Sales Projections
Functions
a. Financial functions
Other Applications of Excel Skills
a. English: Expressing Elements of Literature
b. Geography: Create a contour map
Closing Remarks
CPA Conference March 9, 2013, EXCELlent Strategies Presented By Andrew J. Nelson
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FINANCIAL LITERACY 2012 LEGISLATION
“The financial world in which consumers must navigate has changed
significantly and grown more complex, increasing the need for financial
literacy and raising questions regarding consumers’ financial capability.
Financial literacy focuses on the specific knowledge and concepts
consumers need to know to manage their money and build wealth,
depending on an individual’s situation. It may mean learning how to
create and manage a household budget, learning how to invest money for
retirement, or participating in one-on-one coaching and counseling to
determine how to buy a house or start a business. It also can be part of an
overall strategy to increase economic security for lower-income families.
Financial literacy is one factor in the larger analysis of the financial
capability of consumers, which is the broader picture of how consumers
manage their resources and how they use their financial literacy to make
financial decisions.”
Source: http://www.ncsl.org/issues-research/banking/financial-literacy-2012-legislation.aspx, Last
Updated 8/23/2012, National Conference of State Legislatures. This link provides an excellent overview
of legislative trends that raise the profile of financial literacy in the classroom.
CPA Conference March 9, 2013, EXCELlent Strategies Presented By Andrew J. Nelson
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CA BUSINESS FINANCIAL MANAGEMENT PATHWAY
“Students in the Business Financial Management Pathway learn to
provide investment analysis and guidance to help businesses and
individuals with their investment decisions. Students learn that
exploring, applying, and monitoring investment opportunities are
necessary to take advantage of financial opportunities throughout one’s
life. Employment in the securities and commodities sector of the industry
will continue to expand because of the increasing levels of investment in
the global marketplace and the growing need for investment advice.”
Source:
SAMPLE BFM PATHWAY STANDARDS
STUDENTS CREATE AND USE BUDGETS TO GUIDE FINANCIAL DECISION MAKING:
“Create a budget to calculate long-term projections.”
“Analyze past and current budgets to determine financial business needs.”
Source:
CPA Conference March 9, 2013, EXCELlent Strategies Presented By Andrew J. Nelson
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Basic Five Line Real Estate Income Statements
o Gross Income
o Vacancy & Collection Loss
o Effective Gross Income
o Expenses
o Net Operating Income
Real Estate Income With Expanded Revenue &
Expense Projections
Retail Income Statements
Portfolio Tracking
Bond Laddering
CPA Conference March 9, 2013, EXCELlent Strategies Presented By Andrew J. Nelson
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An accounting structure is committed to memory. Annotated
answer sheets using EXCEL permit students to review each
calculation at their own pace. Students more easily observe
patterns of calculation from one cell to the next.
CPA Conference March 9, 2013, EXCELlent Strategies Presented By Andrew J. Nelson
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HIGH SCHOOL MATH STANDARDS
NOW ORGANIZED UNDER SIX “CONCEPTUAL CATEGORIES”






Number & Quantity
Geometry
Algebra
Functions
Modeling
Statistics & Probability
CPA Conference March 9, 2013, EXCELlent Strategies Presented By Andrew J. Nelson
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Interpreting Functions
Understand the concept of a function and use function notation
Interpret functions that arise in applications in terms of the context
Analyze functions using different representations
Building Functions
Build a function that models a relationship between two quantities
Build new functions from existing functions
Linear, Quadratic, and Exponential Models
Construct and compare linear, quadratic, and exponential models and
solve problems
Interpret expressions for functions in terms of the situation they model.
Trigonometric Functions
Extend the domain of trigonometric functions using the unit circle
Model periodic phenomena with trigonometric functions
Prove and apply trigonometric identities
Source: Page 56, K-12 California’s Common Core For Mathematics Updated 8/30/2012
CPA Conference March 9, 2013, EXCELlent Strategies Presented By Andrew J. Nelson
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Interpreting Functions: “Use function notation, evaluate functions for inputs in
their domains, and interpret statements that use function notation in terms of a
context.”
Source: Page 57, K-12 California’s Common Core For Mathematics Updated 8/30/2012
EXCEL deepens students’ conceptual understanding of a function. Inputs and output are
more concrete, and students can directly connect their classwork with future needs.
Evaluation of functions emphasizes two skills: first, the selection of an appropriate output
function to match real world scenarios; and second, proper identification of the inputs
necessary to evaluate the output function. Use of current technology eliminates much of the
tedious, time-consuming calculations that only demonstrate a student can apply PEMDAS
using a calculator. These time savings lead to more complex financial applications with
multiple inputs.
