新加坡数学这几年很火，教学方式被各个国家推崇。“中西合璧”的新加坡数学可谓是集中了中国、西方数学教育各自之长处，又避免了其弊端，它比中国数学教育更为灵活和发散，但又比西方数学难度更高且练习题更多。既注重动手能力、思维和数感的培养，又注重知识的理解和实际运用。教学上侧重图像建模，要求学生通过画模型的方法把抽象概念具体化，帮助孩子通过实际操作和解决问题的方式学习数学，大大提高数学学习效果和兴趣的同时也培养了学生的创造力、逻辑创新思维和解决问题的综合能力，让孩子透彻理解数学概念，解题思路更灵活！
新加坡数学最核心“CPA教学法”，即图像建模法非常符合孩子的思维认知发展规律，通过最简单的日常生活实物，从具象思维逐步过渡到抽象思维，鼓励孩子主动参与和实践，让孩子更容易吸收和理解复杂的数学概念，提高思维逻辑和运用数学知识解决问题的能力。
今天就让我们一起来看看新加坡数学的一些经典例题，熟悉一下新加坡数学的出题方式和解题思路吧！
问题1-10：
1、A bakery and a library are 120M apart. They are located between Hong’s house and Jeya’s house, as shown below. The bakery is exactly halfway between the two houses.
One day, Hong and Jeya started cycling from their houses at the same time and they arrived at the library together. Jeya cycled at 70M/minute while Hong cycled 15M/minute faster than Jeya.
面包店和图书馆相距120M。它们位于Hong家和Jeya家之间，如下所示。面包店恰好位于两间房子的中间。
一天，Hong和Jeya同时开始从家里骑行，他们一起到达了图书馆。Jeya的骑车速度为70M/分钟，而Hong的骑车速度比Jeya快15M /分钟。
a) How much further did Hong cycle than Jeya?（Hong比Jeya多骑了多远？）
b) How far is Jeya’s house from the library?（Jeya家离图书馆有多远？）
2、Jess needs 200 pieces of ribbon, each of length 110CM, to decorate a room for a party. Ribbon is sold in rolls of 25M each.
What is the least number of rolls of ribbon that Jess needs to buy?
Jess需要200根缎带，每条长110CM，来装饰一个聚会用的房间。缎带以每卷25M出售，她最少需要买几卷？
3、Jim bought some chocolates and gave half of them to Ken. Ken bought some sweets and gave half of them to Jim. Jim ate 12 sweets and Ken ate 18 chocolates. The ratio of Jim’s sweets to chocolates becomes 1:7 and the ratio of Ken’s sweets to chocolates becomes 1:4.
How many sweets did Ken buy?
Jim买了一些巧克力，然后把一半给了Ken。Ken买了一些糖果，并将其中一半赠予Jim。Jim吃了12种糖果，Ken吃了18种巧克力。Jim的糖果与巧克力的比例为1：7，而Ken的糖果与巧克力的比例为1：4。Ken买了多少糖果？
4、One machine took 70 minutes while another took 100 minutes to print the same number of copies of a newsletter. The faster machine printed six more copies of the newsletter per minute that the slower one.
一台机器要花70分钟，而另一台机器要花100分钟，才能打印相同数量的报纸。较快的机器每分钟打印的副本比较慢的机器多六份。
a) The slower machine completed the job at 1pm. At what time was the printing started? （打印较慢的机器，在下午1点完成工作，它在几点开始打印？）
b) What was the total number of copies printed by the two machines?（两台机器总计打印了多少？）
5、Jamie and Mark used $61.2 to buy some egg tarts. Jamie has a 15% discount coupon and bought 6 more egg tarts than Mark.
Jamie 和Mark各花了61.2买蛋挞，Jamie 有一个15%折扣劵，比某某多买了6蛋挞。
a) How many egg tarts did Jamie buy?（Jamie买了多少蛋挞？）
b) What is the cost of an egg tart? （一个蛋挞多少钱？）
6、Fill in the graph below by looking at the figure below.
7、Study the pattern below carefully. What is the missing number?
认真研究下图、发现规律，找到缺失的数字是几？
8、Five identical semi-circles are arranged as shown. Find the diameter of one circle.
5个半圆排列如下，求一个圆的直径
9、There are 50 oranges in a box. 3/10 of them are rotten. How many of the oranges are not rotten?
箱子里有50个橙子，其中3/10都是坏了的，请问有多少橙子是好的？
10、The ratio of the cost of a skirt to the cost of a blouse is 8:5. If the skirt costs $24 more than the blouse, find the cost of the blouse.
