Tricks of the Trade
Mathematics is full of patterns. This is why math is both beautiful and fascinating. By learning some of these patterns, we can become faster and more proficient in our calculations as well as more observant of the wonder all around us. There are all kinds of fun mathematical tricks that, hopefully, will help make math more enjoyable to our students/children.
Here's a math pattern for students to use to check their answer when multiplying by 9: the answer or solution will always add up to 9. For example, 8 x 9 = 72; 7 + 2 = 9. 15 x 9 = 135; 1 + 3 + 5 = 9. 342 x 9 = 3078; 3 + 0 + 7 + 8 = 18; 1+ 8 = 9 This method of checking an answer works for any number multiplied by 9.
To learn to do addition problems mentally, I recommend learning to add from left to right the way we normally read numbers rather than from right to left. Adding from left to right enables you to do the problem in your head without using paper and pencil or to write it as you go from left to right. For example, 346 + 795 Think in this way: 7 (hundreds) + 3 (hundreds) = 10 (hundreds) or 1,000. Write the 1 in the thousands column, holding the 0 in your mind. 4 (tens) + 9 (tens) = 13 (tens) or 130. Add the 1 to the 0 from your hundreds column addition, and write 1 in the hundreds column, holding the 3 remaining tens in your mind. Add 6 (ones) + 5 (ones) = 11. Add the 1 ten to the 3 tens from your tens column addition, and write 4 in the tens column. Write the 1 one in the ones column. Answer: 1141
Also, if you learn to subtract upwards rather than downwards, you can learn to do it in your head. It saves time and is less complicated. To do this, you have to start by thinking in terms of 10: what adds up to 10. For example: 73 — 46 Start with 46. Think: 46 up to 50 (6 + ? = 10) = 4. Now I'm using 10s and it's easy: 50 up to 70 = 20 (20 + 4 = 24); 70 to 73 = 3. Answer 27.
Both these methods take practice, of course. But in the end, they are faster and easier. With the upward subtraction method, you skip all the crossing out and borrowing. That method (the downward method with crossing out and borrowing) should be learned and understood, but in order to do subtraction mentally, the upward method is far easier, in my opinion.
If you want to learn a couple fun patterns that enable you to multiply quickly by 11 or by 25 in your head, check out the link below. Your students will love it!
Math patterns are everywhere just waiting for us to discover. Remember: "Math is the language of God." He has embedded the world and the system of numbers it is based on with patterns galore. Hopefully, the more "tricks of the trade" our students learn, the more fun they will have with math. And the more they are able to do math quickly in their heads, the more they will enjoy it. Happy computing!
Multiplying by 11 and by 25 (After the "x 11" video, scroll down and click on "Show step by step solutions" for how to do "x 25" and the video will come up): https://www.onlinemathlearning.com/math-trick-multiply-11-25.html