##
* *Reflection: Student Ownership
Introducing the Addition Algorithm - Section 1: Warm Up

There is great value in helping second graders learn to explain their thinking. I always encourage students to talk about how they solved a problem, what they were thinking, and what strategies they used to solve the problem. At first it was a struggle. Students would say, "I just did it," but they were so unaware of the how or why.

Today, a parent came in to tell me how her child, who has been struggling with math, sat down and explained to her how you can take an addition problem that is written vertically and add the tens and then add the ones and put them together. The child said that you can check your work by finding the smiley face number that each number is close to and add them to see if the two answers were close. This child had internalize the process and was then able to really explain the process she was using, one that was based on place value reasoning.

It is a crucial skill that is worth taking the time to stress in each lesson that you teach. If a child knows what he/she is doing, to the point that they can explain it, they can apply that to future math experiences.

*Explaining Your Thinking*

*Student Ownership: Explaining Your Thinking*

# Introducing the Addition Algorithm

Lesson 8 of 12

## Objective: SWBAT estimate the answer for a 2-digit addition problem and add when the numbers are in columns.

## Big Idea: Students are able to add and subtract when numbers are presented horizontally. They add and subtract tens and ones with appropriate fluency. Today they will be introduced to adding two 2-digit numbers presented vertically.

*45 minutes*

#### Warm Up

*15 min*

I present a series of problems on the board for students to solve. They are all partners of ten, or partners of 100. I present them vertically in preparation for the later part of this lesson.

9 +1=

80+ 20=

7+ 3=

50 + 50 =

60 +40 =

I ask students to write the number sentences in their journals and solve the problems. I then ask for volunteers to come up and show us what they have done. I encourage other students to ask questions if they do not understand what a partner has done.

The Common Core Standards expect students to add and subtract fluently within 100 by the end of the year. While students are developing their fluency skills, most of the work has been done with horizontal number sentences and adding of a 2-digit number to a smiley face (ending in zero) number such as 30 + 19. Today I want to extend student thinking by presenting numbers vertically which they have seen and used, but need more practice with, and by presenting the adding of two 2-digit numbers. The goal today is to introduce students to the addition algorithm which, although it is not required by the Common Core for second grade, it is required by my district. I am giving my students a new structure to use, and I hope that they will be able to use that structure to solve problems (MP7).

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#### Teaching The Lesson

*20 min*

This lesson has 2 parts to share with students. The first is to review smiley face numbers and adding easily with those. The second is to introduce adding vertically in columns using the standard algorithm. The smiley face numbers are a review whereas the algorithm is the new part of the lesson that I hope I can scaffold on to their previous understanding of place value addition.

I begin with the smiley face numbers. I ask if anyone remembers which numbers are smiley face numbers? (Most students will easily recall this.) Next I put 2 smiley face numbers (not partners of 100) 30 + 50 on the board (vertically). I ask if anyone can give me the answer. We discuss the strategies that someone might use to find the answer including a number line, adding 3 tens + 5 tens, using a number grid. I try to get students to generate these strategies because it gives me a sense of what they are relying on. Also if they verbalize what they are doing, their own understanding increases (versus me just saying do this or do this). I am asking them to reason abstractly and quantitatively (MP2) as they solve the problem (MP1)

I tell them that sometimes we use smiley face numbers to help us know if we are doing a problem right. Because we can use the smiley face numbers easily, we can use them as checking numbers. If our direct answer is close to the smiley face answer, we are probably correct but if it is way off then we might have made a mistake.

I put the example 35 + 34 written vertically on the board. I ask students how I might solve the problem. I say ok, using your ideas, I might try 5 ones + 4 ones are 9 ones, and 3 tens + 3 tens are 6 tens so my answer is 6 + 9 or `15. Do you think that is correct? One way to find out is to use our smiley face numbers as we make sense of the problem (MP1). I say ok now lets see if our smiley friends can help us check. 35 is close to 40 and 34 is close to 30 so 30 + 40 = 70. Oh dear.. I got 15 over here (pointing to my original work). Can anyone see what I did wrong? I wait for students to see that I should not have added the 6 and the 9 together. We go back and correct my mistakes. now my answer is 69 which is a lot closer to 70 so I have much more confidence in my answer.

I tell students that today they will solve several problems using their smiley friends and the tens and ones. We review where the tens and ones are in the vertical equation. I hand them a paper that is marked tens and ones. Today none of the ones add up to more than 9 because I want them to get used to adding in columns and checking with their smiley face friends. Once this skill is secure we can begin to add where it will be necessary to regroup.

I put the first 2 problems from their papers on the board and we walk through them together. Then I have students work independently. I circulate around to support students who may be having difficulty.

I have a challenge project available for students who finish more quickly.

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#### Closing

*10 min*

From walking around and observing, I choose 2 problems that I thinks students were having the most difficulty with. I write them both on the board. I ask for volunteers to come up and write what they did. We discuss the strategy they used and students can ask questions and correct their own work.

At the end I collect the papers to correct and assess next steps.

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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: Where is the Question
- LESSON 2: Playing Teacher - Checking Our Work
- LESSON 3: Estimation - an introduction
- LESSON 4: Using Models to Add and Subtract
- LESSON 5: Comparing Temperatures a Science and Math Exploration Part I
- LESSON 6: Comparing Temperatures A Math and Science Comparison Part II
- LESSON 7: Checking Subtraction
- LESSON 8: Introducing the Addition Algorithm
- LESSON 9: Addition Algorithm Rote or Understanding
- LESSON 10: Adding Repetitive Sets of Numbers
- LESSON 11: Adding and Subtracting in Columns
- LESSON 12: Getting Better At Addition and Subtraction Final Project