Addition and Subtraction Strategies
Lessons in this chapter
About Addition and Subtraction Strategies
Together and Apart - II is the mental arithmetic counterpart to the column methods, and it exists because the column method is often the slowest way to get an answer.
Add and Subtract 10 and 100 in 3-Digit Numbers is the quickest win. Adding 100 changes one digit, so 472 + 100 should never be written out, and noticing that is place value paying off directly.
Add and Subtract 3-Digit Numbers by Partitioning breaks numbers into place values and handles each separately, so 472 + 215 becomes 400 + 200, then 70 + 10, then 2 + 5. It is the column method done out loud, and it makes the columns make sense.
Add and Subtract 3-Digit Numbers by Compensation and Grouping is the more inventive one: to add 198, add 200 and take 2 back. Kids who can do this have stopped following a procedure and started looking at the numbers in front of them.
Relate Addition and Subtraction in 3-Digit Numbers, Estimate Sum and Differences of 3-Digit Numbers and Solve 2-Step Word Problems close the chapter. The two-step problems are the real jump: a child has to work out the hidden middle answer before the question can be answered at all.
Add and Subtract 3-Digit Numbers by Partitioning, Add and Subtract 3-Digit Numbers by Compensation and Grouping and Estimate Sum and Differences of 3-Digit Numbers each open as a worksheet in the page, marked as your child works. These are the mental math problems that make the written method quicker rather than replacing it. Six lessons, all free to practice online.
Frequently asked questions
Adding and subtracting 10 and 100 in 3-digit numbers, then partitioning, then compensation and grouping, then the link between addition and subtraction, then estimating sums and differences, and finally two-step word problems. These are strategies rather than new facts, and they sit in Number and Operations in Base Ten (2.NBT) and Operations and Algebraic Thinking (2.OA).
Because the column method is often the slowest route. 472 + 100 should be instant, and 345 + 198 is easier as 345 + 200 − 2 than as a written sum.
Splitting numbers by place value and adding each part: 472 + 215 as 400 + 200, 70 + 10, 2 + 5. It is the column method said out loud, which is why it helps kids understand the columns.
Adjusting to an easier number and correcting after. To add 198, add 200 and subtract 2. It works because the total change is the same.
To have something to check the answer against. Estimation uses the rounding from the previous chapter, which is why the two sit next to each other.
There is an answer in the middle that nobody asks for. The child has to realize it is needed, work it out, and then use it, which is a planning skill as much as an arithmetic one.