##
* *Reflection: Pacing
Doubles Plus or Minus One - Section 3: Independent Practice

Within a few minutes of beginning the independent practice I realized that I had made a leap that was too large for most of the students to make. The warm ups and the game had gone so smoothly with doubling and adding or subtracting one, that I thought an independent practice where students identified whether they were doubling and adding or subtracting one would be relatively easy.

I was so wrong! The students could count to solve the problems but they had no idea how to determine if they were using a double or not. Most of them clearly were solving the problem without doubles and the idea of a double just confused them. So much for good intentions of providing kids with a new strategy.

I tried to stop the independent practice and reexplain what the paper was asking, but even with that I could see that most of the students had no idea what I was asking so I stopped the work.

I asked students to put the papers in the finished work basket (even if they weren't done) and to come to the rug. I told them that I had made a mistake because I had given them a page that I had not really explained. I told them I was sorry if they were confused and that we would back up a little and I would try to explain the idea again.

I drew a dice with 4 dots on the board. I asked for a student to draw another dice to double four and the child drew a dice like mine. Next I asked someone to come up and write the number sentence for adding the two dice. They did this easily. Next I said, what if I added a dot to this die, now how many dots are there on that dice. The students quickly said five. I asked if anyone could write the new number sentence. A student wrote 4 + 5 = 9. I asked if this matched the dice and everyone agreed that it did. I asked how it was similar to the first problem. The students said it was almost like it but there was a five instead of a four and an nine instead of an eight.

We talked about how when we added one to one side of the sentence, we had to add one to the other side to keep the two sides equal or balanced. I used my body as a balance to show what I meant.

We did several similar examples and I stopped there for today. I had made too large of a leap, so I moved back to where the work had made sense for the students and started to build a new bridge for them. I will do more of this bridge building in the next lesson, which focuses on how doubles always come out even, but doubles plus or minus one always come out odd.

# Doubles Plus or Minus One

Lesson 9 of 18

## Objective: SWBAT use what they know of doubles and partners of ten to add or subtract numbers that are one more or one less

#### Warm Up

*10 min*

Today I begin with a quick review of the doubles rhyme that students created in the last lesson, and the partners of ten rhyme that we have been practicing. I have typed up the doubles rhyme and add a copy to each child's notebook as a reference page.

We recite both rhymes and then I call out some mental math problems using doubles and partners of ten.

After this review I ask, *"What if I had 6 + 7 instead of 6 + 6? Is there something I already know that could help me solve this problem?"* I ask several students to give their solution, reminding them I want to know how they would solve the problem, not what the answer is.

I repeat the process with the question, "What if I had 8 + 7, instead of 8 + 8?"

I want my 2nd grade students to look for strategies to be more efficient in computations, including doubles strategies and making tens which supports the Common Core math strategies that students should be developing.

I tell students that today I will teach them a new game using this idea of one more and one less. I bring students together at the rug to learn the game.

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#### Playing The Game

*20 min*

Today I am going to play a game with the students and then have them play on their own. I have created game boards that are mostly just blank playing boards. The game requires cards for each team labeled +1, -1 and =, It also requires a single dice for each person and colored playing chips.

The game I teach students today is called *Doubles More or Less*. I tell students that they will roll one die. I use oversized foam dice to demonstrate. I roll a 4.

I ask, "What's the double of 4?" They say 8.

I tell them that now I must draw a card. If it has a +1 on it, I can move the double of 4, or 8 +1. If it has a -1 then I must move the double of 4 or 8 -1, and if it has an = sign, then I just move the double.

On the board I move my chip 7 spaces because I drew a -1. Next I ask a student to roll. We repeat the process with their roll and they move their piece on my board. We each take one more turn and I ask if everyone understands before partnering students and handing out materials. I tell students that if someone wins the game, they can play again.

I have created game boards for each team of students. Each team also has 2 colored chips, the +/-/= cards and 1 die.

I give students about 10 minutes to play the game.

#### Resources

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#### Independent Practice

*15 min*

Students are given word problems to practice what they've learned. There are several sets of problems, to allow for differentiation.

I circulate around the room, asking students how they are solving their problems. Part of the work students do is to color code their answers as double +1 or doubles -1. This keeps the focus on the new strategy learned today.

As I listen to student thinking about their use of strategies I keep quick notes to guide my future lesson planning.

#### Resources

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#### Closing

*5 min*

I choose one of the additions problems and started the problem on the board (by drawing the first number). Next I ask for a volunteer to come up draw the second number next to it. Together we looked for the doubles fact, and then I circled the one more. I asked for a volunteer to write the number sentence on the board. We talked through the problem about the doubles fact that was close to our problem, and about how our new problem was only one more. I tried to walk the students through finding the double, seeing the one more and just counting up one from the double they already knew.

It was a good opportunity to go slowly, and expand on the "toe hold" I had made when I went back to using concrete representations, step-by-step, to thinking about *doubles plus one.*

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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