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## Appendix F: Explanation of the Unit on Weight

(EXCERPTS FROM)

EXPLANATION OF THE UNIT ON WEIGHT

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Knowing and Learning Mathematics for Teaching Appendix F: Explanation of the Unit on Weight (EXCERPTS FROM) EXPLANATION OF THE UNIT ON WEIGHT

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Knowing and Learning Mathematics for Teaching A. Section One (2 hours): Objectives for the first section: To learn the concept of weight, the meaning of measurement, and the unit of weight [gram (g)]. Hour One and Two: Goal: To understand the concept of weight and the unit of weight, the gram (g). Materials: Dictionary or books A bucket with water Large springs Scale Scissors Compass (the type used to draw circles) Glue Pencil Wooden blocks 1-yen coins (Example of a proposal for teaching this section) Topic 1: “Which book is heavier? Which bucket is heavier?” Activity: Present two kinds of books and two buckets of water. Guidance: Let students compare the weights of both of the objects by holding one in one hand and another in another hand. Allow students to realize the importance of measurements of weights by letting them know that it is not necessarily possible to distinguish the weights of the objects just by holding them. Topic 2: “Which one is heavier? How can we compare the weight of the objects? ” Activity: Present scissors, compass, and glue. Guidance: Have students discuss the different ways to compare the weights of the objects. Even though students may suggest using a regular scale, suggest that they use a justice scale indicated in the textbook. Important Notes: How to introduce the concept of weights: Weight is a difficult concept for students to understand, compared with the concepts of length and volume, because (a) weight is hard to determine visually and (b) weight is not necessarily determined by the size and shape of the objects. Therefore, it is important that more manipulative activities are introduced and that students measure the weights of objects by picking up the objects to feel their weights (direct comparison). In other words, it is important for teachers to introduce them step-by-step to direct comparisons and indirect comparisons, leading to the use of universal units. For the comparison of two objects, it is important to use objects that are tactually discernible in weight and objects that are not tactually discernible in weight, so that students can learn that they cannot measure the weight of the objects just by using their senses. Editor's note: The Japanese teachers' manual includes—in a contrasting color of type, so as to be easily seen—the answers to each of the questions that appear in the children's text.

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Knowing and Learning Mathematics for Teaching The order of guidance for teaching weight: It is important to include the following steps: Direct comparison (by using hands and justice scale); Indirect comparison (by using a regular scale); Arbitrary units (by using wooden blocks); Universal units (e.g., one gram). Purpose of the unit: The purpose of this unit is to remind students of the steps of measurement and weight, which are similar to those with the measurement of volume and length. Let the students realize the necessity of using arbitrary units and universal units. Topic 3: “Let's compare the objects using the justice scale.” Activity: Present a justice scale. Guidance: Be sure to check if students know that when comparing two objects on a justice scale, the heavier side will drop down, and the lighter side will rise, and that if the two weights are the same, the two sides will remain even. In the example on p. 18, the scissors is heaviest, and the compass and the glue have the same weight. Topic 4: “How much heavier are the scissors than the glue? Let's examine and find out by using wooden blocks.” Activity: Continue to weigh using the justice scale. This deals with step two on p. 19. Guidance: First, allow students to realize the difference in the weights of the glue and the scissors. Second, get them to remember how they can measure the length by the number of units (i.e., make a certain unit and count how many units equal a certain length). Third, suggest that they use wooden blocks as units of measurement. Each block should be the same weight. The glue in the textbook illustration equals five wooden blocks, whereas the scissors equals six blocks. Therefore, the scissors is one block heavier than the glue. It may also be a good idea to suggest other items such as nails or paper clips as a unit of measurement. Then explain to the students that there is a unit of weight, a gram (g), and one gram is equal to one coin of one yen. One gram is written as 1g. Topic 5: “What is the weight of the compass? Let's measure it by using oneyen coins.” Activity: This deals with step three on p. 19. Guidance: Let the students measure the weight of the compass by one-yen coins and finally represent the weight in terms of grams. Twenty one-yen coins equals twenty grams. Topic 6: “What are the weights of the glue and scissors, in terms of grams? Let's measure them using one-yen coins.” Activity: This deals with step four on p. 19. Guidance: Let the students measure the objects and then share their findings with the class.

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