(1) (2) (3) (4) 3 ninths 3/9 2/3 = 4/6 2/3 = 8/12 + 5 ninths + 5/9 1/6 = + 1/6 3/4 = + 9/12 ―――――――――― ――――― ――――――――――― ―――――――――――― 8 ninths 8/9 5/6 17/12 IV. Summary: (1) Only like fractions can be added. (2) Change unlike fractions to like fractions. (3) Add the numerators, placing the sum over the common denominator. V. Application: Examples and problems involving similar and dissimilar fractions. Before undertaking to illustrate the discoverer’s method, it may be well to designate in order the evident steps as they would appear to the pedagogue: (1) Motivate the topic to be presented. (2) Bring to mind appropriate “foundation facts.” (3) Make evident the “crucial fact.” (4) Lead to the forming of an hypothesis through analogy. (5) Afford ample opportunity to prove the hypothesis. _Discoverer’s Method Adapted._ Lesson Plan. I. Aim: (1) _By playing upon the curiosity or by exposing a vital need, create a strong desire to know how to add business fractions._ (Motivate the topic.) Curiosity: “We all know what a fraction is and we know, too, how to change fractions to higher or lower terms.” “Now I wonder how many know how to _add_ fractions, such as 2/5 and 1/5?” “Don’t you tell any one, Mary, but just write your answer on a piece of paper and show it to me.” (Mary’s answer shows that she has thought correctly, but figured incorrectly. John, after having raised his hand, shows his answer to the teacher.) “John has the right answer.” “That’s fine, but let us keep the secret, John.” “I wonder how many others there are in this class who will find the right way?” etc., _or_ Vital need: Discuss with the class the various occupations of life and secure expressions of preference. Some may plan to be real estate agents, others contractors or book keepers, etc. “George, you plan to be a book keeper.” “Let us suppose that I have given you the job of book keeper in my factory.” “Show that you are worth your wages by adding these numbers: 124¾, 647⅔.” “What! can’t do it?” “Then I don’t want you!” etc. II. Preparation: (2) Bring to the foreground the necessary _foundational knowledge_. Suggestions: 4 bushels 8 parts + 3 bushels + 2 parts ――――――――――― ――――――――― 7 bushels 10 parts III. Presentation: (3) Make evident the _crucial fact_. Suggestions: Add 2 fifths 3 eighths 3/8 + 1 fifth + 1 eighth + 1/8 ―――――――――― ――――――――――― ――――― 3 fifths 4 eighths