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Understanding multiplying fractions and whole numbers

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The Understanding multiplying fractions and whole numbers exercise appears under the 4th grade (U.S.) Math Mission. This exercise practices the view of fraction multiplication by integers as repeated addition.

Types of Problems

There are three types of problems in this exercise:

  1. Fill in the blank: This problem describes a multiplication problem involving a fraction and an integer. The student fills in a blank with a number that answers the question or balances the equation to make it true.
    File:UMF1.png
  2. Move dot: This problem has a number line and asks the student to move the dot to the correct spot on the number line that represents a multiplication problem. The student is sometimes asked to also provide the answer, but not always.
    UMF2

    Move dot

  3. Select dot: This problem has a number line labeled with four lettered dots. A product is described and the student is asked to select that dot that corresponds to the answer.
    UMF3

    Select dot

Strategies

This exercise is easy to get accuracy badges as long as user is comfortable with multiplication. The speed badges should be considered medium because it seems that the timing is still a little tight, especially when they need to move the dot and count tick marks.

  1. On the Fill in the blank problem concentrate on the numerators and integer multiplication facts to get the answer quickly.
  2. If user floats over the answer box and an acceptable answer type list appears the answer is a fraction. Otherwise it is an integer.
  3. User can make their own number line or count from the end to move more quickly on the number line problems.
  4. On Select dot problems it is far easier to just figure out how the product compares to the integer one and select the correct dot based on that comparison.

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.

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