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Second level: Adjust similarly +\setlist[longenum,2]{ + label=\arabic*., % Label format: "1.", "2.", etc. + leftmargin=2em, % Left margin adjusted to avoid overlap + labelsep=0.25em, % Space between label and text + labelwidth=1.5em, % Reserve enough space for the label + itemindent=0em, % No additional indentation + align=left % Align label to the left +} + +% Third level +\setlist[longenum,3]{ + label=\arabic*), % Label format: "1)", "2)", etc. + leftmargin=2em, % Increase indentation for clarity + labelsep=0.25em, + labelwidth=1.5em, + itemindent=0em, + align=left +} + +% Fourth level +\setlist[longenum,4]{ + label=\alph*., % Label format: "a.", "b.", etc. + leftmargin=2em, % Increase left margin for nested levels + labelsep=0.25em, + labelwidth=1.5em, + itemindent=0em, + align=left +} + +% Fifth level +\setlist[longenum,5]{ + label=\alph*), % Label format: "a)", "b)", etc. + leftmargin=2em, + labelsep=0.25em, + labelwidth=1.5em, + itemindent=0em, + align=left +} + +% Sixth level 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{\normalfont\fontsize{12pt}{14pt}\bfseries\centering}{}{0em}{} + +% % Konfiguracja nagłówków +% \fancyhf{} +% \fancyhead[L]{\textbf{Wewnątrzszkolne Oceniania}} +% \fancyhead[C]{-- \thepage\ --} +% \fancyhead[R]{\textbf{Załącznik Nr 2}} +% \fancyfoot{} + +% Tytuł i odniesienia +\usepackage{titlesec} +\titleformat{\section} + {\normalfont\fontsize{14pt}{16pt}\bfseries\centering}{\thesection}{1em}{} +\titleformat{\subsection} + {\normalfont\fontsize{12pt}{14pt}\bfseries\centering}{}{0em}{} + +% Dodatkowe pakiety dla niestandardowego formatowania +\usepackage{xcolor} +\usepackage{sectsty} +\sectionfont{\centering\fontsize{16pt}{18pt}\selectfont} + +\definecolor{cred}{RGB}{255, 0, 0} +\definecolor{przedmiot}{RGB}{148, 0, 211} +\definecolor{zakres}{RGB}{0, 100, 0} +\definecolor{poziom}{RGB}{0, 0, 255} + +% Definiujemy nowy skrót, który pozwoli odwoływać się do numeru przypisu: +% \newcommand{\footref}[1]{\textsuperscript{\ref{#1}}} +\begin{document} + +% Wyłącz na moment fancyhdr, aby strona tytułowa nie miała nagłówka/stopki +% \thispagestyle{empty} +\thispagestyle{fancy} + + +% \begin{center} +% \textbf{Załącznik Nr 2}\\[0.5em] +% \textbf{do Statutu Zespołu Szkół Licealnych im. Zbigniewa Herberta w Słubicach}\\[3em] + +% {\Large \textbf{WEWNĄTRZSZKOLNE ZASADY OCENIANIA}}\\[1em] +% w~Zespole Szkół Licealnych im. Zbigniewa Herberta w Słubicach +% \end{center} + +% Wyłączenie nagłówków na pierwszej stronie +% \thispagestyle{plain} + +% Główna treść +\begin{flushright} + Zespołu Szkół Licealnych \\ + im. Zbigniewa Herberta w Słubicach \\ +\end{flushright} + +\vspace{1em} + + + \vspace{5em} + + \begin{center} + {\Large \textbf{SZCZEGÓŁOWE OCENIANIE Z \textcolor{przedmiot}{MATEMATYKI}}}\\[1em] + \textbf{\textcolor{zakres}{Zakres Rozszerzonym}, \textcolor{poziom}{Poziom Nauczania: 1}}\\[1em] + \end{center} + + \vspace{5em} + + + System oceniania opracowany w oparciu o: + + \begin{enumerate}[noitemsep] + \item Wewnątrzszkolne Ocenianie\footnotemark[1] jako Załącznik do Statutu Szkoły. + \item Podstawę programową\footnotemark[2]. + \item Rozkład materiału\footnotemark[3]. + \item Rozporządzenie\footnotemark[4] określające szczegółowe warunki oceniania, klasyfikowania i promowania uczniów. + \item Ustawę\footnotemark[5] \emph{Prawo oświatowe}. + \end{enumerate} + + \footnotetext[1]{Wewnątrzszkolne Ocenianie jako integralny załącznik do Statutu Szkoły, regulujący szczegółowe zasady oceniania, klasyfikowania i promowania uczniów.} + \footnotetext[2]{Podstawa programowa kształcenia ogólnego dla szkół ponadpodstawowych, zatwierdzona Rozporządzeniem Ministra Edukacji i Nauki z dnia 28 czerwca 2024 r., określa cele kształcenia, treści nauczania oraz wymagania edukacyjne dla uczniów szkół ponadpodstawowych, takich jak licea ogólnokształcące, technika i szkoły branżowe II stopnia.} + \footnotetext[3]{Rozkład materiału z~\textcolor{przedmiot}{matematyki} dla \textcolor{poziom}{1 poziomu nauczania} na \textcolor{zakres}{zakresie rozszerzonym}, opracowany na podstawie programu nauczania wydawnictwa Nowa Era, zgodny z~Podstawą Programową\footnotemark[2].} + + \footnotetext[4]{Rozporządzenie Ministra Edukacji Narodowej z dnia 25 sierpnia 2017 r. w~sprawie warunków i sposobu oceniania, klasyfikowania i promowania uczniów i słuchaczy w szkołach publicznych (Dz.U. z 2017 r. poz. 1534 z późn. zm.).} + \footnotetext[5]{Ustawa z dnia 14 grudnia 2016 r. – Prawo oświatowe (t.j. Dz.U. z 2021 r. poz. 1082 z późn. zm.).} + + + \begin{flushright} + \begin{minipage}{0.25\textwidth} % Szerokość na 25% strony + \raggedright % Wyrównanie tekstu do lewej wewnątrz minipage + \textit{Autorzy:}\\[0.5em] % Dodanie odstępu pod tytułem + \hspace{1em}M. Markiewicz\\ % Wcięcie dla pierwszego nazwiska + \hspace{1em}J. Góra % Wcięcie dla drugiego nazwiska + \end{minipage} + \end{flushright} + + +\thispagestyle{fancy} +%-------------------------------- +\newpage +\tableofcontents % Polecenie wstawiające spis treści + +\newpage +\section{Postanowienia ogólne} + +%----------------------------------------- +% § 1 +%----------------------------------------- +\paragraf{Cel i zakres Szczegółowego Oceniania (SO)} + +\begin{longenum} + \item \textbf{Cel główny:} Zapewnienie klarownych i jednolitych zasad oceniania + osiągnięć edukacyjnych uczniów, zgodnie z~Wewnątrzszkolnym Ocenianiem (\textbf{WO}). + \item \textbf{Cele szczegółowe:} + \begin{longenum} + \item Ujednolicenie wymagań edukacyjnych oraz sposobów sprawdzania wiedzy. + \item Zapewnienie przejrzystości kryteriów oceniania dla uczniów i rodziców (prawnych opiekunów). + \item Umożliwienie rzetelnej ewaluacji postępów uczniów i wspomaganie ich rozwoju. + \end{longenum} + \item \textbf{Zakres obowiązywania:} + \begin{longenum} + \item Niniejsze zasady dotyczą \textbf{\textcolor{przedmiot}{matematyki} na \textcolor{poziom}{1 poziomie nauczaniu} w~\textcolor{zakres}{zakresie rozszerzonym}}. + % \item SO jest ściśle powiązane z \emph{Wewnątrzszkolnym Ocenianiem (WO)} + % oraz \emph{Statutem Szkoły} i nie może być z nimi sprzeczne. + \end{longenum} +\end{longenum} + +%----------------------------------------- +%----------------------------------------- +% § 2 +%----------------------------------------- + +\paragraf{Szczegółowe Ocenianie obejmuje:} + +\begin{longenum} + \item Wymagania ogólne i~szczegółowe, wynikające z~podstawy programowej \textbf{PP}\footnotemark[2]. + \item Punktację wymagań oraz określenie minimalnej liczby punktów, które zapewniają realizację wymagań edukacyjnych, zgodnie z~rozkładem materiału (\textbf{RM\footnotemark[3]}), w~którym przypisano działy z (\textbf{PP}\footnotemark[2]) do \textcolor{poziom}{1 poziomu nauczania}. + \item Zakres stosowania progów procentowych i~sposób ich przeliczania na oceny. + + % \item Sposoby i formy sprawdzania wiedzy (prace klasowe, kartkówki, odpowiedzi ustne, projekty itp.). + % \item Sposób uwzględniania opinii/orzeczeń poradni psychologiczno-pedagogicznej w ocenianiu. + % \item Zasady gromadzenia informacji o postępach uczniów i formułowania ocen semestralnych/końcowych. +\end{longenum} + +%-------------------------------- +\section{Punktacja wymagań i minimalna liczba punktów} + +\paragraf{Cel i zakres punktacji wymagań i minimalnej liczby punktów} +\begin{longenum} + + \item Celem tak ustalonej punktacji jest \textbf{określenie wagi poszczególnych wymagań} + w procesie oceniania oraz zapewnienie \emph{rzetelnego} odniesienia do treści programowych. %wynikających z podstawy programowej. + + \item \textbf{Minimalną liczbę punktów} \(\,(P_{\min})\) ustala się w celu wyznaczenia + progu \emph{pełnej realizacji} wymaganych treści wynikających z \textbf{PP}\footnotemark[2] dla danego \textcolor{poziom}{poziomu nauczania} w~zadanym zakresie, + przy założeniu, że zostają spełnione wszystkie: + \begin{itemize}[noitemsep] + \item \textbf{Wymagania Szczegółowe}. + \item \textbf{Wymagania Ogólne}. + % \item nie dochodzi do \textbf{wielokrotnego naliczania} tego samego WO, nawet jeśli jest ono powiązane z kilkoma WS. + \end{itemize} + +\end{longenum} + +\paragraf{Punktacja wymagań} +\begin{longenum} + \item Każdemu \textbf{Wymaganiu Szczegółowemu} (oznaczonemu indeksem \(i\)) przypisuje się + \textbf{wagę punktową} \(w_{s_i}\), przy czym minimalna wartość tej wagi wynosi 1. + + \item Każdemu \textbf{Wymaganiu Ogólnemu} (oznaczonemu indeksem \(j\)) przypisuje się + \textbf{wagę punktową} \(w_{o_j}\), przy czym minimalna wartość tej wagi wynosi 1. + + \item \textbf{Łączna liczba punktów} przysługujących