##
* *Reflection: Developing a Conceptual Understanding
Who Makes Mistakes - Section 1: Warm Up

The student problems included both addition and subtraction questions. The first problem was, "I have 8 butterflies and 6 hearts, how many more butterflies do I have?" With the first problem a student asked, "do we add or subtract?" Another raised a hand and wanted to know what the number sentence was.

I don't want to tell the students what to do but I don't want them to be overwhelmed either. I ask if anyone could use a picture to solve the problem. The question had included the words "how many more.." A child came up and drew the 8 butterflies and the 6 hearts. I asked them if we needed to know how many in all? No, well then what do we want to know?

Here I am providing support navigating the language, while not providing either the answer or the number sentence. If I had given them 8 - 6, all of the students would be able to solve the problem. If I had given them 8 + 6 they also would have been able to get the answer. Instead I focused on supporting their mathematical reasoning, which is fundamental to all of their problem solving.

*Do We Add or Subtract*

*Developing a Conceptual Understanding: Do We Add or Subtract*

# Who Makes Mistakes

Lesson 2 of 18

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

#### Warm Up

*10 min*

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.

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#### Teaching The Lesson

*30 min*

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.

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#### Closing

*5 min*

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.

#### Resources

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- UNIT 1: What and Where is Math?
- UNIT 2: Adding and Subtracting the Basics
- UNIT 3: Sensible Numbers
- UNIT 4: Sensible Numbers
- UNIT 5: Everything In Its Place
- UNIT 6: Everything in Its Place
- UNIT 7: Place Value
- UNIT 8: Numbers Have Patterns
- UNIT 9: Fractions
- UNIT 10: Money
- UNIT 11: The Numbers Are Getting Bigger
- UNIT 12: More Complex Numbers and Operations
- UNIT 13: Area, Perimeter and More Measurement
- UNIT 14: Length
- UNIT 15: Geometry
- UNIT 16: Getting Ready to Multiply
- UNIT 17: Getting Better at Addition and Subtraction
- UNIT 18: Strategies That Work

- LESSON 1: Let Me Count The Ways to Get An Answer
- LESSON 2: Who Makes Mistakes
- LESSON 3: Counting Up to Solve Problems
- LESSON 4: Counting Backwards Works Too
- LESSON 5: Counting Bugs
- LESSON 6: Taking Apart the Problem
- LESSON 7: Getting Bigger and Smaller
- LESSON 8: Double It
- LESSON 9: Doubles Plus or Minus One
- LESSON 10: Evens and Odds
- LESSON 11: Plus Ten Minus Ten
- LESSON 12: From Tens to Nines
- LESSON 13: Equal Amounts
- LESSON 14: Understanding Subtraction
- LESSON 15: Skip Counting with 5s, 10s and 100s
- LESSON 16: Balancing Equations and Counting Backwards
- LESSON 17: Counting with Tens and Hundreds
- LESSON 18: Assessment