##
* *Reflection: Rigor
Taking Apart the Problem - Section 1: Warm Up

When I looked back at the results of the 3 minute fact check and thought about what I had witnessed as students worked, I was impressed that all students were able to complete the addition. What I did notice that was disappointing was how much more difficult the subtraction was. With addition I saw many students respond to the problems without counting, or number lines or fingers.

They showed the automaticity with the early facts that the Common Core Standards extends in grade two to numbers to 20. With subtraction there was little automaticity. Students had strategies for figuring out the subtraction. They relied on their fingers, number lines or number grids to find the answers. While relying on the math tools is acceptable at this point in the year, I want students to move away from having to figure everything out, to more automaticity with the subtraction facts. One skill critical to success in subtraction is to be able to count backwards, starting with any number, as fluently as they count up. Students do not get enough practice with counting backwards. Whenever possible, count backwards for and with students, rather than forward. If you are giving the students 20 seconds to clean up, count backwards rather than forwards. Encourage them to join it.

It is important for students to develop subtraction automaticity, because as numbers get larger the cognitive demand increases, but they will be spending that energy and time on the simple computation that should only take a few seconds. (I have tutored a 6th grader who never developed this automaticity and she counted on her fingers for every problem she needed to solve. She became overwhelmed by the task and it was necessary to go back and relearn these second grade skills.)

Developmentally students can understand when things get smaller, but addition makes more sense. As a teacher, I need to continue to develop their understanding of what subtraction is, and how it is a reverse operation of addition, but not something to be afraid of.

*Adding Is Still Easier*

*Rigor: Adding Is Still Easier*

# Taking Apart the Problem

Lesson 6 of 18

## Objective: SWBAT Students will be able to solve problems by taking them apart and determining whether the answer will be larger or smaller.

#### Warm Up

*10 min*

I begin today’s lesson by assessing student command of automaticity adding and subtracting 0, 1, 2, and 3, using a two minute number facts quiz. There are 25 mixed addition and subtraction problems on the page.

At the end of the 2 minutes, I ask students to take out a marker to correct their own paper. I read the problems aloud and take student answers, which I then echo. If incorrect, I'll ask, "Does anyone have a different answer?" Generally someone will have another answer, and I'll ask how they know it is true. Once we've established the correct answer, I repeat the entire problem. I collect the papers for closer review later before going on to the next part of the lesson.

#### Resources

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#### Teaching The Lesson

*35 min*

During the previous lesson students gathered data and created a way to share that data. Today we will use the data to make comparison problems. I hang up two of the charts and pose the problem:

*“How many more bugs with legs did the first group find compared to the second group?” *

I ask how we might figure this problem out, and what information we need to do the work. Students make some suggestions and we explore these, using our best mathematical thinking and vocabulary (MP3).

I show students how I can make a tower of linking cubes to represent the groups of tens and ones for the first group, and then a tower to show tens and ones for the second group. Now I can count the **difference** between the two towers to show how much more one group has than the other.

I tell students that today I will have the groups combine and I will raise several questions for students to solve using the data from each group. They need to think about what they already know about the question, such as how much each group has, and then find a way to compare the two numbers (MP2). I ask students to think about this important question:

*If we are comparing two groups, can our answer can be bigger than the numbers we start with?*

I create an example on the board for students to look at as they think about this question.

The students are now grouped and given a set of comparison questions to solve. They may use manipulatives, drawings and tally marks to complete the work. (MP4) I circulate around to assist groups with thinking by facilitating their use of strategies to use to solve their problems.

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#### Closing

*10 min*

I call students together on the rug. I ask them to bring their solutions with them. I pick one of the questions and each group shares out their solution and how they found it. Students share out and are encouraged to comment on each other's solutions. We note that the answers are always the same or smaller than the starting numbers when we do comparison problems.

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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