David and Jennifer were building houses out of blocks. David used 36 blocks. Jennifer used 51 blocks. How many blocks did they use? Then, we’re asked three questions. Will the answer be bigger or smaller than the numbers in the question? Do you need to add or subtract to find the answer? Find out how many blocks they need.
This problem asks us to find the total number of blocks that both David and Jennifer use altogether. And so the important information in the problem is the number 36 and the number 51. These are the amounts that both children use. Will the answer be bigger or smaller than the numbers in the question?
Let’s sketch a bar model to represent the problem. Here’s David’s amount of blocks. This bar represents the number of blocks that Jennifer uses. And the long bar underneath represents the total that we’re looking for. So we can see that the answer will be bigger than the numbers in the question because it is the sum of them.
Our next question asks “Do you need to add or subtract to find the answer?” There’re two reasons why we know the answer to this already. The first is that, in our bar model, we can see that we need to combine 36 and 51 to find the answer. And the second reason is that we know the answer is going to be bigger. And because the answer is bigger than the numbers in the problem, we know we need to add to find the answer. This is an addition word problem.
Now that we found the number of blocks that each child has and we know we need to add them together, let’s find out how many blocks they need and solve the problem. There’re lots of different ways that we could add these two numbers together. Let’s just go through one method now. And we know that when we add numbers together, we can add them in any order and the total remains the same.
Because 36 is the smaller number, let’s start with the larger number. Now, we don’t need to add on as many. The next thing we can do is to split or to partition the number 36 into tens and ones. 36 is the same as 30 and six. Now, we can add each part to 51. 51 plus 30 equals 81. And now, we’ll add the six. 81 plus six equals 87.
And so the number of blocks that David and Jennifer use altogether is 87. 36 plus 51 equals 87.