Are you wondering in math, what is an area model? In the world of math education, finding new and effective ways to engage students and facilitate understanding is of utmost importance. One such approach that has gained attention is the area model—a visual tool that helps learners grasp complex mathematical concepts with ease. Let’s explore the power of the area model and how it can transform the way we teach and learn math.
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Students struggle when we first introduce multi-digit multiplication and division to them. They do not understand why they need to do the standard algorithm steps and, hence, make a lot of mistakes. The area model helps students visualize what is happening in the standard algorithm and helps bridge them to this more abstract way of solving problems.
Area Model Method in Standards
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.
In Grade 3, students worked with their basic facts and multiplied a single-digit factor times a multiple of ten. A major focus of Grade 4 is to extend previous experiences to multiplying a single-digit factor times a multi-digit factor. Students should understand arrays and area models as well as the properties of multiplication in order to use models and mental strategies to multiply a single-digit factor by a multi-digit factor.
Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Previous work with division in Grade 3 focused on its meaning. By the end of Grade 4, students should be able to model, write, and explain division by one-digit divisor.
Multiplication Area Model
In math, what is an area model? The area model provides a concrete and visual representation of numbers and operations, allowing students to better visualize and comprehend mathematical processes. By breaking down numbers into smaller, more manageable units, the area model helps students make connections between different mathematical operations, such as multiplication, division, and even fractions.
The area model has become a valuable tool for students across various grade levels. In addition, its ability to simplify complex concepts and promote a deeper understanding of math has made it a popular teaching tool.
What is the Area Model Definition for Multiplication?
An area model is a rectangular diagram used in mathematics to solve multiplication problems, in which the factors getting multiplied define the length and width of a rectangle. So the product is the area of the rectangle. Hence, it is known as the “Area model for multiplication”.
When using an area model, you find the area in parts and add those parts together to find the sum.
Area Model Box Method
The area method, also sometimes called the box method, is an alternative to the standard algorithmic method for long (multi-digit) multiplication.
In addition, Both of these methods use the distributive property for multiplication, but they differ in how the partial products are calculated and written.
What is an Area Model Math?
Area models are visual aids used to make multiplication and division problems simple.
With area models, you can:
1. Multiply two and three-digit numbers.
2. Divide two and three-digit numbers.
3. Multiply fractions and decimals.
Before the Area Model- The Meaning of Multiplication
Starting in 3rd grade, students learn about the concept of multiplication and begin to solve problems using multiplication with concrete materials. Students need to understand basic multiplication before they can multiply multi-digit numbers and use the area model.
3.OA.A.1 Interpret products of whole numbers, e.g. interpret 5 X 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 X 7.
Students develop an initial understanding of the multiplication of whole numbers by modeling situations and understanding the meaning of the numbers (factors) and total (product).
The symbol X means groups of (or times).
Teachers should provide students with various multiplication situations to model using concrete materials. Ask students to identify the number of groups, the number of items in each group, and the total number of items. Next, introduce students to numerical representations by writing equations representing their models.
Read more…Do You Need Exciting and Fun Online Multiplication Fact Practice Ideas and Games?
What is an Array in Math Multiplication Example?
A multiplication array is simply an arrangement of rows or columns that matches a multiplication equation. You can make arrays out of objects or pictures, and you can use any sort of shape.
3 rows of 5 or 3 X 5= 15. Students can use arrays with the area model when they are just getting started.
Explain Arrays With Examples
An array is any arrangement in rows or columns:
- Cards laid out into rows to play Memory
- seats arranged in rows for a recital
- numbers arranged in an Excel spreadsheet are all examples of arrays
Read more… What’s a Multiplication Arrays Math Definition and Fun Activities to Use?
Multiplication Word Problems
As students learn about multiplication and division, they can be introduced to word problems to act out.
3. OA. A. 3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
Students need many opportunities to use concrete materials to model the situations and identify the number of groups and items in a group. Then, once students have an understanding, they can begin to draw pictures.
Teach Word Problems Division and Multiplication with these 160 Google Slides and 160 Worksheets. Use the counters to represent the word problems for multiplication and division on the slides. Then, fill in the equations and solve the multiplication and division word problems.
Read more… How to Successfully and Easily Teach Word Problems in Multiplication and Division
How the Area Model Can Enhance Understanding
The area model is a powerful visual tool that can profoundly enhance students’ understanding of mathematical concepts.
By breaking down numbers into smaller, more manageable units, the area model helps students visualize the relationships between different mathematical components.
Furthermore, the area model encourages students to engage in hands-on activities and manipulations, which can be particularly beneficial for visual and kinesthetic learners.
By physically constructing and manipulating area models, students can actively participate in the learning process, fostering a stronger connection between abstract concepts and their real-world applications.
How to Do Area Model Multiplication
The area model provides a concrete and visual representation of the multiplication process, making it easier for students to grasp the underlying concepts.
