幼儿园至二年级Number计划中
Addition, subtraction and place value to 100
Adding as putting together and subtracting as taking away or comparing, the meaning of the equals sign, and place value in tens and ones up to 100.
math.number.addition-subtraction
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前置知识
2 项必需的前置知识（一直追溯到底）
你将学会
- Add and subtract within 20 fluently, and within 100 using tens and ones.
- Explain that the equals sign means 'has the same value as', so that 7 = 3 + 4 and 3 + 4 = 4 + 3 are both true.
- Represent two-digit numbers as tens and ones and use this to compare them.
定义
- Addition combines two collections with no members in common; a + b is the number of members of the combined collection.
- Subtraction a − b (with b ≤ a) is the number left when b members are taken from a collection of a members, or the difference between two amounts.
- In a two-digit numeral, the left digit counts tens and the right digit counts ones.
定理
- Addition is commutative and associative: a + b = b + a and (a + b) + c = a + (b + c).
- Subtraction undoes addition: (a + b) − b = a.
- Adding zero changes nothing.
常见误解
- Reading '=' as 'the answer comes next', so that 7 = 3 + 4 seems wrong.
- Thinking subtraction is commutative, for example that 3 − 5 = 5 − 3.
- Reading 52 as 'five and two' rather than five tens and two ones.
通向
可选发现
- Doing and undoing 'Add 3' and 'take away 3' are actions that undo each other.
- Integers Can we take 5 away from 3? Extending the whole numbers to the integers makes every subtraction possible.
学习路径
延伸阅读
- Hung-Hsi Wu, Understanding Numbers in Elementary School Mathematics (2011)