3.OA 5: Have Fun First & Foremost With New Concepts (#190)


A Year in the Life: Ambient Math Wins the Race to the Top!
Day 190

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
Understand properties of multiplication and the relationship between multiplication and division.
5. Apply properties of operations as strategies to multiply and divide.  Examples: If 6 x 24 – 24 is known, then 4 x 6 = 24 is also known.  (Commutative  property of multiplication.)  3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 = 30.  (Associative property of multiplication.)  Knowing that 8 x 5 = 40 and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56.  (Distributive property of multiplication.)

Wow.  This is very complex for Grade 3, and should be concretized with stories, art, and movement.  Math By Hand teaches these three properties in Grade 2, using these methods.  Here is an excerpt from the Grade 2 Daily Lesson Plans book.

Tell the three stories on the next page, one each day for the next three days. The stories will help to show these three properties in a simplified, fundamental way. Note that they will be revisited later on, with more advanced math and with algebra. The terms used here are concrete, informal versions of the more abstract terms: commutative, associative, and distributive. Parentheses will be given the informal name, “huggers” previewing their later use in algebra.

Commuting Numbers / Tell This Story for Day 8
When numbers swap and switch places on either side of the equals sign, they’re having fun commuting from one side to the other! It’s like being on a seesaw when you are balanced with your partner. Numbers on the seesaw say, “Commute! Commute!” as they hop from one side to the other. Both Plus and Times like to play this game.

Associating Numbers / Tell This Story for Day 9
When numbers are friendly they like to associate, with hugs. Sometimes they will want to change partners for hugs, but they cooperate no matter how they get together, to be sure they always have the same answer. They say “my associate,” meaning “my friend” whenever they hug. This is a favorite game for Plus, but Times likes it too. 

Distributing Numbers / Tell This Story for Day 10
Remember how busy Times can be? Well he loves to rearrange numbers, sometimes asking them to hug and sometimes not. He can be heard calling, “Distribute!” loud and cheery as he hops and jumps into the room. He busily puts numbers in hugging pairs, then takes them apart again. This is a favorite game for Times, but Plus (and sometimes Minus) like it too.

Each story is told on Day 1 and retold by the children on Day 2, after which they do a guided illustration then practice, with many examples.  This practice should include other forms of visual, auditory or kinesthetic memory aids.  For example, an actual seesaw could be set up for the commutative equations, balancing numbers or even children-as-numbers (wearing them as tags) on either side.

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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