Unit 1 A small craft display - fraction multiplication 一 小手艺展示——分数乘法
Lesson 1 The tail of the bird kite is made of 5 pieces of cloth, the tail of the small fish kite is made of 6 pieces of cloth, each piece of cloth is one half meter long. 小鸟风筝的尾巴是由5根布条做成的，小鱼风筝的尾巴是由6根布条做成的，每根布条长都是1/2 米。 What questions can you ask? 你能提出什么问题？ Cooperative exploration 合作探索 1. How many meters of cloth do you need to make the tail of the bird kite? 1. 做小鸟风筝的尾巴，一共需要多少米布条？ One half times five equals to ______(meters) 1/2×5＝______(米) 1/2 times 5 is just trying to figure out what the sum of five 1/2's is. 1/2×5就是求5个1/2相加的和是多少。 I'll do it by addition. 我用加法计算。 Let me multiply it out. 我用乘法算。 2. How many meters of cloth are needed to make the tail of the kite? 2. 做小鱼风筝的尾巴，一共需要多少米布条？ It's usually easier to divide and then calculate. 通常先约分再计算，这样比较简单。 Think about it. How do you compute fractions times integers? 想一想，怎样计算分数乘整数呢？
Lesson 2 Wang Fang is an expert hand knitter in her class. She can knit a scarf for one fifth meter per hour. 王芳是班里的手工编织能手，每小时能织围巾1/5米。 What questions can you ask? 你能提出什么问题？ Cooperative exploration 合作探索 How many meters can Wang Fang knit a scarf in two hours? How about a half hour? How about two thirds hours? 1. 王芳2小时能织围巾多少米？1/2小时呢？ 2/3小时呢？ The formula can be based on "meters woven per hour × time = total meters woven". 可以根据“每小时织的米数×时间＝织的总米数”来列式。 You can use pictures to analyze and understand. 可以借助图画来分析理解。 When you multiply a number by a fraction, you can think of it as trying to figure out what fraction of that number is. 一个数乘分数，可以看作求这个数的几分之几是多少。 How do you compute 1/5 times 1/2 and 1/5 times 2/3? 怎样计算1/5×1/2和1/5×2/3呢？ How does the numerator and denominator of the product relate to the numerator and denominator of the two factors? 积的分子、分母与两个因数的分子、分母有什么关系？ 2. How many meters of scarf can Wang Fang knit in 5/8 hours? 2. 王芳5/8小时能织围巾多少米？ One fifth times five eighths equals to one eighth(metre) 1/5×5/8＝1/8(米) Think about it: how do you multiply fractions by fractions? Does the method of multiplying a fraction by a fraction apply to multiplying a fraction by an integer? 想一想： 怎样计算分数乘分数？分数乘分数的方法适用于分数乘整数吗？
Lesson 3 In the clay sculpture competition held by the school: 在学校举行的泥塑大赛中： Class One made 15 clay sculptures, among which boys made 3/5 of the total. ●一班共制作泥塑作品15件，其中男生做了总数的3/5。 The boys in Class Two made 12 pieces, while the girls made 5/6 of the boys. ●二班男生制作了12件，女生做的是男生的5/6。 What questions can you ask? 你能提出什么问题？ Cooperative exploration 合作探索 1. How many pieces did the Class One boys do? 1. 一班男生做了多少件？ Let's graph it. 我们画图分析。 To figure out how many boys did in class 1, that's to figure out what 3/5 of 15 is, you multiply. 求一班男生做了多少件，就是求15的3/5是多少，用乘法计算。 Fifteen times three fifths equals to _____ 15×3/5＝______ Answer: The boys in Class one did ______ piece. 答：一班男生做了______件。 2. How many pieces did the girls in Class Two make? 2. 二班女生做了多少件？ Let's graph it 我们画图分析 If we want to know how many the girls in Class 2 did, we just want to know what 5/6 of 12 is? 求二班女生做了多少件，就是求12的5/6是多少？ Twelve times five sixths equals to ______ 12×5/6＝______ Answer: The girls in Class two did _______ piece. 答：二班女生做了_______件。
Lesson 4 It takes 60 grams of corn to make a red sandbag. 做一个红沙包需要60克玉米。 It takes 3/4 of the corn to make a green sandbag as much as a red one. 做一个绿沙包所需的玉米是红沙包的3/4。
It takes 7/9 as much corn to make a yellow sandbag as a green one. 做一个黄沙包所需的玉米是绿沙包的7/9。 What questions can you ask? 你能提出什么问题？ Cooperative exploration 合作探索 How many grams of corn does it take to make a buns? 1. 做一个黄沙包需要多少克玉米？ Draw a picture and analyze the quantitative relationship between them. 画图分析它们之间的数量关系。 So let's figure out how many grams of corn we need to make a green sandbag, so let's figure out what 3/4 of 60 grams is, and we multiply. 先求做绿沙包需要多少克玉米，就是求60克的3/4是多少，用乘法计算。 Sixty times three fourths equals to forty five(grams) 60×3/4＝45(克) And then how many grams of corn do we need to make a buns, so we want to know what 7/9 of 45 is, and we multiply it. 再求做黄沙包需要多少克玉米，就是求45的7/9是多少，用乘法计算。 Forty five times seven ninths equals to thirty five (grams) 45×7/9＝35(克) You can write the synthesis. 可以列综合算式。 Sixty times three fourths times seven ninths equals to thirty five (grams) 60×3/4×7/9＝35(克) Answer: It takes 35 grams of corn to make a buns. 答：做一个黄沙包需要35克玉米。 Related links 相关链接 reciprocal 倒数 1. Observe the following formula, what do you find? Can you give some examples of this? 1. 观察下面的算式,你发现了什么?能举几个这样的例子吗？ Five sixths times six fifths is one 5/6×6/5＝1 Seven elevenths times eleven sevenths is one 7/11×11/7＝1 One fifth times five is one 1/5×5＝1 One nineteenth times nineteen is one 1/19×19＝1 I find that their product is 1. 我发现:它们的积是1。 The numerator and denominator of the two factors switch places. 两个因数的分子和分母交换了位置。 Let me give an example: two thirds times three seconds is one twenty times one twentieth is one…… 我举例: 2/3×3/2=1 20×1/20=1…… I find that…… 我发现…… Two numbers whose product is 1 are reciprocal to each other. 5/6和6/5互为倒数,即5/6是6/5的倒数,6/5是5/6的倒数。 Think about it. How do you find the reciprocal of a number? 想一想,怎样求一个数的倒数? Can you write the reciprocal of the following numbers? 2. 你能写出下面这些数的倒数吗? one half two ninths seven fifths four 1/2 2/9 7/5 4 What's the reciprocal of 1? Is there an reciprocal of zero? 1的倒数是多少?0有倒数吗? |
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