Explore how a constant function assigns the same output to every input. Connect the equation of a constant function to its graph, domain, and range.

[i]Answer these open ended questions on your own or with others to form deeper math connections.[/i]

Putting It All Together

Domain and Range of Constant Functions

Tüm Topluluk Kaynaklarını görün

Explore the wide range of resources created by the GeoGebra Content Team to support your students' learning needs

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Küresel GeoGebra topluluğumuz tarafından titizlikle hazırlanmış bir milyondan fazla matematik ve fen etkinliği, alıştırma ve dersten oluşan geniş bir koleksiyonu keşfedin. Kendinizi sizi bekleyen sınırsız olanaklara bırakın.

Dünya çapında birbirine bağlı kullanıcı ağını gösteren bir çizim

Topluluk Kaynakları

İlişkili Konular

Check out some fun and interactive examples handpicked by our staff

Sekundarstufe 1

High School

Middle School

Upper Elementary

Derse Katıl

3B'de fonksiyonları grafikleyin ve hesaplamalar yapın

Fonksiyonları inceleyin, denklemleri çözün, geometrik şekilleri inşa edin

Geometrik kavram ve yapıları dinamik bir ortamda inceleyin

Denklemler ve fonksiyonları, grafikler ve çizimler ile görselleştirin

Etkileşimli grafikler, slaytlar, resimler ve daha fazlasını içeren çevrim içi not alma uygulamamızı inceleyin

Kesirler, istatistik ve üstel fonksiyonlar ile hesaplamalar yapın

Hesap Makineleri

Denklemleri çözmek ve örüntüleri ifade etmek için semboller kullanma

Toplama, çıkarma ve bölme gibi temel işlemlerin uygulamalarını yapma

Dizi ve serileri inceleme, diferansiyel denklemleri çözme

Matematikte girdileri belirli çıktılara gönderen ilişkiler

Matematikte şekilleri, boyutları ve uzamsal ilişkileri inceleme

Uzunluk, ağırlık ve hacim gibi özellikleri ölçme ve karşılaştırma

Sayıları, ilişkilerini ve sayısal akıl yürütmeyi anlama

Toplama, çıkarma, bölme gibi matematiksel işlemleri gerçekleştirme

Olay ve çıktıların belirsizliğini ve olasılığını analiz etme

Açılar, üçgenler ve trigonometrik fonksiyon ve oranları çalışma

GeoGebra'yı kullanmaya bugün başlayın

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Describe three-dimensional figures generated by rotations of plane figures in space.

3-Dimensional Shapes from 2-Dimensional Shapes

Ablesen von Daten aus Kreuztabellen und Vierfeldertafeln und Interpretieren dieser Daten.

Ablesen und Interpretieren von Daten aus Kreuztabellen und Vierfeldertafeln

Ablesen von Daten aus Tabellen und Diagrammen und Interpretieren dieser Daten.

Ablesen und Interpretieren von Daten aus Tabellen und Diagrammen

Ablesen von Koordinaten von Punkten

Ermitteln von einfachen Quadratwurzeln im Kopf; näherungsweises Berechnen und Abschätzen von Quadratwurzeln.

Abschätzen von Quadratwurzeln durch systematisches Probieren

Abschätzen von Rechenergebnissen und Ermitteln von Schranken.

Abschätzen von Rechenergebnissen

Evaluate absolute value expressions to solve number and word problems, including finding horizontal and vertical distances between points and lines.

Mutlak Değerli İfadeler

Determine the absolute value of a number with and without models in number and word problems.

Tam Sayıların Mutlak Değeri

Ermitteln von Abständen zwischen zwei Punkten, zwischen Punkt und Gerade und zwischen zwei parallelen Geraden. 

Abstände zwischen Punkten und Geraden

Addieren von Bruchzahlen

Beschreiben und Anwenden des Additionsalgorithmus für natürliche Zahlen.

Addieren von natürlichen Zahlen

Addieren von nichtnegativen Dezimalzahlen.

Addieren von nichtnegativen Dezimalzahlen

Use addition and subtraction to find unknown measures of non-overlapping angles.

Açıları Toplama ve Çıkarma

Add and subtract decimals using models and pictures to explain the process and record the results.

Ondalık Sayılarla Toplama ve Çıkarma

Add and subtract fractions and mixed numbers with like denominators (without regrouping) in number and word problems.

Paydaları Eşit Olan Kesirlerin veya Tam Sayılı Kesirlerin Toplanması ve Çıkarılması

Add and subtract fractions and mixed numbers with unlike denominators in number and word problems.

Paydaları Farklı Kesirler ve Tam Sayılı Kesirlerle Toplama ve Çıkarma İşlemleri

Add and subtract fractions and mixed numbers using models and pictures to explain the process and record the results in number and word problems.

Kesirler ve Tam Sayılı Kesirlerle Toplama ve Çıkarma İşlemleri

Model or compute with integers using addition or subtraction in number and word problems.

Tam Sayılarla Toplama ve Çıkarma

Polinomlarda Toplama, Çıkarma ve Çarpma

Identify additive inverses (opposites) and multiplicative inverses (reciprocals) and use them to solve number and word problems.

Toplamsal ve Çarpımsal Ters

Rewrite or simplify algebraic expressions including the use of the commutative, associative, and distributive properties, and inverses and identities in number and word problems.

Cebirsel Özellikler

Verbinden von Vorstellungen mit Maßeinheiten für Flächeninhalte; Schätzen von Flächeninhalten anhand von Stützpunktvorstellungen (Vergleich mit Größen aus dem Alltag).

Alltagsvorstellungen von Flächeninhalten

Verbinden von Vorstellungen mit Maßeinheiten für Längen; Schätzen von Längen anhand von Stützpunktvorstellungen (Vergleich mit Größen aus dem Alltag).

Alltagsvorstellungen von Längen

Verbinden von Vorstellungen mit Maßeinheiten für Massen; Schätzen von Massen anhand von Stützpunktvorstellungen (Vergleich mit Größen aus dem Alltag).

Alltagsvorstellungen von Massen

Verbinden von Vorstellungen mit Maßeinheiten für Rauminhalte; Schätzen von Rauminhalten anhand von Stützpunktvorstellungen (Vergleich mit Größen aus dem Alltag).

Alltagsvorstellungen von Rauminhalten

Use a variety of triangles, quadrilaterals, and other polygons to draw conclusions about the sum of the measures of the interior angles.

Üçgenlerin, Dörtgenlerin ve Çokgenlerin İç Açıları Toplam Özellikleri

Identify the congruent and supplementary relationships of the angles formed by cutting parallel lines by a transversal.

Paralel Doğruların Oluşturduğu Açılar

Identify and label the vertex, rays, and interior and exterior of an angle. Use appropriate naming conventions to identify angles.

Açılar

Anwenden des pythagoräischen Lehrsatzes für Berechnungen in ebenen Figuren; Aufstellen von Formeln.

Anwenden des Satzes des Pythagoras in ebenen Figuren

Berechnen einer Größe aus einer (einfachen) Formel, wenn alle anderen Größen gegeben sind.

Anwenden von Formeln

Lösen von Aufgaben mit direkten und indirekten Proportionalitäten; Beschreiben, Vergleichen und Begründen von Lösungswegen sowie kritisches Betrachten von Ergebnissen und deren Genauigkeit.  

Anwenden von Proportionalitäten in Sachsituationen

Berechnen aller Lösungen einer linearen Gleichung; Darstellen der Lösungen im Koordinatensystem. 

Anzahl der Lösungen von linearen Gleichungen

Use theorems about congruent chords and arcs and the relationships of a radius of a circle to a tangent to solve problems.

Çemberlerde Yay, Kiriş ve Teğet Özellikleri

Estimate and calculate areas with scale drawings and maps.

Ölçekli Çizimlerde ve Haritalarda Alan

Use various methods, including trigonometric relationships or Heron's Formula, to find the area of a triangle in number and word problems.

Area of a Triangle Using Trigonometry

Determine the area of rectangles, squares, and composite figures using nonstandard units, grids, and standard units in number and word problems.

Dikdörtgenlerin, Karelerin ve Birleşik Şekillerin Alanı

Use grids to develop the relationship between the total numbers of square units in a rectangle and the length and width of the rectangle (l x w); find area using the formula in number and word problems.

Izgaralı Dikdörtgenlerin Alanı

Recognize the effect of scale factors or ratios on areas and volumes of similar geometric figures; use formulas to solve number and word problems.

Benzer Geometrik Şekillerin Alan ve Hacimleri

Recognize and extend arithmetic sequences and geometric sequences. Identify the common difference or common ratio.

Aritmetik ve Geometrik Diziler

Kennen und Unterscheiden von verschiedenen Arten von Brüchen (Stammbruch, gemischte Zahl, uneigentlicher Bruch, unechter und echter Bruch).

Arten von Brüchen

Beschreiben und Anwenden der Eigenschaften von spitzwinkligen, rechtwinkligen, stumpfwinkligen, gleichschenkligen und gleichseitigen Dreiecken.

