Understanding Subtraction

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SWBAT subtract one and two digit numbers and explain their strategy for solving the problem.

Big Idea

Understanding subtraction is as key to Common Core Standards as is understanding addition and it is usually much harder for students to grasp.

Warm Up

15 minutes

I put 2 number sentences on the board. One is a partner of 10 addition sentence and one is the related partner of 10 subtraction sentence. (7 + 3 =    and 10 - 7 =   ) .

I ask students what they notice. (It is all the same numbers, it is a fact family, etc.)

I repeat the process with related doubles sentences (8 + 8 =     and 16 - 8 =    ) .

I put up several other examples for students to attempt. I keep the number sentences to under 20 for this exercise because I want students to notice not only the relationship between addition and subtraction, but also how the partners of 10 help us with this. 

The Common Core Standards work towards fluency with numbers under 100, so to expect a clear understanding of numbers to 20 at this point in the year is a logical expectation. This work is the foundation for working with larger numbers later on.

Teaching the Lesson

15 minutes

I start by asking students to come to the rug where I have snap blocks available. Each student is given a tower of 18 blocks to use for modeling their thinking.

I ask, "What would happen if I were to subtract 5 from the tower? Would my new tower be taller or smaller than what I started with?" I wait for students to say that the new tower would be smaller.

I ask, "How many blocks are left after you take the 5 away from the 18?" Students manipulate their blocks to determine the solution.

"Can anyone put a number sentence on the board to match what we just did?" After the addition sentence is on the board, I ask if they can turn it around and make a subtraction sentence to show how we ended up with less blocks. 

I repeat the process with several other numbers forming subtraction sentences.

I ask students to build 2 towers of ten and one tower of 4. How many blocks do they have? Now I ask, "What if we take away 12, how might we do that?" I let students experiment with getting an answer. Some may realize that they can take away a tower of 10 and then 2 more from the tower of 4. Others may just count twelve without realizing that they can use the tower of 10. We will write the number sentence in the same way. 

It is  important to let students work this out for themselves. I want them to conceptualize how they can combine numbers and take them apart. I let students work on their own. After everyone has made an attempt at this, we review what was done. Here I am providing the scaffolding for those that may have not fully understood the process, and I am providing feedback for those who understood.  

The Common Core MP standards suggest that students should be able to use models to solve problems. If I do the modeling for students, they are watching, but not seeing how they can use those models themselves. I want students to see that using things such as blocks is not just for "little kids," but can be helpful at all levels of solving math problems.

 I repeat the process with several other 2 digit from 2 digit numbers. 

I tell students that today they will be working with word problems that will ask them to subtract. I ask students to generate ways they might solve the problems and what tools they might use. We post a list of student ideas such as number line, number grid, base 10 blocks, snap blocks, tally marks, in their heads, with pictures, etc.  Here I am encouraging students to develop independence in their math reasoning. If I always tell students what to do, they may not develop the skills they need when I am not there to walk them through a difficult math problem.

I send students back to their seats and hand out the pages they will work on. I put out the materials students have suggested, reminding them that they can help themselves to materials if they wish. I also remind students I will be walking around asking how they are solving the problems they are working on. I also let them know that not everyone has the same set of problems.

Independent Practice

15 minutes

Students will work independently on the problems I have given them. Some of the problems are more basic, and others are more complex. 

I also put out a challenge paper for students who may work more quickly. 

I circulate around and talk to students about their understandings of subtraction.


5 minutes

I tell students that I want to post something that will help us all understand the difference between addition and subtraction. I ask for student definitions of both and record them on a chart. I will post the chart to refer to later on.