Addition and Subtraction of Numbers
Lessons in this chapter
About Addition and Subtraction of Numbers
Addition and Subtraction of Numbers is the longest chapter in 3rd grade, and it is long because it covers three different ways to get an answer rather than one.
Add and Subtract 4-Digit Numbers, without regrouping and then with, extend the column method one more column. By now the method should be familiar enough that the extra width is routine, and borrowing across more than one zero is the only genuinely new difficulty.
Relate Addition and Subtraction in 4-Digit Numbers and Understand Properties of Addition and Subtraction in 4-Digit Numbers name what kids have been using informally. Addition is commutative and subtraction is not, and stating that explicitly is what stops a child rewriting 400 − 150 as 150 − 400 when it looks easier.
Use Mental Strategies to Add and to Subtract 4-Digit Numbers carry forward partitioning and compensation from 2nd grade, now at a size where choosing the right approach saves real effort.
Estimate Sum and Difference of 4-Digit Numbers and Solve 2-Step Problems close the chapter. Estimation is the habit that catches a misplaced digit, and two-step problems are where a child has to find the unasked middle answer before the question can be answered.
Add 4-Digit Numbers with Regrouping, Use Mental Strategies to Subtract 4-Digit Numbers and Solve 2-Step Problems on 4-Digit Numbers are three of this chapter's ten lessons, and each opens as a worksheet in the page, marked as you answer. It is the longest chapter in 3rd grade because the written method, the mental math problems and the estimation each need their own practice. All ten are free.
Frequently asked questions
Adding and subtracting 4-digit numbers without regrouping and then with it, how the two operations undo each other, the properties of addition and subtraction, mental strategies for each, estimating sums and differences, and finally two-step word problems. It sits in Number and Operations in Base Ten (3.NBT), with the two-step problems in Operations and Algebraic Thinking (3.OA).
Mainly the width. The method is the same as 3rd grade's predecessors, but borrowing can now cross several columns, including more than one zero in a row.
Commutative and associative. 5 + 3 and 3 + 5 are equal, but 5 − 3 and 3 − 5 are not, which is why the order in a subtraction cannot be swapped for convenience.
Because it is the check. Rounding 4,182 + 2,935 to 4,000 + 3,000 tells you the answer should be near 7,000, which catches a misplaced digit instantly.
The middle answer nobody asks for. A child has to realize it is needed, calculate it, and then use it, which is planning as much as arithmetic.
Partitioning by place value and compensation, both from 2nd grade. At four digits they matter more, because the written method is slower.