Arten von Dreiecken

Einteilen der Winkel ihrer Größe nach (spitzer, rechter, stumpfer, gestreckter, erhabener und voller Winkel); Erklären des Gradmaßes für Winkel.

Arten von Winkeln

Aufstellen von Gleichungen zu vorgegebenen Texten und Formulieren von Texten zu vorgegebenen Gleichungen; Anwenden von linearen Gleichungen in Sachsituationen. 

Aufstellen und interpretieren von Gleichungen

Aufstellen und Interpretieren von Termen in unterschiedlichen Kontexten.

Aufstellen und Interpretieren von Termen

Organize, display, and interpret information in bar graphs.

Sütun Grafikleri

Berechnen von Quadrat- und Kubikwurzeln mittels Technologieeinsatz.

Berechnen von Quadrat- und Kubikwurzeln

Berechnen von relativen Häufigkeiten und deren Angabe in Bruch-, Dezimal- und Prozentdarstellung.

Berechnen von relativen Häufigkeiten

Erklären und Anwenden des Betrags einer Zahl; Deuten des Betrags auf der Zahlengeraden als Abstand vom Nullpunkt.

Betrag einer Zahl

Nachvollziehen eines Beweises des pythagoräischen Lehrsatzes.

Beweisen des Satzes des Pythagoras

Bilden und Benennen von Winkeln

Herleiten, grafisch Veranschaulichen und Anwenden der drei binomischen Formeln.

Binomische Formeln

Organize, display, and interpret information in box-and-whisker plots.

Kutu ve Bıyık Grafikleri

Deuten von Brüchen als Anteile eines Ganzen bzw. als Anteile von mehreren Ganzen; Ergänzen von Brüche auf Ganze.

Brüche als Anteile von Ganzen

Estimate and calculate using numbers expressed in scientific notation.

Bilimsel Gösterim Kullanarak Hesaplama

Indicate the probability of a chance event with or without models as certain, impossible, more likely, less likely, or neither likely nor unlikely using benchmark probabilities of 0, 1/2, and 1.

Kesin, Olası, Olasılıksız, İmkansız Olaylar

Complete the square to identify characteristics of relations or functions and verify graphically.

Fonksiyonların ve Grafiklerinin Özellikleri

Identify and use appropriate scales and intervals in graphs and data displays.

Grafikler İçin Ölçek ve Aralıkların Seçilmesi

Organize, display, and interpret information in circle graphs using ratios and percents.

Daire Grafikleri

Identify combinations of fractions that make one whole.

Kesir Kombinasyonları

Compare data and distributions of data, numerical and contextual, to draw conclusions, considering the measures of center and measures of variability.

Veri Dağılımlarının Karşılaştırılması

Compare decimals (tenths and hundredths) with and without models.

Ondalık Sayıları Karşılaştırma

Compare and order fractions using common numerators or denominators.

Kesirleri Karşılaştırma

Compare and order integers with and without models.

Tam Sayıları Karşılaştırma

Compare and order numbers less than 10,000.

10.000'den Küçük Sayıları Karşılaştırma

Write a ratio or rate to compare two quantities

Nicelikleri Oranlarla Karşılaştırma

Compare and order rational numbers with and without models.

Rasyonel Sayıları Karşılaştırma

Bir Olayın Tümleyeni

Define and identify complementary and supplementary angles.

Tümler ve Bütünler Açılar

Solve quadratic equations by completing the square.

İkinci Dereceden Denklemleri Çözmek İçin Kareye Tamamlama

Tam Sayılı Kesirler

Find the inverse of a function or relation. Verify that two functions are inverses using their graphs or composition of functions.

Bileşke ve Ters Fonksiyonlar

Model the concept of percent and relate to the value in decimal or fractional form.

Yüzdeler ile Kesirler veya Ondalık Sayılar Arasında Dönüşüm

Locate points in all quadrants of the coordinate plane using ordered pairs in number and word problems.

Koordinat Düzlemi ve Sıralı İkililer

Locate a point in Quadrant I of a coordinate grid given an ordered pair; name the ordered pair for a point in Quadrant I of a coordinate grid.

Koordinat Düzlemi

Use models to make predictions and interpret the correlation coefficient of the model; distinguish between correlation and causation.

Korelasyon Katsayısı, Korelasyon ve Nedensellik - Farklılıklar, Tasarım ve Örnekler

Use proportions to express relationships between corresponding parts of similar figures.

Benzer Şekillerin Karşılıklı Parçaları

Estimate and compute the cost of items greater than $1.00; make change.

Ürünlerin Maliyeti ve Para Üstü Verme

Determine the sample space for an event using counting strategies (include tree diagrams, permutations, combinations, and the fundamental counting principle).

Örnek Uzaylar İçin Sayma Stratejileri

Describe cross-sectional views of three-dimensional figures.

Katı Cisimlerin Kesitleri

Use geometric models and equations to investigate the meaning of the cube of a number and the relationship to its cube root.

Küp ve Küp Kökler

Derive a quadratic or exponential function that models a set of data (curve of best fit) using calculators. Use the model to make predictions.

En İyi Uyum Eğrileri

Darstellen von Daten in Kreuztabellen und Vierfeldertafeln. 

Darstellen von Daten in Kreuztabellen und Vierfeldertafeln

Darstellen von Daten in Tabellen und Diagrammen (Säulen- und Balkendiagramme, Piktogramme, Liniendiagramme).

Darstellen von Daten in Tabellen und Diagrammen

Grafisches Darstellen und Ablesen von natürlichen Zahlen am Zahlenstrahl.

Darstellen von natürlichen Zahlen

Wechseln zwischen der Funktionsgleichung und dem Funktionsgraph, insbesondere mithilfe von Steigungsdreiecken unter Verwendung der Parameter k und d; Interpretieren des Funktionsgraphen einer linearen Funktion als Gerade. 

Darstellungsformen linearer Funktionen

Nutzen von verschiedenen Darstellungsformen reeller Funktionen (Funktionsgleichung, Wertetabelle, Funktionsgraph); Wechseln zwischen den Darstellungsformen.

Darstellungsformen von Funktionen

Describe data using or selecting the appropriate measure of central tendency; choose a measure of central tendency based on the shape of the data distribution.

Veri, Veri Dağılımı ve Merkezi Eğilim

Read, write, and compare numbers with decimal place values to the thousandths place or numbers greater than one million.

Bir Milyondan Büyük Ondalık Sayılar

Determine the measure of an angle in degree mode or in radian mode.

Açıların Derece ve Radyan Cinsinden Ölçüsü

Deuten von Brüchen als Quotienten

Deuten von Brüchen als relative Anteile und relative Häufigkeiten.

Deuten von Brüchen als relative Anteile und Häufigkeiten

Deuten des Potenzierens mit einem positiven ganzzahligen Exponenten als wiederholtes Multiplizieren derselben Zahl; Interpretieren und Anwenden der Potenzdarstellung mit positiven ganzzahligen Exponenten.

Deuten von Potenzen

Use dimensional analysis to rename quantities or rates

Boyut Analizi

Write equations to represent direct variation and use direct variation to solve number and word problems.

Doğru Orantı

Use the discriminant to determine the number and nature of the roots of a quadratic equation.

İkinci Dereceden Bir Denklemin Diskriminantı ve Kökleri

Use the distance formula to find the distance between two points. Use the midpoint formula to find the coordinates of the midpoint of a segment.

Uzaklık Formülü ve Orta Nokta Formülü

Calculate distances from scale drawings and maps.

Ölçekli Çizimlerde ve Haritalarda Uzaklık

Use the distributive property to represent and simplify numerical expressions.

Dağılma Özelliği

Dividieren von Brüchen; Deutung des Dividierens als Multiplizieren mit dem Kehrwert des Divisors.

Dividieren von Bruchzahlen

Beschreiben und Anwenden des Divisionsalgorithmus für natürliche Zahlen.

Dividieren von natürlichen Zahlen

Represent division of fractions and mixed numbers with and without models and pictures in number and word problems; describe the inverse relationship between multiplication and division.

Kesirler ve Tam Sayılı Kesirlerle Bölme İşlemi

Divide two fractions or a fraction and a whole number in number or word problems.

Kesirlerle Bölme İşlemi

Represent division of a unit fraction by a whole number or a whole number by a unit fraction using models to explain the process in number and word problems.

Birim Kesirleri Bölme

Model division in a variety of ways including sharing equally, repeated subtraction, rectangular arrays, and the relationship with multiplication.

Bölme Modelleri

Write and graph special functions (step, constant, and piecewise) and identify the domain and range.

Özel Fonksiyonların Tanım ve Değer Kümeleri

Draw and measure angles using a protractor. Understand that a circle measures 360 degrees.

Açı Ölçer Kullanarak Açı Çizme ve Ölçme

Durchführen der Primfaktorenzerlegung

Describe the effect of operations on size and order of numbers.

İşlemlerin Sayılar Üzerindeki Etkisi

Identify outliers and determine their effect on the mean, median, and range of a set of data.

Aykırı Değerlerin Veri Kümelerinin Ortalaması, Ortancası ve Açıklığı Üzerindeki Etkisi

Determine the effects of changes in slope and/or intercepts on graphs and equations of lines.

