Making Math Real: Mental Percent Problem Solving Intensive

Making Math Real: Mental Percent Problem Solving Intensive

  Online 4-day mini-course via Zoom

Spring 2021 Dates:  Saturdays & Sundays – April 17-18 & May 22-23 |  9am-1pm  
Registration Fee:  $529
Mandatory Prerequisite: 
* Permitted to register if currently enrolled in the Spring 2021 Pre-Algebra course.

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The focus of the Mental Percent Problem Solving Intensive will be on:

  • Reactivating the concrete connections of fraction-percent equivalence
  • Reactivating the fraction-percent “Landmarks”
  • Reconnecting to “Fractionizing and Decimalizing”: the structures for removing the “% logo” for problem solving applications
  • Presenting the structure, definition, and parameters of the two categories of mental percent problem solving
  • Structuring the three forms of solving within each mental percent category: 1) solving for “part” 2) solving for “total” 3) solving for “percent”
  • Providing the specific sequential incrementation for teaching the three forms of solving within each mental percent category
  • Learning to create prescriptive practice sets for both numerical and word form problems.
  • Helping students synthesize, activate, and apply each mental percent structure within comprehensive mixed practice problem sets
  • Distinguishing between mental percent solving versus algebra solving based on the numerical values and relationships

Mental Percent Problem Solving Intensive Course Description

Percent problem solving has consistently been an area of significant challenge for students, which explains the frequency of its inclusion in standardized testing, especially including the SSAT, ISEE, SAT, ACT, etc. Percent problem solving typically represents the largest category of problem solving within these standardized tests. Furthermore, the most common style of percent problem solving on these timed standardized tests presents numerical relationships that allow for mental problem solving that would require no extra time spent doing computational side work. Indeed, the specific purpose of percent problems that can be solved mentally helps distinguish those students who have integrated the number sense to solve these problems instantly from those (wishing they had access to a calculator) who must write down the problems and solve them computationally, which requires substantial extra time.

The following problem is representative of the types of percent problem solving on the standardized tests which can be solved by using mental structures to generate the solution in moments: 23 of 60 is what percent of 64? The following mental process presents one way in which mental structures could be used:

  • 13 of 60 is 20, so 23 is 40
  • 4064 is 58 which is 62.5%

The ability to apply these mental strategies requires the integration of fraction-percent “landmarks”, which are the most commonly used and most easily learned fraction-percent equivalences.

In addition to fraction-percent landmarks, there is another category of mental percent solving, which is categorized by the numerical relationships of multiples of 10% of a number that is also a multiple of 10, e.g., 70% of 60 = 42.

These two categories of mental percent problem solving will be the bases for the Mental Percent Problem Solving Intensive. In addition to providing the best preparation for percent problem solving on timed standardized tests, the mental structures presented in this intensive provide excellent practical applications for percent problem solving that occur in our everyday lives as well as the direct connection to all percent problem solving using algebra in which the numerical values and relationships would be overwhelming to apply mentally, e.g., 23.5 is what percent of 31? Most notably, the integration of mental percent solving provides for the ongoing intensive development of symbol imaging of the 100 multiplication and 100 division facts in its comprehensive applications of the 9 Lines-based numerical relationships that comprise and define the parameters of mental percent problem solving.

Required Course Materials: All of your notes for mental percent problem solving from the Pre-Algebra course (already in participant’s possession).