4.NF 3d: Beyond Adding & Subtracting Fractions (#263)


A Year in the Life: Ambient Math Wins the Race to the Top!
Day 263

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.  The CCSS math standards are listed here in blue followed by their ambient counterparts.

Number and Operations – Fractions 4.NF
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
3. Understand a fraction a/b with a> 1 as a sum of fractions 1/b.
d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to solve the problem.

The Math By Hand / Grade 4 / Kit 2 / Fractions is a thorough, seamless approach to teaching and learning fractions.  As in Grade 1 when all 4 processes were learned at once so relationships and correspondences between them were clear, so are all 4 processes with fractions introduced and learned at the same time.  A basic, clear “rules” booklet is used as a reference as long as it’s needed.  

Here’s a page from the addition and subtraction section of the booklet.  The choice here was either slightly out of focus or too small to see, but note that the originals are perfectly clear and sharp.  (The booklet is a compact pocket guide that is only 8 pages long and measures 4 1/4″ x 5 1/2″ very portable!)



Along with many other basic tools and strategies for understanding the fundamentals of fractions and how they relate to each other through the 4 processes, a comprehensive overview enables confidence and the ability to apply all rules to any situation, including multi level word problems.

Though the Math By Hand materials do not include word problems per se, a plethora of such problems and worksheets can be found online or in textbooks.  However, before implementing them, it’s a good idea to research the ins and outs of word problem construction, to circumvent any comprehension problems that may arise.  Building the foundation for understanding by using clear, pictorial, graphic, hands-on materials comes first and then continues to be used as support while applying it to any purpose.

And as always, there’s the artful side.  Here’s another wonderful image from the waldorftoday.com gallery of main lesson book drawings: a study of the eagle from the human and animal block.  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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