Doğruların Eğim ve Kesen Noktalarındaki Değişikliklerin Etkileri

Beschreiben der Eigenschaften linearer Funktionen f mit f(x) = k ∙ x + d.

Eigenschaften linearer Funktionen

Beschreiben und Anwenden der Eigenschaften von besonderen Vierecken (Rechteck, Quadrat, Parallelogramm, Rhombus/ Raute, Drachenviereck/ Deltoid, Trapez). 

Eigenschaften von besonderen Vierecken

Beschreiben von grundlegenden Eigenschaften von Quadern mithilfe geeigneter geometrischer Begriffe (Ecken, Kanten, Flächen, parallel, normal). 

Eigenschaften von Quadern

Beschreiben von grundlegenden Eigenschaften von Punkten, Strecken, Strahlen und Geraden.

Eingeschaften von Strecke, Strahl, Gerade

Ermitteln von Laplace-Wahrscheinlichkeiten bei einstufigen Zufallsexperimenten; Interpretieren dieser Wahrscheinlichkeiten als Vorhersagewerte für relative Häufigkeiten.

Einstufige Zufallsexperimente

Einzeichnen von Punkten mit gegebenen Koordinaten auf den Achsen und in allen vier Quadranten des Koordinatensystems.

Einzeichnen von Punkten im Koordinatensystem

Geçen Süre

Write the equation of a line parallel or perpendicular to a given line through a given point.

Bir Doğruya Paralel veya Dik Olan Doğrunun Denklemi

Write an equation to describe the algebraic relationship between two defined variables in number and word problems, including recognizing which variable is dependent.

İki Değişkenli Denklemler

Solve equations involving powers and roots by using inverse relationships.

Üsler ve Kökler İçeren Denklemler

Use the definition of rational numbers to convert decimals and fractions to equivalent forms.

Ondalık Sayıların ve Kesirlerin Eşdeğer Biçimleri

Convert fractions and terminating decimals to the thousandths place to equivalent forms without models; explain the equivalence.

Denk Kesirler ve Ondalık Sayılar

Use models to write equivalent fractions, including using composition or decomposition or showing relationships among halves, fourths, and eighths, and thirds and sixths.

Denk Kesir Modelleri

Write equivalent fractions with smaller or larger denominators.

Denk Kesirler

Use reasoning with equivalent ratios to solve number and word problems.

Denk Oranlar

Erkennen von direkten und indirekten Proportionalitäten in Sachsituationen; Begründen oder Widerlegen von Proportionalitäten.

Erkennen von Proportionalitäten in Sachsituationen

Ermitteln von absoluten Häufigkeiten

Determine precision unit, accuracy, and greatest possible error of a measuring tool. Apply significant digits in meaningful contexts.

Bir Ölçüm Aracı Hatası

Erweitern und Kürzen von Brüche (auch mithilfe von Visualisierungen).

Erweitern und Kürzen von Brüchen

Erklären, dass durch die Erweiterung der rationalen Zahlen zu den reellen Zahlen die Zahlengerade lückenlos ausgefüllt wird.

Erweiterung der rationalen zu den reellen Zahlen

Estimate and compute sums and differences with decimals.

Ondalık Sayılarla Toplama ve Çıkarma İşlemlerinde Tahmin Yapma

Estimate the measure of an object in one system given the measure of that object in another system.

Ölçümleri Tahmin Etme

Estimate, measure and compare capacity using appropriate tools and units in number and word problems

Kapasite Tahmini ve Ölçümü

Estimate, measure and compare length using appropriate tools and units in number and word problems

Uzunlukları Tahmin Etme ve Ölçme

Estimate, measure and compare weight using appropriate tools and units in number and word problems

Ağırlıkları Tahmin Etme ve Ölçme

Estimate and compute products of whole numbers with multi-digit factors.

Tam Sayıların Çarpımlarını Tahmin Etme

Estimate products and quotients of decimals or of mixed numbers.

Ondalık Sayıların ve Tam Sayılı Kesirlerin Çarpım ve Bölümlerini Tahmin Etme

Apply appropriate types of estimation for number and word problems that include estimating products and quotients.

Çarpımları ve Bölümleri Tahmin Etme

Estimate and solve division problems with multi-digit divisors; explain solution.

Tam Sayılarda Bölüm Tahmini

Estimate the square root of a number between two consecutive integers with and without models. Use a calculator to estimate the square root of a number.

Kareköklü İfadelerin En Yakın Tamsayı Değerinin Tahmin Edilmesi

Estimate sums and differences with fractions and mixed numbers.

Kesirlerin ve Tamsayılı Kesirlerin Toplamlarını ve Farklarını Tahmin Etme

Apply appropriate type of estimation for sums and differences.

Toplamları ve Farkları Tahmin Etme

Evaluate algebraic expressions in number and word problems.

Cebirsel İfadelerin Değerlendirilmesi

Solve exponential equations by rewriting expressions with like bases.

Üstel Denklemler

Use exponential notation and repeated multiplication to describe and simplify exponential expressions.

Üslü İfadeler

Write the equation of and graph exponential equations or functions, including f(x) = ab^x and f(x) = a(1+r)^x, in number and word problems; identify and interpret critical values.

Üstel Fonksiyonlar - Denklem, Grafik ve Kritik Değerler

Evaluate expressions and use formulas to solve number and word problems involving exponential functions; classify exponential functions as exponential growth or decay.

Üstel Fonksiyonlar

Simplify numerical expressions that may contain exponents.

Factor quadratic polynomials, including special products.

İkinci Dereceden Polinomları Çarpanlarına Ayırma

Understand that many whole numbers factor in different ways.

Tam Sayıların Çarpanları

Identify and make figures with line symmetry.

Simetriye Sahip Şekiller

Calculate the areas of triangles, parallelograms, trapezoids, circles, and composite figures in number and word problems.

Üçgenlerin, Paralelkenarların, Yamukların, Dairelerin ve Bileşik Şekillerin Alanını Bulma

Find the fractional part of a whole number or fraction with and without models and pictures.

Kesirli Kısmı Bulma

Identify or generate numerical and geometric patterns; correct errors in patterns or interpret pattern features.

Bir Sayı Örüntüsünün Kuralını Bulma

Use models to find volume for prisms and cylinders as the product of the area of the base (B) and the height. Calculate the volume of prisms in number and word problems.

Taban ve Yükseklik Kullanarak Hacim Bulma

Näherungsweises Ermitteln des Flächeninhalts von Kreisen; Anwenden der Formel für die Berechnung des Flächeninhalts von Kreisen, insbesondere auf Halbkreise, Viertelkreise und Achtelkreise. 

Flächeninhalt eines Kreises

Ermitteln von Flächeninhalten von Rechtecken durch Zerlegen in passende Einheitsquadrate; Anwenden der Formel zur Berechnung des Flächeninhalts eines Rechtecks.

Flächeninhalt von Rechtecken

Anwenden und Begründen von Formeln für die Flächeninhalte von besonderen Vierecken (Parallelogramm, Trapez, Deltoid, Raute).

Flächeninhalte von besonderen Vierecken

Use models to develop the relationship between the total distance around a figure and the formula for perimeter; find perimeter using the formula in number and word problems.

Çevre için Formül

Use models to develop formulas for finding areas of triangles, parallelograms, trapezoids, and circles in number and word problems.

Üçgenlerin, Paralelkenarların, Yamukların ve Dairelerin Alanı İçin Formüller

Find the lateral area and surface area of a right prism, pyramid, right circular cylinder, and cone using formulas.

Katı Cisimlerin Yanal Yüzey Alanı Formülleri

Formulieren des pythagoräischen Lehrsatzes für vorgegebene rechtwinklige Dreiecke unter Verwendung verschiedener Bezeichnungen.

Formulieren des Satzes des Pythagoras

Represent division of whole numbers as a fraction in number and word problems.

Bölme Olarak Kesir

Use frequency tables, dot plots, and other graphs to determine the shape, center, and spread of a data distribution.

Sıklık Tabloları ve Nokta Grafikleri

Interpret probability models for data from simulations or for experimental data presented in tables and graphs (frequency tables, line plots, bar graphs).

Sıklık Tabloları, Çizgi Grafikleri ve Sütun Grafikleri

Use and interpret function notation in number and word problems; determine a value of the function given an element of the domain.

Fonksiyonlar ve Fonksiyon Gösterimi

Beschreiben und Interpretieren von Funktionen als eindeutige Zuordnungen; Erkennen und Begründen von funktionalen Zusammenhängen.

Funktionen als eindeutige Zuordnungen

Generate a set of ordered pairs using a rule which is stated in verbal, algebraic, or table form; generate a sequence given a rule in verbal or algebraic form.

Sıralı İkililer ve Diziler Oluşturma

Bennenen und Untersuchen von geometrischen Körpern.

Geometrische Körper

Deuten von Prozent als "von Hundert"; grafische Darstellung von Prozenten.

Grafische Veranschaulichung von Prozenten

Lösen von linearen Gleichungssystemen durch grafische Darstellung.

