Checking Subtraction

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SWBAT improve their fluency with subtraction.

Big Idea

Students need to develop fluency in subtraction, and by understanding how subtraction is related to addition, they can make the connections that can improve fluency and understanding.

Warm Ups

10 minutes

Today I start with a 2 minute fact practice exercise. I make the practice pages on That way I can tailor the pages to the current level of my students. I want to encourage students to develop automaticity with basic math facts. I use a 2 minute fact test that includes 25 addition and 25 subtraction fact problems within 20. I also regularly use materials such as Math Bingo on the IPAD, and computer games homework to encourage this automaticity. There are a myriad of addition and subtraction fact apps for the IPAD that allow students to practice basic facts. I look for programs that are quick and colorful. I want a program that lets students know if they are right or wrong and doesn't just keep going on with out any feedback for students. I also know students will stay more engaged if there are fun things going on such as things that grow as you get more right, or a rewarding game with aliens, etc. after you complete a level. 

I hand out the paper and give the students 2 minutes to complete as many problems as they can. They have a number line and number grid on their desks if they wish to use it, but I am hoping that they will know many of the facts without having to count. 

After 2 minutes I have them switch from pencil to marker and we correct the page together. By correcting the paper, the students can see how well they are doing and become more aware of what they need to practice. If I just collect and correct the papers, the students may never really see what they have missed. I want them to learn from their own mistakes.

One way to show students their own improvement is to have them look over the paper after it is corrected and then provide a similar math fact page for them to do in another 2 minute block. They can look to see if they improved just by reviewing the facts for a few minutes. 

Teaching the Lesson

30 minutes

I start by writing the problems 8 + 9 = 17 and 17 - 8 = 9 on the board and then saying the math problem 8 + 9 = 17. As I say the problem I walk forward across the front of the room. Next I say 17 - 8 = 9. As I say this I walk backward to where I started from. I repeat the process with another relationship within 20. I ask students what they notice? (That the problems have the same numbers, or that one is addition and one is subtraction.) I tell the students that today we are going to see if it is always true that if you add 2 numbers and get an sum, you can subtract one of the numbers from the total and get the other number. I ask them to predict if it will always work the way the examples on the board did. I record how many say yes and how many say no. 

I tell students that today they will work with partners for a few minutes at their seats. They will be modeling with math how addition is related to subtraction (MP4) They will roll two 8-sided dice and write an addition sentence. Next they will draw the total as a series of dots (or other quick items) and then cross out one of the numbers that they rolled and see if they end up with the other. They will then write the subtraction sentence.

If I roll an 8 and a 6, I would write 8 + 6 = 14. Next I would draw 14 dots and cross out 8 and I should have 6 left. I would write 14 - 8 = 6.

I ask students to try it with at least 4 rolls and record their findings.

I ask students if it always worked that when they added, and then subtracted they got the number they started with? (There will probably be a few that drew the wrong number of dots and will say no  I show students how I might have made a mistake in counting that could make it not work, but that if we are careful and attend to the precision of drawing the right number of dots (MP6), it will always work.) I demonstrate the problem 3 + 2 = 5 but I draw 6 dots. I cross out 2 and now have 4 left. I ask if I drew the right number of dots carefully? (no) Drawing the dots carefully is very important to this lesson.

Now I ask students to return to their seats. I want them to generalize the idea of the reciprocity of addition and subtraction with low numbers, to higher numbers. I ask students to work independently on a worksheet to see if the same rule applies to larger numbers. I ask them to complete the addition and subtraction problems on the paper. I do not initially tell them that the problems are related. I do not want them to just fill in numbers without actually doing the addition and subtraction operations. 

When they are done I ask them if they can find any fact family pairs among the addition and subtraction problems. I ask them to draw a line from the addition to the subtraction problem that matches it. We share our findings.

As students work I circulate around to ask students if they see any connection between the addition and the subtraction sentence? I ask them if they notice any patterns in their work?


10 minutes

After most of the students are done I bring students together. I ask them if they can tell anything they discovered with the larger numbers when adding and subtracting? (There are fact families for even larger numbers, that you can add and then go backwards and subtract to get back where you started.) 

I take one of the problems from the paper and walk backwards and forwards the way I did with the easier numbers.

Finally, I put a subtraction problem on the board:

48 - 25 =

I tell students that I think the answer is 13 but I want to check it. I ask them what I could do to see if I am right? (Students may want to count, use a number grid, number line or other math model that we are familiar with. If no one suggests it, I will ask students if anything we did today could help us with checking my work? I will walk back and forward to encourage the connection. (It is my hope that as I scaffold this understanding onto what they are already capable of, students will realize that they can use subtraction to check addition, and that if they know the addition sentence, they also know a subtraction sentence, or that partners in addition are the same as partners in subtraction.