danemu działowi określonemu w~\textbf{PP}\footnotemark[2], uwzględniająca wszystkie powiązania + między Wymaganiami Szczegółowymi i Wymaganiami Ogólnymi, obliczana jest według następującej formuły: + + % \begin{equation} + % P_{\text{sum}} + % = + % \sum_{i=1}^{N_{W_S}} + % \Bigl( + % w_{s_i} \times \sum_{j=1}^{N^i_{W_O}} w_{o_j} + % \Bigr), + % \label{wzor:punktacja} + % \end{equation} + % gdzie: + % \begin{itemize}[noitemsep] + % \item \(N_{W_S}\) oznacza całkowitą liczbę Wymagań Szczegółowych w danym dziale, + % \item \(N^i_{W_O}\) oznacza liczbę Wymagań Ogólnych powiązanych z \(i\)-tym Wymaganiem Szczegółowym. + % \end{itemize} + + \begin{equation} + P_{\text{sum}} = \sum_{i=1}^{N_{W_S}} \Bigl( w_{s_i} \times \sum_{j=1}^{N^i_{W_O}} w_{o_j} \Bigr) + \label{wzor:punktacja} + \end{equation} + + gdzie: + \begin{itemize}[noitemsep] + \item \(N_{W_S}\) oznacza całkowitą liczbę Wymagań Szczegółowych w~danym dziale, + \item \(N^i_{W_O}\) oznacza liczbę Wymagań Ogólnych powiązanych z~\(i\)-tym Wymaganiem Szczegółowym, + \item \(N^i_{W_O} \geq 1\) dla każdego \(i\). + \end{itemize} + + {\small + \textbf{Uwaga:} Wzór (\ref{wzor:punktacja}) służy do określenia \emph{całkowitej} liczby punktów możliwej + do uzyskania za pełne zrealizowanie danego działu, z uwzględnieniem konkretnych + powiązań pomiędzy Wymaganiami Szczegółowymi i Wymaganiami Ogólnymi. + } + + \item Celem tak ustalonej punktacji jest określenie wagi poszczególnych wymagań edukacyjnych + w~procesie oceniania osiągnięć edukacyjnych. + + \item \textbf{Punktacja} przypisana poszczególnym działom oraz łączna liczba punktów + \(\bigl(P_{\text{sum}}\bigr)\), obliczona zgodnie ze wzorem~(\ref{wzor:punktacja}), + znajduje się w~\textbf{Rozdziale~1~załącznika~1}. + +\end{longenum} + +\paragraf{Ustalanie minimalnej liczby punktów} +\begin{longenum} + \item \textbf{Minimalną liczbę punktów} \(P_{\min}\) opisaną wzorem (\ref{eq:pmin}) ustala się w celu wyznaczenia + progu \emph{pełnej realizacji} wymaganych treści wynikających z~\textbf{PP}\footnotemark[2]. + +\begin{equation} + P_{\min} = \min \left\{ \sum_{i=1}^{N_{W_S}} \left( w_{s_i} \times w_{o_j(i)} \right) \right\} + \label{eq:pmin} + \end{equation} + Gdzie: + \begin{itemize} + \item \( P_{\min} \) to minimalna wartość całkowitej punktacji, + \item \( N_{W_S} \) to liczba wymagań szczegółowych, + \item \( w_{s_i} \) to waga \( i \)-tego wymagania szczegółowego, + \item \( w_{o_j(i)} \) to waga wybranego wymagania ogólnego dla \( i \)-tego wymagania szczegółowego, + \item \( j(i) \) to indeks wybranego wymagania ogólnego dla \( i \)-tego wymagania szczegółowego. + \end{itemize} + + \begin{equation} + \forall i \in \{1, \dots, N_{W_S}\}, \quad \exists j(i) \in \{1, \dots, N_{W_O}^i\} + \label{eq:warunek} + \end{equation} + Warunek określony wzorem (\ref{eq:warunek}) zapewnia, że dla każdego wymagania szczegółowego wybrane jest dokładnie jedno wymaganie ogólne, a jednocześnie wszystkie wymagania są zrealizowane. + + \textbf{Uwaga:} W przypadku, gdy każdemu Wymaganiu Szczegółowemu i Ogólnemu przypisuje się \textbf{1~punkt}, wówczas minimalna liczba punktów \( P_{\min} \) realizujących obowiązkowe wymagania edukacyjne z~podstawy programowej dla danego działu wyraża się wzorem (\ref{eq:min_points}). + + \begin{equation} + \label{eq:min_points} + P_{\min} = N_{W_S} + \end{equation} + + Gdzie \( N_{W_S} \) oznacza liczbę Wymagań Szczegółowych. + + \item Minimalna liczba punktów \(\bigl(P_{\text{sum}}\bigr)\) realizująca obowiązkowe wymagania zgodnie z \textbf{PP}\footnotemark[2], znajduje się w~\textbf{Rozdziale~1~załącznika~1}. + +\end{longenum} + +%--------------------------------- +\section{Punktacja zadań} + +\paragraf{Cel i zakres punktacji zadań} +\begin{longenum} + \item Punktacja zadań, określona niniejszym przepisem, służy do dokonywania oceny osiągnięć edukacyjnych, realizowanych zgodnie z zasadami zawartymi w \textbf{Szczegółowym Ocenianiu}, opartymi na kryteriach stanowiących integralną część \textbf{Wewnątrzszkolnego Oceniania}. + + \item Każde zadanie stanowi integralny element systemu oceny, przy czym realizacja co najmniej jednego \textbf{Wymagania Szczegółowego} przypisanego co najmniej jednemu \textbf{Wymaganiu Ogólnemu} jest warunkiem koniecznym. + + \item Ocena zadania ustalana jest na podstawie procentowego udziału punktów zdobytych przez ucznia w stosunku do maksymalnej liczby punktów możliwych do uzyskania przy realizacji danego zadania. +\end{longenum} + +\paragraf{Punktowanie zadania} +\begin{longenum} + \item Zadanie podlega ocenie według kryterium procentowej realizacji wymagań, przy czym procentowe progi przyznawania poszczególnych ocen ustalono zgodnie z wytycznymi określonymi w systemie \textbf{Wewnątrzszkolnego Oceniania (WO)}. + + \item Każdemu z wymagań, zarówno ogólnym, jak i szczegółowym, przypisano określoną wagę, która wyznacza jego znaczenie w procesie oceny zadania. + + \item Łączna liczba punktów przypisywana zadaniu stanowi sumę punktów przyznanych za realizację poszczególnych wymagań, przy czym uzyskanie oceny pozytywnej wymaga realizacji co najmniej jednego \textbf{Wymagania Szczegółowego} oraz osiągnięcia minimalnego progu punktowego. + + \item Procentowy udział zdobytych punktów oblicza się według wzoru: + \begin{equation} + \% = \frac{\sum_{i=1}^{n} p_i}{\sum_{i=1}^{n} P_i} \times 100\% + \label{wzor:procent} + \end{equation} + gdzie: + \begin{longenum} + \item \(p_i\) – liczba punktów zdobytych za realizację \(i\)-tego wymagania, + \item \(P_i\) – maksymalna liczba punktów przypisana do \(i\)-tego wymagania. + \end{longenum} + + \item Ocena końcowa zadania, zwana dalej „oceną”, ustalana jest według następujących progów: + \begin{longenum} + \item \textbf{Ocena 6 (celująca)} – przyznawana w przypadku uzyskania co najmniej 95\% maksymalnej liczby punktów, + \item \textbf{Ocena 5 (bardzo dobra)} – przyznawana w przypadku uzyskania co najmniej 80\% maksymalnej liczby punktów, + \item \textbf{Ocena 4 (dobra)} – przyznawana w przypadku uzyskania co najmniej 65\% maksymalnej liczby punktów, + \item \textbf{Ocena 3 (dostateczna)} – przyznawana w przypadku uzyskania co najmniej 50\% maksymalnej liczby punktów, + \item \textbf{Ocena 2 (dopuszczająca)} – przyznawana w przypadku uzyskania co najmniej 30\% maksymalnej liczby punktów, + \item \textbf{Ocena 1 (niedostateczna)} – przyznawana w przypadku uzyskania wyniku niższego niż 30\% maksymalnej liczby punktów. + \end{longenum} + + \item Ustalenie oceny, zwanej dalej „daną oceną”, następuje w sytuacji, gdy osiągnięty zostanie minimalny próg realizacji zarówno \textbf{Wymagań Ogólnych}, jak i \textbf{Wymagań Szczegółowych}, określony w niniejszym przepisie. W szczególności: + \begin{longenum} + \item Aby przyznać ocenę \textbf{3 (dostateczną)}, wymagane jest zrealizowanie co najmniej 50\% wymagań przypisanych do zadania. + \item W odniesieniu do pozostałych ocen, minimalny procent realizacji wymagań musi być równy lub przekraczać progi określone w odpowiednich punktach. + \end{longenum} + + \item W przypadku stosowania dodatkowych progów lub wymogów, takich jak system „50 na 50”, warunki te muszą być wyraźnie określone w opisie kryteriów oceny zadania, a uczniowie powinni zostać o nich uprzednio poinformowani przed przystąpieniem do wykonania zadania. +\end{longenum} + + +%------------------------------------ +%------------------------------------ + +\section{Wymagania ogólne i szczegółowe} + +\paragraf{Cel i zakres wymagań ogólnych i szczegółowych} + +\begin{longenum} + \item \textbf{Cel:} Zapewnienie jasnych i jednolitych zasad oceniania osiągnięć uczniów + z~\textcolor{przedmiot}{matematyki} na \textcolor{zakres}{zakresie rozszerzonym} na \textcolor{poziom}{1 poziomie nauczania} liceum ogólnokształcącego, + zgodnie z \textbf{Podstawą Programową}\footnotemark[2] i~\textbf{Rozkładem Materiału}\footnotemark[3]. + + \item \textbf{Zakres:} Wymagania określone w niniejszym dokumencie obowiązują nauczycieli realizujących treści kształcenia z~\textbf{\textcolor{przedmiot}{matematyki} na \textcolor{poziom}{pierwszym poziomie nauczania} (\textcolor{zakres}{zakres rozszerzony})}, uwzględniając: + \begin{longenum} + \item Działy z \textbf{RM}\footnotemark[3] – obszary tematyczne przypisane do pierwszego \textcolor{poziom}{poziomu nauczania}, które wyznaczają strukturę nauczania \textcolor{przedmiot}{matematyki}. + \item Pełną realizację obowiązkowych wymagań edukacyjnych – zgodnie z~wytycznymi zawartymi w~aktualnej \textbf{PP}\footnotemark[2], które określają minimalne wymagania do opanowania przez uczniów w ramach~każdego