Grafisches Lösen linearer Gleichungssysteme

Graph absolute value functions and their corresponding inequalities.

Mutlak Değer Fonksiyonlarının ve Eşitsizliklerinin Grafiğini Çizme

Use ordered pairs derived from tables, algebraic rules, or verbal descriptions to graph linear functions.

Sıralı İkililer Kullanarak Doğrusal Fonksiyonların Grafiğini Çizme

Graph quadratic functions. Identify and interpret the intercepts, maximum, minimum, and the axis of symmetry.

İkinci Derece Fonksiyonların Grafiğini Çizme

Graphically solve systems of linear equations.

Doğrusal Denklem Sistemlerinin Grafiğinin Çizilmesi

İkinci Dereceden Denklemleri Grafik Çizerek Çözme

Find and interpret the maximum, the minimum, and the intercepts of a quadratic function.

İkinci Dereceden Fonksiyonların Grafikleri

Organize, display, and interpret multiple sets of information in the same graph including multiple bar, multiple stem-and-leaf, and multiple line graphs.

Birden Fazla Bilgi Kümesi İçeren Grafikler

Organize, display, and interpret information in graphs containing scales that represent multiple units.

Birden Fazla Birimi Temsil Eden Ölçeklere Sahip Grafikler

Find factors, common factors, and the greatest common factor of numbers; explain.

En Büyük Ortak Bölen

Organize and compare one set of information in histograms and bar graphs.

Histogramlar ve Sütun Grafikleri

Organize, display, and interpret information in histograms.

Histogramlar

Identify proportional parts of similar figures using rulers and protractors.

Ölçüm Kullanarak Orantılı Kısımları Belirleme

Recognize that a statistical question is one that will require gathering data that has variability.

İstatistiksel Soruları Belirleme

Describe the intervals for which a function is increasing or decreasing.

Artan ve Azalan Fonksiyonlar

Graph or identify simple inequalities using symbol notation >, <, ≤, ≥, and ≠ in number and word problems.

>, <, ≤, ≥ ve ≠ Sembolik Gösterimlerini Kullanan Eşitsizlikler

Make inferences about a population based on a sample and compare variation in multiple samples.

Örneklemlerden Çıkarımlar

Use concepts of positive numbers, negative numbers, and zero (e.g., on a number line, in counting, in temperature, in "owing") to describe quantities in number and word problems.

Tam sayılar

Identify and interpret the intercepts of a linear relation in number and word problems.

Doğrusal İlişkilerin Kesenleri

Use properties, definitions, and theorems of polygons to solve problems related to the interior and exterior angles of a convex polygon.

Çokgenin İç ve Dış Açıları

Use remainders in problem-solving situations and interpret the remainder with respect to the original problem.

Kalanları Yorumlama

Identify, draw, and name: points, rays, line segments, lines, and planes.

Geometriye Giriş

Use models to investigate the concept of the Pythagorean Theorem.

Pisagor Teoremini İnceleme

Erklären und Begründen, dass es Zahlen gibt, die nicht als Bruch darstellbar sind (irrationale Zahlen).

Irrationale Zahlen

Angeben von Klammer- und Vorrangregeln; Erklären und Anwenden von Klammer-Punkt-Strich-Regel.

Klammer- und Vorrangregeln

Konstruieren von besonderen Vierecken (mit Zirkel, Lineal und Geodreieck oder DGS).

Konstruieren von besonderen Vierecken

Konstruieren von Dreiecken (mit Zirkel, Lineal und Geodreieck oder DGS).

Konstruieren von Dreiecken

Skizzieren und Konstruieren von Rechecken und zusammengesetzten Figuren, die aus Rechtecken bestehen. 

Konstruieren von Rechtecken

Lösen von Konstruktionsaufgaben mit parallelen oder normalen Geraden, Strahlen und Strecken. 

Konstruktionsaufgaben

Beschreiben von grundlegenden Eigenschaften von Koordinatenachsen; Deuten von Koordinatenachsen als normal aufeinander stehende Zahlengeraden.

Koordinatenachsen

Herleiten und Anwenden von Formeln für den Umfang und Flächeninhalt von Kreissektoren.

Kreissektoren

Beschreiben, dass bei jedem Kreis das Verhältnis von Umfang zu Durchmesser die gleiche Zahl π ergibt; Experimentelles Ermitteln von Näherungswerten für π. 

Kreiszahl π 

Beschreiben der Lagebeziehung zwischen Kreisen, Punkten und Geraden; Konstruieren von Tangenten in Kreispunkten.

Lagebeziehung zwischen Kreis und Punkt, Gerade bzw. Kreis

Use rules of exponents to simplify numeric and algebraic expressions.

Üslü İfade Kuralları

Find multiples, common multiples, and the least common multiple of numbers; explain.

En Küçük Ortak Kat

Organize, display, and interpret information in line plots with a horizontal scale in fractional units.

Kesirli Ölçeklere Sahip Çizgi Grafikleri

Write a problem given a simple linear equation or inequality.

Sözel Problemlerde Doğrusal Denklemler ve Eşitsizlikler

Model and solve linear inequalities using the properties of inequality in number and word problems.

Problemlerde Doğrusal Eşitsizlikler

Identify relations as directly proportional, linear, or nonlinear using rules, tables, and graphs.

Doğrusal, Doğrusal Olmayan ve Doğru Orantılı İlişkiler

Identify linear and nonlinear relationships in data sets.

Veri Kümelerindeki Doğrusal ve Doğrusal Olmayan İlişkiler

Define and identify alternate interior, alternate exterior, corresponding, adjacent and vertical angles.

Doğrular ve Açılar

Derive a linear equation that models a set of data (line of best fit) using calculators. Use the model to make predictions.

En İyi Uyum Doğruları

Classify plane figures according to type of symmetry (line, rotational)

Düzlemsel Şekillerde Simetri Doğruları

Identify the number of lines of symmetry in a figure and draw lines of symmetry.

Simetri Doğruları

Solve a literal equation for an indicated variable.

Belirtilen Bir Değişken İçin Harfli Denklem

Divide using single-digit divisors with and without remainders.

Uzun Bölme

Lösen und Interpretieren von Abzählaufgaben

Lösen von Abzählaufgaben

Lösen von (einfachen) Gleichungen durch systematisches Probieren und Veranschaulichen.

Lösen von Gleichungen durch systematisches Probieren

Lösen von linearen Gleichungen durch Umkehren von Rechenoperationen.

Lösen von linearen Gleichungen durch Umkehroperationen

Konstruktives Lösen von Vermessungsaufgaben mithilfe maßstäblicher Zeichnungen.

Lösen von Vermessungsaufgaben

Maßumrechnungen von Raummaßen

Determine the mean absolute deviation (MAD) for one or more sets of data. Describe the meaning of MAD for given data sets.

Veri Kümelerinin Ortalama Mutlak Sapması (OMS)

Veri Kümelerinin Ortalaması

Select the appropriate measure of variability; choose a measure of variability based on the presence of outliers, clusters, and the shape of the data distribution.

Değişkenlik Ölçütleri

Veri Kümelerinin Medyanı (Ortancası)

Ermitteln von Laplace-Wahrscheinlichkeiten bei zweistufigen Zufallsexperimenten (mithilfe von Baumdiagrammen); Interpretieren dieser Wahrscheinlichkeiten; Erstellen und Interpretieren von Baumdiagrammen.

Mehrstufige Zufallsexperimente

Messen von Winkeln

Ordnen von Datenlisten; Ermitteln und Interpretieren von Minimum, Maximum sowie Spannweite.

Minimum, Maximum und Spannweite

Erheben und Interpretieren von Mittelwerten (arithmetischer Mittelwert, Modus, Median).

Mittelwerte

Veri Kümelerinin Modu

Approximate a linear model that best fits a set of data; use the linear model to make predictions.

Verileri Modelleme ve Tahminlerde Bulunma

Construct or complete a table of values to solve problems associated with a given relationship.

Tablolarla Modelleme

Determine the value of sets of coins and bills using cent sign and dollar sign appropriately. Create equivalent amounts with different coins and bills.

Para Hesabı

Add multi-digit numbers with regrouping in number and word problems.

Elde Gerektiren Çok Basamaklı Toplama İşlemi

Subtract multi-digit numbers with regrouping in number and word problems.

Onluk Bozmayı Gerektiren Çok Basamaklı Çıkarma İşlemi

Write a multiplication or a division sentence to represent a number or word problem; solve.

Çarpma ve Bölme İfadeleri

Multiplizieren von Bruchzahlen

Beschreiben und Anwenden des Multiplikationsalgorithmus für natürliche Zahlen.

Multiplizieren von natürlichen Zahlen

Multiplizieren von nichtnegativen Dezimalzahlen.

Multiplizieren von nichtnegativen Dezimalzahlen

Multiply a 1-digit number by a 2-digit multiple of 10.

1 Basamaklı Bir Sayı ile 2 Basamaklı Bir Sayıyı Çarpma

Recognize and use patterns in powers of ten (with or without exponents) to multiply and divide whole numbers and decimals.

