Area Model Multiplication
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Topics
- Partial Products
- Factors
- Multiplication
- Area Model
Description
Build rectangles of various sizes and relate multiplication to area. Discover new strategies for multiplying large numbers. Use the game screen to test your problem solving strategies!
Sample Learning Goals
- 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.
Version 1.2.1
Teacher Tips
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Overview of sim controls, model simplifications, and insights into student thinking ( PDF ). |
Video Primer
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Teacher-Submitted Activities
| Middle School Math Sim Alignment |
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Amanda McGarry | MS | Other | Mathematics | |
| SECUNDARIA: Alineación PhET con programas de la SEP México (2011 y 2017) |
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Diana López | HS MS |
Other | Chemistry Physics Biology Mathematics |
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| PREPARATORIA: Alineación de PhET con programas de la DGB México (2017) |
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Diana López | HS UG-Intro |
Other | Physics Mathematics Chemistry |
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| PRIMARIA: Alineación con programas de la SEP México (2011 y 2017) |
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Diana López | MS K-5 |
Lab Discuss HW Demo Guided |
Chemistry Mathematics Astronomy Physics |
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| Os quadrados perfeitos | Andressa Gomes dos Santos | MS | Guided Discuss |
Mathematics |
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 10.13+, Safari 13+, latest version of Chrome.
Linux Systems:
Not officially supported. Please contact phethelp@colorado.edu with troubleshooting issues.
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