Multi-digit addition
Once numbers have tens, hundreds and more, how do you add them without counting on one at a time?
Where you are 6 inside
What this area is about
Adding big numbers rests on one idea: add like places to like places, tens to tens and ones to ones. The only snag is a place that adds up to more than nine. Ten ones become one ten, ten tens become one hundred, and the rest of the sum goes on as before. Every method in this area is that idea written down a different way.
How these fit together
Place by place, no trades. Adding two-digit numbers without regrouping adds tens to tens and ones to ones, as in 43 + 5 or 27 + 40.
Making a new ten. Adding by making a ten fills up to the next ten, as in 38 + 5. Regrouping in addition is the rule behind it: no place ever holds more than nine.
Written methods. The open number line jumps by tens, then ones. Partial sums adds each place on its own and then combines the parts. The standard algorithm works column by column from the right, carrying into the next place, for numbers of any length.
A path through it
Begin with two-digit sums that need no trade. Then make a ten, and learn regrouping. The open number line fits anywhere after that. Partial sums comes before the standard algorithm, which is where the area ends.
With addition in hand, multi-digit subtraction runs the same ideas in reverse, and estimating sums checks any answer.