Area Models for 3-Digit by 2-Digit Multiplication
Area Models for 3-Digit by 2-Digit Multiplication is a Grade 5 math skill from Illustrative Mathematics Chapter 4 (Wrapping Up Multiplication and Division with Multi-Digit Numbers) where students decompose each factor by place value and apply the distributive property to create six partial products, then add them all together. The area model visually represents each partial product as a rectangle in a 3×2 grid.
Key Concepts
To multiply a three digit number by a two digit number, we can decompose them by place value and apply the distributive property. This creates six partial products, which are the areas of the smaller rectangles in the model. $$(a+b+c) \times (d+e) = (a \times d) + (a \times e) + (b \times d) + (b \times e) + (c \times d) + (c \times e)$$.
Common Questions
How do you use an area model to multiply a 3-digit by a 2-digit number?
Decompose the 3-digit number into hundreds, tens, and ones, and the 2-digit number into tens and ones. Create a 3×2 grid where each cell contains one partial product (the product of the row and column values). Add all six partial products for the final answer.
What is an example of a 3-digit by 2-digit area model multiplication?
To solve 142 × 35: decompose as (100+40+2) × (30+5). Six partial products: 100×30=3000, 100×5=500, 40×30=1200, 40×5=200, 2×30=60, 2×5=10. Sum = 3000+500+1200+200+60+10 = 4,970.
What chapter covers 3-digit by 2-digit area models in Illustrative Mathematics Grade 5?
Area models for 3-digit by 2-digit multiplication are covered in Chapter 4 of Illustrative Mathematics Grade 5, titled Wrapping Up Multiplication and Division with Multi-Digit Numbers.
How many partial products are in a 3-digit by 2-digit area model?
There are 6 partial products: 3 (from the first factor's place value parts) × 2 (from the second factor's place value parts) = 6 cells in the grid.
Why does the area model work for large multiplication problems?
The area model applies the distributive property systematically. By breaking each factor into place value parts and multiplying each pair, every combination of digits is accounted for. Summing the partial products gives the complete product.