działu. + \end{longenum} +\end{longenum} + + + +\paragraf{Wymagania ogólne} +\begin{longenum} + + \item \textbf{Identyfikacja wymagań} – W~tabeli~\ref{tab:wo} zamieszczono wykaz ogólnych wymagań dotyczących przedmiotu \textcolor{przedmiot}{Matematyka} (obejmującego \textcolor{zakres}{zakres rozszerzony}) na \textcolor{poziom}{pierwszym poziomie nauczania}. Wykaz ten sporządzono w~oparciu o~numerację, która stanowi integralną część wytycznych określonych w~\textbf{Podstawie Programowej}\footnotemark[2]. + + \item \textbf{Przydział punktów} – Każdemu z~wymagań, stanowiących integralną część niniejszego systemu oceny, przypisano liczbę punktów, ustaloną w sposób niezmienny i~jednoznaczny, co stanowi podstawę do przeprowadzenia ilościowej oceny osiągnięć edukacyjnych. + + + + + + + +\end{longenum} + + +\input{tables/wo} + + +\paragraf{Wymagania szczegółowe} +\input{tables/ws} + + \section{Przypisane wymagania ogólne do szczegółowych} + + \paragraf{opis} + \begin{longenum} + \item Wymagania ogólne przypisane do wymagań szczegółowych odnoszą się do umiejętności i kompetencji, które uczeń powinien posiadać, aby sprostać wymaganiom szczegółowym. Wymagania ogólne obejmują m.in. sprawność rachunkową, wykorzystanie i tworzenie informacji, interpretowanie reprezentacji matematycznych oraz rozumowanie i argumentację. Każde wymaganie szczegółowe jest powiązane z jednym lub kilkoma wymaganiami ogólnymi, co pozwala na kompleksowe sprawdzenie wiedzy i umiejętności ucznia. + \end{longenum} + +% % \usepackage{graphicx} +% \resizebox{\linewidth}{!}{% +% \begin{longtable}{|p{0.1\textwidth}|p{0.8\textwidth}|p{0.1\textwidth}|} +% \end{longtable} +% } +\input{tables/liczby_rzeczywiste} + + \section{Postanowienia końcowe} + + \paragraf{Zasady obowiązywania} + \begin{longenum} + \item Niniejszy dokument określa szczegółowe zasady oceniania uczniów na \textcolor{poziom}{1~poziomie edukacyjnym} na \textcolor{zakres}{zakresie rozszerzonym} i~obowiązuje wszystkich nauczycieli oraz uczniów w~Zespole Szkół Licealnych im. Zbigniewa Herberta w~Słubicach. + \item Szczegółowe Ocenianie (SO) jest zgodne z: + \begin{longenum} + \item \textbf{Podstawą programową} kształcenia ogólnego\footnotemark[2]. + \item \textbf{Wewnątrzszkolnym Ocenianiem} (WO), stanowiącym integralną część Statutu Szkoły\footnotemark[1]. + \item Obowiązującymi \textbf{przepisami prawa oświatowego}\footnotemark[4]. + \end{longenum} + \item Dokument może być aktualizowany zgodnie z nowelizacją przepisów prawa oraz wewnętrznymi regulacjami szkoły. + \end{longenum} + + \paragraf{Postanowienia końcowe} + \begin{longenum} + \item Każdy uczeń oraz jego rodzice (prawni opiekunowie) mają prawo do pełnej informacji na temat zasad oceniania określonych w~niniejszym dokumencie. + \item Nauczyciel jest zobowiązany do przestrzegania zasad oceniania zgodnie z~wytycznymi zawartymi w~SO. + \item W~przypadku wątpliwości interpretacyjnych związanych z~ocenianiem, decyzje podejmuje nauczyciel przedmiotu w~porozumieniu z~zespołem przedmiotowym. + \item Niniejsze zasady wchodzą w~życie z~dniem zatwierdzenia przez dyrektora szkoły i~obowiązują do momentu wprowadzenia ich nowelizacji. + \end{longenum} + + \begin{flushright} + \textbf{Nauczyciele zespołu przedmiotowego:} \\ + \vspace{2em} % Miejsce na podpisy + \rule{6cm}{0.4pt} \\ % Linia do podpisu pierwszego nauczyciela \\ + \textit{(podpis nauczyciela)} \\[1.5em] + + \rule{6cm}{0.4pt} \\ % Linia do podpisu drugiego nauczyciela \\ + \textit{(podpis nauczyciela)} \\[1.5em] + + \rule{6cm}{0.4pt} \\ % Linia do podpisu trzeciego nauczyciela (opcjonalnie) \\ + \textit{(podpis nauczyciela)} +\end{flushright} + + + +--- +% \begin{longenum} +% \item Nauczyciel, uwzględniając potrzeby i możliwości edukacyjne uczniów, zobowiązany jest do zapewnienia +% realizacji wszystkich powyższych wymagań szczegółowych w ramach programu nauczania przewidzianego +% w klasie pierwszej liceum ogólnokształcącego na poziomie podstawowym. + +% \item Niniejsze wymagania stanowią uszczegółowienie podstawy programowej i są podstawą do +% formułowania \textbf{przedmiotowych zasad oceniania}, w szczególności \emph{Szczegółowego Oceniania (SO)} +% z matematyki, określającego kryteria przyznawania ocen bieżących, semestralnych i końcoworocznych. +% \end{longenum} + + + +% \end{customenum} + +\end{document} + +% Liczby rzeczywiste +% Wyrażenia algebraiczne +% Równania i nierówności +% Funkcje +% Trygonometria +% Planimetria +% Geometria analityczna diff --git a/doc/main.aux b/doc/main.aux new file mode 100644 index 0000000..0c42e8f --- /dev/null +++ b/doc/main.aux @@ -0,0 +1,59 @@ +\relax +\providecommand \babel@aux [2]{\global \let \babel@toc \@gobbletwo } +\@nameuse{bbl@beforestart} +\catcode `"\active +\providecommand\hyper@newdestlabel[2]{} +\providecommand\HyField@AuxAddToFields[1]{} +\providecommand\HyField@AuxAddToCoFields[2]{} +\babel@aux{polish}{} +\@writefile{toc}{\contentsline {section}{\numberline {1}Postanowienia Ogólne}{3}{section.1}\protected@file@percent } 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+ +[15] + +Package fancyhdr Warning: \headheight is too small (12.0pt): +(fancyhdr) Make it at least 14.49998pt, for example: +(fancyhdr) \setlength{\headheight}{14.49998pt}. +(fancyhdr) You might also make \topmargin smaller to compensate: + +(fancyhdr) \addtolength{\topmargin}{-2.49998pt}. + +[16] + +Package fancyhdr Warning: \headheight is too small (12.0pt): +(fancyhdr) Make it at least 14.49998pt, for example: +(fancyhdr) \setlength{\headheight}{14.49998pt}. +(fancyhdr) You might also make \topmargin smaller to compensate: + +(fancyhdr) \addtolength{\topmargin}{-2.49998pt}. + +[17] + +Package fancyhdr Warning: \headheight is too small (12.0pt): +(fancyhdr) Make it at least 14.49998pt, for example: +(fancyhdr) \setlength{\headheight}{14.49998pt}. +(fancyhdr) You might also make \topmargin smaller to compensate: + +(fancyhdr) \addtolength{\topmargin}{-2.49998pt}. + +[18] + +Package fancyhdr Warning: \headheight is too small (12.0pt): +(fancyhdr) Make it at least 14.49998pt, for example: +(fancyhdr) \setlength{\headheight}{14.49998pt}. +(fancyhdr) You might also make \topmargin smaller to compensate: + +(fancyhdr) \addtolength{\topmargin}{-2.49998pt}. + +[19] + +Package fancyhdr Warning: \headheight is too small (12.0pt): +(fancyhdr) Make it at least 14.49998pt, for example: +(fancyhdr) \setlength{\headheight}{14.49998pt}. +(fancyhdr) You might also make \topmargin smaller to compensate: + +(fancyhdr) \addtolength{\topmargin}{-2.49998pt}. + +[20]) + + +Package fancyhdr Warning: \headheight is too small (12.0pt): +(fancyhdr) Make it at least 14.49998pt, for example: +(fancyhdr) \setlength{\headheight}{14.49998pt}. +(fancyhdr) You might also make \topmargin smaller to compensate: + +(fancyhdr) \addtolength{\topmargin}{-2.49998pt}. + +[21] + + +Package fancyhdr Warning: \headheight is too small (12.0pt): +(fancyhdr) Make it at least 14.49998pt, for example: +(fancyhdr) \setlength{\headheight}{14.49998pt}. +(fancyhdr) You might also make \topmargin smaller to compensate: + +(fancyhdr) \addtolength{\topmargin}{-2.49998pt}. + +[22] (./main.aux) + *********** +LaTeX2e <2024-11-01> +L3 programming layer <2024-11-02> + *********** + + +LaTeX Warning: There were undefined references. + +Package rerunfilecheck Info: File `main.out' has not changed. +(rerunfilecheck) Checksum: A50D0C022BB3BB1A43DD0A80321692F5;906. + ) +Here is how much of TeX's memory you used: + 14873 strings out of 473362 + 232773 string characters out of 5723554 + 963400 words of memory out of 5000000 + 37472 multiletter control sequences out of 15000+600000 + 627804 words of font info for 157 fonts, out of 8000000 for 9000 + 1141 hyphenation exceptions out of 8191 + 75i,12n,79p,997b,1030s stack positions out of 10000i,1000n,20000p,200000b,200000s + +Output written on main.pdf (22 pages, 303509 bytes). +PDF statistics: + 343 PDF objects out of 1000 (max. 8388607) + 287 compressed objects within 3 object streams + 132 named destinations out of 1000 (max. 500000) + 38953 words of 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[1][-]{section.5}{\376\377\000P\000o\000s\000t\000a\000n\000o\000w\000i\000e\000n\000i\000a\000\040\000k\000o\001\104\000c\000o\000w\000e}{}% 5 diff --git a/doc/main.toc b/doc/main.toc new file mode 100644 index 0000000..f495c0c --- /dev/null +++ b/doc/main.toc @@ -0,0 +1,6 @@ +\babel@toc {polish}{}\relax +\contentsline {section}{\numberline {1}Postanowienia Ogólne}{3}{section.1}% +\contentsline {section}{\numberline {2}Punktacja i Przyznawanie Wag}{5}{section.2}% +\contentsline {section}{\numberline {3}Przeliczenie Punktów na Oceny}{8}{section.3}% +\contentsline {section}{\numberline {4}Wymagania ogólne i szczegółowe}{10}{section.4}% +\contentsline {section}{\numberline {5}Postanowienia końcowe}{22}{section.5}% diff --git a/doc/py/1 b/doc/py/1 new file mode 100644 index 0000000..f0368cd --- /dev/null +++ b/doc/py/1 @@ -0,0 +1,92 @@ +#!