unit 1: quarter: time frame: fundamentals of geometry 1 3 ... · unit 3: quarter: time frame:...

College Mathematics Curriculum Map 2020-2021 Scottsdale Unified School District – Revised 2/4/2020

College Mathematics Curriculum Map

Unit 1: Quarter: Time Frame:

Fundamentals of Geometry 1 3 - 4 weeks

Essential Questions:

● How can I apply geometric formulas to solve problems?

Key Concepts: Key Vocabulary:

● Recognize the difference between one, two, and three dimensional

objects

● Find the perimeter and area of standard and composite shapes

● Calculate the length of any side of a right triangle

● Find the area and circumference of a circle

● Find the volume of standard 3-dimensional shapes

point, line, line segment, plane, polygon, right triangles, legs, hypotenuse,

Pythagorean Theorem, square, exact answers, approximate answers, area,

perimeter, radius, diameter, circumference, face, Polyhedrons, cube, rectangular

prism, pyramid, cone, sphere, volume, cylinder, cubic units

Priority Standards: Supporting Standards:

● QR.NR.1 Represent quantities, using equivalent forms when

appropriate, to investigate and describe quantitative and geometric

relationships and solve problems in real-world contexts.

● QR.NR.4 Use and justify estimation skills, and know why, how, and

when to estimate results. Assess and justify the reasonableness of

estimations using the context and comparisons to other known values.

● MP.1 – Make sense of problems and persevere in solving them. ● MP.2 – Reason abstractly and quantitatively. ● MP.3 – Construct viable arguments and critique the reasoning of others. ● MP.4 – Model with mathematics. ● MP.5 – Use appropriate tools strategically. ● MP.6 – Attend to precision.

● MP.7 – Look for and make use of structure.

● MP.8 – Look for and express regularity in repeated reasoning.

Instructional Resources/Materials:

College Mathematics Second Edition by SCC: Chapter 1




Measurement & Dimensional Analysis 1 3 - 4 weeks


● How can I apply dimensional analysis to solve problems?

● Why can dimensional analysis produce a quantity in a different unit that is equivalent to the original unit?


● Use dimensional analysis to convert between different units of

measurement for length, mass, and capacity

● Use dimensional analysis to convert between units of measurement in

the metric system

● Use dimensional analysis to convert between the metric and standard

system of measurement

● Use rates and unit rates to problem solve

measurement, unit analysis/dimensional analysis, length, foot, yard, mile, factor

label method, weight, ounce, pound, ton, capacity, fluid ounce, cup, pint, quart,

gallon, US customary measurement system, metric system, meter, gram, liter,

unit equivalents, unit fractions, Kelvin, Fahrenheit, Celsius, rate, unit rate





● QR.NR.3 Understand and compare magnitudes of numbers utilizing

real-world context. Understand the importance and impact of unit

selection.












Equations and Lines 1 and 2 2 - 3 weeks


● How can I use linear equations to model real-world situations?

● How can I use a regression equation to predict an output for a given input?


● Solve one-step, two-step, and multi-step equations

● Recognize a linear equation, and identify the rate of change (slope) and

initial value (vertical intercept)

● Calculate a slope and interpret it as a rate of change

● Use technology to create a scatterplot and find a linear regression

equation

● Interpret the meaning of the slope and initial value (vertical intercept) of a

regression equation

● Use technology to calculate the correlation

● Interpret the correlation from a value of r, or by looking at a scatterplot

algebraic equation, solution, solve an equation, isolating the variable, slope-

intercept form, slope, input variable, output variable, scatterplot, independent

variable, dependent variable, linear regression, linear correlation, correlation

coefficient


● QR.CR.2 Compare, reason, and communicate about proportional and

non-proportional models utilizing real-world contexts.

● QR.CR.3 Identify, create, and use appropriate models for bivariate data

sets (i.e. linear, exponential) to estimate solutions for contextual

questions, identify patterns, and identify how changing parameters affect

the models.

● MP.1 – Make sense of problems and persevere in solving them. ● MP.2 – Reason abstractly and quantitatively. ● MP.3 – Construct viable arguments and critique the reasoning of

others. ● MP.4 – Model with mathematics. ● MP.5 – Use appropriate tools strategically. ● MP.6 – Attend to precision.








Percentages 2 3 weeks


● How can percentages be applied in real world applications?

● How can exponential equations be used to model real world problems?


