Supercharge Your Maths Teaching with ChatGPT & LLMs: Prompts, Tips, and Pitfalls

Large Language Models (LLMs) like ChatGPT are everywhere, and it’s natural to wonder how these forms of artifical intelligence (AI) fit into teaching maths. Can an AI maths solver really help you plan that tricky Year 8 algebra lesson, or create those KS2 geometry problems that are pitched just right?

To get the most out of LLMs like ChatGPT for maths, you need to know how to ask the right questions. Crafting good prompts is key! Evaluate what LLMs give you critically and really understand their limitations.

In this blog, I’ll explore practical ways to use these AI tools, share concrete prompting strategies, highlight the crucial checks you must do, and flag the common pitfalls of using AI like ChatGPT maths.

Key takeaways:

• Be specific: Detailed prompts yield better results.
• Verify everything: Don’t simply trust AI output without checking accuracy and curriculum fit.
• Protect data: Never input identifiable student information.
• Refine and adapt: Use follow-up inputs and your own expertise to improve outputs.
• Stay critical: Understand the limitations and potential pitfalls.

LLMs and ChatGPT maths in education: opportunities and challenges

So, what is an LLM? Think of it as an incredibly sophisticated predictive text generator, trained on millions of examples of natural language and code. Within that data, it searches and analyses patterns. These patterns allow it to generate plausible responses based on your input.

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ChatGPT maths opportunities for teachers:

• Rapid idea generation: Stuck for a starter on percentages? Need a fresh angle for teaching coordinates? LLMs can brainstorm ideas quickly.
• Personalised resource creation: Generate varied math problem sets tailored for different abilities, from simple calculations for fluency to more complex math concepts requiring deeper thought.
• Alternative explanations: Find different ways to explain tricky math concepts like fractions or standard form that might click with a struggling learner. You can ask for step-by-step explanations for specific types of maths problems.
• Time saving (potentially): Speed up drafting initial lesson outlines, creating banks of practice questions to solve problems, or generating marking criteria.
• Make it fun or interesting: Sometimes AI can suggest fun or interesting contexts for maths problems you might not have thought of.

However, using AI for maths, such as ChatGPT and LLMs, also presents some challenges:

Challenges of using ChatGPT for maths teachers:

• Accuracy is not guaranteed: This is a big one. LLMs can and do make mistakes. After all, not all our own predictions are accurate. They might misunderstand nuances, misapply formulas, or generate incorrect solutions, especially, but not always, for more complex math problems. You must verify everything.
• Curriculum misalignment: AI-generated content might not perfectly match your specific scheme of work or year-group objectives.
• Generic outputs: Initial responses are often a bit bland. Good results often mean refining what you feed the LLM and editing what you get back.
• Workload implications: While AI can save time drafting, the time needed to check, edit, and adapt the output can sometimes eat up those savings. 
• Managing prompts: Keeping track of all those useful prompts and outputs can become a large task.
• Data privacy: Inputting sensitive information, such as student data, is a safeguarding concern.

Both the SATs teacher survey and GCSE maths teacher survey highlighted the current lack of training and education provided for teachers around AI and ChatGPT.

Setting up for success: key steps

Before you start generating resources with ChatGPT for maths, take a few crucial steps:

• Check school policies and guidance: Is there an AI policy listing approved platforms and usage guidance? Are there guidelines on data privacy? Get clarity to avoid issues and potentially breaking existing policies such as Safeguarding or Data Protection policies. 
• Account setup and work environment: If you’re setting up accounts, consider using a professional or school email. If your school uses Microsoft, you may be able to access Copilot already. If your school uses Google, you may be able to access Gemini.
• Curriculum alignment: Keep your school’s scheme of work and relevant documents close by. You’ll need them to cross-reference everything the AI gives you for alignment and accuracy. Don’t just trust the AI’s outputs!

TOP TIP:

Any school using AI should have an AI policy. Third Space Learning’s safeguarding leads have created an AI policy template for the use of Skye, the conversational AI maths tutor, and other AI tools. You can download the editable AI policy template for free and adapt it to your school.

Crafting effective prompts: the heart of good AI output

The quality of what you get out of an LLM depends entirely on the quality of what you put in. Vague prompts lead to vague (and often useless) results. Be specific!

