# 4.NF 3b: Fraction Equivalency, Hands-On! (#260) A Year in the Life: Ambient Math Wins the Race to the Top!
Day 260

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.
b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation.  Justify decompositions, e.g., by using a fraction model.  Examples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

Like so much else in math, taking fractions apart and putting them together is best approached with a hands-on format.  Here is a fun and effective lesson plan from the HotChalk Lesson Plans page.

Objective: Students will compare fractions with unlike denominators.

Materials: Fraction game board, Playing Cards

Provide students with a fraction game board (a paper with two fraction bars that specify where the numerator and denominator are) and playing number cards. The game is played like war. Students place cards on the numerator and denominator spaces at the same time. The first person to identify the larger fraction by tapping or placing their hand on the fraction that is larger gets all four cards. As students develop their knowledge of fractions, you can write a denominator for students to use consistently. (For example, have students write 10 in the bottom of the fraction, so that all the fractions are consistently less than one).

This is one area in which Common Core, Waldorf, and Math By Hand agree: hands-on and interactive is the way to go with fractions!  The Math By Hand / Grade 4 / Fractions / Kit 2 includes a DIY set of playing cards with instructions for multiple familiar games that are adapted to learning about fractions.  Here are excerpts from the instructions and the fraction equivalency chart used with the playing cards.

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.  