The Power of One: A Grade 4 Math Adventure
Materials Needed
- Paper and pencil
- Colored pencils or markers
- Index cards or small pieces of paper
- Coins, buttons, LEGO bricks, or other small objects for counting
- A ruler
- Optional: calculator, timer, or digital drawing tool
Learning Objectives
By the end of the lesson, the learner will be able to:
- Explain how the digit 1 changes value depending on its place in a number.
- Read and write numbers containing the digit 1 in standard, word, and expanded form.
- Use multiplication by 1 and addition of 1 to solve real-world problems.
- Create and explain a number puzzle involving the digit 1.
Success Criteria
The learner is successful when they can:
- Correctly identify the value of 1 in at least four different numbers.
- Write at least three numbers in expanded form.
- Solve at least four out of five practice problems correctly.
- Explain their thinking using words, drawings, or equations.
Introduction: The Mystery of One
Hook: Show or write these numbers: 1, 10, 100, 1,000.
Ask:
- What do all these numbers have in common?
- Does the 1 have the same value in every number?
- How can one small digit represent 1, 10, 100, or 1,000?
Explain the learning goal:
Today we will investigate the surprising powers of the digit 1, use it in real-life math, and design our own number puzzle.
Body
I Do: One Digit, Many Values
Write the number 1,111. Explain that each 1 has a different value because of its place:
| Digit | Place | Value |
|---|---|---|
| 1 | Thousands | 1,000 |
| 1 | Hundreds | 100 |
| 1 | Tens | 10 |
| 1 | Ones | 1 |
Model the expanded form:
1,111 = 1,000 + 100 + 10 + 1
Model two more examples:
- 4,125 = 4,000 + 100 + 20 + 5; the 1 is worth 100.
- 7,016 = 7,000 + 10 + 6; the 1 is worth 10.
Quick Check
Ask the learner to state the value of the digit 1 in each number:
- 219
- 1,305
- 6,140
Expected answers: 10, 1,000, and 100.
We Do: Place-Value Detective
Write these numbers on separate cards:
18, 81, 105, 1,250, 4,016, 7,100
Work together to complete the following steps:
- Choose one number.
- Circle the digit 1.
- Name the place of the 1.
- State its value.
- Write the number in expanded form.
Example:
1,250 has a 1 in the thousands place. Its value is 1,000. Expanded form: 1,000 + 200 + 50.
Think-Pair-Share Option
The learner thinks about this question, explains an answer aloud, and then checks the reasoning with a parent, tutor, sibling, or learning partner:
Why is the 1 in 1,250 worth more than the 1 in 81?
We Do: The Rule of Multiplying by One
Explain that multiplying a number by 1 keeps the number unchanged because one group of that number is still the same amount.
- 6 × 1 = 6
- 23 × 1 = 23
- 405 × 1 = 405
Use objects to demonstrate: make one group of 7 buttons. Count the buttons. There are still 7 buttons, so 1 × 7 = 7.
Quick Check
Solve mentally:
- 9 × 1
- 1 × 34
- 512 × 1
Answers: 9, 34, and 512.
You Do: The One-World Challenge
Complete the following problems independently. The learner may use drawings, objects, equations, or a calculator to check work.
- What is the value of 1 in 3,145?
- Write 1,208 in expanded form.
- Write 4,000 + 100 + 30 + 1 in standard form.
- Solve: 76 × 1.
- A library has 1,245 books. A new shelf holds 1 group of all the books. How many books are on the shelf?
Answers
- 100
- 1,000 + 200 + 8
- 4,131
- 76
- 1,245 books
Hands-On Application: Design a Number Puzzle
Create a puzzle using the digit 1. Choose one of these formats:
- Place-Value Puzzle: Write a number containing at least three 1s and ask the solver to identify each 1’s value.
- Number Riddle: Give clues such as, “I am a four-digit number. My thousands digit is 1. My tens digit is 1.”
- Real-Life Challenge: Write a shopping, building, travel, or collection problem that uses multiplication by 1.
- Creative Poster: Design a poster showing how the value of 1 changes in different places.
Include:
- A clear question or challenge.
- At least one number containing the digit 1.
- A solution or answer key.
- A short explanation of the mathematical thinking used.
Real-World Connection
Discuss examples of how the number 1 appears in everyday life:
- One dollar can be represented as 100 cents.
- One kilometer equals 1,000 meters.
- A recipe may need 1 cup of an ingredient.
- A store may sell one item for $10 or $100.
- One group of objects has the same number of objects as the original group.
Ask the learner to choose one example and explain how the value of 1 is being used.
Differentiation and Choice
Support for Learners Who Need More Practice
- Use a place-value chart with ones, tens, hundreds, and thousands columns.
- Build numbers with objects grouped into ones, tens, and hundreds.
- Begin with two- and three-digit numbers before using four-digit numbers.
- Allow the learner to explain answers orally instead of writing every step.
Extension for Learners Ready for More Challenge
- Find a number in which the digit 1 has a value of 10,000.
- Create a number using four 1s that is greater than 5,000.
- Investigate why any number multiplied by 1 stays the same.
- Write and solve a multi-step word problem involving the number 1.
Assessment
Formative Assessment
- Listen to explanations during the Place-Value Detective activity.
- Check answers during the quick checks.
- Ask the learner to explain why the same digit can have different values.
- Observe whether the learner can connect equations to objects or drawings.
Summative Assessment
Ask the learner to complete this exit challenge without assistance:
- In the number 6,121, identify the value of each digit 1.
- Write 2,019 in expanded form.
- Solve: 1 × 638.
- Explain in one or two sentences why multiplying by 1 does not change a number.
- Show one way the number 1 is useful in everyday life.
Simple Rubric
| Skill | Developing | Successful | Advanced |
|---|---|---|---|
| Place value | Identifies some values with help | Correctly identifies the values of the 1s | Explains clearly why position changes value |
| Expanded form | Needs reminders or examples | Writes expanded form accurately | Creates and explains complex examples |
| Multiplication by 1 | Uses a model or prompt | Solves accurately and explains the rule | Applies the rule in a multi-step problem |
| Number puzzle | Includes some required parts | Creates a clear puzzle with a correct answer | Creates a challenging, creative puzzle and explains the strategy |
Conclusion: Tell What You Learned
Return to the opening numbers: 1, 10, 100, and 1,000.
Ask the learner to complete these statements:
- The digit 1 can have different values because __________.
- In the number __________, the 1 is worth __________.
- When I multiply a number by 1, __________.
- One way I use the number 1 in real life is __________.
Finish by having the learner present their number puzzle or poster. Celebrate the idea that one digit can have many different jobs depending on where it stands.
Optional Follow-Up Activity
Go on a “One Hunt” around the home or neighborhood. Find five examples of the number 1 in prices, clocks, labels, measurements, books, signs, or recipes. Record each example and explain what the 1 means in that context.