AI Projects for Math Teachers

I need three parallel practice sets for [grade level or course, Ex. Algebra 1] on [specific skill].

Each set has [number] problems and practices that same skill:
- Set A, entry level. Friendly numbers, one step at a time, no negatives unless the skill requires them.
- Set B, on level. The version I would hand the whole class.
- Set C, stretch. Same skill, harder numbers or one more layer of reasoning.

For every problem in all three sets, show the full solution path line by line, with the answer at the end. Do not just state answers.

Rules:
- The mathematics being practiced has to be identical across the three sets. Change the load, not the skill.
- Keep the arithmetic clean enough that a student who understands the method is not defeated by the numbers.
- Flag any problem where you are less than certain of your own arithmetic.

I am going to work all three sets myself before students see them, so put the key in a separate block at the end where I can cover it.

Write [number] word problems for [grade level or course] on [specific skill].

Set every one of them in my students' actual world. Here is that world: [Ex. our school is Lincoln Middle, the big sport is soccer, half of them work at the grocery store on Route 9, they all play a lot of basketball].

Rules:
- The context has to matter to the problem. If the situation could be swapped for any other noun without changing anything, rewrite it.
- Numbers have to be realistic for the situation. A part-time paycheck is not $4,000.
- No context that assumes something a student in my room might not have (Ex. family vacations, home ownership, expensive hobbies).
- The mathematics stays exactly what a textbook version of this skill would ask. The wrapper changes, the math does not.

For each problem, give me the full solution path with your work shown, then the answer. Number the problems and put the key at the end.

If the arithmetic in any problem gets messy, tell me so I can change the numbers.

Act as a math coach who thinks in terms of student misconceptions.

Course: [grade level or course]. Topic: [topic].
The error I keep seeing: [Ex. students distribute the exponent across addition, so they write (a + b)^2 as a^2 + b^2].

Do this:
1. Explain in two or three sentences what a student is actually thinking when they make that error. Not that they are careless, but what faulty rule is in their head.
2. Write [number] problems built so that a student holding that misconception gets a visibly wrong answer, rather than accidentally landing on the right one.
3. For each problem, show the wrong answer the misconception produces next to the correct answer, with the work shown for both.
4. Write two problems where the misconception happens to give the right answer anyway, so students learn why checking one case proves nothing.
5. Give me the one question to ask a student who is still making the error after all of this.

Show your work everywhere. I will verify every answer before I use it, so mark anything you are unsure of.

Write [number] error-analysis problems for [grade level or course] on [topic].

Each one is a complete worked solution containing exactly one mistake.

Requirements:
- Vary the kind of error across the set: a conceptual error, a sign error, a misapplied rule, steps done out of order, correct method with a wrong final simplification. Identify which is which in the key only.
- The mistake has to be one a real student at this level makes, not a typo.
- Every other line must be correct, so the error is found by reasoning rather than by scanning for the ugly line.
- Do not mark, bold, or hint at the error anywhere in the student copy.

Give me two separate documents: a student copy with nothing marked, and a teacher key.

In the key, for each problem: the line the error sits on, what the student was probably thinking, the corrected work from that line forward, and the right answer. Show all work, and tell me where you are unsure of your own arithmetic.

Build a spiral review set for [grade level or course].

This week's topic: [topic].
Earlier topics I want kept warm: [list three or four, Ex. solving two-step equations, operations with fractions, graphing a line from a table].

Give me [number] problems, mixed rather than grouped, so students have to decide what kind of problem each one is before they start. In the key, label each problem with the topic it hits.

Balance it so roughly a third are this week's topic and the rest spread across the older ones, weighted toward whichever students forget fastest. Tell me which of my older topics you would weight most heavily and why.

Show the full solution path for every problem in the key, with the work, not bare answers.

Then give me the same set again with different numbers, so next week's version is already done. Confirm both versions have the same difficulty, and flag any arithmetic you are not certain of.

Write [number] multi-step problems for [grade level or course] that require students to combine [Ex. proportional reasoning and percent change] inside a single problem.

For each problem give me:
1. The problem exactly as students will see it.
2. The intended solution path, step by step, with the work shown at every step.
3. Which specific idea each step assesses, so I know what a wrong answer at that point tells me.
4. The most likely place a student stalls, plus one hint that does not hand over the next step.
5. The answer, stated separately at the end.

