Comparing Numbers Game: Alligator Chompers

Materials:

• Set of number cards (pre-made cards with a mix of two-digit and three-digit numbers up to 999, including some equal pairs, or two sets of 0-9 cards for creating numbers)
• Large cut-out symbols: >, <, =
• Score sheet or small whiteboards/markers for each pair

Players: 2-4 students per group

Instructions:

1. Prepare: Shuffle the number cards and place them face down in a pile. Place the symbol cards (>, <, =) face up where everyone can see them.
2. Draw Numbers: Each player draws two number cards (or creates two numbers if using single-digit cards, ensuring a mix of two-digit and three-digit numbers). For example, Player A draws 242 and Player B draws 251.
3. Compare and Grab! The goal is to be the first to correctly state a comparison using the symbols AND grab the correct symbol. For example, if Player A has 242 and Player B has 251:
   • Player A might say: "242 is less than 251!" and grab the '<' symbol to place between their cards.
   • Player B might say: "251 is greater than 242!" and grab the '>' symbol.
4. Justify Your Choice: After placing the symbol, the player must explicitly justify their choice using place value language (hundreds, tens, and ones). For example: "I know 242 is less than 251 because both have 2 hundreds, but 4 tens is less than 5 tens."
5. Score a Point: The first player to correctly state the comparison, grab the correct symbol, AND provide a correct place value justification gets a point. (If multiple players correctly state and justify simultaneously, they both get a point).
6. Equal Numbers: If two players draw numbers that are equal (e.g., both make 322), they should grab the '=' symbol and state "322 is equal to 322 because they have the same hundreds, tens, and ones!"
7. New Round: Return cards to the bottom of the pile, shuffle, and start a new round.
8. Winning: Play for a set amount of time (e.g., 10 minutes) or until a player reaches a certain score. The player with the most points wins!

Differentiation for Special Education Students:

• Pre-made Number Cards: Use pre-made two-digit and three-digit number cards rather than having them create numbers from single digits, to reduce cognitive load.
• Symbol Reference Sheet: Provide a personal reference sheet with the symbols and their meanings at their station, including notes on comparing hundreds, tens, and ones.
• Focus on Paired Comparison: Initially, focus on just comparing two numbers at a time (e.g., player A vs. player B) rather than all numbers in the group, to simplify the task.
• Verbal Prompts & Sentence Starters: Provide explicit sentence starters to aid justification, such as: "____ is ____ than ____ because... (compare hundreds, then tens, then ones)."
• Base-Ten Blocks Access: Allow access to base-ten blocks to physically build and compare the numbers if needed, helping them visualize the place value differences.
• Peer Support: Pair with a strong, supportive peer helper who can model the game play and verbal justification.

Comparing Numbers Quiz Answer Key

Instructions: For each pair of numbers, write the correct comparison symbol (>, <, or =) in the box. For questions requiring explanations, refer to the provided thought process.

Example:

145 > 128

• Thought Process: Compare the hundreds digits (both 1). Then compare the tens digits. 4 tens is greater than 2 tens, so 145 is greater than 128.

1. 147 < 229

   • Thought Process: Compare the hundreds digits. 1 hundred is less than 2 hundreds, so 147 is less than 229.

2. 363 < 368

   • Thought Process: Compare the hundreds digits (both 3). Compare the tens digits (both 6). Then compare the ones digits. 3 ones is less than 8 ones, so 363 is less than 368.

3. 211 = 211

   • Thought Process: Both numbers have 2 hundreds, 1 ten, and 1 one. They are exactly the same, so they are equal.

4. 54 < 145

   • Thought Process: Compare the hundreds digits. 54 has 0 hundreds, while 145 has 1 hundred. 0 hundreds is less than 1 hundred, so 54 is less than 145.

5. 700 < 760

   • Thought Process: Compare the hundreds digits (both 7). Then compare the tens digits. 0 tens is less than 6 tens, so 700 is less than 760.

6. 923 > 921

   • Thought Process: Compare the hundreds digits (both 9). Compare the tens digits (both 2). Then compare the ones digits. 3 ones is greater than 1 one, so 923 is greater than 921.

7. Which number is greater?

   Circle the greater number: 387 or 837

   • Thought Process: Compare the hundreds digits. 8 hundreds is greater than 3 hundreds, so 837 is the greater number.

