##
* *Reflection: Modeling
Taking Apart the Problem - Section 2: Teaching The Lesson

When I showed students the towers to compare 2 numbers, I was not clear enough about what the two towers represented. Some students did not realize that I was using the towers to represent the data on the graphs. Other students still did not see that if one tower was tall, and another smaller, the distance from the short tower to the tall tower would be the difference of the two numbers.

When I do this part again, I would point to the number and ask a child to build the first number using the blocks. I would then point to the second number and ask another child to build this number. I would then ask the students to put their two towers next to one another. I would ask a child what the towers mean (the different types of bugs). Now I would ask which is larger? How much larger? We would count the blocks in the taller tower that are above those on the smaller tower. I would then say this is the difference between the two numbers.

This is something I need to demonstrate again and also to allow students to practice with me. This will help them conceptualize what difference means when it appears in mathematical problems.

*I Need To Be More Specific*

*Modeling: I Need To Be More Specific*

# 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