##
* *Reflection: Complex Tasks
Let's Compare - Section 3: Independent Practice

Comparison problems are more complex than simple subtraction problems.

First, all word problems are really two-part problems - the first problem is determining which operation to use and the second problem is actually performing the operation. Students are expected to recognize the problem and solve it by putting together or taking apart (2.OA.A1) The difficulty with comparison word problems in particular is that no “action” is being performed - no putting together or taking apart. Students do need to find the difference and conceptually, that is a difficult concept.

Students understand how to carry out a subtraction problem, but when asked to compare 2 objects they have trouble deciding whether to add or subtract. Visually I can show the students that if they add they will have an answer bigger than they started with, and that would not be a comparison. I often do this with snap blocks. I show a tall tower and a smaller tower. I ask how much taller the first is than the second? I put one tower on top of the other and say would the small one be THAT much taller? (NO - they all see that). So then how can I find the difference? (count up from the small to the tall, or subtract the small from the tall).

The comparison is something that must be shown visually before students can understand what the idea of bigger than or smaller than is really asking them to do.

*Comparisons*

*Complex Tasks: Comparisons*

# Let's Compare

Lesson 8 of 10

## Objective: SWBAT take two objects and compare them using mathematical equations.

#### Warm Up

*15 min*

Yesterday students drew monsters on grid paper and counted to find the area of each monster. They also compared the area of their monster to that of 2 or 3 other monsters. Today I ask a group to show us their monsters and give us the equation to compare 2 different monsters. The group shows 2 of their monsters, tells us the area of each, and writes a number sentence on the board. The rest of the class tries to find the difference by solving the number sentence.

I give each group a chance to share their monsters from yesterday.

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#### Comparing 2 Heights

*15 min*

I ask students to line themselves up by height, from smallest to tallest. I then ask students to help me find the middle of the line. I take the two middle people and ask them to go and partner with the 2 ends. I take the next to from the middle and send them to find partners from the ends of the line. This continues until everyone has a partner. I do this so that I end up with students of different heights so they have something to compare. If I just allowed them to find a partner, there might be partners of the same heights.

Next I bring out tape measures and ask students to measure the height of their partner in inches and to record it. (2.MD.A4) Now I ask the students to compare their height to the height of their partner. How much smaller is one partner than the other? Comparing heights is easier for students than comparing the monsters because they can easily see that their partner is only a little different from them, so they would not add one person's height on top of the other. Next time I might do this lesson first.

I want students to use one of their subtraction strategies to solve the problems. I ask them to write a number sentence on the front of a 3 x 5 card and the answer on the back.

We now record the differences on the board. We are going to find the median and mode for height differences between second graders in our room. We find the most common difference between partners (mode) and then we put the data in order and find the median by crossing off the two ends of the data until we reach a midpoint. While this is not a Common Core expectation, it is a district expectation to introduce these terms to second graders. I use this opportunity to introduce the idea to the students but I do not expect mastery.

If we have any "Way out" answers we look to see how those partners got their answers and we review possible strategies for comparing 2 numbers.

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#### Independent Practice

*15 min*

I ask students to now look at different objects in the room. I tell them that they will be moving about the room measuring 2 objects and recording the measurements in inches or centimeters. They will have 5 minutes to find at least 2 objects and to measure them and record the measures on the top of their blank papers. For this assignment I give students a piece of story paper with a blank space at the top and lines for writing the problem at the bottom. The paper is 2 sided.

After 5 minutes I ring the bell and ask students to return to their seats. I tell them that they will now write comparison word problems for the 2 objects they measured. I ask what kind of questions might they ask? (How much longer is ______ than _______? How much shorter is ____ than _____? How much taller…) I tell them that they will need to tell us the size of each object, ask the question and then create a math number sentence to show the problem. Students are expected to write and solve word problems that require them to take away and put together numbers (2.OA.A1)

I tell students that if they finish a first problem, they may write another, and if needed they may go and measure another set of objects.

After 10 minutes I invite students to bring their problems to the rug for a share out. Here students must figure out the problem as a classmate reads it aloud, and then they must persevere in solving it (MP1).

#### Resources

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#### Closing

*10 min*

Students gather on the rug. They take turns reading their problem and inviting a peer to come up to the easel and solve the problem and explain their thinking. If the child makes a mistake, the class tries to work together to come up with a solution.

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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 Are Our Understandings
- LESSON 2: Students As Teachers
- LESSON 3: Students as Teachers Part II
- LESSON 4: Kindness Day Math
- LESSON 5: Manipulation Central
- LESSON 6: More Than One Way to Solve A Problem
- LESSON 7: How Big Is One Thousand
- LESSON 8: Let's Compare
- LESSON 9: Assessment
- LESSON 10: Missing Numbers in Japanese