10'un Kuvvetleriyle Çarpma ve Bölme

Multiply and divide decimals using models and pictures to explain the process and record the results.

Ondalık Sayılarla Çarpma ve Bölme İşlemlerini Modellerle Gösterme

Multiply or divide two decimals or a decimal and a whole number in number and word problems.

Ondalık Sayılarla Çarpma ve Bölme

Model or compute with integers using multiplication or division in number and word problems.

Tam Sayıları Çarpma ve Bölme

Multiply or divide with mixed numbers in number and word problems.

Tam Sayılı Kesirleri Çarpma ve Bölme

Multiply two fractions or a fraction and a whole number in number and word problems.

Kesirleri Çarpma

Multiply a multi-digit whole number by a 1-digit whole number or a 2-digit multiple of 10.

Çok Basamaklı Sayıları Çarpma

Solve multi-step number and word problems using the four operations.

Çok Adımlı Problemler

Identify the nets for prisms, pyramids, cylinders and cones in geometric and applied problems.

Katı Cisimlerin Açınımları

Erkennen von gegebenen Figuren als Netze eines Quaders; Skizzieren und Konstruieren von Netzen eines Quaders.

Netze von Quadern

Determine whether a linear equation has one solution, infinitely many solutions, or no solution.

Denklem Sisteminin Çözüm Sayısı

Read and write word names for numbers from 1,000 to 9,999.

1.000'den 9.999'a kadar olan sayılar

Read, write, and compare whole numbers from 10,000 to less than one million using standard and expanded notation.

10.000'den Bir Milyona Kadar Sayılar

Read and write word names for whole numbers from 101 to 999.

101'den 999'a kadar olan sayılar

Read, write, or model numbers in expanded form using decimal fractions or exponents.

Sayıların Çözümlenmiş Hali

Write whole numbers in scientific notation; convert scientific notation to standard form; investigate the uses of scientific notation.

Sayıların Bilimsel Gösterimi

Anwenden und Begründen von Formeln für die Berechnung von Oberflächeninhalten von Zylindern.

Oberflächeninahlt von Zylindern

Anwenden und Begründen von Formeln für die Berechnung von Oberflächeninhalten von Kegeln. 

Oberflächeninhalt von Kegeln

Anwenden und Begründen von Formeln für den Oberflächeninhalt von (geraden) Prismen; Untersuchen von Auswirkungen von Längenänderungen auf Oberflächeninhalte.

Oberflächeninhalt von Prismen

Anwenden von Formeln zur Berechnung der Oberflächeninhalte von Pyramiden; Untersuchen von Auswirkungen von Längenänderungen auf Oberflächeninhalte. 

Oberflächeninhalt von Pyramiden

Anwenden und Begründen von Formeln zur Berechnung des Oberflächinhalts von Quadern; Untersuchen von Auswirkungen von Längenänderungen auf Oberflächeninhalte.

Oberflächeninhalt von Quadern

Describe a data set by its number of observations, what is being measured, and the units of measurement.

Gözlem, Ölçüm ve Örnekleme

Solve one-step linear equations and inequalities and graph solutions of the inequalities on a number line in number and word problems.

Tek Adımlı Doğrusal Denklemler ve Eşitsizlikler

Perform multi-step operations with rational numbers (positive and negative) in number and word problems.

Rasyonel Sayılarla İşlemler

Use order of operations including parentheses and other grouping symbols to simplify numerical expressions.

İşlem Sırası

Identify outliers and clusters in bivariate data in tables and scatter plots.

Serpilme Diyagramlarında Aykırı Değerler ve Kümeler

Use properties, definitions, and theorems of angles and lines to solve problems related to adjacent, vertical, complementary, supplementary, and linear pairs of angles.

Açı Çiftleri

Determine and interpret the components of algebraic expressions including terms, factors, variables, coefficients, constants, and parts of powers in number and word problems.

Cebirsel Bir İfadenin Bölümleri

Identify parts of a numerical or algebraic expression.

Bir İfadenin Bölümleri

Örüntüler ve Problem Çözme

Solve number and word problems involving percent increase and percent decrease.

Yüzdelik Artış ve Azalış

Calculate or estimate the percent of a number including discounts, taxes, commissions, and simple interest.

Bir Sayının Yüzdesi

Solve number and word problems using percent proportion, percent equation, or ratios.

Yüzde Problemleri

Determine perimeter using concrete models, nonstandard units, and standard units in number and word problems.

Çevre Uzunluğu

Investigate and determine the relationship between the diameter and the circumference of a circle and the value of pi; calculate the circumference of a circle.

Çap ile Çevre Arasındaki İlişki Olarak Pi

Binler Basamağı Değeri

Indicate and compare the place value of each digit in a multi-digit whole number or decimal.

Basamak Değeri

Write the equation of and graph linear relationships given two points on the line.

Bir Doğrunun Nokta-Nokta Biçimi

Write the equation of and graph linear relationships given the slope and one point on the line.

Doğrunun Nokta-Eğim Biçimi

Sayı Doğrusu Üzerindeki Noktalar

Distinguish between a population and a sample and draw conclusions about the sample (random or biased).

Popülasyon ve Örneklem

Make predictions based on results from surveys and samples.

Örneklemlerden Tahminler

Identify prime and composite numbers less than 100.

Asal ve Bileşik Sayılar

Asal Çarpanlara Ayırma

Erklären und Anwenden des Begriffs Primzahl.

Primzahlen

Determine a simple probability using geometric figures.

Geometride Olasılık

Describe the probability of a chance event using a fraction or ratio.

Bir Olayın Olasılığının Kesir veya Oran Olarak İfade Edilmesi

Determine the probability of compound events (with and without replacement).

Bileşik Olayların Olasılığı

Use a coordinate grid to solve number and word problems. Describe the path between given points on the plane.

Koordinat Düzlemindeki Problemler

Recognize and apply algebra techniques to solve rate problems including distance, work, density, and mixture problems.

Oranlarla İlgili Problemler

Use the commutative and associative properties to add or multiply numerical expressions.

Toplama ve Çarpma İşlemlerinin Özellikleri

Verify how properties and relationships of geometric figures are maintained or how they change through transformations.

Geometrik Şekillerin Özellikleri

Interpret and compare properties of linear functions, graphs, and equations.

Doğrusal Fonksiyonların, Grafiklerin ve Denklemlerin Özellikleri

Use manipulatives, pictorial representations, and appropriate vocabulary (e.g., polygon, side, angle, vertex, diameter) to identify and compare properties of plane figures.

Düzlemsel Şekillerinin Özellikleri

Use the commutative, associative, and distributive properties, and inverses and identities to solve number and word problems with rational numbers.

Rasyonel Sayıların Özellikleri

Write a proportion to model a word problem; solve proportions.

Orantılar

Anwenden von Prozenten in Sachsituationen und Bearbeitung von Fragestellungen im Zusammenhang mit der Prozentrechnung; Beschreiben und Vergleichen von Lösungswegen; Kritische Betrachtung von Ergebnissen und ihrer Genauigkeit.

Prozente in Sachsituationen

Bearbeiten von vertiefenden Aufgaben zur Prozentrechnung in ein- und mehrstufigen Situationen (unter Verwendung von Änderungsfaktoren).

Prozentuelle Vermehrung und Verminderung

Use the Pythagorean Theorem and its converse to solve number and word problems, including finding the distance between two points.

Pisagor Teoremi ve Tersi

Write a quadratic equation or quadratic function given its zeros.

Sıfır Noktalarından İkinci Dereceden Denklemler ve Fonksiyonlar

Determine the quartiles or interquartile range for a set of data.

Verilerin Çeyrekleri ve Çeyrekler Arası Açıklığı

Köklü İfadeler

Use rules of exponents to rewrite or simplify expressions with rational exponents or radicals and interpret their meaning.

Köklü İfadeler ve Rasyonel Üsler

Veri Kümesi Açıklığı

Determine the ratio or rate of change of a relation given a table or graph.

Tablo veya Grafik Verildiğinde Oran veya Orantı

Read and write word names for rational numbers in decimal form to the hundredths place or the thousandths place.

Ondalık Biçimdeki Rasyonel Sayılar

Describe the relationship between corresponding terms in two or more numerical patterns or tables of ratios

Oran ve Orantılar

Anwenden und Begründen von Formeln zur Berechnung des Rauminhalts von Pyramiden; Untersuchen von Auswirkungen von Längenänderungen auf Rauminhalte. 

Rauminhalt von Pyramiden

Ermitteln von Rauminhalten von Quadern durch Zerlegen in passende Einheitswürfel; Anwenden und Begründen der Formel zur Berechnung des Volumens eines Quaders; Untersuchen von Auswirkungen von Längenänderungen auf Oberflächeninhalte. 

Rauminhalt von Quadern

Anwenden und Begründen von Formeln zur Berechnung des Rauminhalts von Zylindern.

Rauminhalt von Zylindern

Describe, use, and compare real numbers. Use the definition of rational numbers to derive and distinguish irrational numbers.

