| Full lesson | Create for a teacher a set of content for giving a lesson, beginning with the lesson plan. Each new block of materials must begin with an H1 heading (other subheaders must be H2, H3, etc). When you describe required pictures, write those descriptions in curly brackets, for example: {A picture of a triangle} |
| Which subject | Mathematics |
| What topic | represent the value of the digit in decimals through the thousandths using expanded notation and numerals |
| What length (min) | 30 |
| What age group | Year or Grade 5 |
| Class size | 20 |
| What curriculum | |
| Include full script | |
| Check previous homework | |
| Ask some students to presents their homework | |
| Add a physical break | |
| Add group activities | |
| Include homework | |
| Show correct answers | |
| Prepare slide templates | |
| Number of slides | 5 |
| Create fill-in cards for students | |
| Create creative backup tasks for unexpected moments |
Representing the Value of Digits in Decimals through the Thousandths using Expanded Notation and Numerals
Year/Grade 5
Mathematics
20 Students
| Step Number | Step Title | Length (minutes) | Details |
|---|---|---|---|
| 1 | Introduction to Decimals | 5 | Introduce the concept of decimals and their importance in everyday life. Discuss place values of decimals. |
| 2 | Place Value Review | 5 | Review whole number place values and extend understanding to decimals, focusing on hundredths and thousandths. |
| 3 | Introducing Expanded Notation | 10 | Explain expanded notation for decimals, demonstrating how to break down numbers into their place value components. |
| 4 | Guided Practice | 5 | Conduct interactive practice with the students. Work through examples together, converting standard and expanded forms. |
| 5 | Independent Practice | 3 | Distribute worksheets for students to complete on their own, allowing them to apply what they have learned. |
| 6 | Homework Assignment | 2 | Review the homework assignment instructions, ensuring clarity on tasks to be completed at home. |
| 7 | Conclusion and Q&A | 5 | Summarize key points from the lesson. Open the floor for any questions-related topics discussed. |
This lesson aligns with the Common Core State Standards for Mathematics, focusing on understanding decimal place value and representation in expanded forms.
Assign relevant practice problems on expanded notation and decimals to reinforce the lesson concepts.
Feel free to adjust any sections to better fit your specific teaching style or objectives!
“Good morning, class! Today, we are going to dive into the world of decimals and understand just how important they are in our daily lives. Think about all the things we measure—money, time, distance. Decimals help us express those measurements more precisely. Who can tell me what they think a decimal is?”
Pause for student responses.
“Great answers! Now, let’s talk about something called place value. Can anyone remind us what place value means, especially in whole numbers? Yes, very good! Each digit in a number has a specific place. Today, we’ll extend that understanding to decimals. Let’s observe the place values for decimals—tenths, hundredths, and thousandths.”
“Now that we have an understanding of whole number place values, let’s expand that to decimals. On the board, I’m going to write the number 3.456. Can anyone tell me what each digit represents? Yes, the ‘3’ is in the units place, the ‘4’ is in the tenths place, the ‘5’ is in the hundredths place, and the ‘6’ is in the thousandths place.
Let’s remember that as we move from left to right, each place value is ten times smaller than the one before. So, if I have 3.4, what do you think 3.45 is compared to it? Correct, it is a little larger because we are adding more value in the hundredths place. Now, with your partner, take a moment to look at some other decimal numbers and identify the value of each digit. I’ll give you two minutes.”
Allow time for partner discussion.
“Wonderful teamwork, everyone! Now, let’s discuss a different way to represent decimals—expanded notation. Expanded notation shows each digit multiplied by its place value. For example, in the number 2.473, how could we break that down? The ‘2’ is 2 ones, the ‘4’ is 4 tenths, the ‘7’ is 7 hundredths, and the ‘3’ is 3 thousandths.
So in expanded notation, we would write it as 2 + 0.4 + 0.07 + 0.003. I will demonstrate this on the whiteboard. As I write, think about how each part corresponds with the number.
Can anyone explain why we use expanded notation? Yes, it helps us see the value of each digit clearly! Let’s try one together—write down the number 5.309. How can we express that in expanded notation?”
Guide students through the process of creating expanded notation.
“Now that we have a solid understanding of expanded notation, let’s do some guided practice! I’ll provide a few examples, and I want you to work with me.
Let’s start with the number 7.216. Who can help break that down into expanded notation? Fantastic! Yes, that would be 7 + 0.2 + 0.01 + 0.006.
Now let’s try converting it back to standard form. If I say 5 + 0.3 + 0.04 + 0.002, what would that be in standard form? Yes, that’s right! It’s 5.342. Great job! I’ll write a few more on the board, and you can solve them with your neighbor.”
Provide several examples for interactive work.
“Excellent work, everyone! Now it’s time for some independent practice. I’m handing out worksheets that have exercises on expanded notation. Make sure you read the directions carefully! You have three minutes to complete these problems on your own. Go ahead!”
Distribute worksheets and monitor student progress.
“Now that we’ve wrapped up our practice, let’s talk about your homework. I’d like you to complete the assignment packet I’m providing. The homework will include a few problems that ask you to represent numbers in expanded notation and convert them back to standard form.
Make sure you have a clear understanding before starting! I’ll give you a minute to ask any questions about the homework assignment.”
Allow time for questions regarding the homework.
“To sum up, today we learned about decimals and how to express them in expanded notation. Remember, the value of each digit is crucial! Does anyone have any questions about what we covered today?
Pause for questions and end with:
“Great job today, everyone! Make sure to practice your homework, and I look forward to seeing your progress on expanded notation. Have a wonderful day!"
What is a decimal? Provide an example in your explanation.
Define the term "place value" and explain how it applies to decimal numbers.
In the decimal number 4.672, what is the value of the digit '6'?
Write the decimal number 3.085 in expanded notation.
If a decimal is represented as 7 + 0.3 + 0.02 + 0.005, what is the standard form of this number?
Convert the decimal number 5.432 into expanded notation.
What place does the digit '3' occupy in the decimal number 2.346? Explain its value.
Write the following decimal numbers in expanded notation: a) 1.204 b) 6.789
For the number 8.091, identify the value of each digit.
Explain why expanded notation can be useful when working with decimals.
Convert the following expanded notation back into standard form: a) 9 + 0.5 + 0.06 b) 3 + 0.4 + 0.003
Describe how the value of each digit decreases as you move from left to right in a decimal number.
Provide a real-life example where decimals are used to express quantities more accurately.