A Year in the Life: Ambient Math Wins the Race to the Top!
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.
4. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed. And between what two whole numbers does your answer lie?
Since this standard is so similar to 4.NF 3d below, I will repeat portions of that post here. The same operation, multiplying a fraction by a whole number, is required for the last three standards. This repetitiveness seems counterproductive, roast beef or no. And the sorts of practical applications posited by word problems can be readily accomplished when skills are in place.
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.
Today’s standard requires multiplication rather than addition. Here is the multiplication page from Math By Hand’s little reference guide, Fraction Rules & Keys. Examples are given on the facing page of the booklet.
This is a no-nonsense guide to anything that might need to happen involving multiplication with a fraction or mixed number. Note that the two elements that are most relevant are shortened to RCF (reduce/cancel first) and GCF (greatest common factor). A picture is worth 1,000 words of course, so the examples make all of this so much clearer. The rest of this post duplicates post #263, because the essence of both standards are so similar. (With the exception of the art, because there are so many outstanding Grade 4 images to choose from!
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 a sketch for a Celtic Knot cross-stitch project by a fourth grader from fiveofus.ca on Pinterest. The joyful process of creating something from scratch looms large for all of us, but especially for children, because there is no more effective way of finding one’s true path in the world. And no boring worksheet or standardized test prep should get in the way of that journey. 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.