Label Your Work!
Updated: Jan 26
Why it is critical for children to label their answers when solving math story problems and how this small step can make a world of difference in building mathematical understanding.
Imagine a world without labels. And I don't mean labels like 'boy' or 'girl,' or 'popular' and 'unpopular.' I mean a world where no one labels anything that they are talking about.
Picture this: you go to a carryout restaurant and are ordering a meal for your family. You want to order three cheeseburgers, two side salads, one order of fries, and three lemonades. For the record, my family would eat way more than this, but let's just use it as an example. But instead of being specific and labelling your thinking when you order, you say 'Can I please have three of those, two, one, and then three." You take out the 'labels' cheeseburger, side salad, fries, lemonade. You remove the specific and important information from the conversation. Then the cashier tells you that your total will be 24 (and instead of saying 24 dollars, they just say 24--removing the important label of dollars). Think about how this interaction might go. You could dig in your purse for 24 pennies, or 24 quarters, or 24 paperclips, or 24 hair ties, or 24 toy cars...you get the idea. Anything but dollars because you didn't realize that it cost 24 dollars. And then when the cashier brings you your food, you end up with three chicken sandwiches, two ice cream cones, one fruit cup and three cokes. This would be extremely confusing, and frustrating!
So now let's put that in the context of the math classroom. When a child doesn't label their answer, it is essentially like a person not 'labelling' what they want at the restaurant. You're removing the very important context from the equation, so to speak. And math word problems depend on the context in order to make sense! And that context is exactly what helps children understand the value of math in the real world!
Let's break it down. Take a look at the following math story problem (geared towards a second grade learner--addition and subtraction within 100).
The green marbles in this problem are not relevant to the question being asked (and this is very common in math story problems because the goal is to help children become sense makers and problem solvers and be able to think carefully about the question being asked). A student solving this problem could label their answer, before they've even solved the problem. This is a critical step to making sense of story problems and also determining what operation to use and how to solve. So they might label their answer 'marbles.' Which is better than no label at all, but since the story problem is talking about only marbles, then it's actually not that helpful. In this case, the label obviously isn't cows, or eggs, candy bars or yards. So a more specific label would be useful. Ask yourself, would the answer be labelled 'total marbles,' 'red marbles,' 'green marbles,' 'blue marbles,' 'more red than green marbles,' 'more red than blue marbles,' or 'more green than blue marbles?' There are a lot of different ways to label these marbles. But if a child carefully reads the problem they would see that the label would read ______more red than blue marbles. **And if that is too much writing for a second grader, they can write, 'more R than B' to represent red and blue (and hey! That connects to using variables in math at a younger age--but more on that in another blog post)!
So by pre-labelling their answer before solving the problem, it helps a student see that, in this case, they need to subtract 17 from 32 to find the difference between the red and the blue marbles, and that they can leave the green marbles alone for this problem. Then they can dive into a solution strategy.
Labelling answers is a critical step of checking work as well. Whenever my students start a math story problem, I ask them to make a quick estimate, and when they finish, I always ask 'how do you know your answer makes sense.' If a student, let's say added the red and blue marbles, instead of subtracted, their answer would say '49 more red marbles than blue marbles.' But if they stop to check to see if it makes sense, they would realize that 49 is more than the red or the blue marbles, so that can't possibly be the difference between the two. That answer would not be reasonable. This label helped the child to pay more careful attention to sense making and reasonableness.
Think about how the label would change if the problem changed slightly.
Now the answer would be labelled 'total marbles.' Labelling this answer would help a child see that they need to add the marble all together to find the total. This label change can clue a child in to the operation that they need to use to solve the problem, and what numbers are involved in problem solving. (In this case, they would be adding all three numbers together).
One of the Mathematical Practice Standards is 'Attend to Precision,' basically stating that good mathematicians pay careful attention to accuracy and precision when problem solving. This precision may not seem overly important or critical at the second grade level. If Deeyansh's marble count is off, lives won't be impacted, the world won't come crashing to an end, right? So some children might wonder why this is so important. But let's look at a higher-level problem that could have a bigger impact. Consider the following fifth and sixth grade measurement conversion problem.
In this scenario, it is critical, and potentially life saving that the drone returns to base to be charged. Consider the impact if it doesn't. The battery could die and it might fall out of range and then may not be able to continue the search and rescue mission. What would happen to the people lost on the mountain if the drone couldn't fly? Many questions could be asked about the potential scenarios if this drone was unable to operate.
But take a careful look at the labels in the problem. It first refers to yards and then feet. So a student has to carefully consider these labels and then label their answer accurately. If they inaccurately label their answer as yards, then the pilot might think he can actually go farther than he can, and the drone battery will die. ? Also, in order to solve the problem, the student must convert feet to yards (otherwise they would be subtracting 32,736 from 15,136 resulting in a negative number). It's all about what makes sense! Problems like these--or really any problems in the real world can help children see the importance of labelling. Cooking and baking is another great example (less critical, but still important), because if you use cups instead of quarts, or teaspoons instead of tablespoons, the recipe will not turn out right and you might have a mess in your kitchen (trust me, I've made that mistake)!
Okay so we understand that children need to read the labels in story problems, and accurately label their answers. But what if they do label their answer and still have trouble understanding the problem? Let's look at the following problem with Deeyansh and his marbles.
Now, if a student reads this second grade math story problem quickly, they might just pull the two numbers 28 and 14 and look at the word total. Using these context clues they may just decide it is an addition problem, and that they should add the numbers 28+14 to get a total of 42 marbles. Take a moment and consider, where did this student go wrong? What was misunderstood about the math story problem?
The student assumed that 28 and 14 were both numbers of marbles in the collection and since it asked for the total, they just added those two numbers together. What they should have done, was first solve for the number of green marbles and then added the total green marbles to the number of red marbles to find the total number of marbles. A bar model is a great tool for understanding what this problem is asking! Check out the example below and read my Blog Post for more on tools like this!
Labelling answers is a critical step in the math story problem solving process. We don't just label answers for fun. We do it to build understanding, reasonableness and to check our work for accuracy. Check out my latest Instagram Reel for an example to show your students!