I have taught RightStart Math for years and we have met and continue to meet with great success. I wanted to share the importance of learning multiplication by visualizing arrays using the AL Abacus.
Please refer to the Math Card Games book and the chapter on multiplication which, in my edition, is pages 65 – 84.
I would like to take an excerpt from page 65:
Paragraph two: “….Memorizing the multiplication facts is approached through visualizing the multiples ( also called skip counting ) patterns AND THROUGH VISUALIZING ARRAYS. The children should not recite in order to find a multiplication fact.”
The next paragraph explains in detail the patterns a child will discover with the multiples. The multiples are shown on this page and they are included on the envelopes and in the Appendix.
On page 66 is a paragraph on arrays. Here is another except:
“…The AL Abacus gives the children a wonderful visual image for remembering the multiplication facts: seeing groups of twos, fives and tens is key…”
Included in this paragraph are three examples with pictures of the arrays:
In the case of 6 taken 3 times, the child will see 5 x 3 + 3 for 18.
In the case of 4 taken 4 times, the child will see 8 + 8 = 16. (The child can use the Dot Patterns for this example.)
In the case of 9 taken 8 times, the child will see 10 x 8 – 8 = 72.
Now I can give personal testimony to this. When I began teaching multiplication to one of my children, we entered 9 taken 4 times on the abacus. He entered the beads and looked up at me and immediately said 3 ten 6. I told him yes, how did you know? He stated that he knew 4 rows of 10 was 4 ten, and 9 is one less than 10, so you take 4 off 4 ten and you get 3 ten 6.
My son understood a fact because he could relate quantities to other quantities and this is what teaching for understanding is all about. RightStart Math recommends playing games and games reinforce the concepts of the lessons. There are approximately 300 games in the Math Card Game book and the game book is an integral part of this method. For those who incorporate the playing of games you will see the results as your children continue to make discoveries.
I taught RightStart first edition, and in this edition around Level C, every sixth lesson was a review lesson. It included games to be played, but I found the review sheet often took enough time to fill up our lesson time and the child tended to be tired after a review sheet or two. So on the next day I played the games, then on the following day I resumed with the next lesson. In this manner I built in time to play the games and I put notes in my games book margin to give my opinion of the games.
As another option for families who desired to reinforce multiplication, I would recommend at least the following games for multiplication: Multiples Memory, Sum Rummy, Mystery Multiplication Card, Treasure Hunt (the kids love this one), and Multiplication Memory with the AL Abacus. Play this game a lot, because this game is so helpful!! I have often played more than one set with this game as well. What’s on Top is a very good for the child who struggles with sequencing. Multiples Solitaire, Square Memory, Ring Around the Products, Multiplying Three One Digit Numbers, and Corners Three where the child keeps score. Of course you can play other games as well but these were ones we liked and I saw value in these games. We did play the game Multi-Fun but in my notes I felt there were better games for us, so not every game may click with a particular child but it is good to try a new game and learn. Playing all these games more than once is important because another round of the same game can produce entirely different results.
When you create time for a game day you can relax and take time to play, observe your child or children and see if they can sort, shuffle, hold cards in their hands, organize cards, and help keep the cards neat and ready for the next game session. I have a few extra sets of cards and if I know I am going to play a game again I may keep the cards ready for a quick set up. It is also possible to play with a smaller set of cards to get the concept but keep the game short and sweet. Game playing can also work with more than one child or just mom and a child. I asked my darling husband if he would like to play a math game in the evening after his work day. He was not that motivated. Hence managing games was my job. I have a fishing tackle box and I store all the cards in order in the tackle box, and have done this for years. I elected to order a second set of multiplication cards which made things much faster for us. Previously I had to raid the envelopes and return the cards which I found took too much of my time.
Playing a Corners game is always a great fall back. Super easy to set up and there is continued value in this game along with its many variations. Toss the Corners Cards, a score pad and some pencils into a Ziplock bag on the way to the doctor, dentist or any appointment. While you wait, play a game. While one child is at band practice, play a game with another child.
I just want to mention that RightStart Math has a philosophy behind the curriculum. Dr. Cotter writes that flash cards are not an ideal way for a child to learn their facts. I would like to expand on this. There are 400 facts for a child to learn, spanning addition, subtraction, multiplication and division.
Let us take the following numbers.
8 + 4 = 12
8 – 4 = 4
8 x 4 = 32
8 / 4 = 2
Flash cards expect a child to look at two numbers and relate it to a third, using an operation symbol and an equals symbol.
The operation symbol changes and then the child looks at the same two numbers and needs to relate them to a different answer and this will occur over 4 operations, so the child needs to memorize 400 separate pieces of information.
However the child who learns math by relating numbers to one another, can reason and deduct the facts based understanding.
So let us take the Corners Game. The child plays a game and in this game they will learn to make 5, 10, 15 and 20 as sums, and add these sums for a score for each turn they take. The arrive at 15 with a 10 and 5, a 9 and 6 or an 8 and 7.
Now when they need to read and answer an equation, if they see the equation 15 – 8 they know it is 7 because they played the Corners game (frequently). Furthermore they know 14 – 8 is 6 because they know 15 – 8 is 7.
The child who reads the flash card 15 – 8 = 7, will probably not make the connection to the fact 14 – 8. For the child who uses flash cards each fact is an individual fact, and relationships are not really formed.
Those who are taught with flash cards think there are 400 separate facts to learn.
The child who learns by understanding applies addition knowledge when learning both subtraction and multiplication. They apply multiplication knowledge when learning division. Understanding fuels more understanding.
