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* *Reflection: Developing a Conceptual Understanding
Less Than or Greater Than - Section 2: Develop the Concept

Students in second grade often come into these math lessons using incorrect terminology. They will often say things like " 37 is bigger than 21." I try to steer them away from this language by writing the following on the board: Greater Versus Bigger

I ask the students if they still think that the statement " 37 is bigger than 21" is true. Many will say no. I remind them that the correct mathematical terms are "greater than and less than" not "bigger than or smaller than." I find that the visual representation of these numbers helps to clarify these misconceptions.

*Developing a Conceptual Understanding: Greater Versus Bigger*

# Less Than or Greater Than

Lesson 2 of 6

## Objective: The students will be able use the less than and greater than symbols to compare two-digit numbers.

#### Activator and Materials

*10 min*

I begin this lesson by showing the students two balls. I use a small squishy ball and a large alphabet ball because that's what I have. I ask the students to turn and talk about how they could compare the two balls. I listen for the students to talk about how the balls are different (size, shape, material) and how they are the same (they are both balls, we use them both for morning meeting). I then have the students talk about what it means to compare. I am listening for the students to talk about how things are different and how they are the same.

Then I take out 8 glue sticks in a group and two glue sticks in a group. I ask the students to compare the two groups of glue sticks. How are they the same? How are they different? I'm listening for the students to be talking about how they are both groups of glue sticks but one group has more.

#### Resources

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#### Develop the Concept

*10 min*

I think that expectations reminders are only fair for 2nd graders. They are still quite young. Because we are using manipulatives today, I have the students review how they should organize their ones cubes and tens rods on their name tag. Then I have the students take out their place value mat and work in partners to build the number 5 and 8 using their ones cubes. I ask the students to talk with a neighbor about how they could compare the two numbers.

Next, I ask the students if they have ever seen the following symbols: <, >. If any students have seen them, I have them share what they might know about them. I explain to the children that we can often think of the two symbols as alligator mouths. I explain that the alligator is hungry, and that he will always eat the greater number. I teach the students the Comparing Numbers Song to help them remember.

Using the two numbers that the students have just built in partners, I ask the students to use their individual whiteboards to write the symbol that they think they could use to compare the numbers. I remind them that the alligators mouth should be open to the greater number because he is ready to eat it.

I then write the two-digit numbers 34 and 72 on the board. I have the students work in partners. One student builds the first number using tens rods and ones cubes, while the partner builds the other number. I ask the students where they think I should look to find out which number is greater. I remind the students that they should always begin by looking in the place that is greatest (in this case it is the tens place)and then compare the same place value between the two numbers. Because I'm not trying to trick my students, I don't yet have them compare numbers that have differing place values (e.g., 54 and 254).

Students practice building numbers in partners a few times until I feel that they are comfortable with comparing. When I see this, I usually give the students numbers that have the same digit in the tens place. I might joke that I can't compare them because the alligator can't choose which number to eat. I am looking for the students to stop me and tell me that if the digits are the same in the tens place then I look at the next greatest place value column and compare those digits. If students don't think of looking in the ones place, we build the two numbers using place value blocks and think about what makes one more than the other.

Finally, I write the numbers 45 and 45 on the board. I ask the students to talk with their partner about how they could compare the two numbers. I am listening for the students to be talking about how they could look at the tens and ones. I ask a few of the students to share what they noticed about the numbers. Which number would the alligator choose to eat? I am looking for the students to recognize that the numbers are both the same, and therefore the way to compare them would be to put the equal symbol between them.

I usually have my students practice building and writing the comparison number sentences for several numbers. Once I feel that they are showing me they understand I would would move on to the Practice section of the lesson. If there are a few students I feel are still having difficulty, I would pull them in a small group to work with me to practice a bit more.

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#### Practice the Concept

*20 min*

Now I will let the students practice this concept in partners using the Greater Than, Less Than game. Each student will need a pair of dice or 18 basic dominoes, a game board (one per pair), a game paper, a place value mat, tens rods, and ones cubes . I like to give the students the chance to practice with both because it helps them be able to recognize the patterns of the dots on both the dominoes and the dice. However, I find that most teachers have dice readily available in their classroom.

Working partners the students roll both of their dice (or each places a domino on their game board) and they build the two-digit number on their place value mat. Then they discuss how they could compare the two numbers using the greater than (>), less than (<), or equal to (=) symbols. They each would write the number sentence on their game paper. They continue doing this until they have completed every space on their paper.

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#### Summarizer

*10 min*

I have the students come back together as a class, either in our rug area or at their desks. I write 17 ___ 71 on the board. I have the students turn and talk about how they could compare those two numbers. I then have one student tell me how they could find out which symbol to use. I am looking for the students to look first at the tens place because it is the greatest place value column. In this comparison, the students don't need to go any further than the tens place.

Then I write 48 ___ 42 on the board. I have the students turn and talk again about the process that they would go through to compare these two numbers. I then have another student share his/her thinking. I am looking for them to go one step further, because when they look at the tens place the digits are the same, so they would have to look at the ones to compare.

Then I write 31___31 on the board. I have the students compare these numbers using the same process as before, having one student share their thinking with the class. I use this time to wrap up the lesson and solidify understanding while identifying any students that may still need further development.

Finally, I will write 265 ___ 261 on the board. Now that the students understand how to compare two digit numbers I like to see who can carry that understanding to a higher level. I always make sure to refrain from just telling the students "start in the tens place" because they need to understand the structure of the concept.

Throughout this lesson, students have been focused on reasoning quantitatively - to make sense of quantities and their relationships (MP2).

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