A Blog by Carnegie Learning
Teaching the ‘why’ and not just the ‘how’ builds deeper understanding, problem-solving and analytical skills in our kids.
I recently noticed a video making the rounds on Facebook: Japanese Multiplication - Multiply Using Lines (Math Trick)
Pretty cool, right? It might even seem like magic.
In reality, this technique is not as different from the "traditional" one we're used to as you might think.
When you draw the lines, you are performing the same multiplication as you might otherwise.
Calculate the 1s place of the product:
Calculate the 10s place of the product:
Calculate the 100s place of the product and add everything together:
In the Japanese example, the lines that are drawn represent different values: 1s, 10s, and 100s. When you draw the lines and count their intersections, you are performing the exact same multiplications and additions as you did in the traditional method:
In fact, you might ask yourself: Why does the traditional way work? It can also seem magical, but it’s simply an issue of place values. For example, the 42 must be shifted over to the left (rather than directly under the 63) because it is actually 420, not 42.
My son’s in fourth grade, and he's being taught to break it up like this to understand the 'why' beyond just the 'how' (the formula):
Twenty-one twenty-threes is twenty twenty-threes plus one twenty-three: 21*23 = (20+1)*23 = 20*23 + 1*23. And twenty twenty-threes is twenty twenties plus twenty threes: 20*23 = 20*(20+3) = 20*20 + 20*3.
Both of the above “magic methods” end up doing exactly the same multiplications and additions that we arrive at by breaking up the problem in this intuitive way: 20 × 20, 20 × 3, 1 × 20, and 1 × 3.
This type of conceptual understanding will help my son as he solves problems -- mathematical or not -- in the future. It’s really great to see how it’s become second nature to him to break up complex problems into simpler parts!
Parents can get frustrated when their children come home with math assignments that they don't understand and can't help with. When that happens, it’s important to remember that just because something was always done a certain way doesn’t mean it’s the best way to do it! Teaching the ‘why’ and not just the ‘how’ builds not only deeper understanding in our kids, but problem-solving and analytical skills that they will use throughout their lives.
You never know -- you might even learn something from your kids if you let them explain their math homework to you!
Matt is a Senior Software Developer on Carnegie Learning’s Intelligent Tutoring Systems team. He’s been with Carnegie Learning for 18 years, and has worked on pretty much every part of the MATHia platform at some point during that time. He enjoys spending time with his family, biking, coding, and swing dancing in his spare time.Explore more related to this author
Parents can get frustrated when their children come home with math assignments that they don't understand and can't help with. When that happens, it’s important to remember that just because something was always done a certain way doesn’t mean it’s the best way to do it!
Matt McHenry, Senior Software Developer, Carnegie Learning