Explaining calculations in your IB Math Internal Assessment (IA) is one of the most delicate balancing acts. Write too little, and your reasoning becomes unclear. Write too much, and examiners get lost in unnecessary detail. The key is clarity—communicating your mathematical thinking without losing the rigor that makes your work impressive.
Using RevisionDojo’s Explanation Builder, this guide shows you how to describe your calculations effectively, maintain mathematical depth, and make your IA feel logical, coherent, and examiner-friendly.
Quick Start Checklist
Before you begin writing your explanations, make sure you have:
- A clear mathematical aim guiding your analysis.
- All calculations organized, labeled, and verified for accuracy.
- Consistent notation for symbols, equations, and variables.
- A plan for where explanations fit naturally in your structure.
- Tools like the Explanation Builder to refine your reasoning into clear, concise language.
When each calculation connects smoothly to your argument, examiners can easily trace your logic—and reward it.
Why Clear Explanation Matters in the IB Math IA
Mathematics is about reasoning as much as results. The IB rewards students who show how they think, not just what they find.
In Criterion C (Communication) and Criterion D (Reflection), clarity plays a major role. Your explanation should:
- Guide the reader through each mathematical step.
- Justify why a formula or method is used.
- Demonstrate understanding of underlying concepts.
- Connect results back to your aim.
A clear explanation turns complex work into something readable, logical, and persuasive.
The Ideal Balance: Clarity + Depth
The best explanations maintain a perfect balance between mathematical rigor and reader accessibility. Think of it like teaching—if you can explain it clearly, you truly understand it.
Clarity means:
- Short, focused sentences.
- Logical sequencing of ideas.
- Smooth transitions between steps.
Depth means:
- Correct and detailed mathematical reasoning.
- Inclusion of relevant formulas and derivations.
- Context for why methods are used.
Your goal is to show understanding, not just show working.
Structuring Your Explanations
A consistent structure for explanations helps maintain logical flow. Try this step-by-step format for every calculation:
1. Introduce the Purpose
Start by explaining what you’re about to calculate and why it matters.
Example:
“To determine how fast the population grows, I calculated the rate of change using the derivative of the logistic function.”
2. Present the Formula
State the formula clearly and define all variables.
Example:
“The rate of change is given by dy/dt = ky(1 – y/L), where k is the growth constant and L is the carrying capacity.”
3. Substitute and Solve
Show substitutions neatly, one line at a time. If steps are repetitive, summarize them efficiently instead of listing every minor operation.
4. Interpret the Result
Explain what your final answer represents in context.
Example:
“This value of k indicates that the model predicts the population will double every 4.2 years under current conditions.”
5. Reflect or Compare
After major calculations, briefly reflect on the reasonableness of your result or compare it to expectations.
Example:
“This matches observed data closely, suggesting the logistic model fits better than the exponential model.”
This structured explanation method ensures that every number has meaning—and every step contributes to understanding.
Using the Explanation Builder for Clarity
RevisionDojo’s Explanation Builder guides students through writing step-by-step reasoning that matches IB expectations. It prompts you to:
- Link each calculation to your IA’s aim.
- Write one explanatory sentence for every major mathematical operation.
- Highlight reasoning words such as therefore, since, and as a result.
- Keep equations aligned with text for readability.
This tool ensures your IA reads like a structured argument rather than a dense list of computations.
Common Mistakes When Explaining Calculations
Even strong students fall into traps that weaken their communication. Here’s what to avoid:
- Jumping straight to results:
Examiners need to see the path to your solution, not just the destination. - Overloading with algebra:
Don’t include every tiny arithmetic step—focus on key transformations that show reasoning. - Ignoring units or context:
Always include correct units and explain what your result represents in real-world or theoretical terms. - Using inconsistent notation:
Keep variable definitions consistent throughout your IA to avoid confusion. - Repeating explanations word-for-word:
Summarize similar calculations rather than copying text blocks.
These mistakes can reduce your Communication score, even if your math is perfect.
Techniques for Writing Clear Mathematical Explanations
Here are strategies that help balance detail and readability:
- Use connecting phrases: “To find…,” “Since this value…,” “Therefore…”—they guide the reader logically.
- Integrate text and math: Place equations within sentences where appropriate.
- Use paragraph breaks strategically: Each paragraph should represent one completed idea or stage of reasoning.
- Label every major formula: (Equation 1), (Equation 2), etc., so readers can easily refer back.
- Include visual aids when needed: Graphs or tables can replace paragraphs of explanation.
Think of your writing as a mathematical narrative—every sentence should build on the one before it.
How Much Detail Is “Enough”?
Students often ask how much explanation is necessary. The general rule is simple: write enough that another IB Math student could follow your logic.
If someone with your same background can understand how you got from one step to the next, you’ve included the right level of detail.
For advanced topics—like differential equations, modeling, or statistics—add brief conceptual summaries before or after complex math to help maintain flow.
Reflection: Showing Understanding, Not Just Process
Strong IAs show reflection within the explanation. For instance:
- After calculating, comment on what your result means mathematically.
- Acknowledge if the outcome differs from expectations and why.
- Discuss how minor assumptions affected the process.
This approach demonstrates intellectual maturity and boosts your Criterion D (Reflection) mark significantly.
How Examiners Assess Explanation Quality
Examiners look for evidence of comprehension, not just completion. They want to see that:
- You know why each step was necessary.
- You can link calculations to your stated goal.
- You can explain results in mathematical and contextual terms.
- Your writing flows logically and concisely.
They’re not just checking if your answer is right—they’re checking if your reasoning makes sense.
Frequently Asked Questions (FAQ)
1. How much text should I include for each calculation?
Include one or two explanatory sentences per major step. Minor algebraic manipulations don’t need detailed explanation unless they introduce a new concept.
2. Should I show every line of working?
Show enough to demonstrate understanding. For repetitive processes (like substitution), summarize after a few examples.
3. Can I use bullet points to summarize steps?
Yes, but sparingly. Bullets can organize multi-step reasoning, but continuous prose reads more professionally.
4. What if my math is too complex for simple explanation?
Use short summary paragraphs before and after long derivations. Phrases like “To simplify the integral…” or “The result confirms that…” keep readers oriented.
5. How can I check if my explanations are clear?
Have a classmate read a section without your guidance. If they understand what you did and why, your clarity is on point.
Conclusion
Explaining calculations clearly is the secret to transforming your IB Math IA from a technical document into a persuasive piece of reasoning. When you write with clarity and precision, your math becomes more accessible, and your arguments become more powerful.
Using RevisionDojo’s Explanation Builder, you can craft explanations that are both logical and sophisticated—helping you earn higher marks for communication, reflection, and mathematical depth.
RevisionDojo Call to Action:
Communicate your mathematics with clarity and confidence. Use RevisionDojo’s Explanation Builder to write concise, coherent explanations that strengthen your IA and impress IB examiners.
