Who Makes Mistakes

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SWBAT realize that mistakes in math are a part of the learning process.

Big Idea

Students in upper grades are asked to show their work. Second graders hide that work. This lesson encourages students to share their work, even without the correct answer.

Warm Up

10 minutes

Yesterday students wrote addition or subtraction word problems, sharing their work at the end of the lesson.

We will continue that conversation today, inviting those that have not shared and ask these students to read their problems.  The listeners work alongside the presentation, to solve the presented problems in their math journals. The reader calls on 2 - 3 people to share their solutions.  We talk about whether those solutions match what the writer was thinking and why or why not.

If the answer does not match the writer's thinking, I ask students if they can figure out what is different. Sometimes the new answer also fits the problem. I stress with students that there may be more than one answer, or more than one way to see the problem and also that sometimes we make mistakes when we are counting forward or back to get an answer.

I ask students to put away their journals, stretch and then walk with 15 hops to the rug.

Teaching The Lesson

30 minutes

I start with a blank writing surface (such as an easel or interactive white board). I tell students I am going to make the number 9, but I make a mistake and make a 6 instead. "Oops, I say, does that look like a 9?" The students laugh and I say, well I made a mistake, let me try again. This time I make a squiggle that is sort of like a nine. The children laugh and I ask what is wrong? They assure me that I have not made a 9. I say, "Oh, but it looks like a neck of a giraffe" I say and I proceed to quickly outline the rest of my giraffe (or whatever it most looks like). Then I tell the children that I was going to write a word problem about 9 giraffes so my mistake was really a good thing. 

I write the giraffe word problem on the board. There were 9 giraffes. Three couldn't reach the tallest leaves. How many ate the tallest leaves? We solve the problem together, but using the following steps purposefully and deliberately:

  • Read the problem
  • Determine what the problem is asking you to do.
  • Figuring out if the answer will be bigger or smaller than the numbers presented in the problem
  • Deciding how we want to represent the problem (e.g., picture or tally marks).
  • And, then using our strategy to get the answer. 


These are the steps I want students to understand when they are faced with a word problem. 1. What do I need to know? 2. What do I already know? 3. Will my answer get bigger or smaller than what I start with? 4. Can I use a picture, or other visual to help me figure out the answer. 

In this lesson I also have weaved in making mistakes, with the understanding that we all make mistakes. I want students to view word problems as something they can do, rather than as something they can't. 

Next I tell students that I was going to make a 3 on a paper, but I made a mistake. I would like them to turn my mistake into something they can write a word problem about. I tell them they will have 5 minutes to "fix" my mistake. I hand them the paper and send them to their seats to work.

At the end of 5 minutes I tell students that we will now work with partners that I will assign. (This stops them grabbing hands before I have finished with directions). In partners, they will write a word problem about the two things in their pictures. They must use numbers whose digit in the tens place is less than 3 and whose digit in the ones place is greater than 4.

I write these as sentences on the board and ask a volunteer to come up and write the number the words represent. We review the digits and greater and less than words. Next I hand out numbered cards 1 - 9. I tell them they each have a digit and they must find the person with the same digit to be their new partner. Once they have found their partner, they must come get a word problem page, and then work together to write a problem, question and number sentence. These we will share and then mount for others to view. 


5 minutes

I ask students to mount their pictures and word problems on a larger paper. I tell them to fold the answer under because we will hang the pictures and problems in the hall for others to solve.

I want students to have a sense that there work is worthwhile. If I always just send it home, there is no celebration of their accomplishments. Also, if I expect perfection, students may become discouraged and stop trying. By realizing that this is early in second grade, I can put up quality work that may not be perfect, but which is worthy of displaying. Students were proud to see their work hanging in the hall.

Other staff were able to see what students were working on, and to praise students for their attempts to create math problems. 

Students are encouraged to read the problems of other groups and to figure out the answers to the problems.