● Convert between fractions, decimals, and percentages

● Solve for part, whole, or percent given any two of the three values

● Calculate and interpret both absolute and relative change

● Recognize an exponential equation and identify both the growth factor

and initial value

● Determine the growth or decay rate from an exponential equation

percent, absolute change, relative change, decreased, percentage points, linear

growth, initial value





● QR.NR.2 Reason, model, and communicate with and about percentages

(change, incorrect, deceptive, relative and absolute).

● QR.CR.1 Analyze and compare growth and decay using absolute and

relative change utilizing real-world contexts.

● QR.CR.2 Compare, reason, and communicate about proportional and

non-proportional models utilizing real-world contexts.

● QR.CR.3 Identify, create, and use appropriate models for bivariate data

sets (i.e. linear, exponential) to estimate solutions for contextual

questions, identify patterns, and identify how changing parameters affect

the models.









Savings 2 2 - 3 weeks


● What are the financial effects of simple interest versus compound interest?


● Recognize that simple interest grows linearly

● Correctly apply the simple interest formula to solve for A, r, t, or 𝑃0

● Recognize that compound interest grows exponentially

● Correctly apply the compound interest formula to solve A, r, or 𝑃0

● Recognize the compound interest formula is used for solving when you

have a one-time, lump sum deposit

● Calculate the APY for an account earning compound interest

principal, annual percentage rate (APR), compounding, annual percentage yield

(APY)








● QR.FR.3 Use models to solve and communicate about contextual

financial questions such as credit card debt, installment savings,

amortization schedules, mortgage and other loan scenarios.







College Mathematics Curriculum Map Unit 6: Quarter: Time Frame:

Annuities and Loans 2 2 - 3 weeks


● How can I solve real world problems that involve both planning for retirement and withdrawing from retirement accounts?


● Recognize an annuity involves equal, regular payments or deposits

● Apply the saving annuity formula and solve for any unknown using the TVM solver

● Apply the payout annuity formula and solve for any unknown using the TVM solver

● Apply the loan formula for amortized loans and solve for any unknown using the

TVM solver

● Recognize how the proportions of a payment going toward principal and interest

change over the life of a loan.

savings annuity, payout annuity, present value, future value,

remaining loan balance


● QR.NR.1 Represent quantities, using equivalent forms when appropriate, to

investigate and describe quantitative and geometric relationships and solve problems

in real-world contexts.

● QR.NR.4 Use and justify estimation skills, and know why, how, and when to

estimate results. Assess and justify the reasonableness of estimations using the

context and comparisons to other known values.

● QR.FR.3 Use models to solve and communicate about contextual financial

questions such as credit card debt, installment savings, amortization schedules,

mortgage and other loan scenarios.

● QR.FR.4 Identify and explain personal and societal consequences of financial

decisions.

● MP.1 – Make sense of problems and persevere in solving

them. ● MP.2 – Reason abstractly and quantitatively. ● MP.3 – Construct viable arguments and critique the

reasoning of others. ● MP.4 – Model with mathematics. ● MP.5 – Use appropriate tools strategically. ● MP.6 – Attend to precision.


● MP.8 – Look for and express regularity in repeated

reasoning.






Chapter 7 3 2 - 3 weeks


● How can I model relationships between sets using Venn diagrams?


● Distinguish between a subset and a proper subset

● Use correct set notation and terminology

● Find intersection, unions, and complements of sets

● Recognize and be able to apply cardinality notation

● Use cardinality notation and formulas to solve Venn diagrams

set, elements, empty set, subset, proper subset, union, intersection, complement,

universal set, Venn Diagrams, cardinality,


● QR.SPR.3 Represent numerical summaries and visual displays of real-

world data to make informed decisions. Reason, communicate, and

describe strengths, limitations, and fallacies of various displays.









Introduction to Probability 3 3 weeks


● How do you distinguish between subjective, experimental, and theoretical probability?


● Be familiar with probability terminology and properties of probabilities

● Use the complement formula to find probabilities

● Be able to calculate odds for and/or against an event

● Create tables to calculate expected values for real world applications including

insurance and product warranties

subjective, experimental, theoretical, probability, outcome, event, simple

event, sample space, impossible, certain, complement, odds against,

expected value,


● QR.NR.3 Understand and compare magnitudes of numbers utilizing real-

world context. Understand the importance and impact of unit selection.