Gerçek, Rasyonel ve İrrasyonel Sayılar

Describe graphically, algebraically and verbally real-world phenomena as functions; identify the independent and dependent variables and any constraints of the domain or range.

Fonksiyon Olarak Gerçek Dünya Olguları

Angeben, Erklären und Anwenden von Rechengesetze (Distributiv-, Assoziativ-, Kommutativgesetz).

Rechengesetze

Beschreiben, Anwenden und Begründen elementarer Rechenregeln für Potenzen.

Rechenregeln für Potenzen

Angeben und Anwenden der Regeln √(a ∙ b) = √a ∙ √b und √(a / b) = √a / √b angeben und anwenden; Begründen, dass im Allgemeinen √(a ± b) ≠ √a ± √b ist.

Rechenregeln

Kennenlernen von Grundbegriffen (Grundwert, Prozentanteil, Prozentsatz); Rechnen mit Prozenten in vielfältigen Situationen; Verwenden von additiven und multiplikativen Berechnungen und Begründen entsprechender Zusammenhänge.

Rechnen mit Prozenten

Lösen von linearen Gleichungssystemen durch Berechnung; insbesondere durch Lösungsverfahren (Einsetzungsverfahren, Gleichsetzungsverfahren, Eliminationsverfahren).

Rechnerisches Lösen linearer Gleichungssysteme

Find indicated terms, the common ratio, or the common difference using recursive sequence formulas; write recursive sequence formulas.

Tekrarlı Dizi Formülleri

Locate, given the coordinates of, and graph plane figures which are the results of translations or reflections in all quadrants of the coordinate plane.

Koordinat Düzleminde Yansımalar

Define and distinguish between relations and functions, dependent and independent variables, and domain and range; identify whether relations are functions numerically and graphically.

Bağıntılar ve Fonksiyonlar

Relate a percent to its equivalent fraction or decimal.

Yüzde ile Kesir veya Ondalık Sayı Arasındaki İlişki

Use models to investigate the relationship of the volume of a cone to a cylinder and a pyramid to a prism with the same base and height.

Bir Koni ile Silindir veya Bir Piramit ile Prizmanın Hacmi Arasındaki İlişki

Identify and draw intersecting, parallel, skew, and perpendicular lines and line segments. Identify midpoints of line segments.

İki Doğru Arasındaki İlişki ve Doğru Parçalarının Orta Noktaları

Convert between different representations of relations and functions using tables, the coordinate plane, and algebraic or verbal statements.

Bağıntı ve Fonksiyonların Gösterimleri

Represent fractions concretely and symbolically, including representing whole numbers as fractions.

Kesirleri Gösterme

Represent multiplication or division of mixed numbers with and without models and pictures.

Tam Sayılı Kesirlerin Çarpım ve Bölümünü Temsil Etme

Determine or calculate residuals of a distribution.

Bir Dağılımda Artıklar

Rewrite and compare decimals to fractions (tenths and hundredths) with and without models and pictures.

Kesirleri ve Ondalık Sayıları Yeniden Yazma

Use properties, definitions, and theorems to solve problems about rigid transformations and dilations of plane figures.

Düzlemsel Şekillerin Katı Dönüşümleri ve Ölçeklemeleri

Locate, given the coordinates of, and graph plane figures which are the results of rotations (multiples of 90 degrees) with respect to a given point.

Koordinat Düzleminde Döndürmeler

Round decimals to a given place value; round fractions and mixed numbers to a whole number or a given fractional place value.

Ondalık Sayıları, Kesirleri ve Tam Sayılı Kesirleri Yuvarlama

Round whole numbers to a given place value.

Tam Sayıları Yuvarlama

Given a list of ordered pairs in a table or graph, identify either verbally or algebraically the rule used to generate and record the results.

Sıralı İkililer Oluşturma Kuralları

Runden von Zahlen

Lesen und Schreiben von Zahlen in römischer Zahldarstellung; Erklären der Vorteile (bei Berechnungen) mit dem dezimalen Stellenwertsystem im Vergleich zur römischen Zahldarstellung.

Römische Zahlen

Bearbeiten von Sachaufgaben zu Quadern, insbesondere Berechnen von Massen und Dichten.

Sachaufgaben zu Quadern

Darstellen von Sachverhalten (Neigungen, Drehungen) durch Winkel; Erkennen von Größenbeziehungen zwischen Winkeln in geometrischen Figuren.

Sachaufgaben zu Winkeln

Bearbeiten von Aufgaben in Sachsituationen zum Maßstab; Arbeiten mit Plänen und Landkarten.

Sachaufgaben zum Maßstab

Sammeln und Ordnen von Daten nach verschiedenen Gesichtspunkten.

Sammeln und Ordnen von Daten

Erklären, Anwenden und Begründen des Satzes von Thales. 

Satz von Thales

Determine and use scale factors to reduce and enlarge drawings on grids to produce dilations.

Ölçek Çarpanı

Organize, display, and interpret information in scatter plots. Approximate a trend line and identify the relationship as positive, negative, or no correlation.

Serpilme Grafikleri

Skizzieren von Schrägrissen von Quadern.

Schrägrisse von Quadern

Schätzen von Wahrscheinlichkeiten mithilfe empirisch gewonnener relativer Häufigkeiten.

Schätzen von Wahrscheinlichkeiten

Schätzen von Winkelgrößen

Describe, or graph plane figures which are the results of a sequence of transformations.

Koordinat Düzleminde Dönüşümler Dizisi

Use set notation to describe domains, ranges, intersection, and union of sets. Identify cardinality of sets, equivalent sets, disjoint sets, complement, or subsets.

Küme Teorisi

Verwendung eines intuitiven Wahrscheinlichkeitsbegriff zur Quantifizierung von Sicherheit.

Sichere, wahrscheinliche, unwahrscheinliche und unmöglich Ereignisse

Use proportional reasoning to solve problems related to similar polygons.

Benzer Çokgenler

Use properties of triangles to solve problems related to similar triangles and the relationships of their corresponding parts.

Benzer Üçgenler ve Eşleme

Identify corresponding parts of similar and congruent figures.

Benzerlik ve Eşlik

Determine a simulation, such as random numbers, spinners, and coin tosses, to model frequencies for compound events.

Bileşik Olayların Olasılıklarını Tahmin Etmeye Yönelik Simülasyonlar

Describe the slope of a line given in the context of a problem situation; compare rates of change in linear relationships represented in different ways.

Değişim Hızı Olarak Eğim

Write the equation of and graph linear relationships given the slope and y-intercept.

Bir Doğrunun Eğim-Kesen Biçimi

Find the slope of a line given two points on a line, a table of values, the graph of the line, or an equation of the line in number and word problems.

Bir Doğrunun Eğimi

Identify from a set of numbers which values satisfy a given equation or inequality.

Eşitsizlikleri Çözme

Solve linear equations using the associative, commutative, distributive, and equality properties and justify the steps used.

Doğrusal Denklemleri Çözme

Determine algebraically or graphically the solutions of a linear inequality in two variables.

Doğrusal Eşitsizlikleri Çözme

Solve systems of equations or inequalities algebraically and graphically that include nonlinear relationships.

Doğrusal Olmayan Denklem ve Eşitsizlik Sistemlerinin Çözümü

Determine whether a system of equations has one solution, multiple solutions, infinitely many solutions, or no solution using graphs, tables, and algebraic methods; compare solutions of systems of equations.

Doğrusal Denklem Sistemlerini Çözme

Use geometric models and equations to investigate the meaning of the square of a number and the relationship to its positive square root. Know perfect squares to 625.

Kare ve Kare Kökler

Determine measures of spread (standard deviation).

Standart Sapma

Relate standard and expanded notation to 3- and 4-digit numbers.

3 ve 4 Basamaklı Sayıların Standart ve Çözümlenmiş Gösterimi

Contrast statements about absolute values of integers with statements about integer order.

Tam Sayıların Mutlak Değerlerini İçeren İfadeler

Erklären und Anwenden des Stellenwertsystems für natürliche Zahlen.

Stellenwerte von natürlichen Zahlen

Erklären und Anwenden des dezimalen Stellenwertsystems; Erklären und Anwenden des Prinzips „Bündeln in Zehner-Schritten“.

Stellenwerte von rationalen Zahlen

Organize, display, and interpret information in stem-and-leaf plots.

Gövde ve Yaprak Grafikleri

Beschreiben von grundlegenden Eigenschaften von Streckensymmetralen (Mittelsenkrechten); Konstruieren von Streckensymmetralen (Mittelsenkrechten).

Streckensymmetrale (Mittelsenkrechte)

Subtract 2- and 3-digit numbers with and without models for number and word problems that require regrouping.

2 ve 3 Basamaklı Sayılarla Çıkarma İşlemi

Subtrahieren von Bruchzahlen

Subtrahieren von ganzen Zahlen

Beschreiben und Anwenden des Subtraktionsalgorithmus für natürliche Zahlen.

Subtrahieren von natürlichen Zahlen

Subtrahieren von nichtnegativen Dezimalzahlen

Use nets or formulas to find the surface area of prisms, pyramids, and cylinders in number and word problems.

