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Comparing Numbers: Who Has More?

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Lesson Plan

Comparing Numbers: Who Has More?

Students will be able to solve comparison word problems within 300 using various strategies, demonstrating their understanding of place value and comparative language.

Understanding how to compare numbers helps students make sense of quantities in the real world, from comparing scores in a game to understanding prices at a store. This lesson builds crucial foundational math skills.

Audience

3rd Grade Students

Time

30 minutes

Approach

Students will work in visibly random groups on a compelling problem, sharing strategies.

Materials

Whiteboards or chart paper, Dry-erase markers, Warm Up: Number Line Challenge, Comparison Problem Worksheet, Slide Deck: Who Has More?, Teacher Script: Comparing Numbers, and Cool Down: Exit Ticket

Prep

Preparation Steps

15 minutes

Step 1

Warm-Up: Number Line Challenge

5 minutes

  1. Distribute the Warm Up: Number Line Challenge.
    2. Instruct students to place given numbers on a number line.
    3. Review answers as a class, discussing strategies for estimating number placement.

Step 2

Introduce the Problem

5 minutes

  1. Use the Slide Deck: Who Has More? to display the main comparison problem.
    2. Read the problem aloud using the Teacher Script: Comparing Numbers, ensuring students understand the scenario and what they need to find.
    3. Facilitate a brief discussion to clarify any vocabulary or initial thoughts, but avoid giving away strategies.

Step 3

Collaborative Problem Solving

15 minutes

  1. Divide students into visibly random groups of 2-3 (e.g., using a deck of cards or popsicle sticks).
    2. Provide each group with a whiteboard/chart paper and markers.
    3. Instruct groups to work together to solve the problem on the Comparison Problem Worksheet. Encourage them to show all their thinking and strategies.
    4. Circulate among groups, observing strategies, asking probing questions (e.g., "How did you decide which number was larger?", "Can you show me another way?"), and providing support without solving for them.
    5. Remind students that the goal is to reach a consensus within their group and be prepared to share their solution.

Step 4

Share and Discuss

5 minutes

  1. Ask a few groups to share their solutions and strategies with the whole class, explaining their thinking.
    2. Use the Slide Deck: Who Has More? to guide the discussion, highlighting different approaches and the use of mathematical vocabulary (greater than, less than, hundreds, tens, ones).
    3. Affirm correct answers and provide constructive feedback on strategies.

Step 5

Cool-Down: Exit Ticket

5 minutes

  1. Distribute the Cool Down: Exit Ticket.
    2. Students independently complete the exit ticket to assess their individual understanding of comparing numbers within 300.
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Slide Deck

Who Has More?

Let's find out how to compare numbers!

Welcome students and introduce the day's math challenge. Explain that today we'll be comparing numbers and solving a problem together.

The Great Marble Mystery!

Sarah has 245 marbles.
David has 254 marbles.
Who has more marbles?

How do you know? Be ready to explain your thinking!

Display the problem clearly. Read it aloud twice. Ask students to identify key information and what they need to find. Reiterate that they will be working in groups.

Sharing Our Thinking

What strategies did your group use?
How did you decide who had more?
Did anyone use a different method?

After groups have worked, call on a few to share their strategies. Highlight different methods like place value comparison, using a number line, etc. Encourage respectful discussion.

Key Idea: Comparing Numbers

To compare numbers, we look at the place value starting from the hundreds place.
If the hundreds are the same, look at the tens place.
If the tens are the same, look at the ones place!

Summarize the key takeaways about comparing numbers. Emphasize looking at the hundreds place first, then tens, then ones. Reinforce vocabulary.

Time for a Cool-Down!

Show what you know about comparing numbers!

Transition to the cool-down activity, explaining its purpose as an individual check for understanding.

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Script

Teacher Script: Comparing Numbers

Warm-Up: Number Line Challenge (5 minutes)

"Good morning, mathematicians! Let's get our brains warmed up with a quick number line challenge. Everyone should have a worksheet in front of them. Your task is to place the numbers on the number line in their approximate positions. Remember to think about what numbers come before and after, and how far apart they are. You have about 3 minutes to work on this independently."

(Circulate and observe students working. After 3 minutes, bring the class back together.)

"Alright, let's look at our number lines. Who would like to share where they placed 150? Why did you put it there? How about 275? Or 80? Great thinking! It's important to remember that a number line helps us visualize the order and relative size of numbers."

Introduce the Problem (5 minutes)

"Now that our brains are warmed up, let's dive into our main challenge for today! I have a really interesting problem for us to solve together. Take a look at the screen/board." (Display Slide Deck: Who Has More? - Slide 2: The Great Marble Mystery!)

"Can I get a volunteer to read the problem aloud for the class?" (Allow a student to read.)

"Thank you! So, we have Sarah with 245 marbles and David with 254 marbles. Our goal is to figure out who has more marbles? And just as importantly, we need to be able to explain how we know."

"Before we jump into solving, does anyone have any clarifying questions about the problem? What does 'more' mean in this problem?" (Guide students to understand they are looking for the greater quantity.)

"Excellent! This is a problem we're going to tackle in groups today, and I want to see all your amazing thinking!"

