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RP1 · Research and present a mathematical event or area of interest

Learn to research and present a mathematical event or area of interest through clear examples and targeted practice.

Alberta Grade 11 Mathematics

Mathematics Research Project

A practical guide to choosing a mathematical topic, checking information, and explaining what you learn

Mathematics appears in events, inventions, art, games, sports, and everyday decisions. A research presentation connects a topic you care about to mathematical ideas and explains that connection to an audience. The goal is not to collect the most facts or use the hardest mathematics. The goal is to make accurate, understandable claims and show how the mathematics helps explain the topic.

What you will learn

Choose a mathematical event or area of interest that can be explored with reliable information.
Check that research claims and calculations are supported by sources or clear working.
Organize a presentation so an audience can follow the topic and its mathematics.
Use suitable visuals, units, and explanations to communicate mathematical ideas.

1. Start with a focused question

A topic is the general subject you want to explore. A research question is a focused question that guides what you look for and what you include. For example, “mathematics in sports” is broad. “How does a change in a basketball player’s shooting percentage affect the number of successful shots in 40 attempts?” is more focused.

Before researching, briefly review two useful skills. A claim is a statement that can be checked, such as a date, measurement, or numerical result. A source is where information comes from, such as a book, museum page, data table, or interview. Keep track of the source as you work so you can identify where each important claim came from.

Choose an event or area that has enough trustworthy information and a clear mathematical connection. An event might be the development of a measurement tool or a mathematical idea used in a historical project. An area of interest might be patterns in music, chance in a game, or how scale is used in a design. Ask yourself: What is the mathematics? What question can I answer? Can I explain the answer using information I can check?

Turn a broad subject into one manageable research question.
Identify the mathematics before building the presentation.
Record the name and location of sources while researching.

2. Gather and check evidence

Evidence is information that supports a claim. For a mathematical presentation, evidence can include a reliable description, a supplied set of measurements, a published graph, or your own calculation based on stated values. Make clear which kind you are using. A calculation is not a source for a historical date, and a source’s numerical claim should not be treated as your own calculation.

Check important claims against a dependable source. Look for who created the information, why it was created, and whether it gives enough detail to check the claim. When possible, compare important facts with another reliable source. If sources disagree, do not quietly choose the number you prefer. Explain the difference or leave the claim out if you cannot resolve it.

Write down values with their units and context. A value of 12 is unclear unless the audience knows whether it means 12 centimetres, 12 years, or 12 items. If you calculate from supplied values, show the operation and explain what the result means. Check that the answer’s unit fits the question and that it is a reasonable size.

Use your own wording to explain what you learned. A short quotation may help when the exact wording matters, but identify it as a quotation and name its source. Give credit for ideas, images, data, and words that are not your own. Follow the format your teacher requests; if no format is specified, make the source easy for an audience to identify.

Separate sourced facts from your own calculations and interpretations.
Keep units and context attached to numerical values.
Credit information and visuals that you did not create.

3. Explain the mathematics and shape the presentation

A clear presentation has a beginning, a middle, and an ending. Begin with the topic and research question. In the middle, give the evidence and explain the mathematical connection. End by answering the question and stating the main idea the audience should remember.

Explain a mathematical term before relying on it. For instance, a rate compares two quantities with different units, such as kilometres per hour. If your presentation uses a rate, identify both quantities and explain what the rate describes. If you use a graph or table, label it and explain what the audience should notice. A visual should help explain a claim, not just decorate a slide.

Use only mathematics that helps answer your question. Show enough working for a reader to follow a calculation. State what each number represents, keep units consistent, and interpret the result in context. If a value comes from a source, name the source. If you make an estimate or assumption, say so. Do not make a precise claim from evidence that is only approximate.

Plan for your audience. Use short sections, readable labels, and a small number of main ideas. Practise explaining the mathematics aloud without reading every word from a slide. A useful final check is to ask someone else to tell you the question, the main mathematical idea, and the conclusion after hearing your presentation.

Connect each calculation or visual to the research question.
Define terms, identify quantities, and explain the result in context.
Finish with a direct answer and a check that the audience understood.

4. Review before presenting

Read or view the presentation as an audience member. Can you follow the order? Are claims supported? Are units, labels, and source credits visible? Check calculations again, including the meaning of each value. A correct numerical result can still mislead if it is attached to the wrong unit or described as more certain than the evidence allows.

Keep a short research record. It can list your question, the sources you used, useful facts or data, calculations, and the changes you made after checking. This record makes it easier to answer questions about where information came from and how you reached a conclusion.

The standard is clear communication, not decoration or complexity. A focused presentation with a careful explanation is stronger than a crowded presentation with many facts that do not answer the question.

Check the question, evidence, calculations, units, and source credits.
Make the conclusion answer the research question directly.
Prefer a few well-explained ideas over a long list of unrelated facts.

Worked example

From a broad interest to a research question

A student is interested in bicycle travel and wants to make a short presentation. Show how the student could narrow the topic and decide what to research.

