Pinta-ala ja algebra

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Käynnistä klikkaamalla
Käytä tätä HTML-koodia näyttääksesi kuvakaappauksen, jossa lukee "Käynnistä klikkaamalla". Polynomit Factors Tuotteet PhET-projektia tukevat ja opettajat kuten sinä.

• Polynomit
• Factors
• Tuotteet

Description

Build rectangles of various sizes and relate multiplication to area. Discover new strategies for multiplying algebraic expressions. Use the game screen to test your multiplication and factoring skills!

Esimerkkejä oppimistavoitteista

• Develop and justify a method to use the area model to determine the product of a monomial and a binomial or the product of two binomials.
• Factor an expression, including expressions containing a variable.
• Recognize that area represents the product of two numbers and is additive.
• Represent a multiplication problem as the area of a rectangle, proportionally or using generic area.
• Develop and justify a strategy to determine the product of two multi-digit numbers by representing the product as an area or the sum of areas.

Standards Alignment

Common Core - Math

3.MD.C.7
Relate area to the operations of multiplication and addition.
3.MD.C.7c
Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.
3.MD.C.7d
Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.
4.NBT.B.5
Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
6.EE.A.3
Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
6.EE.A.4
Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for..
6.NS.B.4
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2)..
7.EE.A.1
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
7.NS.A.2c
Apply properties of operations as strategies to multiply and divide rational numbers.
8.EE.C.7b
Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
Version 1.2.1

Teacher Tips

 Opettajan opas (pdf) sisältää PhET-tiimin vinkkejä. ( PDF ).

Teacher-Submitted Activities

Games Remote Lesson ideas Trish Loeblein YK
L
K-5
UG-Intro
Remote
Kotiteht
Kemia
Matematiikka
Fysiikka
Expanding and Factoring Algebraic Expressions Amanda McGarry YK Guided Matematiikka
Algebraic Expressions Amanda McGarry YK Guided Matematiikka
Exploring Factoring as Undoing the Distributive Property Sarah Hampton L
YK
Guided Matematiikka
Middle School Math Sim Alignment Amanda McGarry YK Muu Matematiikka
Using the area model with expressions Jennifer Knudsen, Teresa Lara-Meloy, Amanda McGarry YK Discuss Matematiikka
SECUNDARIA: Alineación PhET con programas de la SEP México (2011 y 2017) Diana López YK
L
Muu Matematiikka
Biologia
Kemia
Fysiikka
PREPARATORIA: Alineación de PhET con programas de la DGB México (2017) Diana López L
UG-Intro
Muu Fysiikka
Kemia
Matematiikka
Would You Rather ... Karen Gann L Guided Matematiikka
Area Model Algebra - Multiplying Polynomials Carolyn Felknor YK Guided Matematiikka
ARTICULANDO ÁLGEBRA E GEOMETRIA: O CASO DAS EQUAÇÕES ALGÉBRICAS NO ESTUDO DE ÁREAS Verusca Batista Alves; Ana Carolina Costa Pereira YK Kotiteht
Labra
Matematiikka
Distributive Property Review Tim Kissinger and Larry Peters YK Guided
Discuss
Matematiikka
Modelo de Áreas, Cambio de Expresiones Andrés Gualberto Palomo Cuevas L Remote
Kotiteht
Matematiikka
Albania All shqip Modeli Syprinës: Algjebër
Arabia All العربية جبر نموذج المساحة
Bosnia All Bosanski Matematički model površina - Algebra
Brasilian portugali All português (Brasil) Modelo de Área: Álgebra
Englanti All English Area Model Algebra
Espanja All español Modelo de Áreas: Álgebra
Espanja (Meksiko) All español (México) Modelo de Áreas: Álgebra
Espanja (Peru) All español (Perú) Modelo de Área con Álgebra
Gudžarati All Gujarati બીજગણિતનું ક્ષેત્રફળ મોડેલ -નિકુંજ સવાણી
Hindi All हिंदी  बीजगणित -नमूने का क्षेत्रफल
Hollanti All Nederlands Algebra van oppervlakte
Italia All italiano Rappresentazione grafica della moltiplicazione in algebra
Japani All 日本語 面積と式の展開
Kazakki All Kazakh Ауданды есептеу
Kiina - perinteinen All 中文 (台灣) Area Model Algebra_面積模型與代數
Kiina - yksinkertaistettu All 中文 (中国) 面积模型代数
Korea All 한국어 면적 모형: 대수
Kreikka All Ελληνικά Υπολογισμός εμβαδού
Latvia All Latviešu Laukuma modeļa algebra
Mongoli All Монгол (Монгол) Талбайн загварын Алгебр
Persia All فارسی جبر مدل مساحت
Portugali All português Modelo de Área: Álgebra
Puola All polski Model pola - wyrażenia algebraiczne
Ranska All français Modélisation par les aires - Algèbre
Ruotsi All svenska Areamodellen och algebra
Saksa All Deutsch Flächenmodell Algebra
Serbia All Српски Математика преко површина - Алгебра
Sinhali All Sinhalese වර්ගඵල ආකෘති වීජ ගණිතය
Tamili All Tamil மாதிரி உருவின் எண்(அட்சர) கணிதம்
Tanska All Dansk Arealmodel, algebra
Turkki All Türkçe Alan Modeli İle Cebir
Ukraina All українська Площинна модель. Алгебра
Unkari All magyar Területmodell: algebra
Venäjä All русский Вычисление площади
Vietnam All Tiếng Việt Đại số với mô hình diện tích

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iOS 12+ Safari

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Suunnitteluryhmä Kolmannen osapuolen kirjastot Kiitokset
• Jonathan Olson (developer)
• Karina Hensberry
• Susan Miller
• Ariel Paul
• Kathy Perkins
• Mariah Hermsmeyer (artwork)
• Diana López Tavares (artwork)
• almond-0.2.9.js
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• FileSaver-b8054a2.js
• font-awesome-4.5.0
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• seedrandom-2.4.2.js
• text-2.0.12.js
• TextEncoderLite-3c9f6f0.js