Adding and Subtracting in Columns

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SWBAT add and subtract in columns where no regrouping is required.

Big Idea

Students are working to develop their fluency with adding and subtracting numbers to 100. Working with numbers in columns reinforces place value understanding.

Warm Up

10 minutes

I begin today by reviewing adding and subtracting with partners of 100. I orally ask how much is 60 + 40. I ask students to raise their hands to respond. I repeat with 80 + 20. I ask how much is 100 - 70?, 100 - 10? 

Does anyone remember what all of these are called? (Partners of 100)

Now I ask a few oral questions that are not partners of 100 and I tell students that these are not partners of 100, but they are Smiley Face numbers. 

How much is 30 + 50?  80 - 40? 60 + 20? 90 - 50? 

With each question I call on a student to give the answer and then ask other students if they agree. If they all agree we move on. If some students do not agree, we think of ways to check our answer such as the number grid, or counting up or back by tens.

Teaching The Lesson

15 minutes

I begin today by gathering all students on the rug. I have base 10 blocks for each pair of students. I have also drawn "houses" that are divided into 3 floors and 2 sides (the tens apartment and the ones apartment). We will model with mathematics (MP4) as we build and manipulate the two numbers.

I tell students that today we will do some adding and subtracting with base 10 blocks. I start by asking one of the partners to build the number 42 upstairs ( 4 tens rods and 2 ones cubes). Now I ask the other partner to build 36 downstairs (3 tens rods and 6 ones). I tell students that we will now move all the blocks to the basement and count them. "What do you think will happen when we move all of the blocks together to the basement? Can you predict the total number of blocks that there will be?" They count 7 tens and 8 ones for 78. I write the problem on the easel drawing the house first and then putting in the numbers we just worked with. 

I repeat the process with the numbers 26 and 61. I walk through the steps with the students. I write the problem on the board and we check by adding tens and ones together to see if our block answer matches what we think the answer should be. (Adding with Manipulatives).

If I feel that students are comfortable with the process, I ask them if they can solve 33 + 56 on their own using the blocks?  I want them to make sense of the problem and try to solve it on their own (MP1). I tell them to raise their hand when they have the answer displayed on their "house," I circulate around the group and help any children who may be having difficulty.  We compare answers and students check their house.

I repeat the process with a second problem 24 + 72.

I tell students they are doing a great job and that we can also use the house for subtraction. I have students build 67 upstairs with 6 tens rods and 7 ones. I have them build 24 downstairs. Now I show them how we will match downstairs to upstairs and take those away. We can match up 2 tens rods from upstairs with 2 from downstairs and take them away from the house, and 4 ones cubes from downstairs with 4 cubes from upstairs. Now we count how many are left in the house. There should be 4 tens and 3 ones for 43.  It is possible to just build the upstairs number and then take away the blocks, but by matching, when students begin to borrow, they can see that the upstairs pile is smaller than the downstairs pile meaning that they will have to find more blocks (by borrowing) to complete the problem. 

We repeat this process together for 58 - 31.

I am watching to see if students are correctly modeling addition and subtraction during this activity. I have chosen to show both addition and subtraction so students see the two processes as similar and not one as harder than the other. I make sure that none of the problems require borrowing or carrying at this point. 

I put up additional problems on the easel for students to solve with their partners. I will not have them work independently today as I want to make sure that they are comfortable with the blocks. It is a bit cumbersome at first to build all of the numbers, so working in partners makes the process quicker, especially for those students who would prefer just to get the answer in their heads. I do require all students to work with the manipulatives today because when we do begin borrowing or carrying, they may need the visuals to help them.  This process will help when students are ready to regroup for addition and subtraction. 


5 minutes

In closing today I have a discussion with students about why the house helps us when we are adding or subtracting larger numbers (it keeps the 2 columns in order, it reminds us of tens and ones, it helps us to take apart the larger number into its parts so its easier to work with).

I also ask for a thumbs up, across or down to show how well students think they did with this assignment.