A powerful multiplication pattern
A silent-teacher activity! Comparing two products on a number line -- a number times itself, and the number's neighbors times each other -- gives excellent fact practice and reveals a pattern that both helps the students learn their facts, and gives them a bonus!
Setup of activity
See Think Math! website for the image and how to run this activity.
Purpose: Practice embedded in a very surprising pattern-finding activity. The pattern helps children remember some of the facts they’re not sure about, but also lets them do surprising mental math “tricks,” like multiplying 49 × 51 in their heads. Being able to do 49 × 51 mentally is not important for anything, but the skills they use as they get that answer -- multiplying 50 × 50 mentally, subtracting 1 from that mentally, keeping track of all that in their mind -- are all very important. Because the teacher is silent during the pattern search, the kids feel “smart” at finding the pattern (nobody’s told them anything!), and they typically feel very smart when they can perform the fancy multiplications mentally. Feeling smart helps them put in effort that nobody is willing to put in when they don’t expect success. The website shows how to extend this activity to cover other math facts and do other “smart” mental multiplication “tricks.”
On their own
Students can explore what happens when they take two steps away from the central number (the number that is multiplied by itself), like this:
This new exploration (and see http://thinkmath.edc.org/index.php/Difference_of_squares for more) continues the fact practice because a new set of facts are being rehearsed, and leads to another discovery that children can “show off” with, multiplying 28 × 32 in their heads.
It is especially important for students who see themselves as mathematically weak to discover “amazing” things that they can do mentally, because nobody -- no corporation and no child -- puts effort into a venture that they doubt will succeed. Only when they really believe that they can win the game is it worth the work; realizing what surprising things they can do helps them put more effort in.
This section is incomplete. You can help by expanding it. Need some worksheets here.