Guided course - 5 chapters

Statistics basics: A Practical Course with Noah Stein

Noah Stein teaches Statistics basics through five practical chapters that move from a clear foundation to guided work, applied decisions, and revision. You will finish with a worked solution set with a reasoning note, a tutor-ready capstone, saved notes, and a repeatable way to continue practicing.

Curious beginners to intermediate analysts 2 hrs 30 min Practice and checkpoints Free curriculum

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Next: chapter 1

What you will learn

Build knowledge, use it, and leave with evidence of progress.

Explain the essential Statistics basics vocabulary through a connected mental model.
Follow and explain a reliable quantitative reasoning workflow in guided practice.
Apply Statistics basics to a realistic scenario with visible constraints and tradeoffs.
Evaluate and revise a worked solution set with a reasoning note using evidence-based success criteria.
Complete a capstone and leave with a specific next-practice plan.

Before you start

Basic arithmetic and comfort reading a short problem
A calculator is useful but not required for every activity

Useful materials

Paper or a digital scratchpad
Calculator or spreadsheet when appropriate
A place to keep an error log

Suggested rhythm

Complete one 30-minute chapter at a time: learn for 10 minutes, practice for 15, then use 5 minutes for the checkpoint and notes.

Course capstone

Statistics basics reasoning casebook

Solve a connected set of Statistics basics problems and explain how each representation, method, and check supports the answer.

What you will submit

Three fully worked problems
An error analysis for one tempting wrong approach
A one-page method guide

How it will be reviewed

Setups match the information given
Steps are mathematically sound
Answers are checked
Explanations connect results to the question

Course chapters

Learn, practice, check, and record what matters.

2 hrs 30 min total

Chapter 1

Statistics basics: Foundations and vocabulary

Build a dependable mental model for Statistics basics before trying to memorize isolated details. You will define the essential vocabulary, inspect a worked example, and turn the ideas into a reference you can actually use.

27 min Not complete

Learning objectives

Explain the purpose of Statistics basics in your own words.
Use the chapter vocabulary accurately in a short example.
Distinguish a strong example from a common misconception.
Create a compact reference for later practice.

Key terms

Start with the purpose

Place Statistics basics inside a worked problem where the setup matters as much as the answer. Name the result a learner is trying to produce and the constraints that make the skill useful.

How Statistics basics actually works

These are the load-bearing ideas. Everything later in the course is an application of one of them, so it is worth reading slowly and returning to when something stops making sense.

Mean and median answer different questions. The mean uses every value and is dragged by outliers, while the median is the middle value and resists them. For skewed data such as income or response times, the median describes a typical case far better than the mean does.
Sample variance divides by n - 1. Dividing squared deviations by n underestimates the population variance, because the deviations were measured from the sample mean rather than the unknown true mean. Dividing by n - 1 instead removes that bias.
A p-value is not the probability a hypothesis is true. A p-value gives the probability of observing data at least as extreme as yours assuming the null hypothesis holds. It says nothing about the size or importance of an effect, which is why an effect size and confidence interval should always sit beside it.

Misconceptions worth clearing early

Each of these is common, understandable, and expensive to leave in place. Recognising them now saves rework later.

Reading correlation as causation. A strong correlation coefficient feels like an explanation of the mechanism. Fix: Correlation is equally consistent with reverse causation or a shared confounder. Only a controlled experiment or a carefully designed natural experiment supports a causal claim.
Comparing means without checking spread. Two averages are trivially easy to place side by side. Fix: Report the standard deviation or an interval alongside them. A difference of 2 carries no weight when the spread within each group is 30.
Sign errors when rearranging. Moving several terms in one written step hides the operation being applied. Fix: Apply one operation to both sides at a time and write the step down, even when it feels obvious.

Build the mental model

Connect the key terms as a process rather than a word list. Use this sequence: represent the information, choose a method, calculate carefully, and verify the result.

Catch the common miss

Compare a surface-level attempt with one that shows a correct setup, visible steps, checked units or assumptions, and a clear interpretation. Explain the single difference that matters most.

Equation in context

Arithmetic mean

\bar{x}=\frac{1}{n}\sum_{i=1}^{n}x_i

The mean balances all observations around one central value.

Live data

Balance the values against their mean

Move any value and watch the mean line shift to keep the whole set in balance.