Choose a direction
“Bicycles” is too broad because it could include design, history, safety, or travel. The student chooses travel time as the part they want to understand.
Ask a focused question
A useful question is: “How long would a 12-kilometre bicycle trip take at a stated average speed?” This question names a distance and asks for a time, so research can focus on a suitable speed value and its source.
Plan the evidence
The student should find a trustworthy source for an average speed that fits the situation, record its units and context, and explain that different riders and conditions can change travel time. The student should not present one speed as true for every rider.

Answer: The narrowed question is specific enough to guide research: it identifies a distance, asks about travel time, and requires a sourced speed value.

Check: The question is manageable because it asks for one result and makes clear what information is still needed.

Worked example

Explain a calculation with its source and units

A presentation uses a published average speed of 15 kilometres per hour for a particular route and asks how long a 12-kilometre trip would take at that speed. Show a clear calculation and interpretation.

Identify the quantities
The distance is 12 kilometres. The average speed is 15 kilometres per hour, taken from the stated published source. Time can be found by dividing distance by speed.
$t=\frac{d}{v}$
Calculate the time
Substitute the distance and speed. The kilometre units cancel, leaving hours.
$t=\frac{12\text{ km}}{15\text{ km/h}}=0.8\text{ h}$
Interpret the result
Since 0.8 of an hour is 48 minutes, the estimated trip time is 48 minutes at the stated average speed. The presentation should say that this is an estimate based on that speed, not a guarantee for every trip.
$0.8\times60=48\text{ min}$

Answer: At an average speed of 15 kilometres per hour, a 12-kilometre trip would take an estimated 48 minutes.

Check: The units reduce to time, and 48 minutes is reasonable: at 15 kilometres per hour, a trip shorter than one hour should cover less than 15 kilometres.

Worked example

Build a presentation from a mathematical event

A student researches the use of measurement in making a historical map. The student finds a museum source describing the map and a scale printed on it: 1 centimetre represents 5 kilometres. Plan a focused explanation for a map distance of 3 centimetres.

State the question and evidence
The student can ask how the map scale represents a measured distance. The map scale and its meaning are evidence from the map or its museum description. The student should identify the source and explain what the scale compares.
Calculate the represented distance
Each centimetre represents 5 kilometres. For 3 centimetres, multiply the map length by the number of kilometres represented by each centimetre.
$3\text{ cm}\times5\text{ km/cm}=15\text{ km}$
Explain the conclusion carefully
The 3-centimetre map distance represents 15 kilometres. The centimetre units cancel in the calculation. The conclusion describes the scale relationship; it does not claim that every route between the same places is exactly 15 kilometres.

Answer: According to the stated scale, 3 centimetres on the map represents 15 kilometres.

Check: The answer is larger than the map measurement because each centimetre represents several kilometres. The units cancel to kilometres, as needed.

Common mistakes and how to avoid them

Choosing a topic so broad that the presentation becomes a collection of unrelated facts.

Correction: Write one focused question and include information that helps answer it.

Using a numerical claim without saying where it came from or what its units mean.

Correction: Name the source and give the value with its units and context.

Showing a calculation without explaining what the answer means.

Correction: State the result in words and connect it to the research question.

Treating an estimate or average as a result that must apply in every situation.

Correction: Explain what the supplied value represents and identify reasonable limits to the conclusion.

Adding visuals or facts because they look interesting, even when they do not support the main point.

Correction: Keep material that helps answer the question; remove or explain the rest.

Lesson summary

Choose an event or area of interest, then turn it into a focused research question.
Use sources that let you check important claims, and keep track of where information comes from.
Show calculations clearly, attach units, and explain what the result means.
Organize the presentation around the question and end with a direct conclusion.
Check accuracy, source credit, and clarity before presenting.

Check your understanding

Question 1

Which is the most focused research question for a presentation about music and mathematics?

What is music?
How can a repeated rhythm be described using a pattern the audience can hear?
Why is mathematics important?
What are all the ways people use numbers?

Show answer and explanation

How can a repeated rhythm be described using a pattern the audience can hear?

It names a specific connection that can be explored and explained. The other options are too broad.

Question 2

A calculation in a presentation gives a distance of 8 kilometres. What should the student do next?

Remove the unit so the number looks simpler.
State what the distance represents and connect it to the question.
Add more decimal places to make it more reliable.
Present it as a fact from a source even if it was calculated.

Show answer and explanation

State what the distance represents and connect it to the question.

A result needs context. The unit and explanation help the audience understand what the number describes.

Question 3

A source gives an average travel time for one route. Which conclusion is most careful?

Every traveller will take exactly that long.
The average describes the supplied information, but individual trips may differ.
The source proves that no other travel time is possible.
The value can be used without identifying its source.

Show answer and explanation

The average describes the supplied information, but individual trips may differ.

This conclusion stays within what an average can support and does not claim that every case is identical.

Key terms

Topic: The general subject a presentation explores.
Research question: A focused question that guides what information to find and explain.
Source: A place or person that provides information, such as a book, data table, or museum page.
Evidence: Information or a calculation that supports a claim.
Claim: A statement that can be checked using information or reasoning.
Rate: A comparison of quantities with different units, such as kilometres per hour.

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About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Alberta Grade 11 Mathematics (Math 20-2), expectation RP1. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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