Adding two digit numbers on a number line

We're told that Cara had a tower with 42 blocks. She added 12 red blocks, 14 more blue blocks, and 16 purple blocks. So, what we want to do in this video is think about how many total blocks Cara now has. To help us with that, we are going to set up a little bit of a number line here, and this number line keeps going in both directions.

I'm going to set it up so that this big thick hash mark here is 40. I want to make sure that I can include 42 here, and you can see we go 41, 42, 43, 44, 45, 46, 47, 48, 49, 50. So, each of the thick ones are 10 more, so that's 50, 60, 70, and 80. What I'd like you to do is pause this video, think about where 42 is on this number line, and then think about how do we add these blocks on this number line to think about how many total blocks Cara now has.

All right, now let's do this together. So, let's start with her starting point, the 42 blocks right over here. So we see this is 40. So we go 41, 42; so this right over here is Cara's starting point. That is 42 blocks. Now, first she adds 12 red blocks. So you could just count on the number line. So if you add 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, you get right over there. So this right over here is all of us adding 12 blocks.

Now, where does that get us to? Well, we can see that we are now 1, 2, 3, 4 past 50. So we are now at 54 right over there. You could have done it another way; you could have just added right from the get-go. You could have said, "All right, I'm going to add 12," so it takes me 8 to get to 50, and then I have 4 more left. That gets me to 54.

And then we need to add those 14 more blue blocks. So let's add 14 from here: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, and that gets us right over there. So we add another 14, and we get over there. And now, what number are we at? Well, there's two ways to think about it. You can see that we are one, two, three, four, five, six, seven, eight above 60, which would tell us where it's 68, or you could see that we are two below 70, which would also be 68. So we're now at a total of 68 blocks.

Then we add the 16 purple blocks. So let's do that. Let's add 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, and we get right over there. We're very lucky that our number line just happened to have the right number of marks right over here. So then we add 16, and we can see that we are 1, 2, 3, 4 past 80. So we're at 84 total blocks.

Another way you could have thought about it is it would have taken us two blocks to go to 70, then we would have 14 left, another 10 to get to 80, and then we would have four left, and then you get to 84. But now Cara has a total of 84 blocks.