The mean is not just a formula output — it is the balance point of the data, and one extreme value can drag it surprisingly far.

Push one value to the top of its range and watch how far the mean moves.
Make the mean land exactly on 5 in two different ways.
Which single value currently has the most pull on the mean?

Side-by-side comparison

Two solutions with the same final answer

Both attempts look plausible from a distance. Toggle the highlights and study where they part ways.

Aspect	Answer-only work	Auditable solution
Setup	Numbers pulled straight into a half-remembered formula	Defines what each symbol stands for and what is being asked
Steps	Jumps a reader cannot check	Each operation follows from the last and can be verified
Check	Stops at the first number produced	Compares the result against an estimate and the units

When the answer is wrong, only the second solution shows you where.

Practice round

Match the Statistics basics vocabulary

Tap a term, then the definition it belongs to. Wrong guesses cost nothing but honesty.

Retrieval beats rereading: pulling a definition from memory strengthens it far more than recognizing it on the page.

Clear the board once, shuffle, and beat your attempt count.
Say each definition aloud before tapping — then check yourself.

Practice activity - 12 min

Make a one-page field guide

Create a compact field guide that would help a new learner recognize and begin using Statistics basics.

Write a one-sentence definition and purpose.
Add the four key terms with a plain-language example.
Include one non-example and explain why it misses.
Finish with a three-step starter checklist.

Deliverable

One annotated page or slide that can be reused in later chapters.

Success looks like

The definition is specific.
Examples match the vocabulary.
The checklist is usable without extra explanation.

Knowledge check

Which response best shows a usable foundation in Statistics basics?

1 question

AIt defines the idea, shows it in context, and explains why the example fits. BIt copies a list of terms without connecting them. CIt starts the final project before identifying the purpose. DIt chooses an answer without checking the situation.

Chapter notes Not started

2
Chapter 2
Data cleaning: Guided demonstration

Follow a complete Data cleaning example from setup to result, pausing at the decisions that experts often make silently. Then repeat the process with support and check your work against visible criteria.

29 min Not complete
Learning objectives

Sequence the main steps in a reliable Data cleaning workflow.

Explain why each important decision is made.

Complete a supported example without skipping verification.

Use a checklist to identify one correction.
Key terms
1

Watch the whole process

Trace a model from the initial prompt to a worked solution set with a reasoning note. Mark each point where the learner must observe, choose, or verify rather than act automatically.
2

Worked example: Computing both variances for 2, 4, 4, 4, 5, 5, 7, 9

Follow each step and predict the next before you read it. Predicting first is what turns a demonstration into practice.

The eight values sum to 40, so the mean is 5.

Deviations from the mean are -3, -1, -1, -1, 0, 0, 2 and 4, and their squares are 9, 1, 1, 1, 0, 0, 4 and 16.

Those squared deviations total 32, so the population variance is 32/8 = 4 and the population standard deviation is exactly 2.

Sample variance is 32/7 = 4.571, giving a sample standard deviation of about 2.14.

Identical data produces two different standard deviations, so the correct answer depends entirely on whether those eight values are the whole population or a sample drawn from one.
3

Where this usually goes wrong

Watch for these while you work through the demonstration rather than afterwards.

Reading correlation as causation. A strong correlation coefficient feels like an explanation of the mechanism. Fix: Correlation is equally consistent with reverse causation or a shared confounder. Only a controlled experiment or a carefully designed natural experiment supports a causal claim.

Comparing means without checking spread. Two averages are trivially easy to place side by side. Fix: Report the standard deviation or an interval alongside them. A difference of 2 carries no weight when the spread within each group is 30.

Sign errors when rearranging. Moving several terms in one written step hides the operation being applied. Fix: Apply one operation to both sides at a time and write the step down, even when it feels obvious.
4

Practice with scaffolding

Repeat the model with one detail changed. Keep the prompts visible and say or write the reason for each choice before continuing.

5

Check before feedback

Use a correct setup, visible steps, checked units or assumptions, and a clear interpretation as the quality test. Make one self-correction before asking the tutor to review the result.
Equation in context
Sample variance

s^2=\frac{\sum_{i=1}^{n}(x_i-\bar{x})^2}{n-1}

Variance measures spread by averaging squared distances from the sample mean.
Data lab
Find the value that lies

Cleaning is mostly outlier judgment. Drag the suspect value and see exactly how much damage it does to the mean.

