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The first instance of Properties of multiplication 1 was under the 3rd grade (U.S.) Math Mission. This exercise discovers properties of multiplication. In particular the commutative and associative properties of multiplication are given a lot of attention for discovery and use.

Types of Problems

There are two types of problems in this exercise:

  1. Discover commutativity: This problem has several answers that are to be filled in. At each stage the user is expected to fill in the blank with the correct answer. At the end, users should discover that the multiplying numbers in their given order or reversed order does not matter.
    Multprop

    Discover commutativity

  2. Discover associativity: This problem has several answers that are to be filled in. At each stage the users are expected to fill in the blank with the correct answer. At the end, the users should discover that when multiplying the order in which one chooses to multiply (grouping) does not matter.
    Multprop2

    Discover associativity

Strategies

This exercise is easy to get accuracy badges because of the simplicity of the steps moving from one step to the next. It is medium difficulty to attain speed badges because there are many blanks to fill in. If user is concentrating on just this problem type, it is certainly possible to get speed badges, but they need to be concentrated on this one.

  1. Mechanical rules should be able to be determined for the problem types.

Real-life Applications

  1. Multiplication is needed and used by mechanics for repairing cars by multiplying when they overhaul the engine, measure the pistons or just to put in a new gearbox or engine.
  2. By learning multiplication and memorizing the times tables, users provide themselves with essential building blocks to do higher learning math, like division, fractions and even algebra.
  3. Multiplication is necessary for a career in the stock market.

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