Adding and subtracting within 20
A child can find any sum up to twenty by counting from one. What ways of thinking let them know it instead, and why is ten at the center of most of them?
Where you are 7 inside
What this area is about
Every sum and take-away up to 20, such as 8 + 5 or 13 - 5, can be found by counting. This area is about knowing them instead: by seeing a picture, by building a new fact from a known one, and above all by using ten as a landmark. Each way is a reason the answer must be right, never a list to learn by heart.
How these fit together
The first facts. Adding within five and ten starts from seeing small groups at a glance, adding one more and adding nothing, then uses five, bonds and doubles to reach ten. Subtracting within ten reads those facts backwards.
Counting, but less of it. Counting on to add and counting back to subtract start from one part or the whole; both suit a small number.
Facts from facts. Doubles and near doubles: 6 + 6 = 12 is two equal rows, and turns into 6 + 7 = 13.
Using ten. Ten more and ten less finds 10 + 4 = 14 without counting: only the tens change. Making ten and bridging through ten finds 8 + 5 = 8 + 2 + 3 = 13 and 13 - 5 = 13 - 3 - 2 = 8.
Adding three numbers, pairing first the two that make ten or a double, now lives with the properties of addition.
A path through it
Adding within five and ten, then subtracting, counting on and back, and doubles. Then ten more and ten less, and last making ten, which needs bonds to ten and subtracting within ten.
This opens adding two-digit numbers, the first step of multi-digit addition, where the same tens and ones do the work.