● QR.NR.4 Use and justify estimation skills, and know why, how, and when to

estimate results. Assess and justify the reasonableness of estimations using the

context and comparisons to other known values.

● QR.SPR.1 Reason and communicate about the validity of claims based on

empirical, theoretical, and subjective probabilities. Draw conclusions or make

decisions related to risk, pay-off, expected value, and false negatives/positives

in various probabilistic contexts.

● MP.1 – Make sense of problems and persevere in solving them. ● MP.2 – Reason abstractly and quantitatively. ● MP.3 – Construct viable arguments and critique the reasoning of

others. ● MP.4 – Model with mathematics. ● MP.5 – Use appropriate tools strategically. ● MP.6 – Attend to precision.




College Mathematics Second Edition by SCC: Chapter 8 ● Instructors will want to review the parts of a deck of cards (ie: What is and what are the suits? What is a face card?)




Probability and Counting 3 3 weeks


● How can I use permutations and combinations to find probabilities?


● Calculate “and”/”or” probabilities

● Determine if two or more events are independent

● Determine if two or more events are mutually exclusive

● Use tables and tree diagrams to model possible outcomes in counting

problems

● Use permutations and combinations for counting

independent events, conditional probability, dependent, mutually exclusive, tree

diagram, permutations, combinations


● QR.NR.3 Understand and compare magnitudes of numbers utilizing

real-world context. Understand the importance and impact of unit

selection.




● QR.SPR.1 Reason and communicate about the validity of claims based

on empirical, theoretical, and subjective probabilities. Draw conclusions

or make decisions related to risk, pay-off, expected value, and false

negatives/positives in various probabilistic contexts.









Statistics 4 4 weeks


● How can I design a research study?

● How can I graphically display qualitative and quantitative data?


● Distinguish between a population and a sample

● Categorize data as either qualitative or quantitative

● Identify the type of sampling method used

● Identify the potential bias in a statistical study

● Determine whether a statistical study is an experiment or an

observational study

● Classify the type of experimental study

● Use bar graphs and pie charts to graphically display data

● Use a histogram to graphically display data

population, parameter, sample, statistic, sampling bias, random sample, simple

random sample, sampling variability, stratified sample, cluster sampling,

systematic sampling, convenience sampling, voluntary sampling, voluntary

response bias, self-interest study, response bias, perceived lack of anonymity,

non-response bias, loaded or leading questions, question order, observational

studies, experiments, treatment, confounding, control group, placebo effect,

placebo, placebo controlled experiment, comparison group, blind study, double-

blind study, qualitative data, quantitative data, frequency table, bar graph, pareto

chart, pie chart, pictogram, histogram


● QR.SPR.2 Analyze statistical information and identify limitations,

strengths, or lack of information in studies including data collection

methods (e.g. sampling, experimental, observational) and possible

sources of bias. Identify errors or misuses of statistics to justify

particular conclusions.












Describing Data 4 2 - 3 weeks


● How can I use the center, shape, and spread to describe and compare data sets?


● Identify distribution shapes from histograms

● Calculate and interpret the mean, median, and mode

● Compute and interpret the range and standard deviation

● Calculate and interpret the quartiles, 5 number summary, and boxplots

distribution, shape, outliers, center, spread, SOCS, symmetric distribution,

skewed distribution, outlier, arithmetic mean, mean, median, mode, range,

standard deviation, 5-number summary, first quartile, second quartile/median,

third quartile, boxplot


● QR.SPR.2 Analyze statistical information and identify limitations,

strengths, or lack of information in studies including data collection

methods (e.g. sampling, experimental, observational) and possible

sources of bias. Identify errors or misuses of statistics to justify

particular conclusions.




● QR.SPR.4 Represent center, shape, and spread of two or more data sets.

Reason, communicate, and compare data sets in context.









The Normal Distribution 4 2 - 3 weeks


● How can I use the normal distribution to make predictions about data sets?


● Be familiar with properties of the normal distribution

● Be able to apply and interpret the Empirical Rule to a normally

distributed variable

● Calculate and interpret the meaning of z-scores

● Find the area under specified regions of the standard normal distribution

● Use z-scores to find the percentage of observations with a specific

location for a normally distributed variable

Normal distribution, standard score (z-score)








● QR.SPR.4 Represent center, shape, and spread of two or more data sets.

Reason, communicate, and compare data sets in context.






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