Analogies require learners to use analytical skills.
To understand analogies, students should be familiar with vocabulary but must also understand relationships, such as comparing, contrasting, and sequencing.
In introducing a math lesson on analogies, you may wish to start with some simple examples from other disciplines, such as:
Hot is to Soup as Cold is to _____ .
4 : 12 :: 1 : _____ .

Here are some examples of kinds of relationships that can be presented to the students:

    1. Purpose Relationship
        ruler : line :: compass : circle

    2. Part : Whole Relationship
        ray : line :: arc : circle

    3. Part : Part Relationship
        vertex : side :: center : radius

   4. Cause : Effect
        5 : 25 :: 25 : 625

    5. Action to Object Relationship
        bisect : segment :: prove : theorem
        or the reverse:
        equation : solve :: perpendicular : construct

    6. Position Relationship
        perimeter : surrounding :: area : interior

    7. Degree Relationship
        cm : km :: oz : ton

    8. Synonym Relationship
        cube : hexahedron :: average : mean

    9. Antonym Relationship
        parallel : intersecting :: acute : obtuse

    10. Charisteristic Relationship
        square : rectangle :: rhombus : parallelogram

    11. Sequence Relationship
        mono : bi :: tri : quad

    12. Numerical Relationship
        1/2 : 50% :: 1/3 : 33 1/3%