Weak vs. strong ChatGPT maths prompts

TOP TIP:

A good, straightforward approach for those new to prompting is to think about these key elements:

1. Format: Specify how you want the output presented. For example, present the questions clearly numbered, and provide the answer key separately at the end.
2. Role: Tell the AI who you want it to be. For example, act as an experienced primary maths teacher.
3. Task: Clearly state what you want it to do. E.g. Create a worksheet.
4. Context: Provide all the necessary details and limitations like in the strong prompt example above. This is crucial for maths!

Types of prompts for maths teachers

In addition to using Chat GPT to reduce report writing time, prep for parents’ evening, complete CPD and other administrative tasks, the examples below are likely the most common types of prompts maths teachers will use.

Lesson plans and outlines

Example: Year 8 linear equations lesson plan

Act as an experienced Key Stage 3 maths teacher teaching in England. Design a 60-minute lesson plan for a Year 8 class introducing linear equations in the form y=mx+c. Assume students have prior knowledge of plotting coordinates and substituting values into expressions. 

Include a starter activity specifically designed to recap plotting coordinates in all four quadrants. 

Cover the main teaching points of understanding gradient ('m') and the y-intercept ('c') and how they relate to the graph. 

Include a practical activity where students plot graphs of linear equations from a table of values and a plenary task to check understanding of the relationship between the equation and the graph. 

Suggest specific differentiation strategies for both lower and higher attaining students. 

Present the lesson plan as a table with columns for Time, Activity, Teacher Notes/Key Questions, Resources, and Adaptations.

Caution: The AI might miss prerequisite knowledge or suggest unrealistic timings. Treat it as a draft.

Resource creation (worksheets and problem sets)

Example: SATs preparation materials

Act as an experienced primary maths teacher teaching in England who is creating SATs preparation materials. 

Generate 10 multiple-choice questions suitable for Year 6 SATs preparation, covering ratio and proportion topics from the UK National Curriculum. 

Include distractors that are plausible and specifically reflect common misconceptions Year 6 students have with ratio and proportion. Ensure questions vary in context (e.g., recipes, scaling, sharing quantities). 

Each question must have only one clearly correct answer among the options provided. Distractors should be well-formed and appear equally plausible to students who hold common misconceptions, avoiding obvious incorrectness. 

Ensure the language and context of each question are clear, concise, and unambiguous for a Year 6 student. 

Avoid grammatical clues or patterns in the options that might inadvertently reveal the answer. 

If units are relevant (e.g., cm, g, £), ensure they are used correctly and consistently. 

Provide the correct answer for each question. 

Present each question clearly numbered, followed by four answer options (A, B, C, D). 

List the correct answers separately at the end.

Caution: Always double-check calculations, language, and difficulty. Ensure diagrams or contexts are clear.

Marking and feedback

Example: Specific Year 10 GCSE feedback

Act as an experienced GCSE Maths teacher. Provide constructive feedback for a Year 10 student who incorrectly solved the equation 3(x + 2) = 2(x - 1) and got x = -8. 

The feedback should explain the likely error, specifically focusing on a sign error that might have occurred during the expansion of the brackets. 

It should guide the student towards the correct method for solving the equation step-by-step, but without giving them the final correct numerical answer for x. 

The tone should be encouraging and focus on understanding the process. 

Present the feedback as a concise comment suitable for writing on a student's work or in an online feedback box.

Caution: AI feedback can be generic. It lacks knowledge of the individual student. Never input names or full scripts.

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Refine outputs and use custom instructions

Sometimes, AI will come up with outputs that you did not anticipate. Don’t just accept the first output! Use follow-up prompts to adapt the outputs from the LLMs.

For example, while writing money questions, the LLM may have used dollars. Instead of writing the whole prompt again, ask the LLM to “Regenerate the worksheet but make the questions UK-centric (£ and metric units).” 

Check accuracy and curriculum alignment: the teacher’s crucial role

I cannot stress this enough: You are the expert in the room, not the AI. All it is doing is predicting what comes next. You must check the accuracy and alignment:

• Verify everything: Treat AI outputs as drafts. Always cross-reference mathematical content with reliable sources and your own knowledge.
• Spot-check: Work through generated questions and solutions before presenting them to your class. Did the AI make errors? Are the step-by-step explanations logical?
• Check for conceptual gaps: Did the explanation miss a crucial math concept? Does the sequence of questions build understanding logically?
• Curriculum: Does the content precisely match your year group and school curriculum or exam board? Check the terminology is correct.
• Teacher as curator: Be prepared to heavily edit or even discard AI content if it’s not up to scratch. Your professional judgment is paramount.

