3.OA 9: Patterns! Make Math Meaningful & Exciting (#195)


A Year in the Life: Ambient Math Wins the Race to the Top!
Day 195

For one year, 365 days, this blog will address the Common Core Standards from the perspective of creating an alternate, ambient learning environment for math. Ambient is defined as “existing or present on all sides, an all-encompassing atmosphere.”

And ambient music is defined as: “Quiet and relaxing with melodies that repeat many times. Why ambient? A math teaching style that’s whole and all encompassing, with themes that repeat many times through the years, is most likely to be effective and successful. CCSS math standards are listed here in blue, followed by ambient math suggestions.

Operations and Algebraic Thinking 3.OA
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
9. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.  For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

Patterns! are what Math By Hand and Waldorf Education and math itself is all about!  This post will focus on patterns taken from the Math By Hand Grade 3 curriculum, with illustrations.  Patterns abound here because they are the true heart of math, of life itself.  When a math curriculum aligns with and reflects the basic, underlying principles that structure virtually everything around us, that deep relevance is what carries the day and makes for a happily successful math student.

Now for some Math By Hand Grade 3 goodies, taken from the supplemental booklet called, “Tricks & Patterns.”  Note that these are just a few of the many fascinating, motivating patterns found in the Math By Hand / Grade 3 / Kit 2: Rhythms & Stories & Patterns.


Palindromes are words, phrases, or numbers that read the same backwards and forwards.
PALINDROME WORDS: /madam /kayak /level /net-ten /gel-leg /trap-part /step-pets
PALINDROME PHRASES: / don’t nod / never odd or even / no lemon, no melon / bird rib
NUMBER PALINDROMES: / 2772 / 33 / 6776 / 112211 / 11 / 535 / 779977 / 4884 / 22

Here’s how to make a number palindrome:
1)Start with any whole number.
2)Reverse it.
3)Add it to the original number.
4)Reverse the answer and add it.
5)Continue this process until you see a number palindrome. Does it always work?  Try it!  
Here’s an example:  3782 + 2873 = 6655 + 5566 = 12221


0x9 + 1 = 1
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1,111
1234 x 9 + 5 = 11,111
12345 x 9 + 6 = 111,111
123456 x 9 + 7 = 1,111,111
1234567 x 9 + 8 = 11,111,111
12345678 x 9 + 9 = 111,111,111
123456789 x 9 + 10 = 1,111,111,111

See below for the absolute jewel of all number patterns, Pascal’s Triangle.  Note the patterns!  The first row is 1’s, the second row is the counting numbers, the third row is the overlapping, alternating square and triangle numbers, and the very best, the hockey stick pattern, goes like this: go down any number of numbers on a diagonal, add them, then make a sharp turn right or left for the answer.  Again, these are just a few of many, many Math By Hand patterns.

Knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of knowledge as a worthy goal. Tune in tomorrow for more Grade 3 math CCSS and their ambient counterparts.





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