Check numbers are a method of checking addition. Sometimes, this is called Casting out Nines. Check numbers also works with subtraction, multiplication, and division. I like to think of check numbers as a cool tool for my math toolbox. Some people use check numbers frequently, others, not so much. However, if we don’t let people know about these cool things, we’ll never know who might use them!

Let’s look at how to find check numbers, then how to apply them. We also have a presentation on check numbers for you to review. Check numbers are first taught in RightStart™ Mathematics Level D, starting in lesson 47, and Level E, lesson 4, and Math Card Games, game #A63.

Finding Simple Check Numbers

Check numbers are one digit numbers from 0 to 8. We will designate the check numbers by using parenthesis.

Let’s start with a simple two-digit number:    17

Add the digits together:                                 1 + 7 = 8

Check number of 17 is (8).

Now let’s try another:       49

Add the digits together:  4 + 9 = 13

Remember check numbers are only one digit, so we’ll need to take the 13 found above, and continue to add the digits together:  1 + 3 = 4

Check number of 49 is (4).

Another:                              99

Add the digits together:      9 + 9 = 18

And again:                                      1 + 8 = 9

However, remember we said that check numbers are from 0 to 8? There are no 9s. Now what? Well, all 9s are 0s. So, on this example, we have 1 + 8 = 9, and 9 = 0.

Check number of 99 is (0).

Because all 9s = 0s, we have a quick shortcut to help find check number.

Let’s back up to our second example:                 49

If 9 = 0, then it looks like this:                             4 + 0 = (4),

which is what we had the “long” way. Neat, right?

Let’s reapply to our third example:                      99

Well, that’d be:                                                   0 + 0 = (0)

Remember the other name for Check Numbers is Casting Out Nines. If we “cast” the 9s out, which is the same as 0, our work is simplified!

Finding More Check Numbers

Let’s find check numbers with a four-digit number:   4639

Add the digits together:                                            4 + 6 + 3 + 9 = 22

And again:                                                                                        2 + 2 = 4

Check number of 4639 is (4).

Let’s try this again using some of our newly discovered shortcuts.

Remember, 9 = 0.                                                     4639

We can “cast out” the 9, so now we have:           4 + 6 + 3 + 0

But 6 + 3 = 9, so let’s “cast” that out too!            4 + 0 + 0 + 0 = 4

Well! That was easy! Check number of 4639 is quickly found as (4).

Another one:                                                              7326

See anything to “cast”? How about 7 & 2 and 3 & 6? Check number is (0).

Applying Check Numbers

So now that we can find check numbers, let’s use them!

Consider the following equation:

.   4639

+  7326

. 11965

If you’re like me, you wonder if you added it correctly and often will double check either by recalculating and/or checking on a calculator. We can check accuracy by using check numbers!

So, figure the check numbers:

.   4639  (4)

+  7326  (0)

. 11965  (4)

Look at the check numbers! (4)+(0)=(4)!

Let’s do another:

.     364

+  4426

Calculate the answer then calculate the check numbers. Did you do it right?

Should look like this:

.     364  (4)

+  4426  (7)

.   4790  (2)

and the check numbers are correct too.

Now, let’s assume you came up with a wrong sum (which happens) and it looked like this:

.     364  (4)

+  4426  (7)

.   4780  (1)  ERROR

Notice now how the check numbers don’t add up. (4) + (7) does not equal (1). This becomes our check! We now know something is wrong and needs to be corrected.

More Applying Check Numbers

As we can see, check numbers are a method of checking and verifying addition calculations. If the check numbers are not adding up, the answer is probably wrong.

Remember that check numbers work with subtraction, multiplication, and division? We’re going to save that for another post. Meanwhile, play around and see what you discover! Stay tuned……

Kulm Public School, located in Kulm North Dakota, is using the RightStart™ Mathematics curriculum. In November, they had a math day for the entire elementary school with great success. Let me tell you all about it.