Third Space Learning provides one-to-one conversational AI maths tutoring sessions with Skye. Maths teachers and experts create and review every single lesson Skye delivers to ensure that it aligns with the curriculum and accurately covers the mathematical methods and procedures students need. Every lesson covers misconceptions that may arise, so nothing is left to chance. Human expertise is embedded in every single step of Skye’s voice-based AI tutoring lessons.

Find out more about online one to one maths tutoring with Skye:
Online one to one AI maths tutoring for primary schools
Online one to one AI maths tutoring for secondary schools

Advanced or specialised ChatGPT maths topics

LLMs like ChatGPT can sometimes struggle with higher-level maths requiring deep, abstract reasoning, such as advanced calculus and complex proofs.

• Increased scepticism: If requesting content for A-Level or complex GCSE higher-tier topics, be extra vigilant. The AI might give answers that look plausible but have subtle errors.
• Consider specialist tools: For checking complex math equations or symbolic manipulation, dedicated computational tools like Wolfram|Alpha or Symbolab might be more reliable than a general LLM. You could use an LLM to generate a problem, then a solver to verify the solution.

Safeguarding concerns: navigating the risks of ChatGPT maths

Using LLMs effectively means being aware of the potential downsides:

• Incorrect or misleading content: Over-relying on unverified AI content can lead to teaching misconceptions.
• Data privacy: Never input any personally identifiable student data into a public LLM. This includes names, detailed assessment results linked to names, or personal circumstances. This breaches GDPR and school policies. Use anonymised examples to seek feedback. E.g., “A student struggled with simple algebra formulas.
• Teacher workload paradox: It’s not always time-saving if verification and editing become too much. How many times have you searched the internet for that resource when creating it yourself would have been quicker? Be strategic: use AI where it offers genuine efficiency like question variations, not for everything.
• Risk of over-reliance: Don’t let AI replace your creativity or subject knowledge. Use it as a tool, not a crutch. Too much over-reliance can lead to de-skilling yourself.
• Model use for learners: If students know you use AI, model responsible usage. Show them how you use it for ideas, but emphasise the critical thinking and verification steps. Discuss ethical use and the importance of developing their own understanding.

Real-life ChatGPT maths prompts

Here are some real-world prompts in action, showing how the structure above can provide accurate but imperfect outputs.

AI outputs below are illustrative examples. If you use the same prompt you may get different results.

ChatGPT maths example 1: Year 4 multiplying and dividing by 10 and 100 lesson starter

Input:

Act as an experienced primary maths teacher teaching in England. Create a starter activity for a Year 4 class to recap multiplying and dividing whole numbers by 10 and 100 that should take approximately 5 minutes. 

Make it engaging and interactive, suitable for whole-class participation (e.g., using whiteboards, quick-fire questions). Include a mix of multiplication and division questions. Provide the answers for the teacher. 

Present the activity as a clear set of numbered instructions for the teacher to follow.

Output example:

Alright class, settle down everyone! Let’s get our maths brains warmed up with a quick-fire round. Get your whiteboards and pens ready!

Here’s what we’re going to do:

1. “Ten Times Bigger!”
   I’m going to say a number, and you need to quickly write down the number that is ten times bigger. Ready?
   
   What is 6 multiplied by 10?
   What is 23 multiplied by 10?
   What is 10 multiplied by 10?
   What is 70 multiplied by 10?
   
2. “Hundred Times Bigger!”
   Now, let’s make them even bigger! This time, write down the number that is one hundred times bigger than the number I say.
   
   What is 4 multiplied by 100?
   What is 15 multiplied by 100?
   
3. “Ten Times Smaller!”
   Okay, now we’re going to shrink those numbers! Write down the number that is ten times smaller than the number I say.
   
   What is 80 divided by 10?
   What is 320 divided by 10?
   
4. “Hundred Times Smaller!”
   Last one! Write down the number that is one hundred times smaller than the number I say.
   
   What is 500 divided by 5?
   What is 1200 divided by 100?