Katıların Cisimlerin Yüzey Alanları

Calculate the surface area and volume of a sphere in number and word problems.

Kürenin Yüzey Alanı ve Hacmi

Write and solve systems of linear equations in two or more variables algebraically in number and word problems.

İki veya Daha Fazla Değişkenli Doğrusal Denklem Sistemleri

Doğrusal Eşitsizlik Sistemleri

Organize, display, and interpret information in tables and graphs (frequency tables, pictographs, and line plots).

Tablolar ve Grafikler

Angeben und Anwenden von Teilbarkeitsregeln; Begründen von Teilbarkeitsregeln; Begründen und Widerlegen von Aussagen zur Teilbarkeit.

Teilbarkeitsregeln

Beschreiben von grundlegenden Eigenschaften von Kreisen (Kreislinien, Kreisflächen) und Kreisteilen (Kreisbogen, Kreissektor, Kreissegment); Zeichnen von Kreisteilen.

Teile eines Kreises

Erkennen und Ermitteln von Teilern von natürlichen Zahlen; Ermitteln des größten gemeinsamen Teilers (mit Rechenverfahren).

Teiler von Zahlen

Determine the probability from experimental results or compare theoretical probabilities and experimental results.

Teorik ve Deneysel Olasılık

Identify the place value of each digit in a multi-digit number to the thousandths place.

Ondalık Sayılarda Binde Birler Basamağı

Transform (translate, reflect, rotate, dilate) polygons in the coordinate plane; describe the transformation in simple algebraic terms.

Koordinat Düzleminde Dönüşümler

Identify transformations on nonlinear parent functions using function notation, algebraic equations, or graphs.

Doğrusal Olmayan Ana Fonksiyonlara Uygulanan Dönüşümler

Use models or points in the coordinate plane to illustrate, recognize, or describe rigid transformations (translations, reflections, and rotations) of plane figures.

Düzlem Şekillerini Dönüştürme

Locate, given the coordinates of, and graph points which are the results of rigid transformations in all quadrants of the coordinate plane; describe the path of the motion using geometric models or appropriate terms.

Koordinat Düzleminde Noktaların Dönüştürülmesi

Translate between models or verbal phrases and algebraic expressions.

Cebirsel İfadelerin Çevrilmesi

Write a linear equation or inequality to represent a given number or word problem; solve.

Doğrusal Denklemlerin ve Eşitsizliklerin Çevirisi

Translate between models or verbal phrases and numerical expressions.

Sayısal İfadelerin Çevrilmesi

Recognize conditions of side lengths that determine a unique triangle, more than one triangle, or no triangle.

Üçgen Eşitsizliği Teoremi

Use trigonometric ratios to represent relationships in right triangles to solve number and word problems.

Trigonometrik Oranlar

Solve two-step linear equations and inequalities and graph solutions of the inequalities on a number line.

İki Adımlı Doğrusal Denklemler ve Eşitsizlikler

Write number sentences using any combination of the four operations that represent a two-step word problem; solve.

Dört İşlem Kullanılarak Çözülen İki Adımlı Problemler

Construct and interpret a two-way table to display two categories of data from the same source.

İki yönlü tablolar

Identify and draw angles (acute, right, obtuse, and straight).

Açı Türleri

Distinguish between types of events (conditional, mutually exclusive, independent, dependent, etc.). Use the appropriate formula to determine probabilities of random phenomena using addition rule, multiplication rule, or Venn diagrams.

Olay Türleri (Koşullu, Ayrık, Bağımsız, Bağımlı vb.)

Name polygons by the number of sides. Distinguish quadrilaterals based on properties of their sides or angles; relate quadrilaterals based upon their hierarchical attributes.

Dörtgen Çeşitleri

Identify and classify triangles according to the measures of the interior angles and the lengths of the sides; relate triangles based upon their hierarchical attributes.

Üçgen Türleri

Anwenden der Formel für die Berechnung des Umfangs von Kreisen, insbesondere auf Halbkreise, Viertelkreise und Achtelkreise.

Umfang eines Kreises

Anwenden und Begründen einer Formel für den Umfang von Rechtecken.

Umfang von Rechtecken

Umformen von Termen durch Ausmultiplizieren, Zusammenfassen, Herausheben oder Kürzen. 

Umformen von Termen

Lösen von Umkehraufgaben zu Kreisen, inbesondere durch Umformen von Formeln.

Umkehraufgaben zu Kreisen

Lösen von Umkehraufgaben zu Quadern, insbesondere durch Umformen von Formeln.

Umkehraufgaben zu Quadern

Lösen von Umkehraufgaben zu Rechtecken, insbesondere durch Umformen von Formeln.

Umkehraufgaben zu Rechtecken

Lösen von Umkehraufgaben zu Vierecken, insbsondere durch Umformen von Formeln. 

Umkehraufgaben zu Vierecken

Umschreiben eines Vierecks mit einem Kreis und Einschreiben eines Kreises in ein Viereck. Konstruieren von Umkreis und Innkreis von Rechteck und Quadrat.

Umkreis und Innkreis von Vierecken

Umrechnen von Flächenmaßen

Umrechnen von Längenmaßen

Umrechnen von Massenmaßen

Ausführen von Maßumrechnungen von Geldbeträgen.

Umrechnung von Geldbeträgen

Umrechnung von Zeitmaßen

Convert measures of length, area, capacity, weight, and time expressed in a given unit to other units in the same measurement system in number and word problems.

Uzunluk, Alan, Hacim, Ağırlık ve Zaman İçin Birim Dönüştürme

Use models to represent a fraction as a product of a whole number and a unit fraction in number and word problems.

Birim Kesirler

Given a proportional relationship represented by tables, graphs, models, or algebraic or verbal descriptions, identify the unit rate (constant of proportionality)

Birim Oran ve Orantı Sabiti

Calculate unit rates in number and word problems, including comparison of unit rates.

Birim Oran

Calculate unit rates of ratios that include fractions to make comparisons in number and word problems

Kesirlerle Birim Oranlar

Use benchmark numbers (zero, one-half, one) and models to compare and order fractions.

Kesirli Sayılarla Referans Rakamların Kullanımı

Solve quadratic equations using properties of equality.

Eşitlik Özelliklerini Kullanarak İkinci Derece Denklemleri Çözme

Use slopes to determine if two lines are parallel or perpendicular.

Eğim Kullanarak Paralel ve Dik Doğruları Belirleme

Solve quadratic equations using the quadratic formula.

İkinci Derece Denklemleri Çözmek için İkinci Derece Formülünü Kullanma

Use definitions and theorems of angles formed when a transversal intersects parallel lines.

Paralel Doğruların Oluşturduğu Açılarla İlgili Teoremlerin Kullanılması

Make predictions based on theoretical probabilities or experimental results.

Tahminlerde Bulunmak İçin Teorik ve Deneysel Olasılığın Kullanılması

Find the value of a variable in a number sentence.

Bir Sayı Cümlesinde Değişkenin Değeri

Analyze graphs, identify situations, or solve problems with varying rates of change.

Değişken Değişim Oranı

Ven Diyagramları

Veranschaulichen der Addition; Deutung des Addierens als Zusammenfügen von oder Weiterzählen bei natürlichen Zahlen; Deuten und Darstellen der Addition der Form z + n mit  z ϵ ℤ und n ϵ ℕ als Bewegungen auf der Zahlengeraden; diese Deutung verwenden, um entsprechende Rechenaufgaben zu lösen.

Veranschaulichung und Deutung der Addition

Veranschaulichen der Division; Deutung des Dividierens als Teilen, als Messen oder als Umkehren des Multiplizierens.

Veranschaulichung und Deutung der Division

Veranschaulichen der Multiplikation; Deutung des Multiplizierens mit natürlichen Zahlen als wiederholtes Addieren derselben Zahl oder als Vervielfachen; Deutung des Multiplizierens mit Bruchzahlen als Teilen und nachfolgendes Vervielfachen, als Vervielfachen und nachfolgendes Teilen oder als Ermitteln eines relativen Anteils.

Veranschaulichung und Deutung der Multiplikation

Veranschaulichen der Subtraktion; Deutung des Subtrahierens als Abziehen, als Ergänzen, als Ermitteln des Unterschieds oder als Umkehren des Addierens; Deuten und Darstellen der Subtraktion der Form z - n mit  z ϵ ℤ und n ϵ ℕ als Bewegungen auf der Zahlengeraden; diese Deutung verwenden, um entsprechende Rechenaufgaben zu lösen.

Veranschaulichung und Deutung der Subtraktion

Vergleichen und Messen von Flächeninhalten.

Vergleichen und Messen von Flächen

Vergleichen und Messen von Geldbeträgen.

Vergleichen und Messen von Geldbeträgen

Vergleichen und Messen von Längen

Vergleichen und Messen von Massen

Vergleichen und Messen von Rauminhalten

Vergleichen und Messen von Zeitspannen

Vergleichen und Ordnen von ganzen Zahlen (mithilfe der Zahlengerade); Interpretieren von ganzen Zahlen auch in außermathematischen Situationen.

