Multiplication and Division, Part 2
This unit is also about multiplication and division, but with larger numbers. The same ideas apply, knowing more than one strategy to solve problems, communicating the thought process(es). We will work with larger numbers, so knowing the times table is very important. Showing the work in detail is important so difficulties can be identified and clarified. Simply saying "I did the work in my head" or "I just knew it" won't be acceptable for problems other than single digit times single digit multiplication.
Clustering, which means taking big problems and breaking them into smaller, easier ones will be a large part of instruction, as will rounding and estimating combined with managing zeroes. For example the problem 31 x 22 = can be worked by getting a quick estimate by rounding 31 to 30 and 22 to 20.
Our quick estimate is 30 x 20 which is just 3 x 2 with 2 zeroes attached, or 600. Now we have an idea of what our answer should be. Let's see how it goes. 31 x 22 can be broken into 31 x 20 added to 31 x 2. Those pieces are easily obtained by this way. 31 x 20 is just 31 doubled with a "0" attached, 62 and attach 0 for 620, then add the 31 x 2 part which is 62. Keeping our place value correct, we add 620 and 62 to get 682, which is not far from our quick estimate of 600.