Rules:
- Two or three ideas per problem, not six. I want depth, not a scavenger hunt.
- Nothing solvable by guessing or by working backward from options, because there are none.
- Keep the numbers clean enough that the reasoning is the hard part.

Do not skip steps in the solution paths. I am using them to plan the discussion, and I will work each problem myself first.

Build a bank of 15 number talks or warm-ups for [grade level or course], each designed to run in five to eight minutes.

Skill area: [topic]. What my students can already do: [brief description].

Sequence them so the strategies students are likely to use get progressively more sophisticated across the bank. Do not sort by how big the numbers are, sort by the thinking each one invites.

For each, give me:
- The prompt exactly as it goes on the board, nothing extra.
- The two or three strategies students at this level are most likely to use, in the order they usually surface.
- The strategy I am hoping for, and the question that draws it out if nobody offers it.
- One follow-up that connects a student's strategy to the mathematics I am building toward.

Keep each prompt short enough to write large on a board. Show the arithmetic behind every anticipated strategy so I can check it before class.

Write a problem set for [grade level or course] on [topic] in this format: [Ex. multiple choice, four options, in the style of our state test].

Number of problems: [number].
Here is a sample item from the format I am matching: [paste one, or write "none"].

If the format is multiple choice, every distractor must be the answer a real student error produces. In the key, name the error each distractor corresponds to. No random wrong numbers, no absurd options, no "none of the above."

Also:
- Vary where the correct answer sits across the set.
- Keep wording and reading level consistent with the format I named.
- Show the full worked solution for the correct answer, and show the work that produces each distractor, so I can confirm every distractor is actually reachable.

Put the key and the error mapping at the end, separate from the student copy. Flag any item where your own arithmetic is uncertain.

Explain [specific concept] five different ways for [grade level or course] students:
1. Numerically, through a table or a pattern in the numbers.
2. Visually, described precisely enough that I can draw it on the board (say what goes where, with labels).
3. Verbally, in plain language, using no symbols at all.
4. Algebraically, with the general form and what each piece stands for.
5. With a real-world model that actually behaves the way the mathematics does.

For each version:
- Keep it under 150 words.
- Say which student it tends to land with, and what it hides or oversimplifies.

Then tell me which two you would lead with for a class that [Ex. is strong on procedures and weak on reasoning], and why.

If the model in step 5 breaks down somewhere, say exactly where, so a student who pushes on it does not catch me flat. Check any numbers in the table before you hand them over.

Act as a math teacher who has taught [topic] to [grade level or course] many times.

Before I teach it, tell me:
1. The five most common misconceptions students bring to this topic, most frequent first.
2. For each, the faulty rule the student is actually applying, stated the way they would state it.
3. Where each one comes from. Often it is a rule that was true in an earlier course and quietly stops being true here.
4. One diagnostic question per misconception that reveals whether a student holds it, before I have taught anything.
5. What to do on day one about the top two, instead of discovering them on the quiz.

My students' previous course was [Ex. Pre-Algebra], and what I know about this group is [brief description].

Be concrete. "Students struggle with fractions" is not useful. Show the actual wrong work a student produces, with the arithmetic written out so I can recognize it on paper.

I have only ever taught [topic] symbolically. Build me a concrete-to-abstract sequence for [grade level or course].

Three stages:
1. Concrete. A physical or hands-on model. Name the materials (things a school actually has), what students do with them, and the exact question I ask at the end.
2. Representational. A drawing, diagram, or table that keeps the structure of the model without the materials. Describe it precisely enough for me to draw it.
3. Abstract. The symbols, introduced so each one maps onto something students already handled in stages 1 and 2.

For each stage tell me: how long it takes, the one sentence that bridges it to the next stage, and what breaks if I skip it.

Flag anywhere the concrete model stops being faithful to the mathematics, because a model that lies is worse than no model at all.

Show the arithmetic in every example so I can verify it before class.

Explain why [specific procedure, Ex. why you invert and multiply when dividing fractions] actually works.

Give me:
1. The mathematical reason, written for a teacher, complete and rigorous.
2. The same reason rewritten for a [grade level] student, in plain language, with one worked example.
3. A visual or concrete demonstration of it that I can put on a board.
4. The one sentence I say when a student asks "but why?" mid-lesson and I have thirty seconds.
5. The most common wrong explanation teachers give for this, and why it does not hold up.

Do not skip steps in part 1. Write every line, including the ones that feel obvious, because the skipped line is usually where the justification actually lives.

