Addition and subtraction
Putting groups together and taking them apart look like two jobs. How are they one idea, and what does a child build on it?
Where you are 12 inside
What this area is about
Adding and subtracting are a child’s first operations, and 3 + 4 = 7 is among the first sentences they write. The area runs from what the plus and minus signs mean to many-digit sums and differences. One picture threads through it: a whole made of two parts. Adding finds the whole; subtracting finds a part.
How these fit together
What the signs mean. Addition as putting together and subtraction as taking away come first. Subtraction gains two more meanings: subtraction as the difference (“how many more?”) and subtraction as an unknown addend, where 9 - 4 asks “4 and what make 9?”
The picture that links them. Parts, wholes and number bonds finds every way to split a whole in two. Fact families read one bond as four sentences, or two for a double.
Facts and rules. Adding and subtracting within 20 builds fluent facts with ten as a landmark. Properties of addition: order and grouping do not change a total, and adding 0 changes nothing.
Bigger numbers and stories. Multi-digit addition and multi-digit subtraction work place by place. Addition and subtraction problems in words ask which operation a story needs.
A path through it
Joining, taking away, bonds, facts within 20, then the properties. Comparison fits anywhere between taking away and story problems. Missing parts follow the facts within 20, then fact families, then story problems. Multi-digit addition follows the facts within 20; multi-digit subtraction follows it and fact families.
Next comes repeated addition, the start of multiplication and division.