一条裙子和一件衬衫的价格比为8:5，如果裙子价格比衬衫贵$24，那么衬衫多少钱？
答案1-10：
1、a) Hong travelled 240M further than Jeya. （Hong比Jeya多骑了240M）
b) Jeya’s house is 1,120M from the library.（Jeya家离图书馆有1120M）
2、At least 10 rolls（最少10卷）
3、68
4、a) The printer started at 11.20am. （上午11点20分开始）
b) The total number of copies printed was 2,800. （一共打印了2800份）
5、a) 40 b)$1.8
6、
Figure | 1 | 2 | 3 | 4 | 5 |
White triangles | 1 | 1 | 6 | 6 | 15 |
Grey triangles | 0 | 3 | 3 | 10 | 10 |
Total | 1 | 4 | 9 | 16 | 25 |
7、15 （4+7=11，11-6=5；7+10=17，17-9=8）
8、36
9、35
10、40
问题11-20:
11、A box of cookies cost $6 and a bottle of milk cost $2. After paying for 2 boxes of cookies and 6 bottles of milk, Nicole had $30 left. How much money did she have at first?
一盒曲奇饼$6、一盒牛奶$2，Nicole在买了2盒曲奇饼和6盒牛奶后还剩$30，请问她一开始有多少钱？
12、Peter practices on piano for 1 3/4 hours. Pablo practices for 125 minutes. Who practices for a longer time? How much longer?
Peter练了1 3/4小时的钢琴，Pablo 练了125分钟，他们两谁练琴时间更长？长多少？
13、Area of the triangle = ？求下面三角形的面积
14、A watermelon weighs m kg and a pineapple weighs 2 kg.
一个西瓜重m kg，一个菠萝重2kg。
a) Express the total weight of the fruits in terms of m. 用m来表示水果总重量
b) If the m = 4, find the total weight of the fruits 如果m=4，那么水果总重量是多少？
15、Which of the following can be folded to form of a cube?
以下哪些可以折成立方体？
16、The figure is made of a triangle and a semicircle. (Take π=3.14)
下图由一个半圆形盒一个三角形组成。请计算其面积 （π=3.14）
Area of the figure = ？
17、The total length of three ribbons, A, B and C is 2.6m. Ribbon A is 60cm longer than ribbon B. Ribbon C is 50 cm longer than ribbon B. Find the length of Ribbon A.
ABC三条丝带总长度为2.6米。丝带A比丝带B要长60厘米，丝带C比丝带B要长50厘米，请问丝带A多长？
18、PQRS is a parallelogram. QRT is a straight line. Find ∠b
PQRS是一个平行四边形，QRT是一条直线，求∠b多少度？
19、Jesse drove from Town A to Town B. At 8:30am, he had traveled 2/3 of the trip. He traveled the rest of the trip at an average speed of 80km/h and reached Town B at 8:45am. If his average speed of the whole trip is 90km/h, what time did he leave Town A?
Jesse从A镇开车到B镇。他八点半已经开完了这趟旅程的2/3。剩下的旅程他以平均每小时80km的速度前行，八点45分抵达B镇。如果他整趟旅程的平均速度是90km/h，那么他什么时候离开的A镇？
20、The ratio of the number of the girls to the number of the boys in a swimming club was 3:2 last year. When 15 boys joined the club this year, the ratio became 2:3. Find the total number of the children in the club this year.
去年游泳俱乐部的女生数量和男生数量的比例为3:2。今年15个男孩加入了俱乐部，女生和男生的数量比变为2:3，请问游泳俱乐部今年总人数多少？
答案11-20：
11、$54
12、Pablo practices for a longer time, 20 minutes longer. (Pablo弹琴时间更长，长了25分钟)
13、36in
14、2+m, 6
15、A, F, H
16、90.24
17、110cm
18、66度
19、8:05am
20、45
LingoAce在线数学课吸收了新加坡数学教育的优势，采用CPA教学法，从具象（Concrete）的生活实物，到形象化（Pictorial）模型展示，最终到抽象化（Abstract）的数学符号表达，引导学生用建模思维来理解和解决复杂的数学问题，由浅至深、循序渐进地帮助学生建立独特数学思维方式，举一反三，探索一题多解。 课堂趣味性强，注重应用数学知识解决实际问题的能力、抽象思维能力、逻辑推理能力、归纳能力等。
LingoAce课程将数学建模贯穿始终，老师带领学生把实际问题转化为数学模型，鼓励学生选择不同的数学工具和方法，视觉化地理解题目各条件的逻辑关系，提出估测和假设、进行推理和证明，并对结果进行评估和优化。学生在这个过程中不断践行批判性思考，往往能够创造性地轻松解决问题！
