Area Model Multiplication · Two-Digit × Two-Digit

Teaching Notes

Students calculate all four cells, then add them to find the original product.

Before You Begin

• Place value and partial products

Teaching Steps for Parents and Teachers

1. Identify 20 and 3 at the top and 10 and 4 on the left.
2. In the row labeled 10, write 200 and 30.
3. In the row labeled 4, write 80 and 12.
4. Add all four cells to complete 23 × 14 = □ below the table.

Worked Examples

23 × 14 = 200 + 30 + 80 + 12 = 322

1. Calculate all four combinations of 20 and 3 with 10 and 4. The table is not drawn to scale.

Answer: 322

Common Mistakes and How to Help

Adding only two diagonal cells

Use the partial-product expressions to show that the original multiplication includes all four cells.

Correcting the answer without explaining why

Check the tens values: use 20 and 10, not 2 and 1. Add all four cells. Have the student start again at the first incorrect step.

Questions to Check Understanding

• What multiplication expression does each cell represent?
• What does each number in the worked example represent in the original problem?
• Can you use the same method when the numbers change?

Practice Advice

Work through the example together and have the student explain why the answer is 322. Ask the student to explain the first two problems aloud, then solve the next three independently. Review the intermediate steps as well as the final answers. If an error repeats, return to the difficult teaching step before assigning more problems.

Next Practice

• Choose New Numbers for more practice with the same conditions. Ask the student to explain the reasoning as well as give the answer.
• If the student cannot explain the method independently, use smaller numbers to explore the same relationship first.