Lesson Plan
Value of Digits
Students will be able to identify and represent the value of a digit in whole numbers up to 1,000,000,000 and decimals to the hundredths place.
Understanding place value is fundamental to all future math concepts, from basic arithmetic to advanced algebra. It helps students comprehend the true size and contribution of each digit in a number, making them more confident with numbers in real-world situations like money and measurements.
Audience
4th Grade Students
Time
15 minutes
Approach
Interactive practice and group discussion.
Materials
Value of Digits Slide Deck, Value of Digits Activity Cards, [Whiteboards and Markers](No digital material), and Optional: Base-ten blocks or place value charts
Prep
Prepare Materials
5 minutes
- Review the Value of Digits Lesson Plan and all generated materials.
- Print and cut out the Value of Digits Activity Cards (one set per small group).
- Ensure whiteboards and markers are available for each student or small group.
Step 1
Warm-Up: What's My Value?
3 minutes
- Display a number (e.g., 3,456) on the Value of Digits Slide Deck.
2. Ask students to identify the value of a specific digit (e.g., "What is the value of the 4?").
3. Have students quickly write their answers on whiteboards and show them. Discuss responses briefly.
Step 2
Introduction to Place Value
3 minutes
- Use the Value of Digits Slide Deck to review place value concepts, including whole numbers up to billions and decimals to hundredths.
2. Emphasize that the position of a digit determines its value.
3. Refer to the Teacher Script for specific talking points and questions.
Step 3
Activity: Value Sort Challenge
7 minutes
- Distribute Value of Digits Activity Cards to each small group.
2. Explain that each card has a number and a highlighted digit. Students must sort the cards into piles based on the value of the highlighted digit (e.g., 'Tens', 'Hundredths', 'Millions').
3. Circulate to provide support and assess understanding. Encourage groups to discuss their reasoning.
4. After the activity, briefly review some of the cards and their correct groupings as a class.
Step 4
Cool Down: Quick Check
2 minutes
- Display a new number on the Value of Digits Slide Deck (e.g., 123,456.78).
2. Ask students to write down the value of two specific digits (e.g., 'Value of the 2' and 'Value of the 7').
3. Collect or have students show their whiteboards as an exit ticket.
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Slide Deck
What's My Value?
Every digit in a number has a special job!
Welcome students and introduce the concept of digits having different values based on their position. Start with a quick warm-up to activate prior knowledge.
Warm-Up Challenge!
Look at the number: 3,456
What is the value of the digit 4?
Display the number and ask students to identify the value of a specific digit. For example, 'What is the value of the 4 in 3,456?' Allow students to use whiteboards. Briefly discuss their answers.
Place Value Power!
The PLACE where a digit sits in a number tells us its VALUE.
Today, we'll explore whole numbers up to billions and decimals to the hundredths.
Introduce the main concept: place value. Explain that the position of a digit changes its value dramatically. Emphasize whole numbers and decimals to the hundredths.
Whole Number Values
Let's look at the number: 555,555
- The first 5 is in the hundred thousands place, so its value is 500,000.
- The second 5 is in the ten thousands place, so its value is 50,000.
- ...and so on!
Show an example of whole number place value. Point out how the digit '5' has different values in each position. Use the script for detailed explanations.
Decimal Values
What about after the decimal point?
Look at the number: 0.75
- The 7 is in the tenths place, so its value is 0.7.
- The 5 is in the hundredths place, so its value is 0.05.
Introduce decimal place value. Highlight the decimal point and the places to its right. Explain how decimals represent parts of a whole.
Time for a Challenge!
Work in your small groups.
Sort the Value of Digits Activity Cards into piles based on the value of the highlighted digit.
Discuss your choices with your group members!
Transition to the activity. Explain the 'Value Sort Challenge' and how students will work in groups to sort cards. Remind them to discuss their reasoning.
Cool Down: Quick Check
Look at the number: 123,456.78
- What is the value of the digit 2?
- What is the value of the digit 7?
For the cool-down, display a new number and ask students to write the value of two specific digits on their whiteboards. This serves as a quick check for understanding.
