In today's evolving educational landscape, the use of manipulatives in the classroom is gaining recognition as a powerful tool for enhancing mathematical understanding. In Year 1, students experienced firsthand the benefits of hands-on learning as they explored number bonds to 20 and the concept of commutativity.

教育不断发展和前进的时代，在教学中使用教具以增强学生对数学的理解这一教学方法正在普遍被使用并认可。一年级的学生在学习20以内的数对和交换律时就采用了这样的方法，令他们受益匪浅。

During a recent lesson, Ms. Carly introduced her students to Numicon, a versatile set of coloured shapes representing numbers. This engaging resource allowed the children to visualise and physically manipulate number bonds, making abstract concepts tangible. As they paired different Numicon pieces to make 20, students began to see relationships between numbers, fostering a deeper understanding of addition and subtraction.

课堂上，Ms. Carly向学生们介绍了了Numicon，它是一套带有孔洞的扁平塑料形状教具，每个形状代表一个从 1 到 10 的数字，每个数字都有自己的颜色。教具的使用让课堂更引人入胜，学生们能够直观地看到并实际操作数的组合，使抽象的概念变得具体。学生们将不同的部件组合得到20时，他们发现了数字之间的联系，从而加深了对加法和减法的理解。

To reinforce these concepts, Ms. Carly incorporated a dice game where students rolled to create different number bonds. This playful approach not only added an element of fun but also encouraged collaboration and discussion among peers. Alongside this, ten frames helped students organise their thoughts visually, illustrating how numbers can be combined in various ways.

Ms. Carly用骰子游戏让学生们创造不同的数对组合。这种有趣的方式不仅激发了学习的热情，同时也促进了学生们之间的合作和讨论。十格阵则通过视觉的方式启发学生组织思路，展示了不同的数字组合方式。

The lesson also emphasised the principle of commutativity- the idea that the order of numbers in addition does not change the sum. By using number lines and part-whole models, students were able to explore this concept practically. They discovered that whether they added 8 + 12 or 12 + 8, the result remained the same. This exploration not only solidified their foundational skills but also promoted higher-order thinking as students reasoned through their findings and explained their thought processes.

学生们还学习了交换律的原则——即在加法中，数字的顺序不会改变结果。通过使用数轴、部分和整体模型，学生们能够实际地探索并理解这一概念。他们发现，无论是先加8再加12还是先加12再加8，结果都是一样的。过程中，学生们分析了自己的发现并阐述了思考的过程和推理。这种学习方法不仅加深了他们对基础知识的学习，同时也锻炼了学生们的思维能力。