The mean listens to every value, the median only to the middle one — which is why one billionaire moves a neighborhood's average income and not its typical one.

Drag the outlier to 300 and compare the two centers.

When would you report the mean anyway?
Guided flowchart
A complete Data cleaning practice run

flowchart LR N1["Read the task"] N2["Model one step"] N3["Try with support"] N4["Verify the result"] N1 --> N2 N2 --> N3 N3 --> N4

Pause at each arrow and explain the decision before moving to the next step.

Step 1 of 4: Read the task
Data example
Normalize and filter small records

Python Read-only example

1 2 3 4 5 6 7 8 9 10
rows = [ {"name": " Amina " , "score": "84"}, {"name": "", "score": "missing"}, ] clean_rows = [ {"name": row["name"].strip(), "score": int(row["score"])} for row in rows if row["name"].strip() and row["score"].isdigit() ]

1 / 9

Make state explicit rows = [
A named value is created or updated so later behavior can refer to it.

The transformation makes whitespace, missing names, and numeric conversion rules explicit.
Practice round
Rebuild the Data cleaning method

The steps of this chapter's method, shuffled. Arrange them so they would actually work.

A method is a sequence, not a bag of tips — if the order surprises you, that is exactly the gap worth closing now.

Order the steps, then explain to yourself why step 2 cannot go last.

Shuffle again and solve it in fewer moves.
Practice activity - 15 min
Complete the guided run

Use the chapter workflow to produce a worked solution set with a reasoning note for a slightly changed Data cleaning example.
1. Restate the task and constraints.
2. Follow the model one decision at a time.
3. Record the reason for two key choices.
4. Check the result and revise one issue.
Deliverable
A completed guided example with two decision notes and one correction.
Success looks like

The workflow is complete.

Decisions have reasons.

The final check produces a visible correction.
Knowledge check
During guided Data cleaning practice, when is the best time to explain a choice?

1 question

During guided Data cleaning practice, when is the best time to explain a choice? AAt the decision point, before seeing whether the final result works. BOnly after the tutor supplies the correct answer. COnly when the result is wrong. DAfter deleting the draft and starting over.

Chapter notes Not started

Sign in to save chapter notes to your account.

Ready to complete this chapter? Submit the guided example with decision notes, one self-correction, and the checkpoint response.
3
Chapter 3
Charts and dashboards: Applied scenario

Transfer Charts and dashboards into a realistic scenario where the prompt is less tidy and more than one option may be reasonable. You will define the constraints, choose an approach, and defend the tradeoff.

32 min Not complete
Learning objectives

Extract the relevant facts and constraints from a realistic scenario.

Generate at least two plausible approaches to Charts and dashboards.

Choose an approach using explicit criteria.

Explain the likely consequence of the choice.
Key terms
1

Read the situation

Translate the scenario into a clear task. Separate facts, assumptions, constraints, and information that is interesting but not relevant to Charts and dashboards.
2

Choosing well under real constraints

Applied work is mostly judgement under limits: less time, less information, and more competing goals than a textbook example allows. These are the decision rules that hold up in practice.

Several methods could solve the problem: Choose the one whose setup you can state clearly; a slower method you understand beats a faster one you half-recall.

You are stuck at the setup: Solve a smaller version with easy numbers first, then generalise the structure you used.

The answer looks wrong but the arithmetic checks out: Recheck the translation from words to symbols; the error is usually upstream of the calculation.
3

Reading the situation before acting

Before choosing an approach, state three things explicitly: what result the situation actually requires, which constraints are fixed rather than preferences, and what evidence would tell you the approach is working. Skipping this step is the most common reason competent work solves the wrong problem.

Mean and median answer different questions. The mean uses every value and is dragged by outliers, while the median is the middle value and resists them. For skewed data such as income or response times, the median describes a typical case far better than the mean does.
4

Practitioner notes

Small pieces of working knowledge that rarely appear in introductory material.

Plot the raw data before computing anything. Anscombe's quartet is four datasets with matching means, variances and regression lines but four completely different shapes.

State the sample size next to every percentage. 60% of 5 respondents and 60% of 5000 respondents carry entirely different weight.
5

Compare real options

Generate two workable approaches and test both against the purpose. Do not hide the tradeoff; name what each option improves and what it gives up.

