We received this comment from a Geometry Approach curriculum user: “I’m finding myself very frustrated because there are no explanations of how the answers are obtained. Is there no teacher manual in addition to the answer book? The answer book is nice but it doesn’t tell us how you got the answer if we are confused.”

This is a good point. The RightStart™ Mathematics; A Hands-On Geometric Approach level is a different format than the prior RS levels. Geometric Approach is set up more as exploration of math, which, of course, is more like your child’s future learning.

In high school and college, it is expected that the student will “read between the lines” and extract information that’s not quite specifically stated. My high school senior and three college kids get so very frustrated with this, but that’s the way it works!

Real life is this way too. Think of a baby running a fever. There is no manual that specifically states the answer or provides the steps to the cure. Instead, we need to run with trial and error. Sometimes Tylenol brings the fever down. Sometimes a cool bath. Maybe both are needed. Sometimes it’s a trip to the doctor for antibiotics!

So, how do we help you and your child work through these lessons? Well, two things will help.

First, read (or re-read) the “Hints on Tutoring” found in the front of the lesson book and attached below. A critical excerpt from this page reads “If a paragraph is unclear, the student should reread the paragraph, keeping in mind that sometimes more is explained in the following paragraph. No one learns mathematics by reading the text only once.”

I personally find not rereading the lesson is my greatest error when working through the Geometric Approach. My second most common error is reading too quickly, then jumping to conclusions, which mostly are wrong.

Second, ask us a specific question and we will get an answer to you. Have your student send an email to either info@RightStartMath.com or to JoanCotter@RightStartMath.com, put “Math Student” in the subject line, and we’ll get an answer to you as quickly as humanly possible. You may call us at 888-272-3291 and talk through the question with one of our competent people.

Also, have you and your child watched the “How To Teach” recorded webinar? This will give both of you a firmer foundation in which to work through the program.

Remember, if we did have a teacher’s manual, it would be so tempting to following the instructions item by item, which may stifle true learning. So, although I understand and agree with some of the frustration, think of this as a change in your child’s thinking and learning. It’s now time to explore and think through situations, rather than just follow a rigid algorithm.

Finally, remember to email and/or call us. We are here to help you and your child be the best you can be with your mathematics and with your future learning.

 

Maren has continued to work with her daughter, Aspen. Let’s hear how it’s been progressing…..

January 25, 2012

Aspen has been showing great understanding of organizing items by size in Level A. She is able to take any type of items and organize them both smallest to largest and in reverse. She continues to beg to go through her lessons each night and rarely gets frustrated with anything we’ve encountered thus far. She continues to want to “count items” using her AL Abacus. She wanders around the house and totals up her findings then has to verify that she is correct. When asked if a certain quantity has been added or subtracted, she has been stellar in her grasping of the concept and rarely gets them incorrect. I’m finding that the lessons are clear and concise and that it’s been quite easy to give the instructions to her to follow.

February 22, 2012

Aspen has been flourishing with her Level A lessons. She’s still so very excited when we work a lesson. We were working on parallels and about a week following the lesson as we were driving down the highway, Aspen kept asking to play the “pallellell game”. She definitely has a slight problem pronouncing it, however I was racking my mind trying to figure out what she was talking about. It finally came to me that she wanted to play a game to see if items were or were not parallel. We play our new game now whenever we have a drive, as well as when we are at home. She continues to verify with me if she’s correct when she judges if any two items are parallel or not. Math has been becoming one game after another with her, and it’s such a joy to see her enjoying herself and her new knowledge she’s acquiring.

March 27, 2012

Things are progressing nicely for Aspen, as she continues to enjoy her math. She loves working with the Abacus, and continues to play with it to work on her skills even when we’re not doing a lesson. She’s been working diligently on identifying numbers of items with her tally sticks, abacus and her fingers, and for the most part, she’s been successful. She still struggles with the 7, 8 and 9, but is getting more successful with those all the time. She still has a tendency to try to count those out when she thinks I’m not looking. She was working on them the other night, when her big brother, who’s 18, was watching. She was given an “8″ and she was looking at the abacus to figure out the appropriate beads to move, when her brother said, “Aspen just count them out on your fingers”, in which Aspen replied: “Bohdey, we don’t do it that way, we have to think about it.” He just looked at her and grinned. Maybe a little of this will eventually rub off on him, as he didn’t have the opportunity to take advantage of this product and he struggled all the way through school with his math classes. A mom can always be hopeful!

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.