8. Which number is less?

   Circle the less number: 212 or 121

   • Thought Process: Compare the hundreds digits. 1 hundred is less than 2 hundreds, so 121 is the less number.

9. Fill in the blank to make the statement true:

   555 = 555

   • Thought Process: For numbers to be equal, they must be the same value in every place (hundreds, tens, ones).

10. Fill in the blank to make the statement true:

    110 < (Any three-digit number greater than 110, e.g., 111, 150, 200, 999)

    • Thought Process: To make the statement true, the number in the blank must be greater than 110. For example, 1 hundred, 1 ten, and 1 one (111) is greater than 1 hundred, 1 ten, and 0 ones (110) because the ones digit is greater. Or 200 is greater than 110 because 2 hundreds is greater than 1 hundred.

Comparing Symbols Script

Introduction to Symbols

Teacher: "Yesterday, we were number detectives, figuring out which number was bigger or smaller using our hundreds, tens, and ones! Today, we're going to learn how to write down our discoveries using special math symbols! These symbols are like a secret code that mathematicians use!"

Teacher: "Our first symbol looks like this: > (Draw it largely on the board or point to it on the Comparing Numbers: Day 2 Slide Deck, Slide 2). This symbol means 'greater than'. Can everyone say 'greater than'?"

Students: "Greater than!"

Teacher: "Remember our hungry alligator? Its mouth always opens towards the bigger number! It wants to eat the most! Let me show you with some numbers we've compared."

Teacher: "If we compare 145 and 128, we know 145 is bigger. Why? Because both have 1 hundred, but 145 has 4 tens and 128 only has 2 tens. So, the alligator's mouth will open towards 145! We write: 145 > 128. We read this as '145 is greater than 128.' Let's say it together!"

Students: "145 is greater than 128."

Teacher: "Let's try another one: 91 and 76. Who can tell me which is greater and why, thinking about tens and ones?" (Allow a student to respond). "That's right! 91 is greater than 76 because 9 tens is more than 7 tens. So, 91 > 76."

Teacher: "Now, our next symbol looks like this: < (Draw it largely on the board or point to it on the Comparing Numbers: Day 2 Slide Deck, Slide 3). This symbol means 'less than'. Can everyone say 'less than'?"

Students: "Less than!"

Teacher: "It's still our hungry alligator, and its mouth is still open towards the bigger number! The smaller number just gets its back turned to it. Let's see how this works."

Teacher: "If we compare 334 and 337, they both have 3 hundreds and 3 tens. But 337 has more ones (7 ones vs. 4 ones). So, the alligator's mouth will still open towards 337! We write: 334 < 337. We read this as '334 is less than 337.' Let's say it together!"

Students: "334 is less than 337."

Teacher: "How about 76 and 91? If we start with 76, how would we write that comparison using the 'less than' symbol?" (Allow a student to respond). "Excellent! 76 < 91, because 7 tens is less than 9 tens. The alligator still wants the 91!"

Teacher: "And finally, our easiest symbol: = (Draw it largely on the board or point to it on the Comparing Numbers: Day 2 Slide Deck, Slide 4). This symbol means 'equal to'. What do you think 'equal to' means?"

Students: (Expected response: "They are the same!" or "They are equal!")

Teacher: "Exactly! If two numbers are exactly the same, like 222 and 222, then we use the 'equal to' sign. They have the same hundreds, the same tens, and the same ones! We write: 222 = 222. We read this as '222 is equal to 222.' Let's say it together!"

Students: "222 is equal to 222."

Guided Practice with Symbols

Teacher: "Let's try some together. I'll write two numbers, and you tell me which symbol goes in between them. Remember our steps: Hundreds first, then tens, then ones, then the hungry alligator!"

Teacher: "First one: 163 and 36. Turn and tell your partner which symbol (>, <, or =) you would put in between these numbers and why. Make sure you use our place value language!" (Give 30 seconds for discussion.)

Teacher: "Who can share their answer? What symbol, and why?"

Student: (Expected response: "163 > 36 because 1 hundred is more than 0 hundreds. The alligator wants the 163!")

Teacher: "Excellent! The alligator wants to eat 163! Let's try another one: 250 and 250. Discuss with your partner."

Teacher: "What about this one?"