About a month before the event, Tami Kramlich, the Elementary Principal, wrote to us and said,

“Last year we had a literacy and fitness event that was very well-received. Each classroom had a fitness station where the kids and parents learned some easy to do fitness activities. At the end we all met in the lunchroom for snacks and read a book together. We would like to do something similar with our math event.”

So the planning began. We set the event on Monday, November 21, 2011. The event schedule was set:

1:00 – 1:30—Introduction to RightStart™ Math
1:30 – 1:50—First Station
1:50 – 2:10—Second Station
2:10 – 2:30—Third Station
2:30 – 2:50—Fourth Station
2:50 – 3:10—Fifth Station
3:10 – 3:20—Snacks
3:25—Regular Dismissal

Each station, held in different classrooms, had a one or two of the math games set up. Games chosen were Corners™ (MCG #A9), What Makes 16 Cents (MCG #M6), Short Chain (MCG #A47), Fraction War (MCG #F7 and #F9), Multiplication Memory (MCG #P10), Swim to Ten (MCG #N34) and Memory with Different Sets of Cards (MCG #N17).

Parents and children were placed on teams and rotated from station to station to learn a new math game and spend a few minutes playing that game. In some situations, the group would watch the video, sometimes the teacher would demonstrate the game, or sometimes the group would watch a select few play the game, then everyone would go and play it themselves.

We had a blast! Parents and grandparents were involved, children were proud of their classrooms and their math skills, and everyone was learning. Laughter was heard up and down the halls. When the buzzer sounded to indicate it was time to move to the next station, I’d hear “Hurry up so I can get a turn!” or “Now that was GREAT!”

I challenge you to create a game day. If you’re in a school setting, we have the plan outlined right here. If you are a tutor or homeschooler, maybe set up a couple hour block and play games, changing the game every 15 to 20 minutes.

Let us know how this goes. Post your thoughts on Facebook or Twitter!

Have a great day and play a math card game.

RightStart™ Mathematics Level E is the fifth and final year where the teacher is working with the child directly. The following year, Level G, the student will be more independent and the teacher becomes more of a facilitator than an active teacher.

Here is an email from Heidi, written April 1, 2011. As you read this, notice how the child and other family members are already starting to move towards a cooperative learning style.

     This is a note to tell you how much I’m enjoying the courses you’ve developed.  I was introduced to your program a year ago by a homeschooling friend and have had a wonderful time with my youngest son this past year in Level B.  In fact, I find your methods so interesting that I wanted to introduce them to my older son, and we’ve begun to work through Level E.  

     Yesterday we were poring over Durer’s magic square in Level E and he found some additional patterns! The next morning, my husband and son found more! How incredible is that? …

     When Nathan discovered the first set of corner patterns yesterday it was quite exciting, and we enjoyed more of it this morning together and wanted you to know.

What fun that father and son are excited over math patterns! Side by side, both are exploring and learning. Knowing that Dad is interested, excited, and intrigued by math, I’m thinking the son’s math focus is heightened.

She continues: My older daughter, … was so frustrated [with her current math program] that I thought if she did your geometry program she might move up to Algebra thereafter. I’m encouraging her to do several lessons a day.  She enjoys the artistic element of the work.  

     I know she is meant to read and discover for herself, which I’m encouraging her to do.  I am determined to order a workbook for myself and do the program as well as a refresher, as an example to her of my interest in understanding what she’s doing, and thus hopefully as a motivator.

This mother-daughter team is as effective as the father-son team. Dr. Cotter says it is helpful for two people to do the lessons together. Try to work as an “equal,” not as the “teacher.” After both people do the worksheets, compare the results and then look at the RightStart™ Mathematics; A Hands-On Geometric Approach Solutions. Having the parent/teacher stay ahead of the student is also a good idea.

Heidi concludes: After all these years, anything that seems like a word problem still paralyzes me.  On Worksheet 29 [of RightStart™ Mathematics; A Hands-On Geometric Approach], I had to look in the answer book to get me going.  

