Kids are pattern recognition experts.. Humans recognize patterns. We rely on them in all aspects of life. Highly motivated children are what make a school work.
Yet, when teaching math, we don't fully utilize a child's potential to recognize the patterns math provides. Some of these patterns have become so ingrained into us as adults, we don't even recognize them as something to teach. Modern math education has been moving away from the barrage of facts raining down on our kids. Patterns are being used more to guide children towards understanding. But the
ability to recognize patterns appears early in human development. Very young children can be shown patterns in math which will help them solve problems throughout their life. When guided towards understanding the beauty of math, children learn to self train their mind. This exercising of their logical part of the brain results in easy understanding of many concepts. These math patterns are so easy for children to grasp, that they themselves can become teachers of the pattern math method. When a child is given responsibility to help another child learn, she becomes highly motivated. Often, schools treat children as a problem to control. We need to treat children as a resource. Children are the majority in school. IF we believe in democracy, we need to let them have some choice. When offered, many children jump at the chance to learn a mental math method. The most important of these early ideas is to teach very young children to recognize both how many fingers are held up, and, at the same time, how many are held down. A child can easily learn this by heart before age 5. In my experience, any child who does this becomes a master of early math. I taught this to kids 13 years ago at a pre school in Boston. All of those kids who I taught again as a substitute teacher in Boston over the next 10 years were all near the top of their class in math. I found myself teaching this idea to their fellow 5th graders who still had not memorized how to make 10. The so called "10 fact family" has since become a much more important element of public school math education. (I saw it on a big piece of paper up on the door of a 1st grade class in East Oakland this year for the first time. It made me very happy.) The idea behind mental math goes beyond knowing all the answers. But, there are some answers, if children memorize them early, which can help them recognize patterns automatically. For example, when you add 7, the ones digit will go up 7, or down 3. ( 5+7 = 12 , 5-3 = 2 // 8+7 = 15, 8-3 = 5 )
When you add 5 and carry, you subtract 5 from the ones digit. When you add 6 and carry, you subtract 4 from the ones digit. When you add 7 and carry, you subtract 3 from the ones digit. When you add 8 and carry, you subtract 2 from the ones digit. When you add 9 and carry, you subtract 1 from the ones digit.
5+5 = 10
6+4 = 10
7+3 = 10
8+2 = 10
9+1 = 10
10+0 = 10
There are other simple concepts that can be taught well before most schools teach them. Skip counting is a very simple technique which can be used to teach times tables. Many people use skip counting to teach the even and odd numbers. But few use it for teaching other multiples. For example the threes can be taught by the teacher counting twice, then the child. ( teacher: 1 , 2, student: 3, teacher 4, 5, student: 6, teacher: 7 , 8, student: 9, teacher 10,11, student: 12 etc). Once the student learns the 2s, the fours can be skip counted:
- teacher: 2 , student: 4, teacher 6, student: 8, etc. so can the 6s:
- teacher: 2 , 4, student: 6, teacher 8, 10, student: 12, etc.
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When the student begins to write her numbers, these ideas can be used to teach factoring well before the child learns the word. Most teachers ask their student to write their numbers 10 per line. This is of course a fine way to look at numbers. And there some very nice patterns which show themselves on the 100 chart. But we can also have kids write their numbers 3 per line to learn the 3s, 6s, 9s, 12 and how they relate as factors. Learn the 3s, 6s and 9s by skip counting.
1, 2, 3 = 3 x 1
4, 5 , 6 = 3 x 2 = 6 x 1
7, 8 , 9 = 3 x 3 = 9 x 1
10 , 11 , 12 = 3 x 4 = 6 x = 12 x 1
13 , , = 3 x 5
, , = 3 x 6 = 6 x = 9 x
, , = 3 x 7
, , = 3 x 8 = 6 x = 12 x __
, , = 3 x 9 = 9 x
, , 30 = 3 x 10 = 6 x
, , = 3 x 11
, , = 3 x 12 = 6 x = 9 x = 12 x __
, , = 3 x 13
, , = 3 x 14 = 6 x
, , = 3 x 15 = 9 x
, , = 3 x 16 = 6 x = 12 x __
, , = 3 x 17
, , = 3 x 18 = 6 x = 9 x
, , = 3 x 19
, , 60 = 3 x 20 = 6 x 10 = 12 x __
, , = 3 x 21
, , = 3 x 22 = 6 x = 9 x
, , = 3 x 23
, ,____ = 3 x 24 = 6 x __ = 12 x __
, , = 3 x 25
, , = 3 x 26 = 6 x = 9 x
, , = 3 x 27
, ,____ = 3 x 28 = 6 x __ = 12 x __
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Learn the 2s, 4s, 6s, and 8s by skip counting. Even numbers end in 2 4 6 8 0. Odds end in 1 3 5 7 9 .
1 , 2 = 2 x 1
3 , 4 = 2 x 2 = 4 x 1
5 , 6 = 2 x 3 = 6 x
7 , 8 = 2 x 4 = 4 x = 8 x
9 , 10 = 2 x 5
, = 2 x 6 = 4 x = 6 x
, = 2 x 7
, = 2 x 8 = 4 x = 8 x
, = 2 x 9 = 6 x
, 20 = 2 x 10 = 4 x
, = 2 x 11
, = 2 x 12 = 4 x = 6 x = 8 x
, = 2 x 13
, = 2 x 14 = 4 x
, = 2 x 15 = 6 x
, = 2 x 16 = 4 x = 8 x
, = 2 x 17
, = 2 x 18 = 4 x = 6 x
, = 2 x 19
, 40 = 2 x 20 = 4 x 10 = 8 x
, = 2 x 21 = 6 x
, = 2 x 22 = 4 x
, = 2 x 23
, = 2 x 24 = 4 x = 6 x = 8 x
, = 2 x 25
, = 2 x 26 = 4 x
