Unit three Happy Farm -- Algorithms 快乐农场——运算律 Lesson One 第一课 Campus greening, to buy a number of saplings and seedlings. 校园绿化，要购进一批树苗和花苗。 What questions can you ask? 你能提出什么问题？ How many saplings will be purchased altogether? 1.一共要购进多少棵树苗？ I'll count Holly and willow and then... 我先算冬青和柳树一共多少棵再算… （56+72）+28 =128+28 =156（棵） I'll count how many willows and poplars there are and then count... 我先算柳树和杨树一共多少棵再算… 56+（72+28） =56+100 =156（棵） How many seedlings should I buy altogether? 2.一共要购进多少棵花苗？ I first count the number of Chinese roses and peonies, and then count... 我先算月季和牡丹一共多少棵，再算… (80+88）+112 =168+112 =280（棵） I'll count the peonies and camellias first and then count... 我先算牡丹和茶花一共多少棵，再算… 80+(88+112） =80+200 =280（棵） I found the results of the two equations equal. 我发现两道算式的结果相等。 (56+72）+28=56+(72+28） (80+88）+112=80+(88+112） I see that if I add the first two numbers, I add the third number or if I add the last two numbers, I add the first number 我发现前两个数相加，再加第3个数或后两个数相加，再加第1个数… Is that a rule in addition? So let's verify that. 这是加法运算中的一个规律吗？我们来验证一下吧！ (63+15）+35=63+(15+35） (325+82）+18=325+(82+18） This law is called the associative law of addition, and it is written in letters: (a+b) +C=a+(b+C) 这个规律叫做加法结合律，用字母表示为： (a+b）+C=a+(b+C） I find that when you add two numbers, you switch the addends, and the sum stays the same. 我发现两个数相加，交换加数的位置，它们的和不变。 This law is called the commutative law of addition, and it is written in letters: a+b=b+a 这个规律叫做加法交换律，用字母表示为：a+b=b+a What are the problems that can be solved by applying the laws of addition? 运用加法的运算规律能解决哪些问题呢？ Can make the calculation simple, but also can check the calculation. 可以使计算简便，还可以进行验算。 Lesson Two 第二课 I bought some flower soil and fertilizer. 我购进了一些花土和花肥。 What questions can you ask? 你能提出什么问题？ How many kilos of flower soil have you bought altogether? 1.一共购进了多少千克花土？ I count the number of kilograms of soil per bag, then 20 bags... 我先算每袋花土多少千克，再算20袋… (4×25）×20 =100×20 =2000（千克） I count the number of bags of soil, and then the number of kilograms 我先算一共多少包花土，再算一共多少千克… 4×(25×20） =4×500 =2000（千克） How many kilos of flower fertilizer did you buy altogether 2.一共购进了多少千克花肥？ I first calculate how many kilograms of flower fat per bag, then calculate 10 bags. 我先算每袋花肥多少千克，再算10袋。 (5×8）×10 =40×10 =400（千克） I calculate the total number of bags of fertilizer, then calculate the total number of kilograms... 我先算一共多少包花肥，再算一共多少千克… 5×(8×10） =5×80 =400（千克） I found the results of the two equations equal. 我发现两道算式的结果相等。 This law is called the associative law of multiplication, and it is written as :(a×b) ×c=a×(b×c) 这个规律叫做乘法结合律，用字母表示为：(a×b）×c=a×(b×c） Any other rules in multiplication? 乘法运算中还有其他规律吗？ The commutative law of multiplication is expressed in letters as: 乘法交换律用字母表示为： 3. Can we use the commutative law of multiplication and the associative law of multiplication to make the operation easier? 3.运用乘法交换律和乘法结合律，也能使运算简便吗？ 125×7×8 =125×8×7 =1000×7 =7000 125×7×8 =7×(125×8） =7×1000 =7000 Lesson Three 第三课 Peony stands 12 in a row 芍药每行12棵 There are eight peonies in a row 牡丹每行8棵 What questions can you ask? 你能提出什么问题？ How many peony and peony altogether? 1.芍药和牡丹一共多少棵？ To ask how many peony and peony trees in total, you can first find out the number of peony and peony trees, and then find... 要求芍药和牡丹一共多少棵，可以先分别求出芍药和牡丹的棵数，再求… 12×9+8×9 =108+72 =180（棵） Or you can figure out how many flowers per row, and then you can figure out... 还可以先求每行多少颗花，再求… (12+8）×9 =20×9 =180（棵） How many square meters is the total planting area of peony and peony? 2.芍药和牡丹的种植面积一共是多少平方米？ We can figure out the planting area of peony and peony respectively, and then... 可以分别求出芍药和牡丹的种植面积，再求… 15×8+10×8 =120+80 =200（平方米） well enough 还可以… (15+10）×8 =25×8 =200（平方米） I found the results of the two equations equal. 我发现两个算式的结果相等。 12×9+8×9=(12+8）×9 15×8+10×8=(15+10）×8 This law is called the distributive law of multiplication, and is written as :(a+b) ×c=a×c+b×c 这个规律叫做乘法分配律,用字母表示为：(a+b）×c=a×c+b×c Does the distributive property of multiplication make it easy? 运用乘法分配律能使运算简便吗？ |
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