Is the word atividade the same in Brazilian and European Portuguese?

Yes

The word "atividade" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The primary differences are phonetic. In Brazilian Portuguese, the unstressed vowels are more open, and the "d" is often pronounced as an affricate [dʒ] (similar to the "j" in "jeep") when followed by an "i" sound. In Continental Portuguese, unstressed vowels are heavily reduced or even suppressed (making the final "e" nearly silent), and the "d" retains a dental [d] sound. While the word itself does not change, the surrounding syntax and vocabulary often differ between the two regions.

Brazilian Portuguese Examples

1. Estou fazendo uma atividade física. (I am doing a physical activity.)
2. A atividade de hoje está sendo muito difícil. (Today's activity is being very difficult.)
3. Ele terminou a atividade rapidinho. (He finished the activity very quickly.)
4. Precisamos organizar as atividades da semana. (We need to organize the week's activities.)
5. Essa atividade é muito legal. (This activity is very cool.)

Continental Portuguese Examples

1. Estou a fazer uma atividade física. (I am doing a physical activity.)
2. A atividade de hoje está a ser muito difícil. (Today's activity is being very difficult.)
3. Ele terminou a atividade muito depressa. (He finished the activity very quickly.)
4. Precisamos organizar as atividades da semana. (We need to organize the week's activities.)
5. Esta atividade é muito gira. (This activity is very cool/pretty.)