# Actus Potentia Releases Educational Software for Arithmetic; the Software is Suited for Self-paced and Personalized Learning and is Aligned with the Core Curriculum

## A lesson-planning strategy is described here that fits perfectly with the Educational Software on Arithmetic (http://www.actuspotentia.com/Arithmetic.shtml) that is released by Actus Potentia, Inc. in February 2013.

In recent years, problem-based and project-based learning have become two accepted strategies to engage students in a classroom. To support such learning strategies, Actus Potentia has released an Educational Software for arithmetic. Visual and dynamic displays in the software facilitate understanding of mathematical concepts in engaging lesson plans.

A friend of mine, who has pursued and succeeded in science, once said, “I almost gave up math when I reached fraction division in elementary school.” Sometimes, the introduction to fraction division went somewhat like this – “Fraction division is the inverse of fraction multiplication. To divide 5/8 by 2/3 is to find that number which being multiplied by 2/3 gives 5/8 as the product. But the compound fraction 3/2 of 2/3 is 1. Hence we have the rule – find the product of the dividend and the inverse of the divisor.” The content within the quotes is a typical paragraph that can be found in many arithmetic textbooks. No teacher should read this paragraph to his/her class.

Instead, a lesson plan should be built with EnCad (NCAD) as the backbone. NCAD stands for Need-Concept-Algorithm-Dependencies. The Arithmetic software released by Actus Potentia, Inc. is designed for EnCad.

EnCad is shown in an accompanying diagram. For now, the color coding can be ignored. Here, EnCad is explained in the context of teaching division of fractions, but it applies everywhere. The illustrations are screenshots from the Arithmetic software.

First step in this lesson plan is to impress upon the students why they need to divide one fraction by another. The teacher can show a few examples of this need in the class. The teacher can ask all students to bring fraction division problems they need to solve and promise that all students will engage in solving their own problems.

Each batch of cupcakes requires 3/4 cups of cocoa. If you had 3 1/4 cups of cocoa, how many full batches of cupcakes can you bake and how much cocoa will you have left over?

Next, consider the “Concept” in Jane’s problem where she wants to change the color of her fence from green to yellow. She used one and 7/8 quarts of yellow paint to cover two and 3/4 segments of her fence. How many quarts of paint cover one segment of the fence? Students can be given yellow and green construction paper to do this exercise that mimics the explanation given in the Educational Software on Arithmetic.

Jane used 60 pieces of yellow paint to cover 88 pieces of green fence. Therefore, one quart of yellow paint covers 88/60 (or one and 7/15) sections of green fence.

After the students get comfortable with this idea, the “Algorithm” which is good for number crunching to arrive at the same conclusion as the construction paper exercise should be shown to the students.

•     Convert both the dividend and the divisor from mixed numbers into improper fractions
•     Invert the divisor
•     Multiply the two numbers in the numerator and the two numbers in the denominator
•     Convert the resulting, improper fraction into a mixed number and bring to lowest terms

When students have any difficulty in the algorithmic steps, they should re-examine their abilities in the “Dependencies.”

•     Converting mixed numbers into improper fractions
•     Long multiplication
•     Converting improper fractions to mixed numbers
•     Writing fractions in lowest terms

Students with insufficient abilities in the dependencies are then required to complete remedial work and practice on their own.

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AMBAR MITRA