Comparing Things!

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Objective

Students will use the >, =, and < symbols to compare three-digit numbers based on the meanings of the hundreds, tens, and ones digits.

Big Idea

Students explore numbers in a variety of ways to understand how to compare three-digit numbers based on an understanding of place value.

Anticipatory Setting

5 minutes

Material: Notes

I invite students to the carpet. How many of you like cookies? Students seem excited about cookies. They discuss what type of cookies they like. I proceed to draw two large jars on the board. I draw 20 circles in the first jar and 35 circles in the second jar. I am careful not to say the number amount aloud. I ask students to count along with me as I count the cookies in the first and second jar. I write the number of cookies in large print above each jar. If you could choose, which jar would you take? Of course, they all want the jar with the most cookies. I ask which jar has the greatest amount of cookies in it. (The jar with 35 cookies has the most).

What if I want to use a symbol to compare the two numbers? What symbol could I use?  Some students say the greater-than symbol and some are not quite sure. I write the symbols for comparing numbers on the board. I write a blank line beside each symbol, so that we can discuss the meaning together. 

Symbols Used to Compare Numbers

The symbol < means __________

The symbol > means __________

The symbol = means __________

Who can tell me which symbols represent less than, greater than, or equal to?

Students seem a bit confused. Have you heard about the cookie monster? Well Cookie Monster likes to eat a lot of cookies. If he had to choose a jar from the board, what jar do you think he will choose? Students say the jar with the most cookies in it. Yes! He would choose the jar with the most cookies. Therefore, the open part of Cookie Monster’s mouth would need to face the jar with the most cookies in it. I demonstrate with my hands by opening and closing them in a triangle shape. I pretend that my hand is Cookie Monster’s mouth. He’s pretty hungry. I stand in the middle of each jar, and point the open part of my hand to the jar with the most cookies. I ask students to tell me what number is larger. They all say 35. I repeat this using different numbers, and I invite student volunteers to demonstrate Cookie Monster’s motion to determine what number is greater. This section is focused on reviewing symbols that students were exposed to in first grade (1.NBT.B.3). For students who still confuse these symbols, I support their understanding by asking them to choose the symbol on the board that matches the symbol they are making with their hand. This helps make sure they are not confusing the symbols, and that they understand the value of the two numbers.

 

I continue to probe and question using the following:

How does this relate to…?

What concepts that we have learned before were useful in solving this problem?

Where have you used this concept before? (home/real world connection)

Can you give an example of…? 

 

 

 

Interacting

10 minutes

 

 

In this portion of the lesson I introduce students to an interactive number line video. The activity will allow students to practice sequencing numbers up to 1000. I want my students to gain a deeper understanding of number sense. I hope to help them determine what number comes before, after, and next, so that they are better able to compare three-digit numbers. As students are engaged in this activity, I reinforce their learning skills by asking them to say a number greater than or less than a given number. For instance, in one activity, students are asked to write the number between 225 and 227. After they write the number, I ask them to say a number greater than 227, but less than 300. Of course, students say every number up to 300, but this is a great way to extend the value of the numbers they are choosing. I continue working with them for about 10 minutes or so. 

 

I continue to probe and question using the following:

How does this relate to comparing and ordering numbers/values of digits?

What concepts that we have learned before were useful in solving this problem?

Where have you used this concept before? (home/real world connection)

Can you give an example of…? 

 

Trying it Out

15 minutes

We have just completed an activity on how numbers relate. In this activity, I want students to use what they have learned so far to compare two or more numbers. However, I want them to extend it a bit by identifying the value of the digits. First, I ask students to create their own justification cards. You will use the card to compare two or more numbers. However, you all are going to do this with a twist. Students want to know what the twist is. I begin placing cards on the floor in a line labeled as follows: Thousands, Hundreds, Tens, and Ones. I ask students to gather into their assigned two groups. I explain the following directions:

Follow the steps below to compare two or more numbers.

  1. Line up the numbers being compared, one above the other.
  2. Compare the place value for each digit starting from the left.
  3. Find the first difference. The number with the largest digit is the largest number.
  4. Each student is to represent the number by standing on the correct place value labeled on the floor.

 

I want to make sure students fully understand the given task, so I demonstrate what they will be expected to do.

Example 1:

Compare the numbers 361 and 371.

Solution:

The first number is 371. What number is in the hundreds place? (3) So, I stand on the card that says hundreds. Am I enough to represent 3 hundreds? (NO) How many students do I need up here with me to represent 3 hundreds? (2) Great job! I continue to illustrate until I have successfully represented both numbers. Which number is greater? They seem a bit puzzled, so I ask how many hundreds are in both numbers. (3) How many tens are in both numbers? (6 and 7) Which number has more tens? (371) Ok! What number is greater? (371) I continue this process until students are able to explain how and why a number is greater than, less than, or equal to another number.  In addition, students recognize how to use place value to understand the value of digits.

Sometimes the students themselves become the appropriate tool for the task! (MP5)

After students finish the given task, I ask them to pair with their assigned partner. I give them all a sheet of drawing paper and crayons. I explain that they will work together to illustrate their understanding of comparing numbers. As students are working, I circle the room to check for understanding. I may chime in a time or two to ask probing questions: How do you know? What number is in the hundred, tens, and ones place? How do you know? Explain.

 

 Students work-sample

Assessing the Knowledge!

20 minutes

Student's work samples

After the interactive lesson students should be able to make sense of numbers and compare 3-digit numbers based on an understanding of place value.

I ask students to move back into their assigned  seats. You guys seem to be working well with using place value to better understand comparing 3-digit numbers. I noticed some of you sharpening up your number sense skills as well. I want to see what you can do on your own. I give each student a copy of their work assignment. The assignment includes comparing and ordering numbers, basic number sense, and understanding the value of digits. I explain that they will have about thirty-minutes to complete their task.

As students are working, I circle the room to check for understanding. For instance, I ask some students to tell me what digits are in the hundreds, tens, and ones place. They can accurately provide me with the correct digits. To make sure they understand how to compare two numbers, I ask students to justify their comparison using the value of each digit. For instance, one student has a 5 in the hundreds place for the first number being compared, and a 6 in the hundreds place for the second number being compared. I ask the student to determine which number is larger. (689 is larger because it has 6 in the hundreds place instead of 5) I continue to reinforce students' learning, and I assist when needed. 

 

 

I continue to probe and question using the following:

How does this activity help you understand comparing and ordering numbers/values of digits?

What concepts that we have learned before were useful in solving  this problem?

Where have you used this concept before? (home/real world connection)

Can you give an example of…?