# 4.NBT 3-6: Oh Those Common Core Rectangular Arrays! (#257)

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 257

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 their ambient counterparts.

Number and Operations in Base Ten 4.NBT
Generalize place value understanding for multi-digit whole numbers.
3. Use place value understanding to round multi-digit numbers to any place.
Use place value understanding and properties of operations to perform multi-digit arithmetic.l
4. Fluently add and subtract multi-digit whole numbers using the standard algorithm.
5. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

6. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Are these repetitive and boring?  I thought so, therefore decided to include all of them in one post rather than stretching them out.  The Math By Hand curriculum covers rounding and estimation in regular, daily skills practice, both oral and written.  Place value is taught with large, colorful columns and manipulatives, mid to late second grade.  Long division and multiplication are also taught with the same methods, mid third grade.

As for the rectangular arrays and area models, Math By Hand covers this concept first thing, mid first grade.  Once it’s “gotten,” there is no need to endlessly repeat it, especially with boring worksheets like this one from www.commoncoresheets.com:

Paraphrasing  John Holt, don’t subject children to lessons and activities that adults would never sit still for.  This worksheet certainly qualifies as that!  We need to consider that this kind of teaching wrings the very life out of math.  This youtube beautifully illustrates the same mistaken notion of labor-intensive math “explanations.”

Now back to some Grade 4 fun, like this local geography main lesson book page from Waldorf Today: a map of the route to school, surrounded by local birds and squirrels.  Starting from home at the center, geography radiates outward slowly, until it embraces the entire world in Grade 8.

Or this form drawing pinned by Janet Langley as a Grade 5 drawing, but also suitable as a Grade 4 Human and Animal study, integrated with the weaving forms that are typical in Grade 4.

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 4 math CCSS and their ambient counterparts.

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