Use an Area Model to Divide
Using an area model to divide is a Grade 5 math skill in enVision Mathematics, Chapter 5: Use Models and Strategies to Divide Whole Numbers. The total dividend is treated as the area of a rectangle and the divisor as one side length; students find the unknown other side (the quotient) by breaking the area into manageable partial quotient pieces. This visual approach builds understanding of long division.
Key Concepts
Property To divide a dividend by a divisor, you can use an area model. The dividend is the total area of a rectangle, and the divisor is one of the side lengths. The quotient is the unknown side length. You can break the dividend into smaller parts that are easier to divide, find the partial quotient for each part, and then add the partial quotients together to find the final answer. This uses the idea that $(a+b) \div c = (a \div c) + (b \div c)$.
Examples To solve $368 \div 16$, we can break the dividend $368$ into $320 + 48$. We find the partial quotients: $320 \div 16 = 20$ and $48 \div 16 = 3$. The final quotient is the sum of the partial quotients: $20 + 3 = 23$. To solve $504 \div 21$, we can break the dividend $504$ into $420 + 84$. We find the partial quotients: $420 \div 21 = 20$ and $84 \div 21 = 4$. The final quotient is the sum of the partial quotients: $20 + 4 = 24$.
Explanation Using an area model helps visualize the division process. You represent the dividend as the total area inside a rectangle and the divisor as one of its side lengths. By breaking the total area into smaller, more manageable sections, you can use basic multiplication facts and estimation to find partial quotients. Adding these partial quotients gives you the total unknown side length, which is the final answer to the division problem.
Common Questions
How do you use an area model to divide?
Think of the dividend as the total area of a rectangle and the divisor as one side. Find partial quotients for manageable pieces of the area, then add them for the complete quotient.
What is 276 / 12 using an area model?
Set up a rectangle with area 276 and one side 12. Use partial areas: 12 x 20 = 240, remainder 36; 12 x 3 = 36. Total quotient: 20 + 3 = 23.
How does an area model relate to long division?
Both find the same quotient using partial steps, but the area model shows the process geometrically, making the structure of division more visible.
Where is the area model for division taught in enVision Grade 5?
Chapter 5: Use Models and Strategies to Divide Whole Numbers in enVision Mathematics, Grade 5.
What is a partial quotient?
A partial quotient is one piece of the overall quotient found during one step of the area model. All partial quotients are added to get the final complete quotient.