This is Common Core State Standards Support Video in Mathematics. The standard is 2.MD.5.
This standard dealing with measurement and data states: Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. Now what's interesting here is that there is a related standard over in the operations and algebraic thinking strand. Standard one reads: Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from putting together, taking apart, and comparing, with unknowns in all positions, for example, by using drawings and equations with the symbol for the unknown number to represent the problem. Again notice there is quite a bit of similarity between this standard and the one that we're dealing with in measurement and data, which is really a more specific application of this other standard in the other domain.
Now it's not specifically mentioned, but it's very important that students understand the need for standard units. Let's say you had students measure the length of an object and some students used paper clips, others use crayons, others use some checkers or coins, and some others used spaghetti sticks. Notice that they all got different numbers as far as the length, and of course, the reason being is that the length units were different lengths. So that creates a problem, because some were saying it's a length of four, some were saying a length of six, and so forth. So we need the same unit to be used by all students to get the length measurement. So of course here's where the idea of the standard unit of say an inch comes in. So you'd want students to have some kind of manipulative that's an inch long, some kind of strip of cardboard of whatever you come up with. Just label it one inch, so that the idea starts becoming more familiar to the students that we're dealing with a measurement, a standard unit of one inch.
Let's take one more scenario to again instill this idea of the need for standard units. Let's say the question is well—What's the length of the classroom? Let's say okay the teacher is going to be one of the folks that steps off the distance and then deliberately chooses the shortest student in the class as the other person to walk off the distance. Let's say that the teacher took 17 steps across the room, but the shorter student took 25 steps. Now the unit being used is the same thing, steps. But the teacher’s steps are longer than the student's steps, so they did come out with a different number as far as the length. So again bringing in the idea of a standard unit, let's say in this case a ruler, which would be a foot. So again if students use the rulers to measure the length of the classroom, they should all come up with the same solution instead of something like this situation where one of them was 17 steps, and the other length was 25 steps. Again, it is very important to establish this important idea, the need for standard units.
So let's go ahead investigate some problems, some examples. Here we have a boat, and it left its port and has traveled 23 miles. The port on the other side of the bay is a distance of 67 miles. How much farther does the boat have to go to reach the port across the bay? Well first you want students to have some type of visual, you know some type of picture. It doesn't have to be real elaborate but just something basic where they can again understand the facts and the relationships in the problem. So in this scenario, we've got a situation where we traveled 23 miles and the total distance across is 67 miles. It's always a good idea to establish the relationship in plain English, and in this case we had a partial distance and then plus the remaining distance will be the total distance. Once that is established, then it's a lot easier to go ahead and put in our statement that includes the numeric values. So in this case, we had 23 miles plus some unknown distance, the remaining distance, to get a total of 67 miles. Notice that we didn't try to force fit the equation or the relationship to match what the operation was going to be. Just go with what the logic says, and the operation that's going to be used will be will take care of itself.
Let's take a similar scenario this time. A boat left its port and traveled 18 miles. They stopped to watch the whales. Okay, well the whales went away so they decided let's keep going. So then they traveled another 27 miles to get to the port on the other side. So how far is it from one port to the other? Again you want the students to draw some type of physical, visual representation. So they again can see what the relationships are going to be. In this case, the boat traveled 18 miles and then another 27 miles. So our unknown is how many miles total is that? We write our logic statement; partial distance plus remaining distance equals to the total distance. Then we establish the numeric equation, 18 miles for 27 miles is equal to an unknown number of miles. Then the students can solve the problem and actually do the addition and fill in their solution into this symbol here for the unknown.
Let's try a different scenario. Students are pretty familiar with football. In this case, okay Miguel threw a pass from the fifteen-yard line to thirty-nine yard line. How far did he pass the football? Again it is very important that the students have some type of visual representation. So in this case okay from the fifteen-yard line to the thirty-nine yard line, and then we fill in the rest of the information fifteen and the thirty-nine. Now the logic here is very important, and it is something very common that students will deal with in the future. That's the basic idea of how to get distance, which typically would be that you would take the starting point and subtract it from the ending point. Again it is very important logic. You need to write that down, and again something that students need to become very familiar with that if I take the ending point and subtract the starting point that'll give me the distance or the distance traveled. So in this case, now we just fill in the numeric information. We have thirty-nine yards for the ending point minus the fifteen yards as far as a starting point for him throwing the pass and then all we have to do is the subtraction to get our solution. Again fill it in with the symbol that we used for the unknown.
Let's try one more example. When Michelle's family moved into their new home there was a tree in the backyard that was 4 feet tall. Then after 15 years the tree grew 9 feet. So what's the new height of the tree? Now let's focus on this idea after 15 years, this is in here. For a very deliberate reason, students get accustomed to having problems where whatever numeric values are involved, whatever is given in the problem those get used in the solution. But when they start experiencing problems where there's extraneous information like we have here, then there's confusion. So doing something like this early on starts giving them that experience. But what would really help in this case would be when they do the visual representations and they set up the relationships their statements; that eliminates that problem. So like here the original tree was 4 feet okay, then it grew 9 feet, so there's that information. So logic says well the original height plus the growth would be the new height. So now it's just a matter of filling in our information numerically; 4 feet plus 9 feet. So now we can see that the solution will come from just adding 4 feet and 9 feet and filling in the information here. Which in this case of course would be 13 feet. Now by doing all this I've eliminated the confusion of what to do with this. Kids start to realize that, hey, that was just extra information. Yeah it was nice to know, but it wasn't anything that I had to have in order to solve the problem.