6

Make the reasoning visible

Produce a worked solution set with a reasoning note and attach a short decision note. The note should make the result auditable, not merely confident.
Equation in context
Standard score

z=\frac{x-\mu}{\sigma}

A z-score expresses a value as a number of standard deviations from the mean.
Live data
What a bar chart is made of

Move the values and watch both the bars and their mean line respond — a chart is data you can interrogate, not a picture.

The mean is not just a formula output — it is the balance point of the data, and one extreme value can drag it surprisingly far.

Push one value to the top of its range and watch how far the mean moves.

Make the mean land exactly on 5 in two different ways.

Which single value currently has the most pull on the mean?
Practice round
Match the Charts and dashboards vocabulary

Tap a term, then the definition it belongs to. Wrong guesses cost nothing but honesty.

Retrieval beats rereading: pulling a definition from memory strengthens it far more than recognizing it on the page.

Clear the board once, shuffle, and beat your attempt count.

Say each definition aloud before tapping — then check yourself.
Practice activity - 18 min
Solve the scenario

Apply Charts and dashboards to a scenario from school, work, home, or community life that includes at least two constraints.
1. Write the task, audience, and constraints.
2. Sketch two possible approaches.
3. Choose using three criteria from the chapter.
4. Produce the result and explain one tradeoff.
Deliverable
A scenario response with an option comparison and a short decision note.
Success looks like

Constraints are visible.

Both options are plausible.

The final choice follows the stated criteria.
Knowledge check
What makes an applied Charts and dashboards decision defensible?

1 question

What makes an applied Charts and dashboards decision defensible? AThe chosen approach follows stated constraints and criteria, with the tradeoff acknowledged. BIt is the first idea that came to mind. CIt avoids mentioning uncertainty. DIt copies the guided example without adapting it.

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Ready to complete this chapter? Finish the scenario response, compare two options, and explain the selected tradeoff.

Chapter 4

Machine learning intuition: Review and improve

Learn to diagnose and improve Machine learning intuition work with a focused rubric instead of vague judgment. You will separate symptoms from causes, revise the highest-value issue, and document the before-and-after difference.

30 min Not complete

Learning objectives

Evaluate a draft using explicit Machine learning intuition criteria.
Identify the cause behind the most important weakness.
Choose a revision with high impact and reasonable effort.
Explain how the revision changes the result.

Key terms

Use the rubric, not a feeling

Review the work for a correct setup, visible steps, checked units or assumptions, and a clear interpretation. Record evidence for each judgment so feedback points to something observable.

Diagnostic checklist

Run this before you revise anything. Diagnosing first prevents the common failure of polishing the parts that were already fine.

Check: Reading correlation as causation — is this present in your work?
Check: Comparing means without checking spread — is this present in your work?
Check: Sign errors when rearranging — is this present in your work?
Check: Dropping or mixing units — is this present in your work?

The quality bar

This is what finished work looks like in this field. Use it as the standard for your revision rather than a general sense of improvement.

The setup states what each symbol means, including units
Steps are visible enough for a reader to find the exact point of any disagreement
The result is checked against the original problem and interpreted in context

Diagnose before editing

Name the symptom, then ask what decision or missing step produced it. Choose the cause you can address rather than changing everything at once.

Revise and compare

Make one purposeful revision and compare the two versions. Keep the change only if it improves the intended result without creating a larger problem.

Equation in context

Addition rule

P(A\cup B)=P(A)+P(B)-P(A\cap B)

Subtract the overlap once so shared outcomes are not counted twice.

Evidence lab

Models are hungry for the same √n

ML intuition starts where statistics ends: more examples shrink error slowly. The square-root wall applies to machines too.

Uncertainty is priced in square roots: quadrupling the sample only halves the margin, which is why small surveys are cheap and precise ones are not.

Find the sample where the margin drops below ±3 points.
Explain why 10 000 responses are not 10× better than 1 000.

Revision flowchart

Evidence-led improvement loop

flowchart LR
    N1["Inspect evidence"]
    N2["Find the likely cause"]
    N3["Revise one issue"]
    N4["Compare versions"]
    N1 --> N2
    N2 --> N3
    N3 --> N4

Revise the cause of the highest-value issue, then compare the new result with the original criteria.

