4.OA 4: Factors & Primes, Early On & Colorful (#250)


A Year in the Life: Ambient Math Wins the Race to the Top!
Day 250

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.

Wow, 50 more posts to go!  I have decided to stop at 300 days.  This process has been pretty labor-intensive, so stamina has thinned considerably.  One of my original purposes in writing this blog was to provide a reference to the Common Core in tandem with Math By Hand, for those who need or want it, since I am not able to change the California State and National standards with which the Math By Hand curriculum is currently aligned.

Not able to, and really not wanting to, because I do feel that the former standards are far superior to the Common Core.  So I will end with Grade 4, which aligns with Math By Hand anyway.  I’ve been thinking that I’d like to convert the whole blog into an e-book so it would be easier to use as a reference.  Any comments/feedback on this would be appreciated! 

Operations and Algebraic Thinking 4.OA
Gain familiarity with factors and multiples.

4. Find all factor-pairs for a whole number in the range 1-100.  Recognize that a whole number is a multiple of each of its factors.  Determine whether a given whole number in the range 1-100 is a multiple of a given 1-digit number.  Determine whether a given whole number in the range 1-100 is prime or composite.

This standard is easy-peasy!  Factors are first taught early in Grade 1, then repeated through the grades.  Prime and composite numbers are taught pictorially and intensively in Grades 2, 3, and 4.  As always, a picture is worth a thousand words.  See the factor and prime numbers examples below, as they are illustrated at different grade levels in the Math By Hand curriculum.


“12 is the King of Numbers because it’s the richest!  Even though 13 is a bigger number, it only has two jewels: 1’s and itself.  12 has many jewels: 1’s, 2’s, 3’s, 4’s, 6’s, and itself!”  The factors are introduced early on in Grade 1, only through story and pictures, and very concretely and colorfully, as shown.


LG G2 FACTOR TREET-JPEGFactor trees are created early in Grade 2, as a way of finding patterns and factors within the tables, after creating a large times tables chart.  Individual trees are created for each table, giving a concrete sense of how they break down into factors.



The prime numbers are taught playfully at the end of Grade 2, using the fable, The Rooster and the Pearl.  The chart on the left shows the prime and composite numbers to 100, after taking part of the chart to “sift” the prime numbers or “pearls” from the corn kernels.



Magic Squares are introduced at the beginning of Grade 4, both to reinforce factor concepts and as an introduction to fractions.  This puzzle can be constructed by moving the numbers 1-25 as shown above to create columns that all add up to 65: horizontally, vertically, and diagonally.  This particular pattern is useful for gaining mental flexibility and for addition practice.  Other Magic Squares’ patterns are more directly focused on factor concepts.

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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