| 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 | Multiples and least common multiples |
| What length (min) | 30 |
| What age group | Year or Grade 7 |
| Class size | 10 |
| What curriculum | abeka |
| 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 | 10 |
| Create fill-in cards for students | |
| Create creative backup tasks for unexpected moments |
Grade 7
Mathematics
Multiples and Least Common Multiples
30 minutes
10
Abeka
| Step Number | Step Title | Length | Details |
|---|---|---|---|
| 1 | Introduction to Multiples | 5 minutes | Introduce the concept of multiples with examples. Engage students by asking for multiples of 2, 3, etc. |
| 2 | Finding Multiples | 10 minutes | Guide students through identifying multiples of given numbers. Use a number line for visual aid. |
| 3 | Introduction to LCM | 5 minutes | Explain least common multiples. Illustrate with examples and differentiate between multiples and LCM. |
| 4 | Finding the LCM | 5 minutes | Teach two methods: listing multiples and using prime factorization to find LCM. Work through examples together. |
| 5 | Practice Problems | 3 minutes | Students will work on a few LCM problems independently on worksheets. Monitor and assist as needed. |
| 6 | Homework Assignment | 2 minutes | Assign homework related to LCM. Distribute handouts without asking for presentations. |
"Good morning, class! Today, we are going to explore an exciting topic in Mathematics: Multiples and Least Common Multiples, or LCM for short. To start, let's discuss what a multiple is. Does anyone know what a multiple of a number is? Yes, that's right! A multiple is the product you get when you multiply that number by an integer. For instance, the multiples of 2 are 2, 4, 6, 8, and so on.
Now, can anyone give me a few multiples of 3? Great! I heard a few of you say 3, 6, 9, and 12. Keep those answers in mind as we dive deeper into the lesson!"
"Now that we understand what multiples are, let's practice finding them together! I'm going to write some numbers on the whiteboard. Who can tell me the first three multiples of 4? Excellent! Yes, they are 4, 8, and 12.
Next, I want you to take this number line I've drawn and see if you can identify the multiples of 5. Remember, you'll just keep adding 5 each time.
Let’s jot them down together. What do you get? Yes! They would be 5, 10, 15, 20, and so on. Fantastic work, everyone! You are catching on quickly!"
"Moving on, let’s talk about Least Common Multiples, or LCM. The LCM is the smallest multiple that two or more numbers share. For example, what do you think the LCM of 2 and 3 is? Yes, it’s 6!
Now let's differentiate between just multiples and LCM. While multiples can go on forever, the LCM is the smallest number that appears in the multiples of each number. Can anyone tell me why it's important to find the LCM? It helps in problems involving fractions, ratios, and more."
"Now, let's learn two methods for finding the LCM. The first method is to list the multiples of the numbers involved. For instance, let's find the LCM of 4 and 6. What are the multiples of 4? That’s right: 4, 8, 12, 16, and so on. And what about 6? We have 6, 12, 18, and so forth.
What’s the smallest number that appears in both lists? Yes! It’s 12. So, the LCM of 4 and 6 is 12.
Now, let’s move on to the prime factorization method. Can someone remind me what prime factorization is? Great! It involves breaking numbers down into their prime factors. So, let’s break down 12 and 18.
12 is 2 x 2 x 3 and 18 is 2 x 3 x 3. The LCM will be the highest powers of each prime factor present. Can anyone help me find that? Exactly! It gives us 2² x 3², which equals 36.
Fantastic job, class! You are really getting these methods!"
"Now it’s time for you to try some problems on your own! I’m giving you some worksheets where you will practice finding the LCM of various sets of numbers.
Please take about 3 minutes to work on these independently. I’ll walk around the room to assist you if you have any questions during your practice. Remember, focus on both methods!"
"Great work on your practice problems! For homework, I’d like you to complete a new set of LCM problems. I will hand out the assignment now. Please remember that while I’ll be checking your homework, you won’t need to present it in front of the class tomorrow."
"To wrap up our lesson today, let's recap what we covered. We began by discussing what multiples are, then identified them, before moving on to least common multiples. Remember, the LCM is the smallest number that both multiples share.
Do you have any final questions before we end today's lesson? If not, fantastic! I’m really proud of all the hard work you’ve put in today. I look forward to seeing how you do on your homework!"
| Slide Number | Image | Slide Content |
|---|---|---|
| 1 | {Image: A classroom with students} | - Introduction to Multiples |
| - Definition of a multiple | ||
| - Examples: Multiples of 2 and 3 | ||
| 2 | {Image: Whiteboard with numbers} | - Finding Multiples |
| - First three multiples of 4: 4, 8, 12 | ||
| - Identify multiples of 5: 5, 10, 15, 20 | ||
| 3 | {Image: LCM illustration} | - Introduction to LCM |
| - Definition of Least Common Multiple | ||
| - Example of LCM of 2 and 3: It’s 6! | ||
| 4 | {Image: Two lists of numbers} | - Finding the LCM |
| - Listing multiples of 4: 4, 8, 12 | ||
| - Listing multiples of 6: 6, 12, 18 | ||
| - LCM of 4 and 6 is 12 | ||
| 5 | {Image: Prime factorization illustration} | - Prime Factorization Method |
| - Breaking down numbers: 12 = 2 x 2 x 3 | ||
| - Breaking down numbers: 18 = 2 x 3 x 3 | ||
| - Highest powers for LCM: 2² x 3² = 36 | ||
| 6 | {Image: Students working on worksheets} | - Practice Problems |
| - Practice finding LCM alone | ||
| - Focus on both methods | ||
| 7 | {Image: Homework assignment sheet} | - Homework Assignment |
| - Complete a set of LCM problems | ||
| - No presentation required for tomorrow | ||
| 8 | {Image: Clock ticking down} | - Closure |
| - Recap of Multiple and LCM concepts | ||
| - Encourage final questions | ||
| 9 | {Image: Happy students with thumbs up} | - Teacher's pride in student’s hard work |
| - Look forward to homework findings | ||
| 10 | {Image: Open book on a desk} | - Next Steps |
| - Prepare for further lessons on fractions | ||
| - Encourage practice outside of class |
What is a multiple? Provide an example with the number 5.
List the first five multiples of the number 7.
Calculate the first ten multiples of the number 9.
What are the multiples of 12? List at least five of them.
Define Least Common Multiple (LCM) in your own words.
Find the LCM of the following pairs of numbers:
Using the listing method, determine the LCM of 3 and 9.
Apply the prime factorization method to find the LCM of 15 and 24. Show your work.
Why is finding the LCM important in mathematics? Provide two scenarios where LCM is used.
Create a number line for the multiples of 6 and identify the first five multiples.
If two people are skipping rope at the same time, one every 4 seconds and the other every 6 seconds, how many seconds will it be before they are skipping together again?
For the numbers 14 and 35, what is the LCM? Show how you found your answer using both the listing and prime factorization methods.
Explain a situation in real life where you might need to use the LCM.
Solve the following: What are the first three multiples of 16? Then, find the LCM of those multiples.
Challenge: Create a problem for your classmate involving finding the LCM of two numbers, and write down the solution.