Step 1 of 4: Inspect evidence

Model intuition

Separate training examples from a prediction rule

1 2 3 4 5 6 7 8 9

training = [
    {"hours": 1, "passed": 0},
    {"hours": 4, "passed": 1},
]

def predict_pass(hours):
    return int(hours >= 3)

print(predict_pass(5))

1 / 7

Make state explicit training = [

A named value is created or updated so later behavior can refer to it.

This deliberately simple threshold illustrates features, labels, and prediction without hiding the rule.

Side-by-side comparison

Two solutions with the same final answer

Use this pair as your revision rubric: find which column your current draft sits in, one row at a time.

Aspect	Answer-only work	Auditable solution
Setup	Numbers pulled straight into a half-remembered formula	Defines what each symbol stands for and what is being asked
Steps	Jumps a reader cannot check	Each operation follows from the last and can be verified
Check	Stops at the first number produced	Compares the result against an estimate and the units

When the answer is wrong, only the second solution shows you where.

Practice round

Rebuild the Machine learning intuition method

The steps of this chapter's method, shuffled. Arrange them so they would actually work.

A method is a sequence, not a bag of tips — if the order surprises you, that is exactly the gap worth closing now.

Order the steps, then explain to yourself why step 2 cannot go last.
Shuffle again and solve it in fewer moves.

Practice activity - 16 min

Run a focused revision cycle

Review a previous Machine learning intuition artifact or the supplied flawed example, then improve the most consequential issue.

Score the draft against three criteria.
Quote or point to evidence for the weakest score.
Name the likely cause and revise it.
Write a before-and-after comparison.

Deliverable

A marked-up draft, revised version, and four-sentence change note.

Success looks like

Feedback cites evidence.
The revision addresses a cause.
The comparison explains a measurable or observable improvement.

Knowledge check

Which feedback is most useful for improving Machine learning intuition?

1 question

AA specific observation linked to a criterion and a realistic next action. BA general statement that the work is good or bad. CA complete replacement made by someone else. DA list of unrelated preferences.

Chapter notes Not started

5
Chapter 5
AI prompt literacy: Capstone integration

Integrate the course methods in a compact AI prompt literacy capstone. You will define the brief, plan milestones, produce a complete result, gather tutor feedback, and leave with a repeatable next-practice plan.

37 min Not complete
Learning objectives

Translate the capstone brief into milestones and checks.

Combine the course methods without losing the central purpose.

Present evidence for the quality of the final result.

Choose the next skill to practice from the final review.
Key terms
1

Define a finishable brief

Choose a specific audience, result, and boundary for the AI prompt literacy capstone. Reduce scope until the project can be finished and reviewed in one focused cycle.
2

Bringing the parts together

A capstone is judged on coherence, not on the number of techniques it includes. Return to the core ideas and make sure the work demonstrates them rather than decorating them.

Mean and median answer different questions. The mean uses every value and is dragged by outliers, while the median is the middle value and resists them. For skewed data such as income or response times, the median describes a typical case far better than the mean does.

Sample variance divides by n - 1. Dividing squared deviations by n underestimates the population variance, because the deviations were measured from the sample mean rather than the unknown true mean. Dividing by n - 1 instead removes that bias.

A p-value is not the probability a hypothesis is true. A p-value gives the probability of observing data at least as extreme as yours assuming the null hypothesis holds. It says nothing about the size or importance of an effect, which is why an effect size and confidence interval should always sit beside it.
3

Standards that make the work credible

These are the marks of work that would be taken seriously by someone who does this professionally.

The setup states what each symbol means, including units

Steps are visible enough for a reader to find the exact point of any disagreement

The result is checked against the original problem and interpreted in context
4

Practitioner notes

Small pieces of working knowledge that rarely appear in introductory material.

Plot the raw data before computing anything. Anscombe's quartet is four datasets with matching means, variances and regression lines but four completely different shapes.

State the sample size next to every percentage. 60% of 5 respondents and 60% of 5000 respondents carry entirely different weight.
5

Build with checkpoints

Plan foundation, first draft, verification, and revision milestones. At each checkpoint, save evidence instead of relying on memory.

