Introduction
teaching-cabinet.cc is my personal project which has a simple aim: collect what I think it’s useful to teach: activities, ideas, notes, reflections, etc. But, mainly, activities. You could see as a activity repository. As I’m Mathematics Secondary teacher, then this project has very strong bias to include mathematical stuff.
As a personal project, I made it on my spare time. Therefore, I will create new contents or review old ones when I could, with no pre-established pace.
Autorship
The collection is made by myself, Xavier Bordoy. However, the collection might include contents from diverse sources, mine or from other people. In this sense:
- I always try to make proper attribution: write the authors and the license of their work in explicit way.
- I will only choose free or permissive licenses which could allow, at least, other teachers to use materials without requiring explicit permission (Creative Commons or Public Domain are examples of those licenses).
Anyway, unless otherwise noted, everything here is licensed for reuse under CC-BY-NC-SA 4.0 International.
Resources
You have the source code in git repository. This project has no mailing list or bug triage system. If you want to send any suggestion, comment, bug or whatever, email me. Perhaps in more mature state of the project, I will incorporate those tools.
Contribute
If you want to contribute to this project, you can:
- spread it
- review the contents
- creating new contents
By now, donations are not allowed. Maybe later.
Tools I use
I use mdbook with the extensions: mdbook-indexing and mdbook-linkcheck.
The project is handle in repo.or.cz (previously in sourcehut).
Images are hosted in mathstodon posts, videos on peertube instance tubedu and html output in Moritz Poldrack’s server who offered gracefully after some troubles with sourcehut pages.
Pizzas
Act 1
Possible questions:
- Is the price fare?
- What would cost a pizza with diameter equal to 1 meter?
- Can you estimate the grams per person? What if we cut the pizza in 8 slices?
- In a square dish what percentage of dish the pizza would cover?
Act 2
- Price and diameter of each pizza
- Extract from original menu list if you want to do the same for different pizzas
Notes
- It is useful to have a discussion about the fairness of the price if we attend to the diameter (proportional reasoning). But if we reflect that the external corona of the circle contains more pizza than inner circle and when we double the diameter the mass of the pizzas does not double. Thus, we could attend the area of the pizzas. This way the price is more fair but not completely fair.
- We can do a simulation with geogebra about the price of the pizza depending on its diameter. This would give us the concept of the ratio of price respect to the area or diameter. And also it could involve the line which has the points $(diam_1, price_1)$ and $(diam_2, price_2)$.
About this document
The author of this work is Xavier Bordoy. This work is distributed under CC-BY-NC-SA 4.0 license. Its date of creation is 2021-06-29.
The pizza image is extracted from Alexis Bailey “Pizza” which is licensed under CC-BY 4.0 license.
This work has keywords: “proportional reasoning”, “circumference - circle”, “area”, “fractions”, .
The musical pause. Anna Castillo & Macarena García sing for Whitney Houston
Act 1
Possible questions:
- What is the probability that someone, choosen randomly, guess the retake of the song?
- What is the error to try to guess the music retake?
- How does this error distribute? Is it normal distribution or something else?
Act 2
- The Whitney Houston’s “I will always love you” video
- The Roxette’s “The look” video which has also a sound pause
Development of the activity
- The students sit in pairs
- One student take a pencil and another a mobile phone. The student with the mobile phone needs the camera and chronometer applications.
- Teacher puts the video on without the image, just the sound. Meanwhile the student with the camera records the other student who, when she wants, hits the table with a pencil (or claps her hands).
- Later, with chronometer application students see the time between sound pause and student pencil hit
- Students could measure many times this interval and make the mean.
- Students see that error varies with the help of these means.
- We could answer these questions:
- Is it difficult to guess exactly the sound retake? What precision is necessary?
- If we took this experiment with many people, what would be the mean error?
- What is the variation between the moment when someone guess the retake and the real one?
- What is the probability of one person just have an error of 0.5 seconds from the real retake?
Notes
- A related activity could be counting up to 30 and see what would be the deviation respect to 30 real seconds
- On one hand, this activity could use to introduce the concepts of statistical sample and statistical population. On the other hand, to introduce the concept of experimental probability (a probability which needs to get data from outside to be calculated)
- It seems that the maximum precision is about half milliseconds.
Classroom implementation
The 2018-2019 season I implemented this activity in classroom for the first time:
- Just after implement theorical probability activities, I introduced this activity.
- We saw the Hormiguero video and then the question to answer was “What is the probability that one person guess when the sound returns to the song?”. We saw the nececessity to take an statistical sample (that classroom). I so explained the difference between sample and population.
- By pairs, students recorded partners when song was in the background.
- After that, students saw the time between sound silence beginning and their clap. We made that at least 3 times to dilute errors.
- Then students saw the time between sound silence beginning and the real sound retake.
- We did the same Roxette song.
- To calculate the asking probability, we calculated the percentage between their gap and the real gap of the song. We convene 5% or less is OK and more is a mistake. By this way, we counted the number of persons in the interval [0%, 95%) and [95%, 105%) and more than 105%.
About this document
The author of this work is Xavier Bordoy which is distributed under CC-BY-NC-SA 4.0 license. Its date of creations is 2019-05-13.
The original video belongs to “El hormiguero”: “Anna Castillo y Macarena García cantan por Whitney Houston en ‘El Hormiguero 3.0’” from Antena 3 (Sep 25th, 2017).
The work has keywords: “statistical population”, “statistical sample”, “arithmetic mean”, “error”, “precision”, “experimental probability”, “normal distribution”, “statistical distribution”, “probability”, “statistics”, “when”.
Index
“area”,
Pizzas
“arithmetic mean”,
The Musical Pause
“circumference - circle”,
Pizzas
“error”,
The Musical Pause
“experimental probability”,
The Musical Pause
“fractions”,
Pizzas
“normal distribution”,
The Musical Pause
“precision”,
The Musical Pause
“probability”,
The Musical Pause
“proportional reasoning”,
Pizzas
“ratio”,
Pizzas
“statistical distribution”,
The Musical Pause
“statistical population”,
The Musical Pause
“statistical sample”,
The Musical Pause
“statistics”,
The Musical Pause
“when”,
The Musical Pause
Bordoy, Xavier,
Pizzas,
The Musical Pause
CC-BY-NC-SA 4.0,
Pizzas,
The Musical Pause