CPA Conference March 9, 2013, EXCELlent Strategies Presented By Andrew J. Nelson
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 One Function Evaluation Where
Inputs Are Limited To Single Value
Variables (3-4 Numeric Inputs)
 One Function Evaluation Where
Inputs Include Vectors of Data (“Excel
Arrays”)
 Composed Multi-Function
Evaluation (Using More Than One
Formula)
CPA Conference March 9, 2013, EXCELlent Strategies Presented By Andrew J. Nelson
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Function Notation
OUTPUT
INPUTS
CPA Conference March 9, 2013, EXCELlent Strategies Presented By Andrew J. Nelson
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INPUT OF VALUE1 IS AN ARRAY
OF DATA
INPUT OF VALUE1 IS AN ARRAY
OF DATA
CPA Conference March 9, 2013, EXCELlent Strategies Presented By Andrew J. Nelson
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Building Functions: “Compose functions. For example, if T(y) is the temperature
in the atmosphere as a function of height, and h(t) is the height of a weather
balloon as a function of time, then T(h(t)) is the temperature at the location of
the weather balloon as a function of time.”
Source: Page 58, K-12 California’s Common Core For Mathematics Updated 8/30/2012
EXCEL enables students to better understand the composition process that can be missed
when presented in a solely abstract manner. Composition is taught with more realistic
multivariate contexts. The Common Core composite function example considers a single
input variable, time. Financial functions commonly use a variety of input combination
selected from number of periods, rate, present value, future value and payment.
CPA Conference March 9, 2013, EXCELlent Strategies Presented By Andrew J. Nelson
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Y
SAMPLE COMPOSITE FUNCTION QUESTION
ou are twenty-five years old and currently have no savings or debt. You plan
to retire at age 65 years when you will collect social security payments. Once
you retire, you plan to live another 30 years. When you retire, you want
annual income of $25,000 in today’s dollars to supplement your social security
checks. You anticipate that the overall rate of inflation will be 3% per year. Assume
all savings earn an annual rate of 6%. Beginning at age 25 years, how much of your
income must be saved each year to achieve your retirement goals?
Mathematically, this question involves a composite of three functions
that incorporate three variables each.
In abstract form, the composite function is shown below.
CPA Conference March 9, 2013, EXCELlent Strategies Presented By Andrew J. Nelson
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STEP ONE: Convert a current value of $15,000 in today’s dollars
to an inflation-adjusted value when you reach the age of 65 years.
Students must select the “Future Value (FV)” output formula and
evaluate it using the three inputs (rate, number of periods, and
present value). The result is a future value = $48,931.
CPA Conference March 9, 2013, EXCELlent Strategies Presented By Andrew J. Nelson
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STEP TWO: Determine how much total savings will be required at
the age of 65 years to support the inflation-adjusted target
income per year of $48,931 for 30 years of remaining life.
Students must select the “Present Value (PV)” output formula
and evaluate it using the three inputs (rate, number of periods,
and payment). The result is a present value = $673,521.
EXCEL allows students to observe how the output for question
one becomes an input for question two.
CPA Conference March 9, 2013, EXCELlent Strategies Presented By Andrew J. Nelson
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STEP THREE: Determine how much must be saved each year to
attain your target retirement savings goal of $673,521.
Students must select the “Payment (PMT)” output formula and
evaluate it using the three inputs (rate, number of periods, and
future value). The result is a present value = $4,352.
Notice how EXCEL allows students to trace the composition of the
three functions more clearly than abstract notation alone.
CPA Conference March 9, 2013, EXCELlent Strategies Presented By Andrew J. Nelson
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CPA Conference March 9, 2013, EXCELlent Strategies Presented By Andrew J. Nelson
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Linear, Quadratic & Exponential Models: “Distinguish between situations that
can be modeled with linear functions and with exponential functions.”
Source: Page 58, K-12 California’s Common Core For Mathematics Updated 8/30/2012
EXCEL graphical applications permit students to distinguish between not just linear,
quadratic and exponential functions but also power, 3-6 degree polynomial, and logarithmic
functions.
These applications will be discussed in the
Modeling portion of the presentation.
CPA Conference March 9, 2013, EXCELlent Strategies Presented By Andrew J. Nelson
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Interpreting Categorical and Quantitative Data
Summarize, represent, and interpret data on a single count or
measurement variable
Summarize, represent, and interpret data on two categorical and
quantitative variables
Interpret linear models
Making Inferences and Justifying Conclusions
Understand and evaluate random processes underlying statistical
experiments
Make inferences and justify conclusions from sample surveys,
experiments and observational studies
Conditional Probability and the Rules of Probability
Understand independence and conditional probability and use them to
interpret data
Use the rules of probability to compute probabilities of compound events
in a uniform probability model
Using Probability to Make Decisions
Calculate expected values and use them to solve problems
Use probability to evaluate outcomes of decisions
Source: Page 67, K-12 California’s Common Core For Mathematics Updated 8/30/2012
CPA Conference March 9, 2013, EXCELlent Strategies Presented By Andrew J. Nelson
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Interpreting Quantitative Data: “Use the mean and standard deviation of a data
set to fit it to a normal distribution and to estimate population percentages.
