3.NBT 2: Addition & Subtraction Within 1000+ (#198)


A Year in the Life: Ambient Math Wins the Race to the Top!
Day 198

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.

Number and Operations in Base Ten 3.NBT
Use place-value understanding and properties of operations to perform multi-digit arithmetic.
2. Fluently add and subtract within 1,000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

Math By Hand students add and subtract within 1,000 and more when place value is taught, in the middle of Grade 2.  Four oversized, color-coded columns representing 1’s, 10’s, 100’s, and 1,000’s are placed on the floor for both addition and subtraction.  Students replicate a vertically stacked problem from the board by placing matching numbers (on large index cards) on their respective columns.  The numbers are then added or subtracted, and regrouping happens with small numbers that are walked or jumped to the tops of the columns.

After practicing this for some time, the problems are transposed to workbooks, and at that point addition and subtraction relationships are explored.  This has an excellent foundation since all 4 processes were taught together in Grade 1, along with exploring reciprocal relationships among and between all 4.  Fluency is achieved early on, since lots of practice occurs with exploring intriguing math tricks and patterns.  Here are a few examples from the Grade 3 booklet, “Number Tricks and Patterns.”



1)Subtract the reverse of any 3 numbers from the number.
2)Add the reverse of the answer.
3)The final answer is always 1089! Here ‘s just one example, do try more!



1)Add the digits of any number.
2)Subtract the answer from the number.
3)Add the digits of the answer.
4)Continue adding until you get 9.
You always will. Here’s just one example, do try more!

                                                                             7586312 =(32)                                 

                                                                              –       32                                                                  

                                                                             7586280 =(36) =(9)             


As you can see, very large numbers can be used for this fun version of skills practice.  This is no drill and kill . . . rather it presents interesting and compelling patterns as irresistible incentives.  As always, 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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