I'm going to define some math research projects for 7th grade students. The projects can be both purely mathematical and interdisciplinary. By the way, the students can write simple Pascal codes.
I prefer projects which are not technical or abstract. It's strictly preferable that the projects be completely meaningful for the students.
Do you have ideas or know sources which can help me doing this?
Thanks.
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One idea for a project would be to analyze the game 'hog'. In this game, a player's turn consists of choosing (in advance) the number of dice to be rolled. This number of dice are rolled. If any die comes up 1, the player scores 0 points for the turn; but if none of the dice show a 1, then the player scores the sum of the rolls.
This game lends itself to gathering data by actually playing the game; gathering data by simulation of the game; and to mathematical analysis of the game.
If students actually play the game, they quickly realize that if you roll more dice, you increase your chance for a big score, but you also increase your chance for a 0 score.
They may then wonder about whether there is an optimal number of dice to roll in this game.
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They could investigate compound interest. Some questions they could answer:
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Topology is full of fun math problems/puzzles and kids have good spatial abilities from an early age.
Here are some sources I found on first search, I bet you find more:
https://toomai.wordpress.com/2008/05/25/more-experimental-topology-and-experiments-in-topology/
For example, there a lot of cool knot problems that you can make out of strings.
In fact, I bet there are some open questions (eg. with knots) that kids can get their hands on.
For example, a project could be to classify all possible shapes three bubbles form (to draw them out). I wish I had this project as a kid.
Can they graph functions? Do they understand polynomials? Can they plot a line of the form $y=mx+b$?
A powerful exercise is to give them a series of lines to plot, e.g.
$$y = m_1x + b_1 \\ y = m_2x+b_2\\ \vdots$$
You can pre-compute $m_i$ and $b_i$ so that they are tangent curves to a polynomial. A quadratic would be ideal.
Have them plot these curves on a large sheet of paper. Another option is to use string and thumbtacks on a corkboard.
Eventually, they will begin to curve-stitch a function. It will become abundantly clear. Maybe you can even have them compute the polynomial from its zeros.
Now, ask them to find a pattern in the values of $m$.
You will have introduced them to the most basic idea of differential calculus, but in a way that they could perhaps understand.