/usr/bin/env python3 +# -*- coding: utf-8 -*- + +import sys +import json + +def generuj_wiersze(wezel, wiersze, poziom=0): + """ + Funkcja rekurencyjna: + - Odczytuje z węzła (wezel) pola nr, opis, punkty. + - Dodaje do listy 'wiersze' wiersz tabeli w stylu: + [wcięcie + nr] & [wcięcie + opis] & [wcięcie + punkty] \\ + przy czym każde pole jest dodatkowo wcięte zależnie od poziomu zagnieżdżenia. + - Pomija węzeł "Wymagania ogólne" i jego dzieci. + """ + # Sprawdź, czy bieżący węzeł to "Wymagania ogólne" + if wezel.get("opis") == "Wymagania ogólne": + return # Pomijamy ten węzeł i jego dzieci + + nr = wezel.get("nr", "") + opis = wezel.get("opis", "") + punkty = wezel.get("punkty", "") + + # Wcięcie w LaTeX-u (np. 0.5 em na poziom) zależnie od poziomu + wciecie = r"\hspace{" + f"{0.5 * poziom}em" + "}" # 0.5em na poziom + + # Lista kolorów dla Wymagań Standardowych + kolory_standard = [ + r"\cellcolor{gray!20}", # Poziom 0 + r"\cellcolor{red!40}", # Poziom 1 + r"\cellcolor{blue!20}", # Poziom 2 + r"\cellcolor{yellow!20}", # Poziom 3 + r"\cellcolor{red!30}", # Poziom 4 + r"\cellcolor{red!20}", # Poziom 5 + ] + + # Wybierz kolor na podstawie poziomu + kolor = kolory_standard[poziom % len(kolory_standard)] + + # Tworzymy wiersz: + # [wcięcie + nr] & [wcięcie + opis] & [wcięcie + punkty] \\ + linia = f"{kolor}{wciecie}{nr} & {kolor}{wciecie}{opis} & {kolor}{wciecie}{punkty} \\\\" + wiersze.append(linia) + + # Rekurencja dla dzieci + for dziecko in wezel.get("children", []): + generuj_wiersze(dziecko, wiersze, poziom + 1) + +def main(): + if len(sys.argv) < 3: + print("Użycie: skrypt.py plik_wejściowy.json plik_wyjściowy.tex") + sys.exit(1) + + plik_json = sys.argv[1] + plik_tekstowy = sys.argv[2] + + # 1. Wczytanie danych JSON z pliku + with open(plik_json, 'r', encoding='utf-8') as f: + dane = json.load(f) + + # 2. Bufor na wszystkie wiersze LaTeX + wiersze = [] + + # Dostosowanie szerokości kolumn do 0.1, 0.8 i 0.1 textwidth + wiersze.append(r"\begin{longtable}{|p{0.1\textwidth}|p{0.74\textwidth}|p{0.1\textwidth}|}") + wiersze.append(r"\caption{Lista wymagań szczegółowych}\label{tab:ws}\\") + wiersze.append(r"\hline") + wiersze.append(r"\textbf{Nr} & \textbf{Opis} & \textbf{Punkty} \\") + wiersze.append(r"\hline") + # firsthead -> co ma się powtórzyć na kolejnej stronie tabeli + wiersze.append(r"\endfirsthead") + wiersze.append(r"\hline") + wiersze.append(r"\textbf{Nr} & \textbf{Opis} & \textbf{Punkty} \\") + wiersze.append(r"\hline") + wiersze.append(r"\endhead") + + # 3. Generowanie wierszy tabeli na podstawie JSON-a + for element in dane.get("items", []): + generuj_wiersze(element, wiersze) + wiersze.append(r"\hline") # Dodanie linii odcinającej po każdej sekcji + + # 4. Zakończenie longtable + wiersze.append(r"\hline") + wiersze.append(r"\end{longtable}") + + # 5. Zapis do pliku .tex (z polskimi znakami w UTF-8) + with open(plik_tekstowy, 'w', encoding='utf-8') as f: + f.write("\n".join(wiersze) + "\n") + + +if __name__ == "__main__": + main() diff --git a/doc/py/wo.py-k b/doc/py/wo.py-k new file mode 100644 index 0000000..5a20ca0 --- /dev/null +++ b/doc/py/wo.py-k @@ -0,0 +1,76 @@ +#!/usr/bin/env python3 +# -*- coding: utf-8 -*- + +import sys +import json + +def generuj_wiersze_ogolne(wezel, wiersze, poziom=1, intensywnosc=40): + """ + Funkcja do generowania wierszy dla wymagań ogólnych. + """ + nr = wezel.get("nr", "") + opis = wezel.get("opis", "") + punkty = wezel.get("atrybuty", {}).get("punkty", "") + + # Wcięcie w LaTeX-u (np. 0.5 em na poziom) zależnie od poziomu + wciecie = r"\hspace{" + f"{0.5 * poziom}em" + "}" # 0.5em na poziom + + # Kolorowanie dla wymagań ogólnych + kolor = f"\\cellcolor{{green!{intensywnosc}}}" # Kolor dla Wymagań Ogólnych + + # Tworzymy wiersz: + # [wcięcie + nr] & [wcięcie + opis] & [wcięcie + punkty] \\ + linia = f"{kolor}{wciecie}{nr} & {kolor}{wciecie}{opis} & {kolor}{wciecie}{punkty} \\\\" + wiersze.append(linia) + + # Rekurencja dla dzieci + for dziecko in wezel.get("wymagania", []): + generuj_wiersze_ogolne(dziecko, wiersze, poziom + 1, intensywnosc - 20) + +def main(): + if len(sys.argv) < 3: + print("Użycie: skrypt.py plik_wejściowy.json plik_wyjściowy.tex") + sys.exit(1) + + plik_json = sys.argv[1] + plik_tekstowy = sys.argv[2] + + # 1. Wczytanie danych JSON z pliku + with open(plik_json, 'r', encoding='utf-8') as f: + dane = json.load(f) + + # 2. Bufor na wszystkie wiersze LaTeX + wiersze = [] + + # Dostosowanie szerokości kolumn do 0.1, 0.74 i 0.1 textwidth + wiersze.append(r"\begin{longtable}{|p{0.1\textwidth}|p{0.74\textwidth}|p{0.1\textwidth}|}") + wiersze.append(r"\caption{Lista wymagań ogólnych}\\") + wiersze.append(r"\hline") + wiersze.append(r"\textbf{Nr} & \textbf{Opis} & \textbf{Punkty} \\") + wiersze.append(r"\hline") + # firsthead -> co ma się powtórzyć na kolejnej stronie tabeli + wiersze.append(r"\endfirsthead") + wiersze.append(r"\hline") + wiersze.append(r"\textbf{Nr} & \textbf{Opis} & \textbf{Punkty} \\") + wiersze.append(r"\hline") + wiersze.append(r"\endhead") + + # 3. Generowanie wierszy tabeli na podstawie JSON-a + # Wymagania ogólne + wiersze.append(r"\hline") + wiersze.append(r"\cellcolor{green!60}\hspace{0.0em}- & \cellcolor{green!60}\hspace{0.0em}Wymagania ogólne & \cellcolor{green!60}\hspace{0.0em}- \\") + wiersze.append(r"\hline") + for element in dane.get("wymagania_ogolne", []): + generuj_wiersze_ogolne(element, wiersze) + wiersze.append(r"\hline") # Dodanie linii odcinającej po każdej sekcji + + # 4. Zakończenie longtable + wiersze.append(r"\hline") + wiersze.append(r"\end{longtable}") + + # 5. Zapis do pliku .tex (z polskimi znakami w UTF-8) + with open(plik_tekstowy, 'w', encoding='utf-8') as f: + f.write("\n".join(wiersze) + "\n") + +if __name__ == "__main__": + main() diff --git a/doc/t b/doc/t new file mode 100644 index 0000000..13e6490 --- /dev/null +++ b/doc/t @@ -0,0 +1,97 @@ +\section{System Oceniania na Podstawie Wag i Punktów} + +\paragraf{Przypisywanie Wag i Punktów} +\begin{longenum} + \item \textbf{Przypisywanie wag do wymagań}: + \begin{longenum} + \item Każdemu \textbf{wymaganiu szczegółowemu} (\(WS\)) przypisuje się wagę \(w_{s_i}\), gdzie \(i\) to indeks wymaganego szczegółowego. + \item Każdemu \textbf{wymaganiu ogólnemu} (\(WO\)) przypisuje się wagę \(w_{o_j}\), gdzie \(j\) to indeks wymaganego ogólnego. + \item Wagi są ustalane w oparciu o ich znaczenie w programie nauczania i mogą przyjmować wartości całkowite lub ułamkowe. + \end{longenum} + + \item \textbf{Punktacja dla zadań}: + \begin{longenum} + \item Punktacja zadania obliczana jest na podstawie realizacji poszczególnych wymagań szczegółowych i ogólnych. + \item Maksymalna liczba punktów za zadanie (\(P_{\text{zad}}\)) wyznaczana jest jako suma wag wszystkich realizowanych wymagań: + \[ + P_{\text{zad}} = \sum_{i=1}^{N_{W_S}} \Bigl( w_{s_i} \times \sum_{j=1}^{N^i_{W_O}} w_{o_j} \Bigr), + \] + gdzie: + \begin{itemize}[noitemsep] + \item \(N_{W_S}\) – liczba wymagań szczegółowych w zadaniu, + \item \(N^i_{W_O}\) – liczba wymagań ogólnych powiązanych z \(i\)-tym wymaganiem szczegółowym. + \end{itemize} + \end{longenum} + + \item \textbf{Punktacja dla działów}: + \begin{longenum} + \item Punktacja dla danego działu (\(P_{\text{dział}}\)) obliczana jest jako suma maksymalnych punktów ze wszystkich zadań w ramach tego działu. + \item Minimalna liczba punktów (\(P_{\min}^{\text{dział}}\)) potrzebna do zaliczenia działu wyznaczana jest według wzoru: + \[ + P_{\min}^{\text{dział}} = \min \left\{ \sum_{i=1}^{N_{W_S}} \left( w_{s_i} \times w_{o_j(i)} \right) \right\}, + \] + gdzie \(w_{o_j(i)}\) to waga jednego z wymagań ogólnych dla \(i\)-tego wymagania szczegółowego. + \end{longenum} + + \item \textbf{Punktacja dla poziomu}: + \begin{longenum} + \item Punktacja dla całego poziomu (\(P_{\text{poziom}}\)) obliczana jest jako suma maksymalnych punktów ze wszystkich działów: + \[ + P_{\text{poziom}} = \sum_{k=1}^{N_{\text{działa}}} P_{\min}^k, + \] + gdzie \(N_{\text{działa}}\) to liczba działów w ramach poziomu. + \end{longenum} +\end{longenum} + +\paragraf{Wyznaczenie Minimalnych i Maksymalnych Punktów} +\begin{longenum} + \item \textbf{Minimalne punkty dla zadań}: + \begin{longenum} + \item Minimalna liczba punktów (\(P_{\min}^{\text{zad}}\)) dla zadania to suma minimalnych