Mental math tricks and tips | Kathryn Re

Mental math and estimation are two topics that have been ignored or minimized in schools. If you graduated from high school before 1990, your math education was mostly computation and other processes (mathematicians call these algorithms). That left little time for other math topics. If you are still in school or graduated after 1990, your math education was expanded to include probability, statistics, geometry and problem solving. Even with the general use of calculators to speed up our learning of all the new material, mental math and estimation were again put on the back burner and left there.

Mental math and estimation are two topics that have been ignored or minimized in schools. If you graduated from high school before 1990, your math education was mostly computation and other processes (mathematicians call these algorithms). That left little time for other math topics. If you are still in school or graduated after 1990, your math education was expanded to include probability, statistics, geometry and problem solving.  Even with the general use of calculators to speed up our learning of all the new material, mental math and estimation were again put on the back burner and left there.

Suppose your second-grader is having trouble remembering some addition facts. She comes to you with the problem 5+7 because she cannot remember the fact. Suppose that you don’t tell her the answer, but reply with “What is 5+5?”  She readily answers that 10 is the correct answer.  Then you say, “How much more is 5+7 than 5+5”?  If she can tell you that it is two more, she now can figure out the answer on her own:  5+7= 5+5+2, which is 10+2, which is 12. You and your second-grader have just discovered the strategy of substitution.

Let’s try another one. Let’s use our new strategy to add 17+7.  We think of 17 as 10+7, so we have 10+7+7. The last 7 is really 3+4 (because we had to add something to 7 to get 10). We now have 17+7 is really 10+7+3+4. 7+3 is 10, and 10 added to 10 is 20. Now add the 4 to get 24. Notice that we never really had to “carry” anything.

If you can add 10s to any number, then you can add 9s, too. Since 9 is really one less than 10, we can add a 9 by adding 10, then backing up one.  For example, 23+9 can be thought of as 23+10-1, or 33–1, which is 32.

One last example: At the dinner table, your middle school student asks you what the result of 27+48 is. With your hands occupied with the knife and fork, you can’t do the problem “in the air” and, with the calculator in the next room, you may have to admit to your student that you don’t know the answer. But wait! You now have the strategy of substitution!  Think of 27 as 20+7 and 48 as 40+8. Add the tens first: 20+40 is 60. So now you only need to deal with 7+8.  You know that 7+3 is 10, so you think of 7+8 as 7+3+5 which is 15. So 60+15 is 60+10+5=75.  Again you never had to “carry” anything!

See if you can do these “in your head”.  Then check the answers at the bottom of the column.

1)  37 + 17        2)  19 + 57        3)  286 + 428

————————————–

Answers:

(1)  37 + 17 = 30 + 10 + 7 + 7 = 40 + 7 + 3 + 4 = 50 + 4 = 54

(2)  19 + 57 = 57 + 19 = 57 + 10 + 9 = 67 + 9 = 67 + 10 – 1 = 77 – 1 = 76

(3)  286 + 428 = 200 + 400 + 80 + 20 + 6 + 8 = 600 + 100 + 6 + 8 = 700 + 6 + 4 + 4 = 714

More in Life

Enumclaw High hosts 7th annual Empty Bowls event

The event, held at Enumclaw High School, will help fund the Enumclaw Food Bank and Plateau Outreach Ministries.

Read the first two books before tackling ‘Banished’

Well, look at you. And you do — ten times a day,… Continue reading

Buckley Kiwanis names Students of the Month

For January, students from White River High School, Glacier Middle School and Carbonado Historical School District were chosen.

Local students named to WSU honor roll

Students from Black Diamond to Sumner found themselves on WSU’s President’s Honor Roll.

A small act of kindness can make a big impact | SoHaPP

Join SoHaPP’s book group this February to discuss “Wonder” by R.J. Palacio. Don’t have the book? Check it out at the Enumclaw Library or visit The Sequel.

This book will WOW you | Point of Review

Wow. Just… wow. Did you see that? Wasn’t it awesome? It was… Continue reading

EHS graduate McNab promoted to Lieutenant Colonel

Tom McNab was recently promoted to the rank of lieutenant colonel in the United States Air Force.

White River Valley Museum opens “Suffer for Beauty” exhibit

Corsets, bras, and bustles, oh my! The White River Valley Museum is hosting its new event, “Suffer for Beauty,” which is all about the changing ideals of female beauty through the ages. The exhibit runs through June 17.

Library’s art and writing contest returns to Pierce County | Pierce County Library System

Pierce County teens are encouraged to express themselves through writing, painting, drawing and more for the annual Our Own Expressions competition, hosted by the Pierce County Library System.

‘School of Awake’ offers advice to adolescent girls

Twinkle, twinkle. For as long as you can remember, you’ve known how… Continue reading

Mental health first aid training in Enumclaw | The Summit

Friday, January 19 at 7 p.m., Dr. Michelle Bengtson will kick off the mental health-themed weekend by speaking on Hope for Depression: The World’s Greatest Epidemic. Dr. Bengtson is the author of the award winning “Hope Prevails: Insights from a Doctor’s Personal Journey through Depression.”

Print 3-D creations at Pierce County Library System

Bring a ready-to-print file and watch the magic of 3-D printing bring the file to life at Pierce County Library System’s 3-D Print Shop. The free print shop sessions are offered January through March at Pierce County Libraries, giving people the opportunity to use the 3-D printers to create items, get quick design lessons, and learn the 3-D printing process.