Collaborative Problem Solving (15 minutes)

"Now, for the fun part! I'm going to put you into visibly random groups. When I say 'go,' please move quickly and quietly to your groups. Each group will get a whiteboard or a large piece of chart paper and some markers. Your task as a group is to solve the 'Great Marble Mystery.' Work together to figure out who has more marbles and be ready to show and explain all of your strategies and thinking on your board. Remember, everyone in the group should understand the solution and be able to explain it. You have about 15 minutes to work."

(As students work, circulate and listen to their discussions. Ask open-ended questions to prompt deeper thinking, without giving away answers. Examples: "How are you starting?" "What do the numbers 2, 4, and 5 in 245 represent?" "Can you draw a picture to show your thinking?" "What if the hundreds digit was different?" "Is there another way you could compare these numbers?")

Share and Discuss (5 minutes)

"Alright, mathematicians, bring your attention back to me in 3... 2... 1... Let's see some of the fantastic thinking happening around the room!" (Display Slide Deck: Who Has More? - Slide 3: Sharing Our Thinking)

"Which group would like to share their solution first? Can you show us your board and explain how you figured out who had more marbles?" (Select a group to share. After they share, ask follow-up questions.)

"That's a great strategy! Did any other group use a similar strategy?"

"Did any group use a different way to solve the problem? Maybe you thought about place value, or used a number line?" (Call on another group with a different approach.)

"Fantastic job explaining your thinking! What did we learn about comparing numbers today?" (Display Slide Deck: Who Has More? - Slide 4: Key Idea: Comparing Numbers)

"Remember, when we compare numbers, we always start by looking at the digit in the largest place value. For these numbers, that's the hundreds place. If the hundreds are the same, then we move to the tens place. If the tens are the same, we look at the ones place. That's how we can tell which number is greater or lesser!"

Cool-Down: Exit Ticket (5 minutes)

"To wrap up our lesson, I have a quick exit ticket for everyone. This will help me see what you've learned about comparing numbers today. Please complete this independently before you leave class." (Display Slide Deck: Who Has More? - Slide 5: Time for a Cool-Down!)

"You've all done an amazing job today. I saw some really impressive teamwork and problem-solving!"

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Warm Up

Warm-Up: Number Line Challenge

Instructions: Look at the number line below. Place the following numbers in their approximate locations on the number line. Try to be as accurate as possible!

Numbers to place: 80, 150, 275, 50, 200, 120

0 ---------------------------------------------------------------------------------------------------- 300












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Worksheet

Comparison Problem Worksheet: The Great Marble Mystery!

Problem: Sarah has 245 marbles. David has 254 marbles.

Question: Who has more marbles? How do you know?

Show all your work and explain your thinking below. You can use words, numbers, or pictures!













Challenge Question: If Mark has 249 marbles, does he have more than Sarah or less than David? Explain.












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Answer Key

Answer Key: The Great Marble Mystery!

Main Problem: Sarah vs. David

Question: Sarah has 245 marbles. David has 254 marbles. Who has more marbles? How do you know?

Answer: David has more marbles.

Explanation / Step-by-step thinking:

  1. Understand the Numbers: We need to compare 245 and 254.
  2. Compare Hundreds Place: Both numbers have a 2 in the hundreds place (200). Since they are the same, we move to the next place value.
  3. Compare Tens Place: Look at the tens place. Sarah has 4 tens (40) in 245. David has 5 tens (50) in 254. Since 5 tens is greater than 4 tens, we already know that 254 is greater than 245.
  4. Conclusion: Because David's number (254) has a greater digit in the tens place, David has more marbles than Sarah.

Visual Representation (Optional, for student reference):

245: Hundreds: 2 | Tens: 4 | Ones: 5
254: Hundreds: 2 | Tens: 5 | Ones: 4

Comparing 4 and 5 in the tens place, 5 > 4.

Challenge Question: Mark, Sarah, and David

Question: If Mark has 249 marbles, does he have more than Sarah or less than David? Explain.

Answer: Mark has more marbles than Sarah but less than David.

Explanation / Step-by-step thinking:

  1. Compare Mark (249) and Sarah (245):

    • Hundreds: Both have 2. (2 = 2)
    • Tens: Both have 4. (4 = 4)
    • Ones: Mark has 9 ones, Sarah has 5 ones. (9 > 5)
    • Conclusion: Mark (249) has more than Sarah (245).

  2. Compare Mark (249) and David (254):

    • Hundreds: Both have 2. (2 = 2)
    • Tens: Mark has 4 tens, David has 5 tens. (4 < 5)
    • Conclusion: Mark (249) has less than David (254).

Therefore, Mark has more marbles than Sarah but less than David.

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Cool Down

Cool Down: Exit Ticket

Name: ________________________

  1. Compare the numbers using >, <, or =.

    a) 178 _______ 187

    b) 203 _______ 230

    c) 199 _______ 199




  1. Maria collected 156 stickers. Tom collected 165 stickers.
    Who collected fewer stickers? Explain how you know.












  2. Write a number that is greater than 210 but less than 220.




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Comparing Numbers: Who Has More? • Lenny Learning