wag wymagań niezbędnych do zaliczenia tego zadania. + \end{longenum} + + \item \textbf{Minimalne punkty dla działów}: + \begin{longenum} + \item Minimalna liczba punktów (\(P_{\min}^{\text{dział}}\)) dla działu to suma minimalnych punktów z wszystkich zadań w ramach tego działu. + \end{longenum} + + \item \textbf{Minimalne punkty dla poziomu}: + \begin{longenum} + \item Minimalna liczba punktów (\(P_{\min}^{\text{poziom}}\)) dla poziomu to suma minimalnych punktów z wszystkich działów w ramach tego poziomu. + \end{longenum} + + \item \textbf{Maksymalne punkty}: + \begin{longenum} + \item Maksymalna liczba punktów (\(P_{\max}\)) dla zadań, działów i poziomu to odpowiednio sumy maksymalnych wag wszystkich wymagań. + \end{longenum} +\end{longenum} + +\paragraf{Przeliczenie Punktów na Oceny} +\begin{longenum} + \item \textbf{Ocena za zadanie}: + \begin{longenum} + \item Ocena za zadanie ustalana jest na podstawie procentowego udziału zdobytych punktów (\(P_{\text{zdobyte}}\)) w stosunku do maksymalnej liczby punktów (\(P_{\text{max}}\)): + \[ + \% = \frac{P_{\text{zdobyte}}}{P_{\text{max}}} \times 100\%. + \] + \item Progi ocen: + \begin{itemize}[noitemsep] + \item Ocena 6: min. 95\%, + \item Ocena 5: min. 80\%, + \item Ocena 4: min. 65\%, + \item Ocena 3: min. 50\%, + \item Ocena 2: min. 30\%, + \item Ocena 1: poniżej 30\%. + \end{itemize} + \end{longenum} + + \item \textbf{Ocena za dział}: + \begin{longenum} + \item Ocena za dział ustalana jest na podstawie średniej arytmetycznej ocen z wszystkich zadań w ramach tego działu. + \end{longenum} + + \item \textbf{Ocena za poziom}: + \begin{longenum} + \item Ocena za poziom ustalana jest na podstawie średniej arytmetycznej ocen z wszystkich działów w ramach tego poziomu. + \end{longenum} +\end{longenum} diff --git a/doc/tables/wo.log b/doc/tables/wo.log new file mode 100644 index 0000000..e69de29 diff --git a/exercise/main.pdf b/exercise/main.pdf deleted file mode 100644 index b5755c156738e637b78f3870e2f11d5f137f7ea4..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 131947 zcma&MQ;;r7(5~6GZQHhO+qS-TueN)&-K%Zewr$(CJ^Reex%ww!PF_@GT~tIxW@J6} zMkcwEm;^mD13L`)+|uwG3@Z^6k)w$X3?Cm1qnx>erK=SYGdnXk(f@5Qj1ty%uIA1} 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{\Large \textbf{Poziom nauczania: Liceum}}\\[5pt] - {\Large \textbf{Zakres: Podstawowy}} -\end{center} - -\vspace{1cm} - -%======================================== -% Treść zadania -%======================================== -\section*{Treść zadania} -Udowodnij, że dla dowolnej liczby całkowitej \( n \) zachodzi: -\[ -n^2 \equiv 0 \quad \text{lub} \quad n^2 \equiv 1 \pmod{4}. -\] -(Innymi słowy, kwadrat każdej liczby całkowitej po podzieleniu przez 4 daje resztę 0 lub 1.) - -%======================================== -% Wymagania szczegółowe (WS) -%======================================== -\section*{Realizowane Wymagania Szczegółowe (WS)} -\begin{itemize}[leftmargin=*, label=--] - \item \textbf{WS1:} Przeprowadza proste dowody dotyczące podzielności liczb całkowitych i reszt z dzielenia. -\end{itemize} - -%======================================== -% Wymagania ogólne (WG) – podstawa programowa dla liceum -%======================================== -\section*{Wymagania ogólne (WG) podlegające ocenie} -\begin{itemize}[leftmargin=*, label=--] - \item \textbf{W1.1:} Sprawność rachunkowa (wykonywanie obliczeń oraz stosowanie praw działań matematycznych). - \item \textbf{W2.2:} Wykorzystanie i tworzenie informacji (używanie języka matematycznego do opisu rozumowań i uzasadniania wniosków). - \item \textbf{W3.1:} Wykorzystanie i interpretowanie reprezentacji (stosowanie obiektów matematycznych i operowanie nimi). - \item \textbf{W4.1:} Rozumowanie i argumentacja (przeprowadzanie rozumowań oraz uzasadnianie poprawności rozwiązań). -\end{itemize} - -%======================================== -% Rozwiązanie – Każdy krok w 2 wierszach -%======================================== -\section*{Rozwiązanie} - -\noindent -\textbf{Krok 1: Uogólnienie liczby całkowitej.}\\[2mm] -Niech \( n \) będzie dowolną liczbą całkowitą. Możemy zapisać: -\[ -n = 2k \quad \text{(dla \( n \) parzystego)} \quad \text{lub} \quad n = 2k+1 \quad \text{(dla \( n \) nieparzystego)}, -\] -gdzie \( k \in \mathbb{Z} \).\\[2mm] -\textit{Realizacja wymagań: \textbf{W3.1, W2.2}.} - -\vspace{0.5cm} - -\noindent -\textbf{Krok 2: Rozpatrzenie przypadku \( n = 2k \).}\\[2mm] -Dla \( n = 2k \) mamy: -\[ -n^2 = (2k)^2 = 4k^2. -\] -Skoro \( 4k^2 \) jest podzielne przez 4, to: -\[ -n^2 \equiv 0 \pmod{4}. -\]\\[2mm] -\textit{Realizacja wymagań: \textbf{W1.1, W4.1}.} - -\vspace{0.5cm} - -\noindent -\textbf{Krok 3: Rozpatrzenie przypadku \( n = 2k+1 \).}\\[2mm] -Dla \( n = 2k+1 \) mamy: -\[ -n^2 = (2k+1)^2 = 4k^2 + 4k + 1 = 4(k^2+k) + 1. -\] -Skoro \( 4(k^2+k) \) jest podzielne przez 4, to: -\[ -n^2 \equiv 1 \pmod{4}. -\]\\[2mm] -\textit{Realizacja wymagań: \textbf{W1.1, W4.1}.} - -\vspace{0.5cm} - -\noindent -\textbf{Krok 4: Wniosek końcowy.}\\[2mm] -Z rozpatrzenia obu przypadków wynika, że: -\[ -n^2 \equiv 0 \quad \text{lub} \quad n^2 \equiv 1 \pmod{4}. -\]\\[2mm] -\textit{Realizacja wymagań: \textbf{W4.1, W2.2}.} - -\vspace{1cm} - -%======================================== -% Podsumowanie oceny – tabela z wagami -%======================================== -\section*{Podsumowanie oceny} -\begin{table}[h] -\centering -\begin{tabular}{|l|c|c|c|} -\hline -\textbf{Wymaganie} & \textbf{Liczba wystąpień} & \textbf{Waga przy wystąpieniu} & \textbf{Łącznie punktów} \\ -\hline -W1.1 & 2 & 0.5 & 1 \\ -\hline -W2.2 & 2 & 0.5 & 1 \\ -\hline -W3.1 & 1 & 1 & 1 \\ -\hline -W4.1 & 3 & 0.33 & 1 \\ -\hline -\end{tabular} -\caption{Waga i procentowy udział poszczególnych wymagań w zadaniu.} -\end{table} - -\noindent -\textbf{Ocena końcowa:} Ocena jest ustalana na podstawie procentowej realizacji wymagań ogólnych. Aby uzyskać daną ocenę, uczeń musi spełnić określoną liczbę punktów w systemie WO, zgodnie z poniższą klasyfikacją: -\begin{enumerate}[label=\textbf{\arabic*.}] - \item \textbf{Ocena 6 (celująca)} – spełnione co najmniej 95\% wymagań ogólnych na 95\% na \%. - \item \textbf{Ocena 5 (bardzo dobra)} – spełnione co najmniej 80\% na 80\%. - \item \textbf{Ocena 4 (dobra)} – spełnione co najmniej 65\% na 65\%. - \item \textbf{Ocena 3 (dostateczna)} – spełnione co najmniej 50\% na 50\%. - \item \textbf{Ocena 2 (dopuszczająca)} – spełnione co najmniej 30\% na 30\%. - \item \textbf{Ocena 1 (niedostateczna)} – niespełnienie żadneggo z powyższych warunków. -\end{enumerate} - -\end{document} - diff --git a/praca-pisemna/main.pdf b/praca-pisemna/main.pdf new file mode 100644 index 0000000000000000000000000000000000000000..85f5dbd3407d18a2de06e1a0e5d1ec662a6b2ddd GIT binary patch literal 296109 zcma&NQ;aUa)~?&O&DpkX+qP}nwr$R~ZQHhOe2v-0Ui;+ilas7{@z>R;q*7I>)W!3@ 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+ } + } +} + +% -------------------------------------------------------- +% Makra do odwołań do WO i WS: +% (Wyświetlają: WO 1.1, T. 1) albo WS 1.2, T. 2) +% -------------------------------------------------------- +\newcommand{\WO}[1]{\textbf{WO #1, T.~\ref{tab:wo}}} +\newcommand{\WS}[1]{\textbf{WS #1, T.~\ref{tab:ws}}} + +\begin{document} + +% -------------------------------------------------------- +% Tytuł +% -------------------------------------------------------- +\begin{center} +{\Large\textbf{Praca pisemna -- Kartkówka (maksymalna liczba punktów cząstkowych: 0--19)}}\\[8pt] +\textbf{Skala ocen w dzienniku: 0--10}\\[2pt] +\textbf{Autorzy: M. Markiewicz, J. Góra} +\end{center} +\vspace{1em} + +% -------------------------------------------------------- +% Zadanie 1 (jedna strona) +% -------------------------------------------------------- +\section*{Zadanie 1} +\textbf{Treść:} Oblicz wartość wyrażenia: +\[ + \sqrt{16} \;+\; 2^{-3}. +\] +Zapisz krótko uzasadnienie każdego kroku (np.