Answers for the Teacher:

1. 6 multiplied by 10 = 60
2. 23 multiplied by 10 = 230
3. 10 multiplied by 10 = 100
4. 70 multiplied by 10 = 700
5. 4 multiplied by 100 = 400
6. 15 multiplied by 100 = 1500
7. 80 divided by 10 = 8
8. 320 divided by 10 = 32
9. 500 divided by 100 = 5
10. 1200 divided by 100 = 12

Here, the LLM has decided to provide a script, using numbers with four digits. If this is not the desired output, you can always refine your prompt to be more specific with what you do and do not want.

Refined input:

Act as an experienced primary maths teacher teaching in England. Create a starter activity for a Year 4 class to recap multiplying and dividing whole numbers by 10 and 100. This should take approximately 5 minutes and suitable for whole-class participation through the use of mini whiteboards only. Include a mix of multiplication and division questions. Provide the answers for the teacher at the end of the output.

Refined output:

Introduction (30 seconds)
“We’re going to do a quick warm-up using our mini whiteboards. You’ll see a number and an instruction — either to multiply or divide it by 10 or 100. Show your working if you need to, but make sure your final answer is big and clear. I’ll give you 10 seconds per question. Ready?”

Questions (display each on the board or say aloud)

Give approximately 10 seconds per question. Prompt pupils to hold boards up once finished.

1. 24 × 10 = ?
   
2. 300 ÷ 10 = ?
   
3. 5 × 100 = ?
   
4. 2,000 ÷ 100 = ?
   
5. 46 × 100 = ?
   
6. 900 ÷ 100 = ?
   
7. 7 × 10 = ?
   
8. 80 ÷ 10 = ?
   
9. 6 × 100 = ?
   
10. 5,000 ÷ 100 = ?

ChatGPT maths example 2: Year 8 calculating area word problems

Input:

Act as an experienced Key Stage 3 maths teacher teaching in England. Generate 5 word problems for a Year 8  class involving calculating the area of triangles and parallelograms. Include at least one problem involving a compound shape made from a triangle and/or a parallelogram. 

Ensure all dimensions and areas use metric units (e.g., cm, m, cm², m²). Make the language clear and concise, suitable for a Year 8 reading level. Ensure the necessary dimensions (base, height, perpendicular height) are provided in each problem. 

Provide the correct answer for each problem, including the correct units. Present each word problem clearly numbered, and list the answers separately at the end.

Output example: 

1. A triangular flower bed in a park has a base of 8 metres and a perpendicular height of 5 metres. What is the area of the flower bed?
   
2. Mr. Jones is designing a new kite in the shape of a parallelogram. The base of the kite is 60 centimetres and its perpendicular height is 45 centimetres. What is the area of the material needed to make the kite?
   
3. A farmer has a field shaped like a triangle. The longest side of the field measures 120 metres, and the perpendicular distance from this side to the opposite corner is 75 metres. Calculate the area of the farmer’s field.
   
4. Sarah is drawing a shape made by joining a parallelogram and a triangle. The parallelogram has a base of 10 centimetres and a perpendicular height of 8 centimetres. The triangle shares the same base of 10 centimetres and has a perpendicular height of 6 centimetres. What is the total area of the combined shape?
   
5. A window in an art studio is in the shape of a parallelogram. The base of the window frame is 1.5 metres and its perpendicular height is 0.8 metres. What is the area of the glass in the window?

Answers:

1. 20 m²
2. 2700 cm²
3. 4500 m²
4. 110 cm²
5. 1.2 m²

Here, the LLM has leaned on its American training data and used imperial metrics. Refine the prompt to ensure that imperial is not used.

Refined input:

Act as an experienced Key Stage 3 maths teacher teaching in England. Generate 5 word problems for a Year 8  class involving calculating the area of triangles and parallelograms. Include at least one problem involving a compound shape made from a triangle and/or a parallelogram. Ensure all dimensions and areas use metric units (e.g., cm and m). Make the language clear and concise, suitable for a Year 8 reading level. Ensure the necessary dimensions (base, height, perpendicular height) are provided in each problem. Provide the correct answer for each problem, including the correct units. Present each word problem clearly numbered, and list the answers separately at the end.

Refined output:

1. A triangular flower bed in a park has a base of 8 metres and a perpendicular height of 5 metres. What is the area of the flower bed?
   