Student: (Expected response: "250 = 250 because they have the same hundreds, tens, and ones. They are exactly the same!")

Teacher: "Perfect! They are equal! Last one together: 177 and 179. Discuss."

Teacher: "And the symbol here is...?"

Student: (Expected response: "177 < 179 because the hundreds and tens are the same, but 9 ones is more than 7 ones. The alligator wants to eat 179!")

Teacher: "You've got it! The alligator wants to eat 179! Now you're ready for your worksheet and our activity!"

Comparing Numbers: Symbols Challenge

Name: _________________________

Instructions: For each pair of numbers, write the correct comparison symbol (>, <, or =) in the box. Remember the hungry alligator always eats the bigger number! Think about hundreds, tens, and ones to help you decide.

Example:

145 > 128

• Thought Process: Both have 1 hundred. Then compare tens: 4 tens is greater than 2 tens, so 145 is greater than 128.

1. 76 ____ 91

   
   
   
   

2. 151 ____ 157

   
   
   
   

3. 222 ____ 422

   
   
   
   

4. 170 ____ 160

   
   
   
   

5. 383 ____ 381

   
   
   
   

6. 615 ____ 516

   
   
   
   

7. 904 ____ 940

   
   
   
   

8. 267 ____ 269

   
   
   
   

9. 333 ____ 333

   
   
   
   

10. 41 ____ 141

    
    
    
    

Challenge!

11. Write two three-digit numbers and use the "<" symbol to compare them. Explain your choice using hundreds, tens, and ones.

    
    
    
    
    
    
    

12. Write two three-digit numbers and use the ">" symbol to compare them. Explain your choice using hundreds, tens, and ones.

    
    
    
    
    
    
    

Alligator Mouth Comparison Activity

Materials: Large printouts of the >, <, and = symbols (or drawn on cardstock), number cards (0-999, including a mix of two-digit and three-digit numbers, and some pairs that are equal).

Players: 2-4 students per group

Instructions:

1. Small Groups/Pairs: Divide students into small groups or pairs.
2. Number Draw: Students take turns drawing two number cards. These numbers can be a mix of two-digit and three-digit (e.g., 72 and 27, or 215 and 251, or even 100 and 100).
3. Alligator Action: Students physically place the correct comparison symbol (the cut-out alligator mouth) between the two number cards to make a true statement. They must decide which number is bigger, smaller, or if they are equal.
   • For example, if they draw 72 and 27, they would place the ">" symbol to show 72 > 27, or "<" if they started with 27 (27 < 72).
   • If they draw 215 and 251, they would place the "<" symbol (215 < 251).
   • If they draw 100 and 100, they would place the "=" symbol (100 = 100).
4. Verbalize and Justify: Students in the group must verbalize the comparison using the correct language and symbols: "72 is greater than 27 because..." or "215 is less than 251 because..." They must also justify their choice by referencing place value (hundreds, tens, and ones).
5. Teacher Observation & Feedback: Circulate among the groups. Listen to their verbalizations and justifications. Provide immediate, explicit feedback, correcting any misconceptions about symbol orientation or place value comparison. Encourage students to help each other understand.
6. New Round: Return cards to the pile, shuffle, and start a new round. Play for a set amount of time.

Differentiation for Special Education Students:

• Symbol Reference Card: Provide a personal reference chart with the symbols and their meanings, including clear visuals and reminders for comparing hundreds, tens, and ones.
• Focus on Two Digits First: If students are struggling with three-digit numbers, initially provide only two-digit number cards until confidence is built, then gradually introduce three-digit numbers.
• Base-Ten Blocks Support: Allow students to use base-ten blocks (including hundreds flats) to build and compare the numbers physically before selecting and placing the symbol.
• Sentence Starters: Provide explicit sentence starters to aid verbalization, such as: "I think ____ is greater than ____ because the hundreds/tens/ones are..." or "I use the ____ symbol because...."
• Peer Modeling: Pair special education students with strong peer helpers who can model the comparison process and verbal justification.

Place Value Visual Cards

*(Teacher: Print and cut these cards. Consider drawing or affixing visual representations of base-ten blocks (flats for hundreds, rods for tens, small squares for ones) next to each number and description for clearer visuals.)