Script
Teacher Script: Value of Digits
Warm-Up: What's My Value? (3 minutes)
Teacher: "Good morning/afternoon, everyone! Let's get our brains warmed up for some math today. We're going to be talking about something super important: the value of digits in numbers. Every digit in a number has a special job, and that job depends on where it sits!"
"To start, take a look at the number I'm putting on the board: 3,456 (refer to Value of Digits Slide Deck, Slide 2). On your whiteboards, I want you to quickly write down: What is the value of the digit 4 in this number? Give me a thumbs up when you have your answer."
(Pause for students to write and show answers. Circulate and observe.)
Teacher: "Great job! I see many of you correctly identified that the 4 in 3,456 is in the hundreds place, so its value is 400. Fantastic! Let's keep that idea in mind as we dive deeper."
Introduction to Place Value (3 minutes)
Teacher: "Today, we're going to explore this idea even further. We'll learn how the PLACE where a digit sits in a number truly tells us its VALUE. This is super important because it helps us understand big numbers, small numbers, and everything in between! We'll be looking at whole numbers all the way up to billions, and even tiny parts of numbers called decimals, down to the hundredths place." (refer to Value of Digits Slide Deck, Slide 3)
"Think about it like this: If you have a dollar bill, a dime, and a penny, they all have the digit '1' in their value, but their place makes them worth totally different amounts! The dollar is worth one whole, the dime is one tenth of a dollar, and the penny is one hundredth of a dollar. Place matters!"
"Let's look at another example with whole numbers. (refer to Value of Digits Slide Deck, Slide 4) Take the number 555,555. Can someone tell me the value of the 5 in the hundred thousands place? How about the 5 in the tens place? Why are they different even though they're both the digit 5?"
(Pause for student responses, guiding them to understand that position dictates value.)
Teacher: "Exactly! The position changes everything. Now, let's explore decimals. (refer to Value of Digits Slide Deck, Slide 5) When we see a decimal point, it means we're looking at parts of a whole. In the number 0.75, the 7 is in the tenths place, so its value is 0.7, or seven-tenths. The 5 is in the hundredths place, so its value is 0.05, or five-hundredths. It's like cutting a pizza into 10 slices (tenths) or 100 tiny pieces (hundredths)!"
Activity: Value Sort Challenge (7 minutes)
Teacher: "Alright, it's time for a challenge! You'll be working in your small groups today. Each group will get a set of Value of Digits Activity Cards. (refer to Value of Digits Slide Deck, Slide 6)
"On each card, you'll see a number with one digit highlighted. Your job is to sort these cards into different piles based on the value of that highlighted digit. For example, if a card has 2,345 on it, and the 3 is highlighted, you'd put it in the 'Hundreds' pile. If another card has 0.78, where the 7 is highlighted, you'd put it in the 'Tenths' pile."
"Work together, discuss your choices, and make sure everyone in your group understands why each card goes where it does. I'll be walking around to help and answer any questions. You have about 7 minutes for this activity. Go!"
(Circulate, listen to discussions, offer hints, and correct misconceptions.)
Cool Down: Quick Check (2 minutes)
Teacher: "Bring your attention back up here, everyone. Great work collaborating on those cards! Let's do a quick check to see what you've learned today."
"On your whiteboards, please write down the answers to these two questions based on the number on the screen: 123,456.78 (refer to Value of Digits Slide Deck, Slide 7)
- What is the value of the digit 2?
- What is the value of the digit 7?
"Show me your whiteboards when you're finished. This will help me see how much you understood about our 'Value of Digits' lesson today!"
(Collect whiteboards or observe responses as an exit ticket.)
Teacher: "Excellent effort today, mathematicians! Remember, the place truly determines the value. Keep practicing, and I'll see you next time!"
Activity
Value of Digits Activity Cards
Instructions: Cut out each card. In your small group, sort the cards into piles based on the value of the highlighted digit.
Card 1
2,345,678
Card 2
12,345.67
Card 3
9,876.54
Card 4
0.12
Card 5
50,000,000
Card 6
4.32
Card 7
789.01
Card 8
1,000,000.00
Card 9
300,000
Card 10
1,234.56
Card 11
0.9
Card 12
567,890.12
Card 13
8,000,000
Card 14
12.3
Card 15
999.99