If there is more than one legitimate justification, give me the one that generalizes best and say what it costs in simplicity. I will check the reasoning line by line before I teach it, so tell me where you are least sure.

My [grade level or course] students are asking when they will ever use [specific topic]. I want an honest answer, not a poster.

Give me:
1. Four situations where this specific mathematics is genuinely used, and who uses it. Not "engineering," but the actual task inside the job.
2. For each, one concrete example with real numbers, worked out, so I can show it rather than assert it.
3. An honest ranking: which of these a student in this room might plausibly run into, and which are true but remote.
4. The applications commonly claimed for this topic that do not hold up, and why.
5. If the real answer is that this topic matters mostly as groundwork for a later one, say that plainly and name the later one.

I would rather have one true answer than five contrived ones, so do not stretch. Mark any thin use as thin, and check the numbers in your worked examples before you give them to me.

Write a proof or derivation of [specific result] for [grade level or course] students.

Requirements:
- Number every step. One logical move per step.
- After each step, state in a short clause what justifies it: a definition, a prior result, an algebraic property, a given.
- Do not skip a step because it is routine. Do not write "it follows that," "clearly," "it can be shown," or "by algebra." If a line takes three moves, write three lines.
- State up front what is assumed and what is being proved.
- Use only tools my students already have: [Ex. no trigonometry, no calculus].

Then give me:
1. The two steps students are most likely to accept without understanding, and the question that checks whether they do.
2. Where the argument breaks if one assumption is dropped.

I am going to check every line, so flag any step you are less than confident is fully justified rather than smoothing over it.

Design a task for [grade level or course] on [topic] that can be solved three genuinely different ways.

Give me:
1. The problem as students will see it, worded so it does not steer them toward one method.
2. Three complete solutions using three different approaches (Ex. algebraic, graphical, numeric or table-based), each worked step by step with the arithmetic shown.
3. For each approach: which student reaches for it, what it makes obvious, and what it hides.
4. The order to put them on the board for the discussion, and why that order.
5. The three questions that drive the comparison, ending with one that gets students to say when they would choose each method.
6. The wrong turn most likely to show up as a fourth approach, and how to use it rather than dismiss it.

All three solutions must reach the same answer. Verify that yourself and show the work, because a comparison discussion falls apart the moment two of the paths disagree.

Build quick checks for [grade level or course] on these objectives: [list them, one per line].

For each objective, give me exactly three problems:
- One a student with the basic idea can do.
- One at the level I actually expect.
- One only a student who understands, rather than mimics, can do.

For each objective also give me:
1. The full worked solution for all three, with the arithmetic shown.
2. What a wrong answer on each specific problem tells me about where the misunderstanding sits.
3. The cut line: how many, and which ones, a student needs right before I move on.
4. My move if more than a third of the class misses the second problem.

Keep each check to something a student finishes in four minutes and I can read at a glance while walking the room. Format all three problems to fit on a half sheet, and put the key on its own page.

Write a rubric for this non-routine math task in [grade level or course]: [paste the task or describe it].

The rubric has to score more than the final answer. Include rows for the reasoning, the choice of approach, the use of representations, the communication of the solution, and the handling of assumptions. Include a row for accuracy, but do not let it dominate the total.

For each row, write four performance levels with descriptors specific to this task. Not "shows some reasoning," but what that looks like on this problem.

Also give me:
1. A student-facing version in plain language, phrased as what to do rather than what will be judged.
2. Two sample responses, one strong and one that reaches the right answer with weak reasoning, plus how each scores row by row and why.
3. The row most likely to cause a grading argument, and how to word it so that does not happen.

Keep the total under [number] points.

Build me a feedback comment bank for [grade level or course] math.

The errors I keep writing about: [list them, Ex. drops the negative when distributing, never checks the solution, no units on the answer, skips so many steps I cannot follow the reasoning, right method with an arithmetic slip].

For each error, write 15 comments I can drop onto student work.

Rules:
- Every comment names the specific mathematical move that went wrong. Never effort, attitude, or "be careful."
- Every comment includes a next action the student takes on this problem, not general advice.
- Vary the length. Some short enough for a margin, some for the bottom of a page.
- Use [NAME] where a name goes.
- Nothing sarcastic, and nothing that reads as a verdict on the student.

Group them by error type. Mark the three per error I should reach for most often, and add one comment per error for the student who made it again after already being told once.

Build two versions of a test for [grade level or course], Form A and Form B, matched closely enough that either one can serve as the retake.

