Pinta-ala ja algebra

Pinta-ala ja algebra kuvakaappaus  Lataa  Upota
  • Polynomit
  • Factors
  • Tuotteet

Sisältö

  • 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 ).

Video Primer

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Teacher-Submitted Activities

Games Remote Lesson ideas A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Trish Loeblein YK
L
K-5
UG-Intro
Remote
Kotiteht
Kemia
Matematiikka
Fysiikka
Expanding and Factoring Algebraic Expressions A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Amanda McGarry YK Guided Matematiikka
Algebraic Expressions A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Amanda McGarry YK Guided Matematiikka
Exploring Factoring as Undoing the Distributive Property A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. Sarah Hampton L
YK
Guided Matematiikka
Middle School Math Sim Alignment This contribution was designed by PhET. Amanda McGarry YK Muu Matematiikka
Using the area model with expressions This contribution was designed by PhET. Jennifer Knudsen, Teresa Lara-Meloy, Amanda McGarry YK Discuss Matematiikka
SECUNDARIA: Alineación PhET con programas de la SEP México (2011 y 2017) This contribution was designed by PhET. Diana López YK
L
Muu Matematiikka
Biologia
Kemia
Fysiikka
PREPARATORIA: Alineación de PhET con programas de la DGB México (2017) This contribution was designed by PhET. 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

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HTML5 sims can run on iPads and Chromebooks, as well as PC, Mac, and Linux systems.

iPad:
iOS 12+ Safari
iPad compatible sims

Android:
Not officially supported. If you are using the HTML5 sims on Android, we recommend using the latest version of Google Chrome.

Chromebook:
Latest version of Google Chrome
The HTML5 and Flash PhET sims are supported on all Chromebooks.
Chromebook compatible sims

Windows Systems:
Microsoft Edge, latest version of Firefox, latest version of Google Chrome.

Macintosh Systems:
macOS 10.12+, Safari 12+, latest version of Chrome.

Linux Systems:
Not officially supported. Please contact phethelp@colorado.edu with troubleshooting issues.

Suunnitteluryhmä Kolmannen osapuolen kirjastot Kiitokset
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  • Amanda McGarry (co-lead)
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  • Karina Hensberry
  • Susan Miller
  • Ariel Paul
  • Kathy Perkins
  • Mariah Hermsmeyer (artwork)
  • Diana López Tavares (artwork)
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