     Analyzing why I struggled, I realized that if I could first state my discovery, then describing the process was no problem.  I don’t know if I would have gotten to it without the teacher’s resource.  Do you recommend I let my daughter have access to that when she stumbles?  I’m afraid it might become too much of a crutch to her.  

     I suppose by working just ahead of her and understanding, then I can lead her to it with appropriate questions or even clearly stating my strategy.

Dr. Cotter responded to Heidi that It is fine for the student to use the Solutions to look at the answer, then go back and work the problem through. This is a common practice in college courses!

Also, let the student know that it is a good practice, after making an error, to write on the back of the worksheet page where they went wrong. With the wrong path identified, the correct path is more evident. Most importantly, remind the student that each lesson needs to be read, not once, but several times, just like a college textbook.

Finally, if a student has questions in Level G, RightStart™ Mathematics; A Hands-On Geometric Approach, they can email Dr. Cotter directly at JoanCotter@RightStartMath.com. Students who put “Math student” in the subject get answered first.

Enjoy your time with your child in Levels A through E. Level G will start them on the path of self-teaching.

Old Main Game (#A4)

This game is spin off of the popular child’s game Old Maid. Rather than pairs being matching cards, pairs are two cards that add up to ten. This helps the children learn and practice their math facts. More importantly, this will provide an application for the newly learned facts.

For each player, use a set of cards from 1 to 9, making sure there is an equal number of 5s. Without looking, remove one card from the deck and set it aside. This will become the unmatched “dead end” card that is to be avoided. Deal all cards to the players. If someone has one more card than another, that’s just fine.

In turn, each person will pick a card from the player on their left. If the new card creates a match (two cards equally 10), they may lay down the pair. If not, the second person will pick a card from the person on their left. Play will go round and round until the one “dead end” card remains.

One mom says “I had my friend’s two daughters (6 and 9) over today for a couple of hours, and with my own two (5 and 8 ) I thought it would be a good time to play a math game. It’s our first one with the kids. We picked Old Main (where the pairs make 10).

“It was a pretty big hit. I cruised around helping a bit, and they played a few hands quite happily. I was particularly relieved that no one was upset to have the last (dead end) card. Instead, our emphasis went to “Oh, Hannah has the mystery match! Okay, so what must the mystery card be?” The older two shouted out what the missing card had to be, we flipped it over, they were happy, and we went on to the next hand.

“Abigail (6) was the cutest. As we first dealt the cards, she said, ‘My mom is starting to do math with me this year. Maybe this will help us learn something!’ Raised eyebrows, I said, ‘Imagine if that happened, how cool would that be?’”

Go to the Dump Game (#A3)

Another game that is dearly loved by children is Go to the Dump. This is the same format as the ever popular Go Fish game. If you would like to see the game in action, click here.

Matches are facts of 10 and players ask for matches to the cards they have in hand. If the requested card isn’t available, the player is sent to the “dump”, the stack of cards in the center of the group.

Dia writes, “Kodi and I played the Go to the Dump game. She got four 1s and then got the giggles so bad, she was crying! All she could ask was ‘Got a 9’? What a fun time to spend with her!”

How much fun is Dia having with her daughter? Do you think they’d have as much fun doing worksheets?

Another mom writes, “Today we played Go to the Dump. Pretty easy stuff for a 10 year old who’s finished Grade 6 math, right? Well, he asked to play it again THREE TIMES.”

Assessment Tool

Games also provide an assessment tool.

Sandi writes, “We are playing the Go to the Dump and Old Main. I want to let you all know that I love this program. My daughter loves it too. I like that in interacting with her during the games, I can see if she understands a concept or not and start addressing before frustration sets in. It is great to play games to let a concept set in and not have to drill or do worksheets over and over to try and understand something. RightStart™ is laid out exceptionally well.”

I like to equate math card games to hugs. You can’t hug your child too much; you can’t play enough math card games. So, go play a math card game!