Objectives and the points each is worth: [list them].
Length: [number] minutes. Formats to include: [Ex. multiple choice, short answer, one extended response].

Requirements:
- Every Form B item assesses the same objective at the same difficulty as its Form A partner, with different numbers and a different context. Not the same problem with the numbers nudged.
- Give me an item-by-item map: which A item pairs with which B item, and the objective each covers.
- Keep the arithmetic burden equal across the forms. If one version has uglier numbers, fix it.

Show the complete worked solution for every item on both forms, then a clean answer key at the end.

Tell me which pairs you are least confident are truly equivalent. I will work both forms myself before either one is given.

Here is the test I am giving my [grade level or course] students: [paste the whole test].

Work backward from it and build the study guide it implies:
1. Group the content by objective, and tell me how many points each objective carries, so students know where to spend their time.
2. For each objective: a two-sentence plain-language reminder of the method, one fully worked example, and two practice problems parallel to the test items without being the test items.
3. The vocabulary and notation this test uses that a student needs to recognize on sight.
4. The three things on this test students are most likely to underestimate.
5. A one-page "if you only have thirty minutes" section at the top.

Show the work in every worked example, and put an answer key for the practice problems at the end with full solution paths rather than bare answers.

Do not reuse a single problem from the test. If any test item does not map cleanly to an objective, tell me, because that is worth knowing before I give it.

Here is a worksheet from my [grade level or course] class: [paste the problems, or describe the skill and give a few examples].

Build a scaffolded version using faded support, not fewer problems:
1. Problem 1 fully worked, every step shown, with a short note beside each step saying what it does and why.
2. Problems 2 and 3 partially completed. Leave out one step, then two, and put the missing work on labeled blank lines so a student knows what kind of thing goes there.
3. Problems 4 through 6 give only a step-by-step prompt list ("first ..., then ...") with all the work blank.
4. The remaining problems exactly as in the original, no support.

Also:
- Keep the same number of problems as the original. A scaffolded worksheet is not a shorter worksheet.
- Add a boxed reminder of any prerequisite fact this skill depends on.

Give me an answer key with full solution paths, and flag any arithmetic you are not sure of.

Here are word problems from my [grade level or course] class: [paste them].

Rewrite each one to cut the reading load without changing the mathematics at all.

Rules:
- The numbers, the operations, and what is being asked stay exactly the same. If the math shifts even slightly, you have gone too far.
- Short sentences, one idea each, active voice. Cut every clause that does not carry information the solver needs.
- Keep the mathematical vocabulary (Ex. "perimeter," "proportional") and gloss it in a short parenthesis the first time. Do not strip the math words out, students need them.
- Swap unfamiliar cultural or contextual references for everyday ones, keeping the structure identical.
- Put the question last, in one line.

For each problem, show the original and the rewrite side by side and list what you cut. Then work both versions and confirm the answer is unchanged, telling me if any rewrite altered the problem at all.

My [grade level or course] students are working on [topic], and some finish in three minutes. I need extensions that go deeper, not more of the same.

Give me [number] extension problems, each a different type:
1. One that generalizes the skill (Ex. what happens for any n, or prove the pattern holds).
2. One that runs it backward, giving the answer and asking for the setup.
3. One that adds a constraint and asks whether a solution still exists.
4. One that asks for the case where the usual method fails, and why.
5. One open modeling or estimation problem with more than one defensible answer.

For each: the problem, a full solution with the work shown, the level of hint to give a student who stalls, and one sentence on the mathematical habit it builds.

Nothing may require content from a later course. These have to be reachable with what a strong student in this class already has. Verify your own solutions and say where you are unsure.

Here are the results from a quiz in my [grade level or course] class: [paste anonymized results, initials or student numbers only, item by item if you have it].

The objectives it covered: [list them].

Do this:
1. Sort students into three groups by what they actually need, not by score. Name each group's specific gap and point to the item data that shows it.
2. Write a 15 minute small-group plan for each: what I say, the two or three problems we work together, and the check at the end that tells me it landed.
3. Give me real independent work for the other two groups while I am with one, tied to the same objectives, that does not need me.
4. Tell me the order to pull the groups in, and why.
5. Name any student whose pattern does not fit the three groups, and what I should look at next for them.

Use initials only in everything you write back. Where the item data does not support a conclusion, say so instead of guessing at a cause.

A student in my [grade level or course] class is missing a prerequisite. Here is the situation:

What we are working on now: [Ex. adding rational expressions].
What the student cannot do: [Ex. add fractions with unlike denominators].
Time I actually have with them: [Ex. 20 minutes, twice].

