3.OA 4: Keeping It Real While Filling In the Blanks! (#189)


A Year in the Life: Ambient Math Wins the Race to the Top!
Day 189

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
Represent and solve problems involving multiplication and division.
4. Determine the unknown whole number in a multiplication or division equation relating three whole numbers.  For example, determine the unknown number that makes the equation true in each of the equations  8  x  ?  =  48,  5  =  __  /  3,  6  x  6  =  ? .

Back to Math By Hand Grade 1 to fulfill this standard!  Much practice occurred with color coded strips in all 4 processes, alone and side-by-side to show equivalency.  A little white square is the color strips’ magic ingredient.  Here’s how it works.  The color strips are divided into 6 sections: they are 18″ long and folded into 3″ squares.  They’re used with manipulatives, the glass gems shown above or counting beans, to represent the numbers in equations.

And here’s the magic part.  A 3″ white square can be placed anywhere on the strip, in any position in the equation, perfectly fulfilling this Grade 3 standard in Grade 1.  And even though the equations never total more than 20, the concept is learned and carried on later, with higher order equations in all 4 processes.  The next step is to use the sets of “real numbers,” lovingly crafted in Grade 1, in place of the gems/beans.

Transitions are made slowly and solidly.  Slow and steady wins the race to the top, after all.  The next step is writing the equations on paper, but this is always paired with using the manipulatives so the numbers and their functions remain grounded and tangible.  This is foundational and can form a strong basis for learning new concepts and all skills practice.

Skills practice needs to be more than merely 2-D with pencil and paper.  For today’s standard, oral practice with a ball or bean bag works well.  Here’s how.  For the equation,  8  x  ?  =  48  say, “eight times,” throwing the ball for the student to catch on the blank.  Then say, “equals forty eight.”  The student throws the ball back saying, “six.”

For the equation,  5  =  __   /  3,  have tambourines or other percussive instruments on hand (preferably made by you and the student(s) and say, “five equals.”  Strike the hand drum or tambourine for the blank then say, “divided by three.”  The student accompanies the answer, “fifteen” with his/her tambourine or drum.

For the equation,  6  x  6  =  ?,  you might modify the game “Simon Says” by using a gesture for the blank, like jumping up and down, making a funny face, or clapping three times after saying, “six times six equals.”  The student then accompanies the answer, “thirty six” with the same gesture.  Have fun with it, 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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