Teaching 2-digit multiplication and estimation

STANDARDS TAUGHT

  • 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.

Required Supplies or Devices

  • Computer and projector, smartboard or other device for class to watch videos
  • 20 math problems 3-digit numbers multiplied by a 2-digit number. Can be shown using projector, in student math books or printed and passed out as worksheets Here is a program to create worksheets of random problems.

Lesson overview

  1. Have the students try to solve 3 to 5 problems- 10 minutes
  2. Watch the first video – 3 minutes
  3. * Optional 2-minute lecture after video 1
  4. Try another 3 to 5 problems – 10 minutes
  5. Watch the second video – 3 minutes
  6. Do another 3 to 5 problems – 10 minutes
  7. Discuss strategies for solving problems with students if any of the strategies helped them solve the problems, and if so, which ones – 10 minutes
Long multiplication and math reality checks: Example 1

Estimation is the most practical math skill

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

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 an hour, you have just lost out on over $2,000!

A different example of estimation

…. comes from the second video . 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.

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

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

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

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