~dlaczego tak liczymy pierwiastek +i~potęgę ujemną). Na koniec podaj krótki przykład \emph{praktycznej interpretacji} potęgi ujemnej. + +\vspace{0.5em} +\noindent +\textbf{Diagram wymagań (Zadanie 1):} +\begin{center} +\begin{forest} + mytree + [Zadanie 1 + [\WS{1.1} + [\WO{1}] + [\WO{1}] + ] + [\WS{1.2} + [\WO{1}] + [\WO{1}] + ] + ] +\end{forest} +\end{center} + + +\subsection*{Tabela punktacji (Zadanie 1)} +\noindent +\begin{center} +\begin{tabular}{|p{0.25\textwidth}|p{0.55\textwidth}|p{0.1\textwidth}|} +\hline +\textbf{WS--WO} +& \textbf{Opis / Weryfikacja} +& \textbf{1/0} \\[3pt] +\hline +\WS{1.1}, \WO{1} & Poprawne obliczenie \(\sqrt{16}\). & \\ \hline +\WS{1.1}, \WO{4} & Uzasadnienie procesu obliczania pierwiastka. & \\ \hline +\WS{1.2}, \WO{1} & Poprawne obliczenie \(2^{-3}\). & \\ \hline +\WS{1.2}, \WO{2} & Interpretacja praktyczna potęgi ujemnej. & \\ \hline +\multicolumn{2}{|r|}{\textbf{Suma punktów (maks = 9)}} & \\ \hline +\end{tabular} +\end{center} + +\vspace{1em} +\noindent +\textbf{Miejsce na realizację:} +\vspace{6em} % Zwiększ w razie potrzeby + +\newpage + +% -------------------------------------------------------- +% Zadanie 2 (jedna strona) +% -------------------------------------------------------- +\section*{Zadanie 2} +\textbf{Treść:} W~trójkącie prostokątnym o~przyprostokątnych 3\,cm i~4\,cm: +\begin{itemize} + \item[(a)] Oblicz długość przeciwprostokątnej (zastosuj Twierdzenie Pitagorasa). + \item[(b)] Wyznacz \(\sin\) oraz \(\cos\) kątów ostrych. + \item[(c)] Krótko uzasadnij, skąd bierze się tożsamość \(\sin^2\alpha + \cos^2\alpha = 1\). +\end{itemize} + +\subsection*{Tabela punktacji (Zadanie 2)} +\noindent +\begin{center} +\begin{tabular}{|p{0.25\textwidth}|p{0.55\textwidth}|p{0.1\textwidth}|} +\hline +\textbf{WS--WO} +& \textbf{Opis / Weryfikacja} +& \textbf{1/0} \\[3pt] +\hline +\WS{4.1}, \WO{1} & Poprawne obliczenie przeciwprostokątnej (Tw.~Pitagorasa). & \\ \hline +\WS{4.1}, \WO{2} & Wykorzystanie danych (np.~rysunku). & \\ \hline +\WS{4.1}, \WO{4} & Uzasadnienie użycia Tw.~Pitagorasa. & \\ \hline +\WS{3.1}, \WO{1} & Poprawne wyznaczenie \(\sin\), \(\cos\) kątów. & \\ \hline +\WS{3.1}, \WO{3} & Interpretacja (który bok do sin, który do cos). & \\ \hline +\WS{3.1}, \WO{4} & Uzasadnienie tożsamości \(\sin^2\alpha + \cos^2\alpha=1\). & \\ \hline +\multicolumn{2}{|r|}{\textbf{Suma punktów (maks = 10)}} & \\ \hline +\end{tabular} +\end{center} + +\vspace{0.5em} +\noindent +\textbf{Diagram wymagań (Zadanie 2):} +\begin{center} +\begin{forest} + mytree + [Zadanie 2 + [\WS{3.1} + [\WO{1}] + [\WO{3}] + [\WO{4}] + ] + [\WS{4.1} + [\WO{1}] + [\WO{2}] + [\WO{4}] + ] + ] +\end{forest} +\end{center} + +\vspace{1em} +\noindent +\textbf{Miejsce na realizację:} +\vspace{8em} % Zwiększ w razie potrzeby + + +\newpage + +% -------------------------------------------------------- +% Podsumowanie punktów, przeliczenie i ocena +% -------------------------------------------------------- +\section*{Podsumowanie punktów} + +\begin{center} +\begin{tabular}{|c|c|c|} +\hline +\textbf{Zadanie} & \textbf{Punkty zdobyte} & \textbf{Punkty maks.} \\ +\hline +1 & \phantom{0} & 9 \\ +\hline +2 & \phantom{0} & 10 \\ +\hline +\textbf{Razem} & & 19 \\ +\hline +\end{tabular} +\end{center} + +\vspace{1em} + +\noindent +\textbf{Przeliczenie punktów na skalę (0--10) do dziennika:} +\[ + P_{\text{dziennik}} \;=\; + \bigl(\text{Punkty zdobyte}\bigr) \times \frac{10}{19}. +\] +\[ + \text{(Przykład: jeśli zdobyto 15\,pkt z 19, to } + 15 \times \frac{10}{19} \approx 7.9 \text{.)} +\] + +\vspace{0.8em} +\noindent +\textbf{Przeliczenie na procenty:} +\[ + \% \;=\; \frac{\text{Punkty zdobyte}}{19} \times 100\%. +\] + +\vspace{1em} +\noindent +\textbf{Przykład uzasadnienia oceny (do wypełnienia przez nauczyciela):}\\ +\begin{itemize} + \item \textbf{Zrealizowane wymagania:} + \begin{itemize} + \item w~Zad.1~(\dots), + \item w~Zad.2~(\dots). + \end{itemize} + \item \textbf{Braki:} + \begin{itemize} + \item nie uzasadniono \(\dots\), + \item brak rysunku \(\dots\) + \item itp. + \end{itemize} + \item \textbf{Suma punktów:} \dots\ (na 19), + \quad\(\Rightarrow P_{\text{dziennik}} = \dots\), + \quad\% = \dots. +\end{itemize} + +% -------------------------------------------------------- +% Wymagania ogólne +% -------------------------------------------------------- +\clearpage +\begin{longtable}{|p{0.1\textwidth}|p{0.74\textwidth}|p{0.1\textwidth}|} +\caption{Lista wymagań ogólnych (WO)}\label{tab:wo}\\ +\hline +\textbf{Nr} & \textbf{Opis} & \textbf{Punkty} \\ +\hline +\endfirsthead +\hline +\textbf{Nr} & \textbf{Opis} & \textbf{Punkty} \\ +\hline +\endhead +\hline +\cellcolor{green!60}- & \cellcolor{green!60}Wymagania ogólne & \cellcolor{green!60}- \\ +\hline +\cellcolor{green!40}1 & \cellcolor{green!40}Sprawność rachunkowa. & \cellcolor{green!40}- \\ +\cellcolor{green!20}1 & \cellcolor{green!20}Wykonywanie obliczeń na liczbach rzeczywistych, także przy użyciu kalkulatora, stosowanie praw działań matematycznych przy przekształcaniu wyrażeń algebraicznych oraz \dots & \cellcolor{green!20}1 \\ +\hline +\cellcolor{green!40}2 & \cellcolor{green!40}Wykorzystanie i tworzenie informacji. & \cellcolor{green!40}- \\ +\cellcolor{green!20}1 & \cellcolor{green!20}Interpretowanie i operowanie informacjami przedstawionymi w tekście, \dots & \cellcolor{green!20}1 \\ +\cellcolor{green!20}2 & \cellcolor{green!20}Używanie języka matematycznego do tworzenia tekstów matematycznych, \dots & \cellcolor{green!20}1 \\ +\hline +\cellcolor{green!40}3 & \cellcolor{green!40}Wykorzystanie i interpretowanie reprezentacji. & \cellcolor{green!40}- \\ +\cellcolor{green!20}1 & \cellcolor{green!20}Stosowanie obiektów matematycznych i operowanie nimi, \dots & \cellcolor{green!20}1 \\ +\cellcolor{green!20}2 & \cellcolor{green!20}Dobieranie i tworzenie modeli matematycznych, \dots & \cellcolor{green!20}1 \\ +\cellcolor{green!20}3 & \cellcolor{green!20}Tworzenie pomocniczych obiektów matematycznych na podstawie istniejących, \dots & \cellcolor{green!20}1 \\ +\cellcolor{green!20}4 & \cellcolor{green!20}Wskazywanie konieczności lub możliwości modyfikacji modelu matematycznego, \dots & \cellcolor{green!20}1 \\ +\hline +\cellcolor{green!40}4 & \cellcolor{green!40}Rozumowanie i argumentacja. & \cellcolor{green!40}- \\ +\cellcolor{green!20}1 & \cellcolor{green!20}Przeprowadzanie rozumowań, także kilkuetapowych, \dots & \cellcolor{green!20}1 \\ +\cellcolor{green!20}2 & \cellcolor{green!20}Dostrzeganie regularności, podobieństw oraz analogii, \dots & \cellcolor{green!20}1 \\ +\cellcolor{green!20}3 & \cellcolor{green!20}Dobieranie argumentów do uzasadnienia poprawności, \dots & \cellcolor{green!20}1 \\ +\cellcolor{green!20}4 & \cellcolor{green!20}Stosowanie i tworzenie strategii przy rozwiązywaniu zadań, również w sytuacjach nietypowych. & \cellcolor{green!20}1 \\ +\hline +\hline +\end{longtable} + +% -------------------------------------------------------- +% Wymagania szczegółowe +% -------------------------------------------------------- +\begin{longtable}{|p{0.1\textwidth}|p{0.74\textwidth}|p{0.1\textwidth}|} +\caption{Lista wymagań szczegółowych (WS)}\label{tab:ws}\\ +\hline +\textbf{Nr} & \textbf{Opis} & \textbf{Punkty} \\ +\hline +\endfirsthead +\hline +\textbf{Nr} & \textbf{Opis} & \textbf{Punkty} \\ +\hline +\endhead +\cellcolor{gray!20}- & \cellcolor{gray!20}Poziom Nauczania: 1 & \cellcolor{gray!20}- \\ +\cellcolor{red!40}- & \cellcolor{red!40}Wymagania szczegółowe & \cellcolor{red!40}- \\ +\cellcolor{blue!20}1 & \cellcolor{blue!20}Liczby rzeczywiste & \cellcolor{blue!20}- \\ +\cellcolor{yellow!20}- & \cellcolor{yellow!20}Zakres podstawowy & \cellcolor{yellow!20}- \\ +\cellcolor{red!30}1 & \cellcolor{red!30}Wykonuje działania (dodawanie, odejmowanie, mnożenie, dzielenie, potęgowanie, \dots) w zbiorze liczb rzeczywistych. & \cellcolor{red!30}1 \\ +\cellcolor{red!30}2 & \cellcolor{red!30}Przeprowadza proste dowody dotyczące podzielności liczb całkowitych i reszt z dzielenia, \dots & \cellcolor{red!30}1 \\ +\cellcolor{red!20}\hspace{1.0em}a & \cellcolor{red!20}\hspace{1.0em}Dowód podzielności przez 24 iloczynu czterech kolejnych liczb naturalnych. & \cellcolor{red!20}\hspace{1.0em}1 \\ +\cellcolor{red!20}\hspace{1.0em}b & \cellcolor{red!20}\hspace{1.0em}Dowód własności: jeśli liczba przy dzieleniu przez 4 daje resztę 3, to nie jest kwadratem liczby całkowitej. & \cellcolor{red!20}\hspace{1.0em}1 \\ +\cellcolor{red!30}3 & \cellcolor{red!30}Stosuje własności pierwiastków dowolnego stopnia, \dots & \cellcolor{red!30}1 \\ +\cellcolor{red!30}4 & \cellcolor{red!30}Stosuje związek pierwiastkowania z potęgowaniem oraz prawa działań na potęgach i pierwiastkach. & \cellcolor{red!30}1 \\ +\cellcolor{red!30}5 & \cellcolor{red!30}Stosuje monotoniczność potęgowania, \dots & \cellcolor{red!30}1 \\ +\cellcolor{red!30}6 & \cellcolor{red!30}Posługuje się pojęciem przedziału liczbowego, \dots & \cellcolor{red!30}1 \\ +\cellcolor{red!30}7 & \cellcolor{red!30}Stosuje interpretację geometryczną i algebraiczną wartości bezwzględnej, \dots & \cellcolor{red!30}1 \\ +\cellcolor{red!30}8 & \cellcolor{red!30}Wykorzystuje własności potęgowania i pierwiastkowania w sytuacjach praktycznych, \dots & \cellcolor{red!30}1 \\ +\cellcolor{red!30}9 & \cellcolor{red!30}Stosuje związek logarytmowania z potęgowaniem, \dots & \cellcolor{red!30}1 \\ +\cellcolor{yellow!20}- & \cellcolor{yellow!20}Zakres rozszerzony & \cellcolor{yellow!20}- \\ +\cellcolor{red!30}1 & \cellcolor{red!30}Spełnia wymagania określone dla zakresu podstawowego. & \cellcolor{red!30}1 \\ +\cellcolor{red!30}2 & \cellcolor{red!30}Stosuje wzór na zamianę podstawy logarytmu. & \cellcolor{red!30}1 \\ +\hline +\hline +\end{longtable} + +\end{document} + diff --git a/strategia/diagram/main.pdf b/strategia/diagram/main.pdf new file mode 100644 index 0000000000000000000000000000000000000000..553792476d9eb1c6dcecb3048968a259ee42f048 GIT binary patch literal 50262 zcma&NQ;aT5)Tr6EwcGCAZCh{Kwr$(CyLa2RZQHhO+dbcz%zrY;nTuITC95tfSvPCt 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$P^{\max}_{\text{zad}}$\\ \textit{(i ew. minima)}}; +\node[block, below=1.5cm of pktZad] (sumDzial) {Sumowanie\\ punktów w dziale}; +\node[block, below=1.5cm of sumDzial] (minmaxDzial) {Wylicz $P^{\min}_{\text{dział}}$\\ i $P^{\max}_{\text{dział}}$}; +\node[block, below=1.5cm of minmaxDzial] (sumPoziom) {Sumowanie\\ punktów w poziomie}; +\node[block, below=1.5cm of sumPoziom] (minmaxPoziom) {Wylicz $P^{\min}_{\text{poziom}}$\\ i $P^{\max}_{\text{poziom}}$}; +\node[block, left=2.5cm of minmaxPoziom] (ocena) {Przeliczanie\\ punktów na oceny}; +\node[block, below=1.5cm of minmaxPoziom] (koniec) {Ocena\\ końcowa}; + +% --- Połączenia (strzałki) --- +\draw[line] (start) -- (ws_wo); +\draw[line] (ws_wo) -- (zadania); +\draw[line] (zadania) -- (pktZad); +\draw[line] (pktZad) -- (sumDzial); +\draw[line] (sumDzial) -- (minmaxDzial); +\draw[line] (minmaxDzial) -- (sumPoziom); +\draw[line] (sumPoziom) -- (minmaxPoziom); +\draw[line] (minmaxPoziom) -- (koniec); + +% Dodajemy rozgałęzienie do bloku „Przeliczanie ocen”. +\draw[line] (minmaxPoziom) -- ++(-2.5,0) -- (ocena); +\draw[line] (ocena) -- ++(0,-1.5) -- ++(2.5,0) -- (koniec); + +\end{tikzpicture} +\end{document} +

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+\usepackage[T1]{fontenc} +\usepackage[utf8]{inputenc} +\usepackage{amsmath,amssymb} +\usepackage{geometry} +\usepackage{xcolor} +\usepackage{hyperref} +\usepackage[polish]{babel} +\usepackage{forest} + +\geometry{margin=2cm} + +% Konfiguracja środowiska do rysowania drzew (forest): +\forestset{ + mytree/.style={ + for tree={ + draw, + rounded corners, + align=center, + edge={->}, + parent anchor=south, + child anchor=north + } + } +} + +\begin{document} + +% -------------------------------------------------------- +% Wzory wykorzystywane w Szczegółowym Ocenianiu (SO) +% -------------------------------------------------------- +\section*{Wzory wykorzystywane w Szczegółowym Ocenianiu (SO)} + +\begin{itemize} + \item \textbf{(Wzór 1) Maksymalna liczba punktów za zadanie:} + \[ + P_{\mathrm{max}}^{\mathrm{zad}} + \;=\; + \sum_{i=1}^{N_{WS}} + \Bigl( w_{s_i} \times \sum_{j=1}^{N_{WO}^i} w_{o_j} \Bigr), + \] + gdzie \(N_{WS}\) to liczba Wymagań Szczegółowych, \(N_{WO}^i\) to liczba Wymagań Ogólnych + przypisanych do \(i\)-tego WS, a \(w_{s_i}, w_{o_j}\) to wagi poszczególnych wymagań. + + \item \textbf{(Wzór 3) Procent uzyskanych punktów (np. do wyznaczenia oceny):} + \[ + \%\;=\;\frac{P_{\text{zdobyte}}}{P_{\text{max}}} \times 100\%. + \] + + \item \textbf{(Wzór 4) Ocena z danej formy (np. kartkówki):} + \[ + O_{\text{forma}} + \;=\; + \frac{\sum_{k=1}^{N_{\text{zad}}} O_{\text{zad}_k}}{N_{\text{zad}}}, + \] + gdzie \(O_{\text{zad}_k}\) to ocena z \(k\)-tego zadania, a \(N_{\text{zad}}\) to liczba zadań + danej formy. + + \item \textbf{(Wzór 5) Ocena z działu:} + \[ + O_{\text{dział}} + \;=\; + \frac{\sum_{k=1}^{N_{\text{form}}} O_{\text{form}_k}}{N_{\text{form}}}, + \] + czyli średnia ocen z~wszystkich form sprawdzania wiedzy w~danym dziale. + + \item \textbf{(Wzór 6) Ocena z poziomu nauczania (np. semestr/rok):} + \[ + O_{\text{poziom}} + \;=\; + \frac{\sum_{k=1}^{N_{\text{dział}}} O_{\text{dział}_k}}{N_{\text{dział}}}. + \] +\end{itemize} + +\bigskip + +% -------------------------------------------------------- +% 1. Wstęp: Szczegółowe Ocenianie (SO) - idea +% -------------------------------------------------------- +\section*{Wstęp: Szczegółowe Ocenianie (SO)} + +\noindent +\textbf{Idea:} Każde zadanie (egzaminacyjne, kartkowe, sprawdzianowe itp.) +zostało rozbite na \emph{Wymagania Szczegółowe (WS)}. +Każdy \textbf{WS} jest dodatkowo oceniany przez pewne \textbf{Wymagania Ogólne (WO)}, +które sprawdzają takie aspekty jak: +\begin{itemize} + \item \textbf{WO$_1$} -- sprawność rachunkowa, + \item \textbf{WO$_2$} -- wykorzystanie i tworzenie informacji, + \item \textbf{WO$_3$} -- wykorzystanie i interpretowanie reprezentacji, + \item \textbf{WO$_4$} -- rozumowanie i argumentacja. +\end{itemize} + +\noindent +\textbf{Punktacja typu TAK/NIE:} +Dla każdego \textbf{WS--WO} sprawdzamy, czy jest \emph{zrealizowane} +(w~rozwiązaniu widać spełnienie tego wymagania) czy \emph{nie}. +Jeśli \textbf{TAK}, przyznajemy ustaloną liczbę punktów (np.~1). +Jeśli \textbf{NIE}, to 0 punktów. +Następnie zliczamy punkty w zadaniu i porównujemy z maksymalną liczbą punktów dla zadania. + +\bigskip + +% -------------------------------------------------------- +% 2. Zadanie 1 +% -------------------------------------------------------- +\section*{Zadanie 1: Wyrażenia z pierwiastkami i potęgami} + +\noindent +\textbf{Treść zadania:}\\ +Oblicz wartość wyrażenia: +\[ + \sqrt{16} + 2^{-3}. +\] +Uzasadnij krótko swoje kroki (np. dlaczego \(\sqrt{16}=4\), +czemu \(2^{-3}=\tfrac{1}{8}\)), a następnie podaj +\emph{praktyczną interpretację} (np.~co oznacza potęga ujemna +w kontekście zmniejszenia skali pewnych wielkości). + +\subsection*{Wymagania Szczegółowe (WS) i przyporządkowane Wymagania Ogólne (WO)} +\begin{itemize} + \item \textbf{WS$_1$:} Wykonuje działania na liczbach rzeczywistych z wykorzystaniem pierwiastków i potęg.\\ + \textit{(podlega ocenie w zakresie WO: WO$_1$, WO$_4$)} + + \item \textbf{WS$_2$:} Stosuje potęgi i pierwiastki w kontekstach praktycznych.\\ + \textit{(podlega ocenie w zakresie WO: WO$_1$, WO$_2$)} +\end{itemize} + +\subsection*{Drzewo wymagań (Zadanie 1) -- schemat} +\begin{forest} + mytree + [Zadanie 1 + [WS$_1$ + [WO$_1$] + [WO$_4$] + ] + [WS$_2$ + [WO$_1$] + [WO$_2$] + ] + ] +\end{forest} + +\subsection*{Wagi i punktacja maksymalna} +Dla uproszczenia przyjmujemy, że każda para \textbf{WS--WO} ma wagę = 1 pkt. +\[ + \underbrace{\text{WS}_1 \times (\text{WO}_1 + \text{WO}_4)}_{2\,\text{pkt}} + \;+\; + \underbrace{\text{WS}_2 \times (\text{WO}_1 + \text{WO}_2)}_{2\,\text{pkt}} + \;=\; + 4\,\text{pkt}. +\] +Zatem: +\[ + P_{\max}^{(\text{Zadanie 1})} = 4. +\] + +\subsection*{Przykład pełnego rozwiązania i oceniania (Zadanie 1)} + +\begin{enumerate} + \item \(\sqrt{16} = 4\). + \begin{itemize} + \item \textbf{WS$_1$, WO$_1$} (sprawność rachunkowa): \textbf{TAK} = 1 pkt + \item \textbf{WS$_1$, WO$_4$} (rozumowanie, uzasadnienie): np.~krótka argumentacja, że \(16=4^2\). + \textbf{TAK} = 1 pkt + \end{itemize} + + \item \(2^{-3} = \frac{1}{2^3} = \frac{1}{8}\). + \begin{itemize} + \item \textbf{WS$_2$, WO$_1$}: dalsza poprawność rachunkowa (0,125). \textbf{TAK} = 1 pkt + \item \textbf{WS$_2$, WO$_2$}: podanie \emph{interpretacji praktycznej} (np.~zmniejszenie 8-krotne). + \textbf{TAK} = 1 pkt + \end{itemize} + + \item Ostateczny wynik: \(4 + \frac{1}{8} = 4{,}125\). (Sama suma nie wnosi kolejnego punktu, + bo i tak weryfikację \emph{rachunkową} już oceniono przy \textbf{WO$_1$}.) +\end{enumerate} + +\noindent +\textbf{Suma punktów:} \(1 + 1 + 1 + 1 = 4 \,(\text{max} =4)\).\\ +\textbf{Procentowo:} \(\frac{4}{4}\times 100\% = 100\%\). + +\bigskip + +\subsection*{Przykład błędu (rozwiązanie częściowo poprawne, ale bez punktów za błędny element)} + +\begin{itemize} + \item \(\sqrt{16} = 4\) -- poprawnie.\\ + \textbf{(WS$_1$, WO$_1$)}: TAK = 1 punkt. + + \item Brak uzasadnienia (dlaczego \(\sqrt{16} = 4\)), + więc \textbf{(WS$_1$, WO$_4$)}: NIE = 0 punktów. + + \item \(2^{-3}\) błędnie podane jako \(-8\).\\ + \textbf{(WS$_2$, WO$_1$)}: NIE = 0 punktów (brak poprawnego rachunku). + + \item Brak jakiejkolwiek interpretacji praktycznej (potęgi ujemne).\\ + \textbf{(WS$_2$, WO$_2$)}: NIE = 0 punktów. +\end{itemize} + +\noindent +\textbf{Suma punktów:} \(1 + 0 + 0 + 0 = 1\).\\ +\textbf{Punktacja maksymalna w~Zadaniu 1:} 4.