K–2NumberPlanned
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
The lesson for this topic has not been written yet. The outline below is part of the curriculum map and has not been reviewed.
Builds on
Required prerequisites, all the way down: 2
You will learn to
- 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.
Definition
- 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.
Theorem
- 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.
Common misconceptions
- 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.
Leads to
Optional discoveries
- 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.
Learning pathways
Further reading
- Hung-Hsi Wu, Understanding Numbers in Elementary School Mathematics (2011)