Flash cards just show two numbers and expect the child to relate a third number to the first two. There are better ways in RightStart Math to achieve recall of multiplication facts than flash cards.
Math wrap ups are very interesting and I am familiar with them. They will also expect the child relate a pair of numbers to another number but the wrap up will have many numbers on each side of a plastic panel. The AL Abacus is more useful than a wrap up, in my opinion.
When mixing other methods, keep in mind the font used. RightStart Math uses a distinct font to help curb reversals and inversions of digits. In RightStart digits 6 and 9 look different and the 8 has a nice tail at the top. This font is very helpful for a child who struggles to visualize symbols. Most other math products do not take the unique symbol into consideration.
Debbie O posted that not all children can memorize information. Dr. Cotter shares that about 15% of the population cannot memorize information well. I have an older son who fell into this category. In his early years he was the unfortunate recipient of rote memorization, rushed instruction, and weak curriculum. He was dyslexic and his ability to learn math was so compromised with his early foundational instruction. I can recall in first grade how he had to do mad minute math drills with a work sheet. He was to answer as many math problems as he could in one minute. This caused him to rush and feel stressed. He learned nothing.
I embarked on home school and for years I tried very hard to help him learn. If this innocent child had the benefit from learning with RightStart from the beginning so much of his difficulty could have been prevented. In contrast his younger brother began with RightStart at age 3 and 4. He learned so well with this method. The confidence my youngest son has in math is wonderful, and I attribute this to his learning with RightStart Math. Yet there is a part of me that will always wonder, what if my oldest could have had this foundation. It is for this reason that I take the time to share my thoughts with families as they desire to educate their children. Please be careful when making decisions regarding math instruction and that learning concepts is the first aspect and recall can be achieved put should not take precedence over understanding.
When a family feels they want to work on multiplication facts here are a few things to consider:
1. Access the child’s addition and subtraction facts first, especially addition facts. I would expect a 3-second recall for all addition facts first. If this is not the case, I would reinforce addition fact and subtraction facts prior to teaching multiplication facts. Use the strategies to achieve this. If memory serves me, I think I spent about six weeks parked on addition and subtraction strategies when we were in Level C. We spent 12 working on these strategies. I spent 13 teaching months on Level C, first edition.
2. Use the AL Abacus. Enter the multiplication equation and look at the patterns to arrive at the product.
3. Isolate the multiplication facts first and strengthen the ones, twos, fives, and tens first. Then add in the threes, fours, sixes, sevens and nines. You can follow the order of this based on your teachers manual. Once there is more understanding you can mix different sets.
4. Skip counting helps the child see patterns. All the twos are even numbers, the fives end in 0 and 5. The bottom row of the fours are twenty more than the top row. The bottom row of the eights are 40 more than the top row. The digits for the products of nines add up to nine. They help with patterns but are not used for recall.
5. If a child choose to skip count his way to arrive at a product, offer them the abacus and have them enter the equation and see the patterns to have a visual representation of a fact.
6. After playing a multiplication game like Multiplication Memory, take out some notebook paper or math journal paper and have the child write out each equation for the fact group you are working on. You might elect to work with gridded paper so the child can align the numbers nicely, keeping place value in mind. Later on if the child makes a mistake, it is okay, but show them their hand written equations to jog their memory a bit.
7. It is perfectly fine to park and reinforce multiplication, by playing games and given written practice for a few weeks. Help the child see a mistake and learn how to correct the mistake. Mistakes are a part of learning and children do not learn a concept because it was covered once. They learn it after a long period of exposure.
8. Be careful when mixing other math curriculum if the methods are contradictory. If one method promotes memorization but another method promotes understanding, the interchange can confuse a child.
9. Determine the need. When is mastery of multiplication age-appropriate? RightStart places a large emphasis on a student really solidifying addition and multiplication. With these two operations as a solid base, subtraction and division come naturally. If a family desires to continue to home school and continues to use RightStart, there is time for the child to learn at their pace for understanding. If the family desires a new method or might enter a child into a school system, rote learning and speed are emphasized, but our nation is by no means a leader in mathematics, so while a large percentage American school children are being taught to learn by memorization and speed, the US does not rank that high as a nation in math proficiency.
10. Keep true to your goals as a family. Why are you home schooling and why did you select this method? Take advantage of the freedom that home schooling affords and teach a child at the pace that makes sense for the child. It is important to teach math correctly. Math builds upon itself. Laying the foundation correctly is vital for all higher level math and for life.
I wish you all the best as you navigate math instruction. The time that a home educator invests in teaching her children is so important today and I cheer you all from the sidelines.
I will leave with this interesting dialog between my sons:
On a rare occasion my boys were seated at the kitchen table and they each got a small bag of potato chips which I picked up at the market. This was a treat because I do not encourage potato chips. My oldest who did not have RightStart Math as his foundation looked at the bag of chips. In the corner the bag showed a little star with a price that said 35 cents and a circle that said 3 for a dollar. My oldest said, mom 35 + 35 + 35 is 1 dollar. His younger brother was sitting on the opposite side of the table and he said no, 35 + 35 + 35 is $1.05. My youngest looked directly at my oldest and told him he was incorrect, 3 bags of chips cost $1.05 My oldest looked at me, questioning me. I explained if you bought 3 bags of chips you got a discount and they took 5 cents off. My oldest looked at me so sad, how could they write that on the bag, how could they trick me. My youngest sat their confidently eating his sandwich and I knew he knew the truth. My youngest learned with RightStart Math.
RightStart Math is an excellent method and one that is worth the time to teach.
Teaching RightStart Math since 2008