Area Model

Definition

The area model is a visual representation that can be used to illustrate and understand the concepts of multiplication and fractions. It provides a concrete way to conceptualize these mathematical operations by relating them to the area of geometric shapes.

5 Must Know Facts For Your Next Test

1. The area model can be used to represent the multiplication of whole numbers by breaking down the factors into their place values.
2. When multiplying fractions, the area model can be used to visualize the relationship between the numerator and denominator.
3. The area of a rectangle can be calculated by multiplying its length and width, which corresponds to the multiplication of the two factors.
4. The area model can help students develop a deeper understanding of the distributive property of multiplication.
5. The area model can be extended to represent the multiplication of polynomials and the division of fractions.

Review Questions

• Explain how the area model can be used to illustrate the multiplication of whole numbers.
  • The area model represents multiplication as the area of a rectangle, where the length and width correspond to the two factors being multiplied. For example, to multiply 23 by 14, the area model would show a rectangle with a length of 20 and 3, and a width of 10 and 4, resulting in four smaller rectangles that, when added together, give the total product of 322.
• Describe how the area model can be used to visualize the multiplication of fractions.
  • When multiplying fractions, the area model can be used to represent the relationship between the numerator and denominator. For instance, to multiply $\frac{1}{2}$ by $\frac{1}{3}$, the area model would show a rectangle divided into 6 equal parts, with 1 part shaded to represent the product of $\frac{1}{6}$. This visual representation helps students understand that the product of two fractions is a fraction whose numerator is the product of the numerators and whose denominator is the product of the denominators.
• Analyze how the area model can be used to develop a deeper understanding of the distributive property of multiplication.
  • The area model can illustrate the distributive property of multiplication, which states that $a(b + c) = ab + ac$. By representing the factors as the dimensions of a rectangle, students can see how the total area can be calculated by breaking down one of the factors into its parts. For example, to multiply 12 by 15, the area model would show a rectangle with a length of 10 and 2, and a width of 10 and 5, demonstrating that $12 \times 15 = (10 \times 10) + (10 \times 5) + (2 \times 10) + (2 \times 5)$. This visual representation helps students understand the underlying mathematical principles and apply the distributive property more effectively.

Related terms

Multiplication: The mathematical operation of finding the product of two or more numbers by repeated addition.

Fraction: A numerical quantity that is not a whole number, expressed as the quotient of two integers with the second one not equal to zero.

Array: A rectangular arrangement of objects or numbers in rows and columns, used to represent multiplication.