Reasoning · Grade 2-1 Addition and Subtraction Word Problems
Problem
Stack the known 6 in the ones and 4 in the tens lined up by place, with 72 underneath.
Lining up tens under tens and ones under ones is the place-value picture every Grade 2 student uses to add two-digit numbers.
2.NBT.A.1Draw A DiagramIn the ones, what added to 6 ends in 2? Only 6, and it carries 1.
Adding within the ones column is single-digit addition you already know; the carried 1 is just the regrouping idea.
2.NBT.B.5Guess And CheckThe ones column on its own fixes the missing ones digit, and any ten it makes is carried up as a single ten.
Only the ones digits of the two numbers can land in the ones place of the answer, so nothing from the tens can disturb that column.
When the two ones digits pass ten, the full ten does not vanish — it moves up as one unit of the next place and the rest stays behind.
The tens must reach 7 from the carried 1 and the 4, so the missing digit is 2 — the number is 26.
Each tens box is worth 10, so balancing the tens column is the same place-value reasoning, just in the tens spot.
2.NBT.A.1Draw A DiagramThe difference is positive, so the number ending in 8 is the bigger one — put it on top, the 30s number below.
A number in the 30s can be at most 39, and 39 is far below any two-digit number ending in 8 that we'd need, so the number ending in 8 must be the larger one.
2.NBT.A.1Draw A DiagramTo leave 9 we borrow ten: 18 − 9 = 9, so the bottom number is 39.
When the top digit is too small we borrow one ten, exactly the regrouping move used in two-digit subtraction.
2.NBT.B.5Guess And CheckThe borrow drops the tens by one, so (□−1) − 3 = 4 gives the top number 88.
After lending a ten, the tens column is plain subtraction again, so the leftover tens have to make 4.
2.NBT.B.5Draw A DiagramStack the numbers in neat columns and the secret digits practically fill themselves in - it's just the place-value adding and subtracting you already do in Grade 2!