Caveat Academy course · Grades 10 to 12

Quantitative Reasoning: math for real decisions

The math you will actually use: check a claim with a quick estimate, see why up 20 percent and down 20 percent is a loss, find what a car loan really costs, spot a bar chart that cheats, read a poll's margin of error, and work out why most positives on a good screening test can still be false alarms. Six modules at your own pace with a calculator, ending with a news claim you take apart yourself.

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$19one-time · every device you sign in on
Buy · $19

Included with the Caveat Academy pass and Whole-school licenses. Or get it in the High school electives library, $119 for 66 items.

6 modules · 18 lessonsabout 12 hours$19

Six modules, eighteen lessons

Each module ends with a practice set that tracks mastery, an explain-it-back prompt, a short written response and a module exam. The final opens when every module is proficient; passing it earns a certificate with a verification code.

  1. Module 1: Numbers in context

    Estimate quantities by orders of magnitude, convert units with dimensional analysis and compare places or products with unit and per-capita rates.

    • Estimation and orders of magnitude
    • Units and conversions
    • Rates, ratios and per capita
    about 2.1 h

  2. Module 2: Percentages

    Compute percent change, successive changes and percentage points, and distinguish relative from absolute risk.

    • Percent and percent change
    • Successive changes and percentage points
    • Relative and absolute risk
    about 2.1 h

  3. Module 3: Money math

    Compute simple and compound interest, loan costs and inflation effects, and evaluate a budget against a guideline.

    • Simple and compound interest
    • Loans and credit
    • Budgets and inflation
    about 2.1 h

  4. Module 4: Reading data

    Choose between mean and median, detect misleading graphs and judge surveys by sampling method and margin of error.

    • Center and spread
    • Graphs that inform and graphs that mislead
    • Samples and surveys
    about 2.1 h

  5. Module 5: Probability and risk

    Compute probabilities and expected values and reason about conditional probability with natural frequencies.

    • Basic probability
    • Expected value
    • Conditional probability and base rates
    about 2.1 h

  6. Module 6: Models and claims

    Compare linear and exponential models, use doubling time and half-life, and evaluate claims for confounding and causation.

    • Linear and exponential models
    • Growth, decay, doubling and half-life
    • Correlation, causation and checking claims
    about 2.1 h

Try it before you start

This is how every lesson works: step through a worked example at your own pace, then answer a check and get the reason right away. Nothing here is saved; the course keeps your progress.

Module 5 · Conditional probability and base rates

Worked example: a positive screening result

  1. Example: a condition affects 1 percent of people. A test catches 90 percent of those who have it, and wrongly flags 9 percent of those who do not.

A lesson check from each module

The checks need JavaScript turned on. The course itself works the same way.

What you get

Academics · High School$19 · included with the Academy pass and Whole-school licenses

What you finish with
A finished semester of quantitative reasoning: you can estimate by orders of magnitude, convert units without losing track, compare places and prices by rate, compute percent change and tell percent from percentage points and relative from absolute risk, work out compound interest, loan costs and inflation, choose mean or median, catch a misleading graph, judge a survey by its method and margin of error, compute expected value, reason through base rates with natural frequencies, tell linear from exponential growth and pull apart correlation and cause. Passing the final earns a Caveat certificate of completion.
Who it is for
Students in grades 10 to 12 who have finished Algebra 1 and want math they will use as adults, students taking a math-for-life or quantitative reasoning course, seniors preparing for college courses with a quantitative requirement, and homeschool families. A phone calculator is enough; the money lessons are general education, not financial advice.
Format
An online self-paced course: 6 modules and 18 lessons with worked examples you reveal step by step, 144 practice and exam items (multiple choice, numeric, fill-in and ordering), an explain-it-back prompt and a rubric-checked short response in every module, module exams with one retake, a 24-question final and a certificate with a verification code. About 12 hours in all; works on a phone or a computer.
Access
$19 one-time, yours on every device you sign in on; the course opens once you are signed in with it. Included with the Caveat Academy pass and Whole-school licenses. Also in the High school electives library ($119) and the Academics Suite pass ($149), and 1 more bundle. Progress is saved in this browser on this device, and the certificate page lets you download your record.
Where it lives
The High School space in Caveat Academics.
Support
Access, a receipt, a refund or a correction to the course: team@caveatacademic.com.

How it works

  1. Open the course and start Module 1. Each lesson takes about 25 to 35 minutes; two or three a week finishes the course in about a semester.
  2. Answer the checks as you read. Every answer shows the reason, and a miss links you back to the lesson that covers it.
  3. Finish each module with its practice set and exam. Proficient on every module opens the final; 70 percent passes it.
  4. Print or download your certificate and record from the certificate page.

Start the course

Sources and accuracy

The lessons are original writing by Caveat Academic Services. Facts were checked against these free, open references, which are also good places to read further.

  1. OpenStax, Contemporary Mathematics, the chapters on money, probability and statistics, a free college textbook: openstax.org
  2. OpenStax, Introductory Statistics 2e, on sampling, bias and margins of error: openstax.org
  3. Consumer Financial Protection Bureau, explainers on APR, auto loans and credit cards: consumerfinance.gov
  4. U.S. Bureau of Labor Statistics, the Consumer Price Index and how inflation is measured: bls.gov
  5. National Institute of Standards and Technology, unit conversion factors (SP 811 and the SI guide): nist.gov

Quantitative Reasoning is a self-paced course from Caveat Academic Services. It follows the sequence of a typical high school quantitative reasoning course but does not replace a school course and awards no credit. Interest rates, prices, salaries, test accuracies and risks in worked problems are labeled examples for practicing the math; they are not financial or medical advice. Support: team@caveatacademic.com.