Subtraction Houses Part 2

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SWBAT use manipulatives to complete double-digit subtraction problems requiring regrouping.

Big Idea

Who lives in each room of the house and do they have what students need to borrow to complete a double-digit subtraction problem?

Warm Up

10 minutes

I want to increase student's automaticity with math facts to 20. For students to be able to perform the addition and subtraction algorithms fluently, they need to have mastery of their basic facts. At this point in the year I often see that students know the easier facts, but still need more time and practice to really learn the 6,7,8 and 9's facts. 

Today I am going to give students a chance to use iPads to complete math fact practice. I have a variety of free math apps on the iPads, including Flash to Pass, Math Bingo, Speed Math. I partner students up and give them 10 minutes to play subtraction practice games. We will be working with subtraction today and I want students to make the connection that their basic facts are a primary component of using the algorithm, even when working with larger numbers. 

At the end of 10 minutes of practice, I ask students to return the iPads to their cart and join me on the rug.

Subtraction Houses Revisited

25 minutes

I ask students if they remember how we used the houses for subtraction and addition yesterday. We use place value mats shaped like houses, where the top floor is the first number in the problem, the middle floor is the number being added or subtracted, and the basement is the sum or product. The houses allows students to build a model of a math problem and then use the manipulatives to solve the problem (MP4). To review and connect to prior knowledge, I ask students how many digits I can put in each side of the house (the house is split into tens and ones), on a single floor (only one). "What about the middle floor?" (one). "Basement?" (one). "Yes," I say, "we can only have one digit in any room on any floor of the house." 

Now I ask students to help me with a problem before we start to pass out the base 10 blocks for our houses.  "What if I have 3 pencils. Can I take away 9 pencils from my 3 pencils?" (No) "Why not?" "Can someone write the math problem for me 3 - 9 = ____.?" " Do I have enough pencils to take away 9 (I hold up 3)." (no) "If I only have 3 pencils (still hold up 3) would it be the same to write 9 - 3? Why or why not?"

This conversation is very important for regrouping. Students often just switch the numbers around when the second number is bigger than the first. They need to really understand that the order of numbers makes a big difference in subtraction even though it didn't in addition. 

I repeat the demonstration with  5 rulers. I ask someone to come up and take away 7. Can they do it? Why not? Can someone write the number sentence for 5 - 7. Is it the same as 7 - 5? Do I have 7 rulers to take 5 away from? (no). So are the 2 number sentences the same? 

Today we are going to learn how to look at our math problems to fix them so we don't just switch the numbers around in a way that is not the same. 

Lets start by building the number 80 upstairs. Okay, now lets build 36 downstairs. Now we are going to check before we start. Look at the ones side of the house. How many ones live upstairs? (0). How many ones live downstairs? (6). I hold up a fist with 0 fingers? Can I take 6 away from this? (no). Is the number 80 bigger than the number 36? (Yes). So I should be able to subtract, but when I try to do it in columns, it doesn't work. Does anyone have an idea of what I can do? I take suggestions and if anyone suggests regrouping, I will build on that.  

If not, I will try to guide the discussion with questions like "How many tens live upstairs" (8). "Do you think they might lend us a ten? I am going to ask. I pretend to knock on the door and ask to borrow a ten. I take the tens rod and put it on the ones side. Now how many ones do I have upstairs (10) and downstairs (6). Can I subtract? (Yes) This would work, but what do I need to do first (trade the 10s rod in for 10 ones). I trade the rod in and ask students to do the same. Now can you subtract the way we did yesterday, moving one from upstairs, grabbing a friend from downstairs and going on out through the basement until there are no friends left? I have students complete the subtraction with the blocks and we get our answer. We can check our answer using another method, such as solving on the number grid. We did it!

I repeat this process at least 3 more times, reminding students to check to make sure that there are more ones upstairs than down. 

If I feel that students are able to complete the process with their partner, without going step by step with me, I give them a paper for partner practice. (For me this step didn't happen. We worked as a group on the subtraction with the manipulatives. The paper can be done next time.)

(I keep students in partners because this is still a new process. The students can support one another as they become more proficient with regrouping.