# Making Math Real: Comparing & Ordering Fractions Intensive

## Making Math Real: Comparing & Ordering Fractions Intensive

#### Online 6-day mini-course via Zoom

LAST OFFERING:  February 13-14, 27-28 & March 13-14, 2021 |  9am-1pm PT
Registration Fee: \$859 (Includes tuition & new course worksheet materials: Fractions III: Comparing & Ordering Fractions [shipped upon registration])
Mandatory Prerequisite: * Permitted to register if currently enrolled in the Fall 2020 Fractions DL course.

The focus of the Comparing & Ordering Fractions Intensive will be on:

• Structuring the four levels of comparing and ordering fractions mentally
• Structuring the eight levels of comparing and ordering fractions mathematically
• Learning to prescriptively use the soon to be published Fractions III: Comparing and Ordering Fractions
• Connecting comparing and ordering fractions mentally to rounding fractions to the nearest whole number and to the nearest ,1-2.
• Structuring the respective scopes and sequences across the grades for both comparing and ordering fractions mentally and mathematically
• Developing the requisite perceptual activations that support fraction number sense

Comparing & Ordering Fractions Intensive Course Description

Comparing and ordering fractions present multiple challenges for students. Research* from as recently as 2017 continues to confirm that national failure rates for US students remain at 80% for concepts and applications with fractions. Additionally, the cognitive demands for the concept applications of comparing ad ordering fractions is the highest order for all K-5 fractions applications. Comparing and ordering fractions require students to activate a comprehensive perceptual understanding of how the relationship of numerical values between numerators and denominators synthesize to express a magnitude of value that does not necessarily reflect the values of each numerator and denominator. E.g., assuming the same size whole, 56 expresses a far greater magnitude value than 23100, despite the latter fraction having greater values in both the numerator and denominator than the fraction of greater value. The ability to successfully compare 56 and 23100 requires the synthesis activation that the relationship of 5 to 6 in the first fraction is expressing an almost complete whole, or close to 1; and the relationship of 23 to 100 is expressing a relatively small amount of a whole, or not at all close to 1.

Ordering three or more fractions increases the cognitive demands of only comparing two fractions, and students’ ability to successfully compare and order fractions both mentally and mathematically provides the highest order development of fraction number sense, the intended goal and objective of comparing and ordering fractions.

The Comparing & Ordering Fractions Intensive will present the two sections for comparing and ordering fractions. The first section will be the full structures for comparing and ordering fractions mentally and the second section will present comparing and ordering fractions mathematically. This intensive course will be based exclusively on the soon to be published book/worksheet master binder: Fractions III: Comparing & Ordering Fractions and is included in the tuition for the course as the required course materials.

* Hard Lessons: Why Rational Number Arithmetic Is So Difficult for So Many People; Robert S. Siegler¹, ² and Hugues Lortie-Forgues³, Current Directions in Psychological Science, 2017, Vol. 26(4) 346–351

Required Course Materials:  In addition to the Fractions III required course reader (shipped upon registration), all of your notes for comparing and ordering fractions mentally (“Hardly Any, Around 12, Almost the Whole Cake”) and mathematically (The Eight Levels of Comparing and Ordering Fractions) from the Fractions, Decimals & Advanced Place Value course (already in participant’s possession).