To illustrate this, let’s consider a simple example of multiplying two-digit numbers, such as 23 x 14. Using the area model, students can break down the numbers into their place value components (20 + 3 and 10 + 4) and visualize the multiplication process as a series of smaller area calculations.
By drawing a rectangle and dividing it into sections corresponding to the place values, students can see how the individual products (20 x 10, 20 x 4, 3 x 10, and 3 x 4) come together to form the final result of 322.
This visual approach not only helps students understand the mechanics of multiplication but also allows them to see the relationships between the different factors involved. As they progress to more complex multiplication problems, the area model can be scaled up, enabling students to tackle larger numbers with confidence.
Area Model Long Division
The area model box method, also known as the box method division, is a strategy that uses a grid or rectangle to visually break down numbers by place value and divide multi-digit numbers:
Break down the number
Step 1: Break the dividend into place values and write the value of each digit in its place inside the box. For example, to divide 125 by 5, you would break it down into 100 in the hundreds place, 20 in the tens place, and 5 in the ones place.
Step 2: Divide by place value. Start by dividing the largest place value by the divisor. For example, to divide 825 by 5, you would start by dividing 500 by 5, which equals 100.
Step 3: Add partial quotients. Continue dividing each place value by the divisor to get partial quotients, then add those partial quotients together to get the final quotient. For example, to divide 825 by 5, you would also divide 300 by 5 to get 60, and 25 by 5 to get 5. Finally, add 100 + 60 + 5 to get the final quotient of 165.
Visualizing Fractions Using the Area Model
The area model is also a powerful tool for helping students understand the concept of fractions. By representing fractions as regions within a larger area, the area model provides a concrete and intuitive way for learners to grasp the relationships between whole numbers and their fractional parts.
For example, to illustrate the fraction 1/4, students can draw a square and divide it into four equal parts, highlighting one of those parts as the representation of the fraction. This visual representation allows students to see how the fraction relates to the whole and how different fractions, such as 1/2 or 3/4, are represented within the same area.
In addition, as students progress to more complex fractional concepts, the area model can be used to demonstrate operations like addition, subtraction, and multiplication of fractions. By dividing the area into corresponding sections and manipulating the visual representations, students can develop a deeper understanding of how fractions work and how they can be combined or compared. This hands-on, visual approach to fractions can be particularly beneficial for students who struggle with the abstract nature of traditional fraction instruction.
Why Should You Use the Area Model in Multiplication?
The standard algorithm (vertical algorithm) is generally faster, but unlike the area or grid methods, it does not promote understanding or encourage the development of mathematical thinking.
Students rarely understand why they are carrying numbers or what that “placeholder zero” is all about in the second row of calculations. It is best to introduce children to long multiplication with the area method/grid method before using the standard algorithm. In addition, the area method supports the important ability to estimate answers.
Using the Area Model in the Classroom
One effective approach is to start with simple, hands-on activities that allow students to construct and manipulate area models physically. This can involve using graph paper, colored blocks, or even digital tools to create visual representations of numbers and operations.
Also, as students become more comfortable with the area model, educators can gradually increase the complexity of the problems, guiding students to apply the area model to more advanced mathematical concepts.
Area Model Multiplication 2 Digit by 2 Digit
Example of the Area Model Multiplication 3 Digit by 1 Digit
Example of the Area Model Multiplication 3 Digit by 2 Digit
Area Model Multiplication Activities
Fortunately, there are numerous resources available to support educators in incorporating the area model into their math instruction.
Check out the Multiplication Area Model
Teach the Multiplication Area Model with these 40 Google Slides and Printable versions. Use the place value blocks and the area model of multiplication to represent the multiplication word problem on the slides. Then, fill in the equations and solve the multiplication word problem.
Math Learning Center – Math App
These free apps are based on the visual models featured in Bridges in Mathematics. Apps are available in multiple versions: a web app for all modern browsers and downloadable versions for specific operating systems and devices (such as Apple iOS for iPad).
area-model-of-multiplication-worksheetEmbracing the Power of the Area Model in Math Education
By providing a concrete and visual representation of numbers and operations, the area model empowers learners to move beyond rote memorization and develop a deeper, more intuitive grasp of the subject matter.
- ☀Download this BONUS Guide with everything you need to cultivate a positive classroom community.
- ➕Includes definitions, lesson ideas, mindset surveys for students and teachers, and printable posters.
- 🧠💪Research shows a link between a growth mindset and math success. Kids with a growth mindset about their abilities perform better and are more engaged in the classroom.
- 👉Includes everything you need to start cultivating a more positive math classroom and students who love math. Download and get started today! Click here to download the Mindset Guide & Survey.
As educators embrace the power of this visual approach, they can unlock new possibilities for their students, fostering a love for mathematics and equipping them with the skills and confidence they need to succeed in the ever-changing world of STEM education. Hopefully, this helped answer the question: In math, what is an area model?
