What is wrong with this homework?
Nothing really. Actually, it showcases an excellent strategy for addition.
What you are supposed to do is make a ten, which makes it easier to add the rest.
Take the example 29 + 52. Look at the first number 9 + 1 = 10, take a 1 away from 52 and add it to the 29 to get 30. Then add the remaining 51 to 30, which can be done in your head.
The publisher even made it simple for you by putting a nice helpful line underneath the number they want you to break apart.
Lets try the first problem. Now go back the the first number and ask yourself 5 plus what equals 10? Yes, 5 + 5 = 10, so I need to take a 5 from the second number (27) and add it to 35 to make a nice round 40.
Then we finish the problem with the left overs from the original addend. I hope you didn’t add 27, because we took the 5 from the 27 leaving ourselves with just 22.
40 + 22 = 62.
Do you understand how to do the math now?
Good, because this is an excellent strategy for addition. To use this strategy requires you to be fluent in your addition facts up to 10, which also happens to be one of the common core standards for 1st grade math.
Then you should be able to add by tens (also a common core standard). It wasn’t explicitly asked for on this sheet, but my son’s teacher was nice enough to give out number lines on which they had practiced adding two digit numbers starting from a ten.
Again, I say this is an excellent strategy for addition, especially addition of two digit numbers. When I shared the picture I asked “What is wrong with this homework?” There is nothing wrong with the math, but everything is wrong with the homework.
What is happening is they are taking an advanced addition strategy and teaching it explicitly, then going back and asking students to practice it over and over again. This is no different than going back to the old days and requiring students to line up the number one above the other and adding down the lines. It is actually worse because that strategy is often the most effective way to add any two random numbers on paper. The strategy above is probably one of the easiest if you were asked to add two numbers in your head. (The second easiest for me at any rate.)
Instead of teaching students how to do this strategy it would be better to contrive a method for discovering this method in the classroom and hope that someone brought it up during a number talk. Even if they didn’t come up with this specific strategy I wouldn’t force it on students, rather the goal is to get them comfortable in discovering and using new strategies and as they progressed through the years they will discover it. You will see in the series of videos some ways to use number discussions in a classroom. Even those non-teachers should watch the first video at least.
Practicing someone else’s strategy for solving math doesn’t teach us how to do math, it teaches us how to follow directions.
Now my question is, “How would you make this problem better?” My suggestions tomorrow.