Vergleichen und Ordnen von ganzen Zahlen

Vergleichen und Ordnen natürlicher Zahlen sowie nichtnegativer Dezimal- und Bruchzahlen.

Vergleichen und Ordnen von nichtnegativen Dezimal- und Bruchzahlen

Vergleichen und Ordnen von rationalen Zahlen; Darstellen von rationalen Zahlen auf der Zahlengeraden.

Vergleichen und Ordnen von rationalen Zahlen

Erkennen und Ermitteln von gemeinsamen Vielfache von natürlichen Zahlen; Ermitteln des kleinsten gemeinsame Vielfachen (mit Rechenverfahren).

Vielfache von Zahlen

Model the concept of the volume of a solid figure using cubic units.

Bir Küpün Hacmi ve Kübik Birimler

Determine the volume of composite figures in number and word problems.

Birleşik Şekillerin Hacmi

Calculate the volume of cylinders, pyramids, and cones in number and word problems.

Katı Cisimlerin Hacmi

Wechseln zwischen Bruch- und (endlicher bzw. periodischer) Dezimaldarstellung.

Wechsel zwischen Bruch- und Dezimalzahldarstellung

Wechseln zwischen Bruch-, Dezimal- und Prozentdarstellung.

Wechsel zwischen Bruch-, Dezimalzahl- und Prozentdarstellung

Begründen und anwenden, dass die Winkelsumme in jedem Dreieck 180° beträgt.

Winkelsumme im Dreieck

Describe the meaning of an unknown in the context of a word problem.

Bir Bilinmeyenli Sözel Problemler

Darstellen von Zahlen unter Verwendung von Zehnerpotenzen und Anwenden der Gleitkommadarstellung.

Zehnerpotenzen und Gleitkommadarstellung

Zeichnen von Winkeln

Identify and interpret zeros of a quadratic function using factoring in algebraic and word problems.

İkinci Dereceden Fonksiyonların Sıfırları

Beschreiben grundlegender Eigenschaften von ähnlichen Figuren; Interpretieren und Anwenden von Ähnlichkeitsfaktoren. 

Ähnlichkeit

Überprüfen von Achsensymmetrie einer ebenen Figur. 

Überprüfen von Achsensymmetrie

Überprüfen, ob ein Dreieck rechtwinklig ist durch Umkehrung des pythagoräischen Lehrsatzes. 

Überprüfen von Rechtwinkligkeit in Dreiecken

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Learn Quadratic Equations - GeoGebra Math Resources

Learn and practice interpreting and graphing quadratic functions with interactive resources from GeoGebra.

Discover over {1} free and ready-to-use GeoGebra resources to improve your skills in rewriting quadratic functions into different forms and determining key characteristics such as the vertex, intercepts, minimum or maximum values, orientation, and axis of symmetry.

Learn Quadratic Functions - GeoGebra Math Resources

Learn and practice working with rational numbers with interactive resources from GeoGebra.

Discover over {1} free and ready-to-use GeoGebra resources for grades 4-8 for exploring and practicing comparing decimals to fractions, ordering rational numbers, and solving problems with properties of arithmetic operations.

Learn Rational Numbers - GeoGebra Math Resources

Learn and practice finding unit rates and solving proportions with interactive resources from GeoGebra.

Discover over {1} free and ready-to-use GeoGebra resources ready for use to learn and practice unit rate calculations and proportion solving in number and word problems for grades 4-8.

Learn Ratios and Rates - GeoGebra Math Resources

Learn and practice working with real numbers with interactive resources from GeoGebra.

Find over {1} free and ready-to-use GeoGebra resources for grades 4-8 to explore and practice real number concepts like classifying real numbers, comparing and ordering.

Learn Real Numbers - GeoGebra Math Resources

Learn and practice working with roots with interactive resources from GeoGebra.

Discover over {1} free and ready-to-use GeoGebra resources for grades 4-8 to practice finding square and cube roots and understanding the relationship between a number and its square or cube root. Explore geometric models and equations.

Learn Roots - GeoGebra Math Resources

Learn and practice writing and converting whole numbers in scientific notation with interactive resources from GeoGebra.

Discover over {1} free and ready-to-use GeoGebra resources for grades 4-8 to learn & practice writing & converting whole numbers in scientific notation. Enhance your math skills with interactive lessons.

Learn Scientific Notation of Numbers - GeoGebra Math Resources

Learn and practice generating ordered pairs from verbal, algebraic, and table rules with interactive resources from GeoGebra.

Discover {1} free and ready-to-use GeoGebra resources for grades 4-8 to learn how to create ordered pairs from verbal, algebraic or table rules.

Learn Sequences and Series - GeoGebra Math Resources

Learn and practice identifying solid figures with interactive resources from GeoGebra.

Find over {1} free and ready-to-use GeoGebra resources for grades 4-8 for exploring and practicing identifying the nets for prisms, pyramids, cylinders, and cones. Learn to calculate surface area and volume of spheres and describe cross-sectional views of 3D figures.

Learn Solids - GeoGebra Math Resources

Learn and practice standard deviation concepts with interactive resources from GeoGebra.

Discover over {1} free, ready-to-use GeoGebra resources to learn and practice the concept of standard deviation, including determining measures of spread.

Learn Standard Deviations - GeoGebra Math Resources

Learn and practice describing data with mean, median, and mode with interactive resources from GeoGebra.

Discover {1} free and ready-to-use GeoGebra resources to learn and practice data description with mean, median, and mode for grades 4-8. Explore and understand outliers and their impact on statistical characteristics.

Learn Statistical Characteristics - GeoGebra Math Resources

Learn and practice identifying statistical questions, measuring variability and making predictions from sample data with interactive resources from GeoGebra.

Explore and practice statistical concepts with {1} free and ready-to-use GeoGebra resources for grades 4-8. Identify statistical questions, measure variability, and make predictions from samples. Enhance your data analysis skills with GeoGebra.

Learn Statistics - GeoGebra Math Resources

Learn and practice subtracting numbers with interactive resources from GeoGebra.

Discover over {1} free and ready-to-use GeoGebra resources for grades 4-8 to practice and explore multi-digit subtraction, including estimating differences.

Learn Subtraction - GeoGebra Math Resources

Learn and practice finding the surface area of different types of solids with interactive resources from GeoGebra.

Discover {1} free and ready-to-use GeoGebra resources for grades 4-8 to practice finding the surface area of solids including prisms, pyramids, and cylinders in real-world math problems

Learn Surface Area - GeoGebra Math Resources

Learn and practice identifying lines of symmetry in shapes with interactive resources from GeoGebra.

Discover over {1} free and ready-to-use GeoGebra resources for grades 4-8 for exploring & practicing symmetry in figures: identify lines & create symmetrical shapes

Learn Symmetry - GeoGebra Math Resources

Learn and practice graphing and solving systems of equations and inequalities with interactive resources from GeoGebra.

Explore over {1} free and ready-to-use GeoGebra resources for grades 4-12 to enhance your understanding of how to solve and graph systems involving a combination of equations and/or inequalities.

Learn Systems of Equations and Inequalities - GeoGebra Math Resources

Entdecke und übe unterschiedliche Zeitmaße mit interaktiven Unterrichtsmaterialien von GeoGebra.

Entdecke über {1} kostenlose und sofort verwendbare GeoGebra-Unterrichtsmaterialien zum Thema Zeitmaße für alle Schulstufen, perfekt zum Entdecken und Üben.

Zeitmaße verstehen & anwenden - Interaktive Mathe-Materialien | GeoGebra

Learn and practice transforming polygons in the coordinate plane with interactive resources from GeoGebra.

Find over {1} free and ready-to-use GeoGebra resources for grades 4-8 to learn & practice transforming polygons in the coordinate plane.

Learn Transformations - GeoGebra Math Resources

Learn and practice identifying and classifying triangles with interactive resources from GeoGebra.

Find over {1} free and ready-to-use GeoGebra resources for grades 4-8 to explore and practice how to identify and classify triangles, learn about angle sum properties, and improve triangle knowledge and skills.

Learn Triangles - GeoGebra Math Resources

Learn and practice trigonometry concepts with interactive resources from GeoGebra.

Discover over {1} free and ready-to-use GeoGebra resources to learn and practice trigonometry, including trigonometric ratios, identities, graphs, unit circle relationships, and modeling periodic phenomena.

Learn Trigonometry - GeoGebra Math Resources

Learn and practice converting measures and using appropriate tools with interactive resources from GeoGebra.

Discover {1} free and ready-to-use GeoGebra resources for grades 4-8 to enhance your understanding of converting measures of length, area, capacity, weight, and time to different units. Learn to effectively measure and compare lengths, capacity, and weight through practical exercises in number and word problems.

Learn Units and Measurement - GeoGebra Math Resources

Learn and practice calculating the volume of solids with interactive resources from GeoGebra.

Discover more than {1} free and high-quality GeoGebra resources for grades 4-8 to practice finding and calculating the volume of 3D shapes such as cylinders, prisms, pyramids, cones, and composite figures.

Domain and Range of Constant Functions

Domain and Range of Constant Functions

Putting It All Together

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