Get Your Game on and Subtract Fluently with Multi-digits!

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Objective

SWBAT subtract fluently using a multi-digit standard algorithm.

Big Idea

Students choose between two games to improve critical thought about place value and mastering multi-digit subtraction.

Warm up

10 minutes

My students love this rap in subtraction. We have used it before, and it is a good warm up for a day like today, when we are practicing skills based on fluently subtracting with a standard algorithm.

We listened to it and discussed what errors we are still struggling with in subtraction. We talked about how this rap helps us to remember the "how" of subtraction. 

We listed reasons we needed to fluently subtract large numbers. Afterall, most people use calculators when doing such large numbers. Below is what we came up with.

1. We need to pay attention to numbers and think about if the answer is right.

2. We need to understand place value and regrouping helps us do that.

3. A calculator may not be available.

4. We can use it when we play games. ( This student didn't know he was going to do that today!)

5. My Gramps says it is a life skill that most people need, but don't know it.

 

I told my students that all of these thoughts were good ones and that yes, it is  a life skill, but a math skill that helps them understand other concepts later on.

Partner Work

5 minutes

In order to partner students well, I had given them number cards that were answers to simple subtraction facts. One partner had the expression and the other student had the answer. I was able to differentiate by partnering up my higher end or leaders with students with lower skills. This way, I would be sure that all students would be learning more smoothly. I just used simple 3x5 note cards. This is a great partnering device that avoids any social issues. It is quick too!

Once they were in partners, I asked them to review partner rules and self checks:

1. Respecting each other

2. Listening

3. Working hard or hardly working?

 

We were ready for games!

Two choices

40 minutes

Students had two choices of games: 

Materials: dice, paper, pencils and calculators to check work.

Subtract to Zero: This is great for struggling students!

Roll 4 dice to create a 4 digit number. Partners use one sheet of paper for this. They create the largest number they can with the 4 digits.  Then, they take turns rolling two dice to create a tens digit. They take turns subtracting until they get zero. They miss their turn until they get exactly zero. They need to develop a little number sense with creating the two digit numbers to subtract by figuring out that they should maybe start with subtracting the largest they can create. But perhaps in the end when getting closer to zero, they need to use the smaller number. They have to think a lot with this and because they use the same running problem, they pay attention to each other's subtraction habits.

 

Ask and Give

This game is played by rolling up to 7 dice. I modified the amount of digits for some people to fit their subtraction needs. 

They need two pieces of paper. Each person does their own work separately.

1. The first student asks for a random number.

2. The second student tells them either that: Yes, I have the _____. It is in the  _______ place.

or No. If no, you skip your turn.

3. If it is yes, the first student adds it to their number as the other student subtracts it from his.Ask & Give.pdf

So, if it is a 3 in the hundreds place, the "asker" gets the 300 and the giver loses 300.

They keep doing this to create the largest number they can. The student with the largest number at the end of the game, wins. OR they can also try to give away enough to get to zero. That is a little harder to do, but it changes the strategy to make sure you start with the smallest number you can create in the beginning and hope that you can give away the most. It twists the thinking number sense a little. I have played both ways and I like creating the largest number better. 

I asked students to choose which game they wanted to play. 

Students mostly chose Ask and Give. I am not sure why. One pair of students got bored and switched. I did see one pair choose Ask and Give and try to get to zero. 

Take a Peek in the Classroom: Ask and Give These students were confused on how to play the game. I needed to explain exactly how the numbers are manipulated between the two of them. It is important to rove around and check to make sure that they are adding and subtracting the proper place values. 

AS they played, I roved and checked their progress. I caught a pair of students confusing the two games and needed to spend time working with them to get them going. In this clip, A little confusion, I am straightening out another point of confusion where the student thought she didn't have to subtract the number out when giving. She wasn't understanding the process. These discussions I have with my students during classroom game time reinforce the understanding of place value as well as accuracy, supporting the standard.

There is one student who is struggling terribly with place value. It turned up in this game and she realized it. Finding our mistakes in place value using a game. I discover that she hasn't lined up her places when she is subtracting and adding. She needs to use graph paper to help her line up numbers. I need to work with her one on one to review place value and help her understand that the numbers have a place. It is interesting that a student can name all the places in numbers up to thousands place, but when the ten thousands place is introduced, I often see issues like this. That is why CCSS builds from year to year to help with the developmental process of understanding and number sense.

The other movie clips are just a short peek at some conversations as the games went on. Clarifying Subtract to Zeros is about getting students to understand the importance of accuracy and lining up numbers to subtract. I think it is essential that we insist on neatness and lining up numbers to support accuracy.

After 30 minutes of playing, I asked them to get calculators out and check their work. 

Closure

10 minutes

I asked students to share anything they saw in checking their own work using a calculator. Two paired students said that in Subtract to Zero, they forgot to borrow a group of tens in two instances. They said that they had done it in the tens place when a zero was involved. I asked them if they thought that they were able to find the mistake easily. They said that because in this game they only subtract two digit numbers, that yes, the mistake was easy to see.

  Another student said that it was hard to think of the place value in Ask and Give.I had watched her struggle with place value in general and think that this game, if played more often, would help solve her place value understanding issues.

All of them agreed that they had fun.

I asked them if they knew they were strengthening their skills. The student who was confused about how to play "Ask and Give" (in the clip) said that when she took away a number from her number, she was anxious to get more back when she could add. She was anxious to see how big the number would get. I wondered if she had thought about how to use a strategy to figure out how to get the most back, or if she realized it was just chance.

I told them that these are both good games to practice at home to practice mastering fluency and multi-digit algorithms as expected by Common Core State Standards.

They all thought it was a lot of fun!

 

Homework

5 minutes

IXL math was assigned for more practice. I like C.1 and C.3. I assigned 30 minutes of practice tonight. All work needed to be written on loose leaf to show work. C.3 has missing digits for more advanced students.