Partial Products · Two-Digit × Two-Digit

Teaching Notes

Students break apart both factors by place value and add four partial products.

Before You Begin

• Place value and two-digit by one-digit multiplication

Teaching Steps for Parents and Teachers

1. Write 23 = 20 + 3 and 14 = 10 + 4.
2. Calculate 20 × 10 = 200 and 3 × 10 = 30.
3. Calculate 20 × 4 = 80 and 3 × 4 = 12.
4. Find 200 + 30 + 80 + 12 = 322.

Worked Examples

23 × 14 = 200 + 30 + 80 + 12 = 322

1. Calculate 20 × 10, 3 × 10, 20 × 4, and 3 × 4, then add the four partial products.

Answer: 322

Common Mistakes and How to Help

Stopping after only two partial products

Connect each of the four combinations of parts to its multiplication expression.

Correcting the answer without explaining why

Check all four combinations so the student does not calculate only 20 × 10 and 3 × 4. Have the student start again at the first incorrect step.

Questions to Check Understanding

• Why does leaving out one of the four partial products change the answer?
• 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.