\\ +\[ + \text{Procent} \;=\; \frac{1}{4} \times 100\% \;=\; 25\%. +\] + + + +% -------------------------------------------------------- +% 3. Zadanie 2 +% -------------------------------------------------------- +\section*{Zadanie 2: Trójkąt prostokątny i funkcje trygonometryczne} + +\noindent +\textbf{Treść zadania:}\\ +Mamy trójkąt prostokątny o przyprostokątnych 3\,cm i 4\,cm. +\begin{itemize} + \item[(a)] Oblicz długość przeciwprostokątnej (Twierdzenie Pitagorasa). + \item[(b)] Wyznacz \(\sin\) oraz \(\cos\) kątów ostrych tego trójkąta. + \item[(c)] Uzasadnij krótko tożsamość \(\sin^2\alpha + \cos^2\alpha = 1\). +\end{itemize} + +\subsection*{Wymagania Szczegółowe (WS) i przyporządkowane Wymagania Ogólne (WO)} +\begin{itemize} + \item \textbf{WS$_3$:} Stosuje funkcje trygonometryczne w trójkątach prostokątnych + (obliczanie boków, kątów itp.).\\ + \textit{(podlega ocenie w zakresie WO: WO$_1$, WO$_3$, WO$_4$)} + + \item \textbf{WS$_4$:} Rozwiązuje zadania z Twierdzeniem Pitagorasa.\\ + \textit{(podlega ocenie w zakresie WO: WO$_1$, WO$_2$, WO$_4$)} +\end{itemize} + +\subsection*{Drzewo wymagań (Zadanie 2) -- schemat} +\begin{forest} + mytree + [Zadanie 2 + [WS$_3$ + [WO$_1$] + [WO$_3$] + [WO$_4$] + ] + [WS$_4$ + [WO$_1$] + [WO$_2$] + [WO$_4$] + ] + ] +\end{forest} + +\subsection*{Wagi i punktacja maksymalna} +Każda para \textbf{WS--WO} = 1 pkt: +\[ + \underbrace{(\text{WS}_3 \times 3\,\text{WO})}_{3\,\text{pkt}} + \;+\; + \underbrace{(\text{WS}_4 \times 3\,\text{WO})}_{3\,\text{pkt}} + \;=\; + 6\,\text{pkt}. +\] +\[ + P_{\max}^{(\text{Zadanie 2})} = 6. +\] + +\subsection*{Przykład pełnego rozwiązania i oceniania (Zadanie 2)} + +\begin{enumerate} + \item \textbf{Twierdzenie Pitagorasa (WS$_4$):}\\ + \(c = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5.\) + \begin{itemize} + \item \textbf{WO$_1$} (poprawny rachunek): TAK = 1 pkt + \item \textbf{WO$_2$} (wykorzystanie info, np.~rysunek lub tabela danych): + \emph{jeśli} uczeń załączy krótki schemat lub opis. TAK = 1 pkt + \item \textbf{WO$_4$} (rozumowanie): np.~wyjaśnienie, dlaczego Pitagoras tu działa. TAK = 1 pkt + \end{itemize} + + \item \textbf{Funkcje trygonometryczne (WS$_3$):}\\ + \(\sin\alpha = \tfrac{3}{5}, \;\cos\alpha = \tfrac{4}{5};\;\) + \(\sin\beta = \tfrac{4}{5}, \;\cos\beta = \tfrac{3}{5}\). + \begin{itemize} + \item \textbf{WO$_1$} -- dalsza poprawność rachunkowa: TAK = 1 pkt + \item \textbf{WO$_3$} -- interpretacja kątów, np.~z rysunku: TAK = 1 pkt + \item \textbf{WO$_4$} -- argumentacja: dlaczego akurat \(\frac{3}{5}\) i \(\frac{4}{5}\). TAK = 1 pkt + \end{itemize} + + \item \textbf{Tożsamość} \(\sin^2\alpha + \cos^2\alpha = 1\).\\ + (Zwykle ocenimy w ramach \textbf{WS$_3$, WO$_4$} -- jeżeli uczeń pokaże krótkie uzasadnienie + z interpretacji geometrycznej. Może to też być zaliczone w poprzednim punkcie.) +\end{enumerate} + +\noindent +\textbf{Maksimum:} \(6/6\) pkt \(\to 100\%\). + +\subsection*{Przykład częściowej realizacji: szczegółowa punktacja (Zadanie 2)} + +\noindent +\textbf{Zadanie 2:} (maks. 6 pkt) + +\bigskip +\textbf{WS\textsubscript{4}: Twierdzenie Pitagorasa (3 pkt)} + +\begin{itemize} + \item \textbf{WO\textsubscript{1}} (poprawny rachunek): + \begin{itemize} + \item Uczeń oblicza przeciwprostokątną: \(\sqrt{3^2 + 4^2} = 5\). + \item \(\Rightarrow\) TAK = 1 pkt + \end{itemize} + + \item \textbf{WO\textsubscript{2}} (wykorzystanie informacji / rysunek): + \begin{itemize} + \item Dodany jest prosty schemat trójkąta z zaznaczeniem boków 3 i 4 cm. + \item \(\Rightarrow\) TAK = 1 pkt + \end{itemize} + + \item \textbf{WO\textsubscript{4}} (rozumowanie / argumentacja): + \begin{itemize} + \item Uczeń wyjaśnia, dlaczego używamy Twierdzenia Pitagorasa w trójkącie prostokątnym. + \item \(\Rightarrow\) TAK = 1 pkt + \end{itemize} +\end{itemize} + +\noindent +Suma za WS\textsubscript{4} = 3/3 pkt. + +\bigskip +\textbf{WS\textsubscript{3}: Funkcje trygonometryczne w trójkącie (3 pkt)} + +\begin{itemize} + \item \textbf{WO\textsubscript{1}} (rachunek): + \begin{itemize} + \item Podano \(\sin \alpha = \frac{3}{5}\), \(\cos \alpha = \frac{4}{5}\) – rachunkowo poprawnie. + \item \(\Rightarrow\) TAK = 1 pkt + \end{itemize} + + \item \textbf{WO\textsubscript{3}} (interpretowanie reprezentacji): + \begin{itemize} + \item Uczeń wskazuje, że kąt \(\alpha\) leży przy przyprostokątnej długości 3 (np. z krótkim opisem). + \item \(\Rightarrow\) TAK = 1 pkt + \end{itemize} + + \item \textbf{WO\textsubscript{4}} (rozumowanie i argumentacja): + \begin{itemize} + \item Brak uzasadnienia wzorów lub tożsamości \(\sin^2 \alpha + \cos^2 \alpha = 1\). + \item \(\Rightarrow\) NIE = 0 pkt + \end{itemize} +\end{itemize} + +\noindent +Suma za WS\textsubscript{3} = 2/3 pkt. + +\bigskip +\textbf{Łączna liczba punktów (Zad. 2)}: \(3 + 2 = 5\) / 6. + +\[ + \text{Procent} = \frac{5}{6} \times 100\% \approx 83{,}3\%. +\] + +\noindent +W przykładowej skali progowej (\(80\%-94\%\)) oznacza to ocenę: 5 (bdb). + + +\bigskip + +% -------------------------------------------------------- +% 4. Skala ocen i przeliczanie punktów +% -------------------------------------------------------- +\section*{Skala ocen i przeliczanie punktów na ocenę} + +\subsection*{Krok 1: Suma punktów zadań i obliczenie \%} +\begin{itemize} + \item \(\displaystyle P_{\max}^{(\text{Zadanie 1})} = 4\) + \item \(\displaystyle P_{\max}^{(\text{Zadanie 2})} = 6\) + \item \textbf{Suma maksymalna} w tej formie sprawdzania wiedzy (np.~kartkówce): + \[ + P_{\max}^{(\text{forma})} = 4 + 6 = 10. + \] + + \item Po sprawdzeniu obu zadań, zliczamy \textbf{punkty uzyskane} + (np.~\(P_{\text{zdobyte}} = 8\)). + + \item \textbf{Procent}: + \[ + \%\;=\;\frac{P_{\text{zdobyte}}}{P_{\max}^{(\text{forma})}} \times 100\%. + \] + Przykład: + \(\frac{8}{10} \times 100\% = 80\%\). +\end{itemize} + +\subsection*{Krok 2: Mapowanie procentu na ocenę szkolną (1--6)} +Proponowana \textbf{skala procentowa} (dostosowana do wewnątrzszkolnego oceniania): +\[ +\begin{aligned} + &0\%-29\% &&\;\;\to 1\ (\text{niedostateczny}),\\ + &30\%-49\% &&\;\;\to 2\ (\text{dopuszczający}),\\ + &50\%-64\% &&\;\;\to 3\ (\text{dostateczny}),\\ + &65\%-79\% &&\;\;\to 4\ (\text{dobry}),\\ + &80\%-94\% &&\;\;\to 5\ (\text{bardzo dobry}),\\ + &\ge 95\% &&\;\;\to 6\ (\text{celujący}). +\end{aligned} +\] +\emph{Przykład:} jeśli ktoś uzyskał 80\%, to w tej skali otrzymuje ocenę 5 (bdb). + +\subsection*{Krok 3: Wpis do dziennika (skala 0--10 pkt z kartkówki)} +Czasem nauczyciel wewnętrznie (w dzienniku) woli notować \emph{liczbę punktów 0--10} +zamiast oceny w skali 1--6. +W takiej sytuacji: +\[ + \text{punkty\_0-10} + \;=\; + \bigl\lfloor\, (\% / 100) \times 10 \bigr\rceil \quad + \text{(np. zaokrąglenie do jednego miejsca po przecinku lub do całości).} +\] +\emph{Przykład:} 80\% \(\to\) \((0.80)\times 10=8\) punktów w dzienniku. + +\bigskip + +% -------------------------------------------------------- +% 5. Podsumowanie +% -------------------------------------------------------- +\section*{Podsumowanie: kroki oceniania w praktyce} + +\begin{enumerate} + \item \textbf{Weryfikacja WS--WO} w każdym zadaniu: + \begin{itemize} + \item Sprawdzasz, czy \textbf{WS$_i$, WO$_j$} jest spełnione (TAK = 1 pkt, NIE = 0 pkt). + \item Sumujesz wszystkie przyznane punkty. + \end{itemize} + + \item \textbf{Punkty za zadanie} = liczba zrealizowanych \textbf{WS--WO} / maksymalna możliwa liczba. + \begin{itemize} + \item Np. w Zadaniu~1 \(\max = 4\), w Zadaniu~2 \(\max = 6\). + \end{itemize} + + \item \textbf{Punkty łączne (forma)} = \(\sum\) punktów zadań. + \(\quad P_{\max}^{(\text{forma})} = \sum\) (maksymalna punktacja zadań). + + \item \textbf{Wyznaczenie procentu}: + \[ + \%\;=\;\frac{P_{\text{zdobyte}}}{P_{\max}^{(\text{forma})}} \times 100\%. + \] + + \item \textbf{Określenie oceny (1--6)} na podstawie progu procentowego (tablica powyżej). + + \item \textbf{(Opcjonalnie) Przeliczenie na skalę 0--10} i wpis do dziennika. + \[ + \text{punkty\_0-10} + \;=\; + \bigl\lfloor\, (\% / 100)\times 10 \bigr\rceil. + \] +\end{enumerate} + +\bigskip + +\noindent +\textbf{Przykład końcowy:}\\ +Uczeń w Zadaniu~1 zdobył 3/4 pkt, w Zadaniu~2 zdobył 5/6 pkt, +czyli łącznie 8/10 (co daje \(80\%\)). +Skala procentowa: \(80\%\to5\) (bardzo dobry). +W dzienniku nauczyciel może wpisać \textbf{8/10}~pkt (lub 5 bdb). + +\bigskip + + +\end{document} diff --git a/praca-pisemna/schema/main.pdf b/praca-pisemna/schema/main.pdf new file mode 100644 index 0000000000000000000000000000000000000000..a164dfd91aecd41bdd132ddd26054ead140f6cbf GIT binary patch literal 190859 zcma%hQ?w|-vgEdH+qP}nw$8R~+qR9fZQHhOTXWvbystZJ&Fin~pYH6a?1;$9BvlX* zqh+LHg(96>8eW59Vj^H5ursoP;^Bd!moc?9ceWs4VrFL|_}>>4y_lu7v#BEiy_mJ3 zv#E%wv7L!26dxayle43#p$(M##YkN|Y1aY_laB`^fqVBfOg^CMor-ft6+|l(JK6=qAe-w>j z^pVv4(ScvYg2*Y+c(p|4kx{BQ&Tj{0=`abZPMqDT+p*QP?bKVM72D?UP-HL~ za&8Ph8Zzlyba7hJtq*?$-qfNPExMJ0Y 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