3 Digit by 2 Digit Multiplication Word Problems
Use partial areas to explain three-digit by two-digit multiplication.
Teaching notes for parents and teachers
How to teach it
Split both side lengths by place value. Label the smaller rectangles and add every partial area.
Example to work through together
Use the model below as you explain the example. Have your student point to the quantities as you discuss them.
126 × 24 = 126 × (20 + 4)
= 2,520 + 504 = 3,024 square feet
| Width | 100 feet | 20 feet | 6 feet | Row total |
|---|---|---|---|---|
| 20 feet | 2,000 | 400 | 120 | 2,520 |
| 4 feet | 400 | 80 | 24 | 504 |
All six smaller areas belong in the total. Multiplying only the hundreds by the tens, or forgetting one row, leaves part of the field uncounted.
Ask your student
Which section of the rectangle does this product represent?
If your student needs help
If a partial product is missing, check each row and column of the area model.
Choosing and using the worksheet
Each sheet contains four original rectangle-area stories with lengths from 100 to 999 feet and widths from 10 to 99 feet. Zero digits and multiples of ten can occur, but a set does not guarantee a particular digit pattern. Use the working space for the two partial products, regrouping marks, and their sum. The key supplies the equation and final area; the child still explains the calculation.
Make a practice set
Select the worksheet, answer key, or both. When both are selected, the answer key prints after the questions. Keep it separate if you want your student to work independently.
After your student finishes
Ask the child what the second partial product represents and why its place value differs from the first. Compare the exact answer with an estimate, then check the square-foot unit.
Word problems2 Digit Multiplication Word Problems: Rectangle Area
Multiply two two-digit side lengths to find a rectangular field’s area in square feet.
4 problems · Answer key included
Word problems4 Digit by 1 Digit Multiplication Word Problems
Use place-value partial products to find rectangle area from a four-digit length and a one-digit width.
4 problems · Answer key included
Word problems4 Digit by 2 Digit Division Word Problems
Use estimates and partial quotients to find complete groups with two-digit divisors, then interpret any remainder. Choose a smaller exact-group activity before four-digit totals.
4 problems · Answer key included
More about multiplication · Grade 5 worksheets
Grade 5 selected skill connection: 5.NBT.B.5 (three-digit by two-digit multiplication in rectangle-area contexts). See the Common Core standards for this grade. This worksheet does not cover every requirement in the standard.