Multiplying fractions and whole numbers intuition

The  exercise appears under the 4th grade (U.S.) Math Mission. This exercise explores the geometric representation of fractions and their connection with products with fractions and whole numbers.

Types of Problems
There is one type of problem in this exercise:


 * 1) Select the options that represent the picture: This problem provides a diagram with figures cut into congruent pieces and some shading. The student is asked to select all the options from a multiple-select list that represent the shaded region in the diagram.Mfawni1.png

Strategies
Knowledge of fraction representations and fraction multiplication are encouraged to ensure success on this exercise.
 * 1) The shapes are always cut into the same congruent shapes, so there is no need to make common denominators on this problem.
 * 2) The selected answers will not be simplified but the numbers are generally small so mental simplification can increase efficiency.

Real-life Applications

 * 1) Fractions appear in many fields, from personal finance to advanced mathematics. Familiarity with the names and operations with fractions will increase mathematical ability at almost all levels.
 * 2) The problems in this exercise strengthen the geometric understanding of fractions.