Materials and Devices

  • Computer with a projector, Smartboard or other device for your class to watch videos
  • 20 math problems: 3-digit numbers multiplied by a 2-digit number. You can use what you already have or use the Multiplication Worksheet Generator to make your own worksheet.
  • YouTube access

Lesson Overview

  1. Have the students try to solve 3 to 5 problems. – 10 min
  2. Watch the first video. – 3 min
  3. * Optional 2-minute lecture with Q&A.
  4. Practice 3 to 5 problems. – 10 min
  5. Watch the second video. – 3 min
  6. Practice 3 to 5 problems. – 10 min
  7. Discuss strategies for solving problems. If any of these strategies proved helpful, discuss which ones. – 10 min

Example 1

Estimation is the most practical math skill

There are a lot of math concepts that I use regularly when writing software or computing statistics in my day job. The one skill I use all the time is estimation. (I can tell you that the ability to accurately estimate an answer is not universal.)

Example 1: Long multiplication using “math reality checks.”

In the problem in the video above, we round 892 to 900 and can estimate that our answer should be near to – and less than – 9,900.

Let’s say you type the wrong number in your phone, hitting the 6 instead of the 9, since these two are pretty close and you have big fingers. Now your answer is 7,612. If you have a good grasp of estimation and multiplication, that is clearly wrong. If you’re computing how much money you need to charge a customer based on the 892 hours you expect to work at $11.00 per hour, you have just lost out on over $2,000!

Example 2

This video also gives a strategy for solving difficult problems. That is, break the problem into smaller, easier problems.

Example 2: Use addition to solve a multiplication problem.

Here, because the last digit of one number is 7 and of the other number is 2, you know that 7 x 2 = 14. So, whatever else your answer is, it has to end in a 4.

All of those facts learned, like 2 x 7 =1 4 are the basis for the commutative property of multiplication, reducing numbers to lowest terms, or solving equations by multiplying or dividing both sides by a constant, and more. You need a BASE to work from, problems that can be examples.

The fact is that the more experience you have with numbers, the more problems you solve. The more problems solved, the easier it gets.

Standards Addressed

  • Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations.
  • Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

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