6

Present and continue

Present a worked solution set with a reasoning note with a concise rationale. Use the final rubric to choose one strength to retain and one next practice target.
Equation in context
Confidence interval pattern

\text{estimate}\ \pm\ (\text{critical value})(\text{standard error})

An interval pairs an estimate with a margin that reflects sampling uncertainty.
Writing lab
Clear prompts get better answers

An AI prompt is instructions for a very literal reader. Edit one here until it is short, specific, and unambiguous.

The Flesch score is arithmetic on sentence length and word length — which means both are levers you control in every sentence you write.

Split your longest sentence in two and watch the score move.

Swap one three-syllable word for a plain one — how much did it matter?

Push the score above 60, then decide what you actually prefer.
Visual model
Capstone learning loop

The capstone is a complete cycle: define a finishable brief, build, review evidence, then choose the next practice target.
Structured prompt
Express an AI task as clear JSON

JSON Read-only example

1 2 3 4 5 6 7 8 9
{ "role": "study tutor", "task": "Explain one concept with an example", "learner_level": "beginner", "constraints": [ "Ask one check question", "Do not invent sources" ] }

1 / 7

Label a piece of context "role": "study tutor",
The field name makes the value's purpose readable without relying on position.

Structured fields make the goal, learner context, and boundaries easy to inspect and revise.
Practice round
Match the AI prompt literacy vocabulary

Tap a term, then the definition it belongs to. Wrong guesses cost nothing but honesty.

Retrieval beats rereading: pulling a definition from memory strengthens it far more than recognizing it on the page.

Clear the board once, shuffle, and beat your attempt count.

Say each definition aloud before tapping — then check yourself.
Practice activity - 22 min
Complete the capstone sprint

Create a complete AI prompt literacy artifact for a defined audience and purpose, using the course rubric to review it.
1. Write a brief with scope and success criteria.
2. Create the first complete version.
3. Run a self-check and request focused tutor feedback.
4. Revise, present, and set one next-practice target.
Deliverable
A finished capstone, evidence of one revision, and a next-practice note.
Success looks like

The result answers the brief.

Course methods are visible.

Revision follows feedback or evidence.

The next step is specific and achievable.
Knowledge check
When is the AI prompt literacy capstone ready to finish?

1 question

When is the AI prompt literacy capstone ready to finish? AIt meets the written brief and criteria, includes a reviewed revision, and has a clear next-practice target. BIt contains every possible feature or idea. CThe learner can no longer think of any improvement. DIt looks exactly like the tutor example.

Chapter notes Not started

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Ready to complete this chapter? Submit the completed capstone, revision evidence, rubric review, and one concrete next-practice target.

Make it personal

Turn the public curriculum into your own learning path.

Ask Noah Stein to adapt the sequence to your level, available time, and goal. The personalized path can then be saved in your workspace.

0 of 5 chapters complete

Build knowledge, use it, and leave with evidence of progress.

Before you start

Useful materials

Suggested rhythm

Statistics basics reasoning casebook

What you will submit

How it will be reviewed

Learn, practice, check, and record what matters.

Statistics basics: Foundations and vocabulary

Learning objectives

Key terms

Start with the purpose

How Statistics basics actually works

Misconceptions worth clearing early

Build the mental model

Catch the common miss

Which response best shows a usable foundation in Statistics basics?

Data cleaning: Guided demonstration

Learning objectives

Key terms

Watch the whole process

Worked example: Computing both variances for 2, 4, 4, 4, 5, 5, 7, 9

Where this usually goes wrong

Practice with scaffolding

Check before feedback

During guided Data cleaning practice, when is the best time to explain a choice?

Charts and dashboards: Applied scenario

Learning objectives

Key terms

Read the situation

Choosing well under real constraints

Reading the situation before acting

Practitioner notes

Compare real options

Make the reasoning visible

What makes an applied Charts and dashboards decision defensible?

Machine learning intuition: Review and improve

Learning objectives

Key terms

Use the rubric, not a feeling

Diagnostic checklist

The quality bar

Diagnose before editing

Revise and compare

Which feedback is most useful for improving Machine learning intuition?

AI prompt literacy: Capstone integration

Learning objectives

Key terms

Define a finishable brief

Bringing the parts together

Standards that make the work credible

Practitioner notes

Build with checkpoints

Present and continue

When is the AI prompt literacy capstone ready to finish?

Turn the public curriculum into your own learning path.