Recognize that there are data sets for which such a procedure is not appropriate.
Use calculators, spreadsheets, and tables to estimate areas under the normal
curve.”
Source: Page 68, K-12 California’s Common Core For Mathematics Updated 8/30/2012
EXCEL enables students to create visually inspiring graphic displays that demonstrate a deep
knowledge of normal population distributions. Incorporation of an artistic element engages
the marginally interested students while enhancing the communication of the statistical
concepts. These displays document student learning more broadly than most summative
tests. Assessment of these displays focuses on the following specific areas of statistical
knowledge.
 Students show the mean as the center of a normal population distribution.
 Students draw the normal distribution with a symmetric shape, and the horizontal axis
serves as an asymptote for the normal curve.
 Students show a spread for the normal distribution that measures one standard
deviation from its center to the inflection points of the normal curve.
 Create a chart title that clearly delineates and distinguishes between the population
and variable, and includes a unit of comparison.
 Students distinguish between population and sampling distributions through their
correct measure of spread, chart title label, and probability notation.
 Students synthesize their understanding of the P-value in three forms – graphically as
the shaded area under the normal curve, abstractly using probability notation, and
quantitatively using Excel to compute its percentage.
Excel’s organizes worksheets within a workbook with easy to navigate tabs. This
structure can help instructors to breakdown, organize and sequence instruction for
complex tasks.
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The Finished Product
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Use The Rules of Probability: “Find the conditional probability of A given B as the
fraction of B’s outcomes that also belong to A, and interpret the answer in terms
of the model. Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and
interpret the answer in terms of the model. . . . “
Source: Page 69, K-12 California’s Common Core For Mathematics Updated 8/30/2012
Annotated answer worksheets can be created with Excel. These worksheets allow students
to self-assess their work outside the classroom. The ability of students to open formula
windows and observe cell contents allow them to delve deeply in the calculations. Color
coding of concepts and instructional elements are easily incorporated.
To avoid students accessing inappropriate materials during assessments, worksheets with
gaudy borders are created and posted on the website. Students must remain on the
assigned worksheet until the test is completed. From the back of the room, these borders
are easily visible. Any non-conforming screens are a red flag that students may be cheating.
Excel allows entire rows or columns can be highlighted which connects well with the concept
of conditional probability in a data table context. Students can visually observe the reduced
size of the sample set imposed by a “given” condition. Substantial improvement was
documented when instruction included this strategy.
CPA Conference March 9, 2013, EXCELlent Strategies Presented By Andrew J. Nelson
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SAMPLE DISCRETE PROBABILITY QUESTION
SAMPLE EXCEL WORKSHEET FOR CALCULATIONS
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SAMPLE EXCEL ANNOTATED ANSWER SHEETS
SAMPLE EXCEL WORKSHEET FOR CALCULATIONS
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“Modeling links classroom mathematics and statistics to everyday life,
work, and decision-making. Modeling is the process of choosing and
using appropriate mathematics and statistics to analyze empirical
situations, to understand them better, and to improve decisions.
Quantities and their relationships in physical, economic, public policy,
social, and everyday situations can be modeled using mathematical and
statistical methods. When making mathematical models, technology is
valuable for varying assumptions, exploring consequences, and
comparing predictions with data. . . . Real-world situations are not
organized and labeled for analysis; formulating tractable models,
representing such models, and analyzing them is appropriately a creative
process. “
Modeling Standards: “Modeling is best interpreted not as a collection of isolated
topics but rather in relation to other standards. Making mathematical models is
a Standard for Mathematical Practice, and specific modeling standards appear
throughout the high school standards indicated by a star symbol (★).”
Source: Page 67, K-12 California’s Common Core For Mathematics Updated 8/30/2012
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EXCEL MAKES THE ABSTRACT MORE CONCRETE
Benefits Students Who Struggle With Abstract Math
Function Library Reinforces Use Over Memorization
Cells Contain The Inputs That Underlie Its Value
http://www.calcpa.org/Content/26191.aspx
http://www.calcpa.org/Content/Financial_Literacy.aspx
1. Understand that a function from one set (called the domain) to another set (called the range) assigns
to each element of the domain exactly one element of the range. If f is a function and x is an element
of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph
of the equation y = f(x).
4. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it
describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n
engines in a factory, then the positive integers would be an appropriate domain for the function.
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