Parents Frustrated by Common Core Math Homework
There is a viral common core math problem that has been circulating for a while now. Perhaps you have seen it in your Facebook feed or on Twitter. It is a parent’s response to what they see as a ridiculous common core math problem. This parent is not alone. I am constantly coming across pictures that parents post of their student’s common core math homework. Below shows the problem, and here is a link to a HuffPo article.
Your first response might be the same as Frustrated Parent. We all know how to set up a subtraction problem, and it seems ridiculous to complicate things with a number line. If you read the article, the main response from common core supporters is that this type of problem stems from bad curriculum and it is not the fault of the standards. This is a valid point (common core is NOT a curriculum, but rather standards to guide creation of curriculum), but I want to make the case for this type of problem and show you what to do if your child comes home with something similar.
One of the main themes in the common core math standards is to be able to solve problems in a variety of ways. Think about math like a tool box. When you are putting a screw in the wall you might automatically reach for a screw driver. This might be the most obvious choice, but it doesn’t mean it is the only choice. You might want to choose a drill in some circumstances. Maybe you need pliers or a hammer if things don’t work out. In math it is good to have a variety of tools at your disposal. You might not always use the screw driver. Certain situations might call for different tools. It is the same in math. Even if we don’t need all these tools to solve all our problems, it is good to have them in our toolbox, and more importantly we need to know how to use them.
A Better Solution?
OK, back to the problem. Essentially this problem is asking students how to use a number line to solve a subtraction problem. It is also asking students to use their knowledge of base 10 to subtract on that number line. Surprisingly enough, some kids might prefer this type of method. If your child is like me, they enjoy these sort of math puzzles. First, a student will learn to understand that subtraction moves backwards on a number line, or makes numbers smaller. Next, it will help them to see subtraction in steps. In the above example, Jack started by subtracting the hundreds, then the tens, then the ones (although he did make a mistake). Base 10 blocks can be a great tool to help your child with this. Have them start by building 316 (or whatever number they are subtracting). It will look like this:
Now that they can visually see what they are subtracting, especially in base 10 form, it will be easier for them to keep track of these steps on the number line. They can start with the 100’s, like Jack did, or they can start with the 1’s, like you would in a traditional subtraction algorithm. The beauty is that both ways will get them there. Have them try it different ways to show that you will get the same answer.
Look at the number line Jack used, or draw a similar one on paper. Have your student start subtracting their blocks. If they do the 100’s first, they will go from 427 to 327 to 227 to 127. Next try the tens (or in this case, one ten). Since we are working with the tens place, we will go from 127 to 117 (this is where Jack made his mistake). Your student should start to see that the only digit that is changing is the tens digit, since that is what we are subtracting right now. Finally, we will just have 6 ones left. Counting backwards 6 times will get us to 111, which is the correct answer.
What Do You Think?
Still not convinced this was worth your student’s (or your) time? Think about this. If I asked you to subtract 316 from 427 using the traditional method, what have you learned? You have shown that you know how to properly set up a subtraction problem, and that you know the algorithm for subtraction. You also have used some single digit subtraction. Those are important skills, but check this out.
What have you learned doing it my way? For starters, you know how to use a number line, and that subtraction moves backwards on a number line. You have also demonstrated an understanding of base 10. In the traditional method, the 3 was just a number in the hundreds place. Using this method you showed that the 3 stood for 3 hundreds, in fact you also showed that you understand 100’s so well that you can subtract 100 from a three digit number. You did the same thing with the tens and ones place values. Being able to change any number by taking away ones, tens or hundreds is a very crucial skill. Many students who have only memorized the subtraction algorithm don’t know how to do this. On top of that, we did it mentally, using our knowledge of place value to subtract 100, 10 and 1.
Was it more work? Yes. But what is the point of math homework, or any math practice for that matter? Do you really want to know the answer to 427-316? Probably not. What you really want is for your child to put their math skills into practice. Solving a problem in this manner helps them practice so many other skills, and gives them a much better understanding of how numbers work.
If your child comes across a problem like this at the kitchen table, hopefully you now have some tools to pass along to them and fill their math toolbox, rather than being stumped yourself.
Common Core Math Standards
Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.
Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.