Partial Products · Two-Digit × One-Digit

Teaching Notes

Students break a two-digit number into tens and ones to multiply.

Before You Begin

• Place value and multiplication by a one-digit number

Teaching Steps for Parents and Teachers

1. Write 23 = 20 + 3.
2. Calculate 20 × 4 = 80.
3. Calculate 3 × 4 = 12.
4. Find 80 + 12 = 92 and check the answer to the original problem.

Worked Examples

23 × 4 = 20 × 4 + 3 × 4 = 80 + 12 = 92

1. Decompose 23 into 20 and 3, then multiply each part by 4.

Answer: 92

Common Mistakes and How to Help

Multiplying the tens digit without its place value

In 23, the digit 2 means 20. Calculate 20 × 4, rather than 2 × 4.

Correcting the answer without explaining why

The tens digit 2 represents 20. Check that both parts were multiplied by 4. Have the student start again at the first incorrect step.

Questions to Check Understanding

• Why do you add 20 × 4 and 3 × 4?
• 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 92. 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.