Adding lengths in 2nd grade math

The two problems that need adding are Mia's strings $(9 + 6)$ and the joined ropes $(5 + 3)$. Both ask you to combine two lengths into one new total. The stick problem compares lengths, so it needs subtracting.

1. 1Read each problem. Ask: am I combining two lengths into one new total (ADD), or comparing two lengths or finding a missing piece (SUBTRACT)?
2. 2The string problem combines Mia's 9-inch string and her 6-inch string into one total $(9 + 6 = 15$ inches). The rope problem joins a 5-foot rope and a 3-foot rope into one new rope $(5 + 3 = 8$ feet). Both combine two lengths, so both need ADDING.
3. 3The stick problem asks 'how much longer' — that compares the 14-inch stick and the 5-inch twig to find the difference, so it needs SUBTRACTING (14 − 5 = 9). This is a comparing question, not a combining one.
4. 4Select the two problems that need adding: the string problem and the joined-rope problem.

Common mistake. A common mistake is seeing two length numbers in every problem and thinking to add them all. But 'how much longer' is a comparing question — you subtract to find the difference, not add.

The idea underneath. Length word problems can ask you to ADD (combine two lengths into a new total) or SUBTRACT (compare two lengths, OR find a missing piece from a known whole). The question itself — what the unknown is — tells you which operation to use, not just the words you see.

The matching equation is $30 - \Box = 18$. Maya started with $30$ inches, cut off $\Box$ inches, and was left with $18$ inches.

1. 1Look at the story. Maya started with a $30$-inch ribbon. She cut off some inches. Now her ribbon is $18$ inches long.
2. 2Find what we know and what we do not know. We know the start ($30$ inches) and the end ($18$ inches). We do not know how many inches Maya cut off — this is the unknown, so it gets the $\Box$ symbol.
3. 3Cutting off makes the ribbon shorter, so the action is subtraction. The story reads: start minus the cut equals the end.
4. 4Put in the numbers from the story.

Common mistake. A common mistake is picking $30 - 18 = \Box$. That equation finds the answer (how many inches were cut off), but it does not match the story's structure. In the story, the unknown is what Maya cut off — the number that goes between $30$ and $18$, not after the equals sign.

The idea underneath. The equation that matches a story shows where each number lives in the story — start, change, and end. Solving the math comes second. First, place $\Box$ where the story's unknown sits.

The rope is $37$ inches long after Lila cuts off $28$ inches. The computation is $65 - 28 = 37$.

1. 1Look at the action in the story. Lila cuts off $28$ inches from the $65$-inch rope, so the piece that remains is shorter than $65$ inches. To find what is left, subtract.
2. 2Subtract $28$ from $65$. Since $5$ is less than $8$ in the ones place, regroup: take $1$ ten from the $6$ tens, leaving $5$ tens and $15$ ones. Then $15 - 8 = 7$ ones, and $5 - 2 = 3$ tens.
3. 3There are $37$ inches of rope left.

Common mistake. A common mistake is adding $65$ and $28$ to get $93$ instead of subtracting. When something is cut off, the remaining piece is smaller, so subtract.

The idea underneath. In a length word problem, the action in the story tells you the operation: 'cuts off' or 'uses' means the remaining length is smaller (subtract); 'in all' or 'altogether' means combine (add).

The equation is $? - 15 = 34$, and $? = 49$. The rope was $49$ inches long.

1. 1Read the story carefully. We know Tim cuts off $15$ inches and the piece left is $34$ inches. We do not know how long the rope was to start.
2. 2"Cuts off" tells us to use subtraction. The starting length is the unknown, so $?$ goes in the first position. We write the equation with $?$ for the unknown start length.
3. 3To find $?$, add the two known numbers: $34 + 15 = 49$.
4. 4So $? = 49$. The rope was $49$ inches long.

Common mistake. A common mistake is placing $49$ in the result slot and writing $15 + 34 = ?$. That gives the right number but puts $?$ in the wrong position. The story already tells us the remaining piece is $34$ inches — that goes in the result slot. The unknown starting length goes in the first slot.

The idea underneath. Action words in the story tell you which operation to use: "cuts off," "takes away," and "gives away" mean subtraction; "puts together," "adds more," and "altogether" mean addition. When the unknown is the starting amount, place $?$ in the first slot.