Build the shortest possible bridge:
1. Identify the minimum this student needs from the missing skill in order to access today's content. Not the whole skill, just the part that is load-bearing here.
2. A [number] minute sequence that gets them there, with the exact examples in order and the work shown.
3. Where a tool or reference sheet is a fair workaround instead of reteaching, and where that would hide a gap that matters later.
4. The one check that tells me the bridge held.
5. What I would need to come back and fix properly, and when.

Do not give me a full reteach of an earlier grade. If this honestly cannot be bridged in the time I have, say so and give me the fallback.

I am running a lesson where my [grade level or course] students audit AI-generated math for errors.

Topic: [topic].

Give me:
1. Six worked solutions on this topic, written in a confident explanatory voice. Put one real mathematical error in four of them and leave two completely correct. Vary the error type, and do not mark or hint at anything.
2. A separate teacher key: which are wrong, the exact line, what the error is, and the corrected work.
3. A student handout with the audit task: what to check, in what order, and how to record a finding (line number, what is wrong, corrected work, right answer).
4. Three debrief questions, including one about why a wrong solution can still sound authoritative.
5. The closing question that gets students to say what they will do differently the next time a machine hands them an answer.

The two correct solutions matter. If everything is wrong, students stop reading and start pattern-matching. Verify those two line by line.

Design a lesson for [grade level or course] comparing three tools on the same mathematics: a scientific or graphing calculator, a step-by-step solver, and a chatbot.

Topic: [topic].

Give me:
1. Four problems to run through all three tools, chosen so the results actually differ. One routine, one where a chatbot is likely to slip, one where the calculator gives a correct but useless answer, and one word problem where the setup is the hard part.
2. A student recording sheet: tool, output, was it right, and how you would know without already knowing.
3. What each tool is genuinely reliable for and where each one fails, in plain language.
4. Three discussion questions that lead to what "show your work" is actually for, and why the answer alone was never the point.
5. A short closing write: which tool would you trust for what, and why.

Keep it to one [number] minute period. Tell me which outputs to test myself beforehand, since these tools change.

Design assignments for [grade level or course] on [topic] that a chatbot cannot complete for a student.

Give me [number] tasks, each built on something AI has no access to:
- A physical measurement the student takes.
- Data the class generates together in the room.
- A defended estimate where the reasoning is the graded part.
- A choice between methods the student has to justify.
- Work that references something specific we did in class.

For each task:
1. The assignment as students see it.
2. What makes it resistant to being outsourced, in one sentence.
3. What I collect and how I score it, weighted toward reasoning rather than the final number.
4. The workaround a determined student would try, and the small design change that closes it.

Be honest in step 2. If a task is only mildly resistant, say so rather than overselling it. I want to design around the tool, not run an arms race.

Write a letter to families of my [grade level or course] students about helping with math at home.

What we do this year that will look unfamiliar to them: [Ex. multiple strategies before the standard algorithm, writing out reasoning, partial credit for method].
Where homework fights usually start: [Ex. the parent shows their own method and the student says it is wrong].

The letter must:
- Stay under 400 words, plain reading level, no education jargon. No "number sense," no "productive struggle."
- Give three specific things a family member can do, phrased as sentences they can actually say out loud to their child.
- Say clearly that they do not need to know our method, and say what to do instead of teaching one.
- Name what a reasonable amount of homework struggle looks like, and when to stop and email me.
- Never imply their own math education was wrong.

Then give me a version at a fifth grade reading level for translation, and a three-sentence version for a text message.

Two things for [grade level or course] math reporting.

First, a progress-report comment bank. The skills I report on: [list them, Ex. procedural fluency, problem solving, mathematical reasoning, communication of solutions, persistence on non-routine problems].
Write 20 comments per performance level for exceeding, meeting, approaching, and not yet meeting.

Rules:
- Name a specific mathematical skill or behavior. Never effort, attitude, or ability.
- Include a concrete next step in each one.
- Use [NAME] as a placeholder. Two sentences maximum.
- Nothing that would embarrass a student reading it over a parent's shoulder.
- Every comment must be impossible to move to another level without rewriting it.

Second, conference talking points. Here are my notes: [paste them, initials only, no full names].
For each student, give me three: one specific strength with the evidence, one growth area stated as a next step, and one question to ask the family. One line each.

Use initials only in everything you write back.