## What are Dr. Tapp's Mathematical Playgrounds?

Dr. Tapp's mathematical playgrounds is the creating of an environment conducive of learning mathematics. The Playgrounds focus on presenting information in a fun and entertaining way. Playgrounds generally fit into one of four categories: Arithmetic, Geometry, Combinatorics, or Set Theory. The environment created is intended to be inviting and non-competitive.

## How is the Playground Organized?

The playground is organized by activities, and objectives. Activities that are intended to measure progress towards an objective are called stations. A child may be asked to participate in a station several times. Generally, children enjoy seeing how they improve over time. Stations can help students see their progress. Some activities are not intended to support objectives, these activities tend to be more fun and expose students to advanced subjects in an age appropriate way. Some activities could support an objective, but are not useful for evaluating achievement of an objective.

## What are the Objectives?

The objectives of the playground series are:

• Add integers up to five digits.
• Multiply three digit integers by three digit integers
• Subtract integers up to five digits.
• Divide integers by two digit integers, providing answers correct up to five significant figures.
• Completely factor any positive integer less than 529
• Reduce fractions with numerator or denominator less than 529 to lowest terms.
• Add, subtract, multiply, and divide fractions.
• Add, Subtract, multiply decimals with up to four significant digits.
• Divide decimal numbers with up to six significant digits by decimal numbers with two significant digits.
• Compute any number less than 21 raised to a power less than 6.
• Interpret and compute arithmetic expressions, perhaps with aid of a calculator, using correct order of operations.
All objectives are expected to be completed without a calculator unless otherwise stated. Pencil and paper are expected to be used when demonstrating any objective.

## How many years will it take to achieve these objectives?

I'm targeting all objectives being taught to a 6 year-old by the time they are 12. The goal is to have the students prepared for algebra. I consider it ambitious to have the student prepared for algebra at the 12 to 14 year-old range.

## Why have strange numbers like 529 in the objectives?

When looking for factors of a number less than 529 it's enough to check all primes up to 19. If the number is over 529, technically 23 should also be checked as a factor. If a student can factor 411 completely, they should be able to factor a number less than 529 without any more difficulty. In general, objectives need limitations in order to be measurable. Of course, students can always go above and beyond the objectives.