Card 1: Number 23

Tens: 2 rods / 20 blocks

Ones: 3 small squares / 3 blocks

Card 2: Number 32

Tens: 3 rods / 30 blocks

Ones: 2 small squares / 2 blocks

Card 3: Number 45

Tens: 4 rods / 40 blocks

Ones: 5 small squares / 5 blocks

Card 4: Number 28

Tens: 2 rods / 20 blocks

Ones: 8 small squares / 8 blocks

Card 5: Number 125

Hundreds: 1 flat / 100 blocks

Tens: 2 rods / 20 blocks

Ones: 5 small squares / 5 blocks

Card 6: Number 251

Hundreds: 2 flats / 200 blocks

Tens: 5 rods / 50 blocks

Ones: 1 small square / 1 block

Card 7: Number 334

Hundreds: 3 flats / 300 blocks

Tens: 3 rods / 30 blocks

Ones: 4 small squares / 4 blocks

Card 8: Number 337

Hundreds: 3 flats / 300 blocks

Tens: 3 rods / 30 blocks

Ones: 7 small squares / 7 blocks

Comparing Numbers: Hundreds, Tens, and Ones

Name: _________________________

Instructions: Look at each pair of numbers. First, identify the largest place value (hundreds, then tens). Circle that digit in both numbers. Then, compare the numbers. Circle the number that is GREATER in each pair.

Example:

145 vs. 128

(Circle 145)

1. 76 vs. 91

   (Circle the greater number)

   
   
   
   

2. 58 vs. 53

   (Circle the greater number)

   
   
   
   

3. 212 vs. 412

   (Circle the greater number)

   
   
   
   

4. 170 vs. 160

   (Circle the greater number)

   
   
   
   

5. 383 vs. 381

   (Circle the greater number)

   
   
   
   

6. 615 vs. 516

   (Circle the greater number)

   
   
   
   

7. 904 vs. 940

   (Circle the greater number)

   
   
   
   

8. 267 vs. 269

   (Circle the greater number)

   
   
   
   

Challenge!

9. Think of two three-digit numbers where the hundreds and tens digits are the same, but one number is greater than the other. Write them down and circle the greater number.

   
   
   
   
   
   
   

Building Blocks Comparison Activity

Materials: Base-ten blocks (hundreds flats, rods for tens, unit cubes for ones) or LEGO/Duplo blocks (100-stud flat for hundreds, 10-stud long blocks for tens, single-stud blocks for ones).

Instructions:

1. Partners: Students will work in pairs.
2. Number Draw/Teacher Provides: Each pair will be given two two-digit or three-digit numbers by the teacher (e.g., 67 and 76, or 215 and 251).
3. Build the Numbers: Each student in the pair will use their building blocks to represent one of the two-digit or three-digit numbers. For example, if the numbers are 215 and 251:
   • Student A builds 215 (2 hundreds flats, 1 tens block, 5 ones blocks).
   • Student B builds 251 (2 hundreds flats, 5 tens blocks, 1 one block).
4. Compare Step-by-Step: Students will then physically compare their built numbers.
   • Teacher Script: "Look at your numbers. First, compare the largest place value blocks (hundreds). Which number has more hundreds? If the hundreds blocks are the same, then compare the 'tens' blocks. Which number has more 'tens' blocks? If the tens blocks are also the same, then compare the 'ones' blocks. Which number has more 'ones' blocks?"
5. Verbalize: Students will say which number is greater or less using sentences like, "____ is greater than ____ because it has more ____ (hundreds/tens/ones)" or "____ is less than ____ because it has fewer ____ (hundreds/tens/ones)." For special education students, provide sentence frames focusing on place value.
6. Switch Roles: Students will switch numbers or draw new cards and repeat the activity.

Differentiation for Special Education Students:

• Start Simple: Begin with numbers where the hundreds or tens digits are clearly different (e.g., 300 vs. 100, or 250 vs. 210) to build foundational understanding.
• Visual Aid: Provide a checklist or visual reminder of the comparison steps (Hundreds -> Tens -> Ones) at their workstation.
• Guided Comparison: Limit the number of place values to compare initially (e.g., only focus on hundreds, then gradually add tens and ones).
• Pre-built Numbers: For some students, pre-build one of the numbers and have them focus on building and comparing the second number.
• Peer Support: Pair with a strong peer helper who can model verbalization and provide gentle guidance.