2. Mr. Jones is designing a new kite in the shape of a parallelogram. The base of the kite is 60 centimetres and its perpendicular height is 45 centimetres. What is the area of the material needed to make the kite?
   
3. A farmer has a field shaped like a triangle. The longest side of the field measures 120 metres, and the perpendicular distance from this side to the opposite corner is 75 metres. Calculate the area of the farmer’s field.
   
4. Sarah is drawing a shape made by joining a parallelogram and a triangle. The parallelogram has a base of 10 centimetres and a perpendicular height of 8 centimetres. The triangle shares the same base of 10 centimetres and has a perpendicular height of 6 centimetres. What is the total area of the combined shape?
   
5. A window in an art studio is in the shape of a parallelogram. The base of the window frame is 1.5 metres and its perpendicular height is 0.8 metres. What is the area of the glass in the window?

Answers:

1. 20 m²
2. 2700 cm²
3. 4500 m²
4. 110 cm²
5. 1.2 m²

ChatGPT maths example 3: GCSE area and perimeter feedback

Input:

Act as an experienced GCSE maths teacher teaching in England. Provide constructive feedback for a Year 10 GCSE Foundation student who consistently forgets to include units in their answers for area and perimeter questions. 

The feedback should explain why including units is important in maths and real-world contexts. It should suggest a practical strategy or memory aid the student can use to remember to include units. The tone should be encouraging and supportive. 

Assume the context of the GCSE Foundation tier curriculum in England. Present the feedback as a concise comment suitable for writing on a student's work or in an online feedback box.

Output example:

Hi [Student’s Name], you’re doing a great job with the calculations for the area and perimeter questions! Your methods are usually spot on. Just a little reminder about including your units in the final answer. Imagine you’re telling someone the size of a room – saying it’s “20” isn’t very helpful, is it? Is that 20 centimetres squared or 20 metres squared? The units tell us the scale and what we’re actually measuring.

For area, think “squared” because we’re multiplying two lengths (like cm × cm = cm²). For perimeter, it’s just a length (like cm).

A little trick that might help: Area has an “a” and “squared” also has an “a” sound. Perimeter is just a plain length! Keep up the good work – just remember those units!

While this initial output isn’t too bad here, it’s quite lengthy, which means that the pupil will be unlikely to take it all in. There is also nothing there that frames the importance of units outside of doing for the exam.

Refined input:

Act as an experienced GCSE Maths teacher teaching in England. Provide constructive feedback for a Year 10 GCSE Foundation student who consistently forgets to include units in their answers for area and perimeter questions. The feedback should explain why including units is important in maths and real-world contexts. It should suggest a practical strategy or memory aid the student can use to remember to include units. The tone should be encouraging and supportive. Assume the context of the GCSE Foundation tier curriculum in England. Present the feedback as a concise comment suitable for writing on a student's work or in an online feedback box.

Refined output:

Hi [Student’s Name], you’re doing a great job with the calculations for the area and perimeter questions! Your methods are usually spot on. Just a little reminder about including your units in the final answer. Imagine you’re telling someone the size of a room – saying it’s “20” isn’t very helpful, is it? Is that 20 centimetres squared or 20 metres squared? The units tell us the scale and what we’re actually measuring.

For area, think “squared” because we’re multiplying two lengths (like cm × cm = cm²). For perimeter, it’s just a length (like cm).

A little trick that might help: Area has an “a” and “squared” also has an “a” sound. Perimeter is just a plain length! Keep up the good work – just remember those units!

Teaching smarter with the assistance of AI

LLMs like ChatGPT for maths offer genuinely interesting possibilities for maths educators. They can be valuable allies in brainstorming lesson ideas, drafting resources, and exploring different ways to explain math concepts.

When used thoughtfully with specific prompts, critical evaluation, and a constant focus on accuracy and curriculum alignment, they can help streamline aspects of your workload.

However, they are tools, not replacements for your professional expertise. The need for teacher verification, pedagogical judgment, and safeguarding awareness remains paramount. Don’t expect perfect, ready-to-use resources every time; expect drafts that require your input and refinement.

As AI technology keeps improving, staying informed is key. Look out for school CPD, explore resources from reputable educational bodies, and share best practices (and pitfalls!) with colleagues.

Approaching LLMs with informed curiosity and critical awareness can effectively “supercharge” aspects of your maths teaching practice and make learning even more engaging for your class.

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