Subtraction Houses

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SWBAT to employ place value strategies using manipulatives to complete double-digit subtraction without regrouping.

Big Idea

Who lives in each room of the house and can we travel through the house as we subtract?

Warm ups

15 minutes

In order for students to be prepared for the introduction of a new strategy for subtraction (one that several students have shown a readiness for as they attempt to subtract larger numbers in columns the way they do addition), I ask students to write the answers to some mental subtraction questions.

I tell students to write each equation and answer as I say them. I say 18 - 9=, (I give students only 15 seconds to respond in order to practice automaticity with facts before going on. I also realize that with 15 seconds, some students will be able to count up or back to get the answer using the number line on their desk. This is acceptable because it is still requiring them to count quickly and improve their ability to approach the problem ready to solve it.) I say 16 - 7=, (pause), 13 -8= (pause) 15 - 7 = (pause) and 17 - 9=. Now I say the facts again and ask students to raise their hands and give me the answer. I tell students to correct their own problems to see how they did. 

I praise all students for their attempts, acknowledge that not everyone got every problem right, but that we are all learning and getting better, and then I ask if students can share some strategies to figure out one they don't just "know in their head,". I list their strategies on the board. I say to students, "look at these strategies and see if any of them can help you as we do the next set.  Ok, now I will give you 5 more problems to solve. I say 14 - 6= (pause), 16 - 8= (pause), 12 - 7= (pause), 13 - 4= (pause) and 15 - 9 =.

Again I ask students to volunteer to share answers, and I ask everyone to correct their own work. (During all of this warm up, I circulate around the room looking at what students are doing, and noting who is having difficulty with this lesson. This will help me know who to work with in a small group at another point to help them work more automatically with their counting, number lines or number grids to solve subtraction problems. )

I invite students to put away their journals and to meet me on the rug in 30 seconds. I count down from 30 to 0 as they move to the rug. 

Teaching the Lesson

25 minutes

I begin by asking students if they remember using the houses to add large numbers? Students have already gained a basic understanding that one digit of a two digit number goes in the ones place and one digit goes in the tens place. We build the top of the problem upstairs, and the second number downstairs. That leaves the basement to put our answer in.  Could someone tell me what we did when we used them? (We added, we built numbers out of blocks and then added them, We built numbers and counted the blocks. We put the ones in the ones place and the tens in the tens place.) I tell them that we can also use the houses to subtract. I say, "What happens to our answer when we subtract, is it bigger or smaller than the number at the top?" (smaller) "It does get smaller, so today we want to make sure the number at the bottom is smaller than what is at the top. Where does the biggest number go in a subtraction problem? " (At the top). "Where does the biggest number always go in an addition problem?" (At the bottom).  "So last week we ended up with more blocks than we started with, but this week we will end up with less. Are you ready?" Students have worked with parts and wholes already this year. They have a basic understanding that a 2 digit number is so many tens and so many ones. We are taking the number apart and working first with the ones and then with the tens. 

I tell students we will start with the same process we did for addition. We will first build a number upstairs. "Would you build 39. Which digit is in the tens side of the house? (3) Which is in the ones (9). Good, ok, now would you build 25 downstairs." I wait until all numbers are built. 

"Ok, now we are going to be like trains. We are going to move one block from upstairs, find a mate in the middle and take them off the board through the basement. We will start with the ones. Let's check first to make sure there are more ones upstairs than downstairs. (We count 9 upstairs and 5 downstairs.) Does anyone know why we did that? I reinforce that we can't take more away than we have. Ok so grab 1 one from upstairs, find a friend downstairs and send them out through the basement. Keep going. Grab another 1 from upstairs, find a friend downstairs and take them out through the basement. Keep going until there are no more in the downstairs but some left upstairs. Bring those to the basement and keep them there." 

"Ok, now let's do the same with the tens side. Take 1 from upstairs, find a friend downstairs and take them out through the basement. Do that again. Keep going until there are none left in the downstairs. Bring the rest from upstairs to the basement." 

"How many are in the basement? (14). Yes. you just did 39 - 25 and you ended up with 14. Give yourselves a thumbs up for good work." 

It is possible here to only build the upstairs number and then take away the lower number right from the upstairs number (i.e. just build the 39 and then take away 5 ones and 2 tens from the 39 to get the answer, but when students progress to borrowing, it is harder to see that they need to borrow, because they don't have the larger pile of ones downstairs to work with, so I have students move the blocks down and out after they have built both numbers.

I repeat this process with 3 more sets of numbers that do not require borrowing. 

(I wait to introduce borrowing until the second day, because the process is confusing and I want them to be secure before they add the extra steps of borrowing.)

Independent Practice

15 minutes

I hand students a page of mixed double digit addition and subtraction problems tens ones problems to do with a partner. I explain that students can do things in one of two ways. One partner can use the paper and pencil to get the answer while the second partner uses the blocks and houses, and then they switch, or they can work together to build the problem and then write the solution on the paper. I want students to make sense of the problems and persevere in solving them (MP1). I do not limit the paper and pencil strategies. Students may use number lines, number grids, columns, or other strategies that they are comfortable with to solve the problems. 

If they cannot agree on an answer, they will need to work together to build with the blocks again and check again.

I give students about 15 minutes to work in partners and then we come together to discuss how they did.