  This cops-and-robbers" parody involves the visit of the first fraction to a community of whole numbers. The "weird" number, 2/3, steals a piece of cake and then leads the townspeople on a merry chase. He escapes, and "disguises" himself as 4/6 to explain the system of rational numbers and the concept of equivalent fractions. (13 min) |
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| Teacher's Guide“THE WEIRD NUMBER” Discussion Guide • Before Viewing To prepare students for “The Weird Number,” it will help them to know that numerals take the place of people in the film. The first characters are natural, or whole, numbers. Then a new character with one numeral on top and another on the bottom appears. This is called a “rational” number. Students will learn from the film what this new number means and how natural numbers can take the form of rational numbers. • The Weird Number (Rational Numbers) A cops-and-robbers adventure story, “The Weird Number,” introduces second and third grade students to rational numbers (fractions) in this amusing animated film. After seeing the film and completing suggested activities related to it, students should be able to: (1) name rational numbers expressed in written form; (2) identify equivalent rational numbers; (3) describe rational numbers less than one as naming part of a whole; (4) describe natural numbers as being a subset of rational numbers. • Synopsis The film takes place in an imaginary mountain village populated only by natural, or whole, numbers. The mayor is represented by the numeral 1, the chief of police by 763. Thefts never occur in the village, because every inhabitant is identified by the quantity he “takes.” For example, 7 would always take seven units, thereby giving himself away. But one day a “little piece of bread” is missing from the baker’s shop. There’s no clue to the identity of the thief, because the missing piece is not a whole unit. The thief surely is not one of the villagers. 763 (the police chief) and the baker, represented by the numeral 9, search for the culprit. They find a strange-looking creature with a miniature 2 on top and a miniature 3 on the bottom. Caught red-handed, 2/3 leads 763 and 9 on a merry chase before he manages to escape. Another stranger, 4/6, appears and says he is a rational number from the other side of the mountain. (Yes, he knows 2/3—What? He’s been causing trouble?) 4/6 explains rational numbers, and he explains equivalent fractions. After 4/6 returns to the other side of the mountain, the police chief realizes 4/6 is really 2/3 in disguise—or rather, in a different expression of his identity. The film ends with a hint of still another stage in the student’s concept of numbers: the existence of irrational numbers. • After Viewing A discussion of mathematical information presented in the film will help students identify and name rational numbers. When you show on the board a rational number such as 2/3 and then a natural number such as 6, a dialogue such as the following can be useful: How do these two numerals look different from each other? (The first has a numeral at the top and a numeral at the bottom. The second has one numeral only.) If you write just the numeral at the top of the first example, what kind of number have you shown? (A natural, or whole, number) Do all rational numbers fit that pattern? Can they all be shown a numeral on top and a numeral on the bottom? Let’s look at several. Can you find one for which this is not true? (No.) Show a series of rational numbers on the board. Ask the students to name the numbers by reading them aloud (“One-half,” “two-thirds,” “eighteen-twenty-sevenths,” etc.) A brief explanation of why we need rational numbers can be helpful. Students will recognize this need when they partition a whole into two sections and try to solve equations such a n = 1 2. Obviously, this can’t be solved with a natural number. Therefore, rational numbers are necessary. They are expressed as an ordered pair of natural numbers: 1/2, 1/4, 3/4, 2/3, 4/4, 2/2, 9/7 Some rational numbers are equivalent to others: 1/2 = 2/4, 6/8 = 3/4, 4/4 = 9/9 Natural numbers are also rational numbers; they can be expressed as an ordered pair of natural numbers: 1 = 2/2 or 3/3, 4 = 16/4 or 4/1 The discussion may include written work to help students name different kinds of numbers. Ask students to: 1. Write any rational number you can think of. (Such as 3/4.) 2. Write another name for that rational number. (Such as 9/12.) 3. Write any natural number. Write that same number as a fraction. 4. Write the rational number 1/2. Write three different names for that rational number. (2/4, 3/6, 9/18.) • Related Activities 1. A Paper Model With two square sheets of acetate, paper and a piece of stiff white paper the same size, you can demonstrate the meanings of given rational numbers. Mark off one sheet of acetate paper into four equivalent sections, with one section colored green. Mark off the other sheet of acetate paper into two equivalent sections with one section colored red. Place the acetate paper with four sections over the stiff white paper (so it will show up better), and ask what rational number is represented by the entire sheet? (4/4.) By the green section alone? (1/4.) Place the acetate sheet partitioned in two sections over the stiff white paper. What rational numbers are represented by the whole sheet and by the colored sections? (2/2 and 1/2.) Place both sheets over the white paper so the green and red sections do not cover each other. What rational number do the red and green sections combined represent? (3/4.) What rational number does the white sections represent? (1/4.) This can also be done using acetate paper with an overhead projector. 2. Domino Game Mark cards similar to dominoes with two unequal rational numbers on each side of the center dividing line. Students can place equivalent rational numbers end to end: 1/2 2/3 4/6 1/5 2/10 1/3 3. What Comes Next in the Sequence? Start a sequence of rational numbers and ask the class (or smaller groups, or individuals) what comes next. Suggested sequences: 1/1, 2/2, 3/3, 4/4 …………………………………… 1/2, 2/4, 3/6 ………………………………………… 1/3, 2/6, 3/9 ………………………………………… |
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