While multiplying larger numbers involves more steps, it’s not necessarily more challenging. If you know the steps to organize the process. So, what strategies can we use to organize multi-digit multiplication?

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Millions Thousands Ones Hundred Millions Ten Millions Hundred Thousands Ten Thousands Hundreds Tens The most essential step to organizing your work for multidigit multiplication is having a solid understanding of place value. Writing large numbers is based around positional power. So the number 4,368 is a combination of 4 numbers represented by 4 digits. It’s the digit 8 representing 8 ones or just the number 8. The digit 6 which, because of its position to the left of the 8 represents 6 ten or the number 60. The digit 3, which is in the position to the left of the 10s, represents 3 hundreds, or the number 300. And the digit 4, to the left of the hundreds is in the 1,000s position equals 4 thousands or the number 4,000.

Let’s look at multiplying 368 by 7 Let’s look at multiplying 368 by 7. Because there’s 3 places in 368, we’ll be multiplying by 7- 3 times. So here’s how the area model works for larger numbers. We begin with a rectangle, writing our single digit on the left, vertical side. Knowing that we have 3 place values, we’re going to break this rectangle into 3 sections. I like our hundreds section to be slightly larger than our 10s and our 10s space to be slightly larger than our ones. This helps us in our next step. Now, we’re going to write out the number sentence that shows the amount of each individual section. So, our first section has 7 rows with 300 in each row totalling 2,100. Our 10s section has 7 rows with 60 in each row for a total of 420 and finally this says our ones section has 7 rows with 8 in each row for a total of 56.

Now, onto the guts of our lesson. First, enter large rectangle Now, onto the guts of our lesson. First, enter large rectangle. Next step, single digit on the vertical side. Now, we evaluate our 3 digit number. Before we expand it out, we’re going to divide our rectangle into 3 sections, one for each place value and we want to leave a little more room for our hundreds than for our 10s and just a little less for our ones. This gives us the visual reminder that each section’s product should be bigger than the next, plus it gives us a bit more room to work as the factors and products take up more space. On to finding the value of each part of our larger rectangle. I’m going to write out my number sentence in each section- Now, all that’s left to do is add the sections together. Now, personally, I like to work in descending order- largest first. So, I’m going to take 300 x 7 now when I take 60 x 7 it’s like I get a little extra reminder to line up the places. So, now I know that 7 groups of 360 is 2,520 and if I look back at my model, I can see that’s these 2 sections here.

We’re going to get to all of the specific steps in a moment but for right now, notice there are 3 separate parts to this problem. This means that you’ll be multiplying to find 3 products then adding those 3 products together. Mucho steps. Notice the difference in the way I’ve recorded the products under the multiplication column. Now look at the way I’ve done so under addition. See how I’ve lined up all of the places. It breaks my poor heart to see students correctly set up their problems, correctly multiply out all of the pieces, then get the whole thing wrong because they added a 5000 instead of 50 because they thought their 5 was in the 100s column. Don’t break your teacher’s poor heart because of this error.

We’re going to get to all of the specific steps in a moment but for right now, notice there are 3 separate parts to this problem. This means that you’ll be multiplying to find 3 products then adding those 3 products together. Mucho steps. Notice the difference in the way I’ve recorded the products under the multiplication column. Now look at the way I’ve done so under addition. See how I’ve lined up all of the places. It breaks my poor heart to see students correctly set up their problems, correctly multiply out all of the pieces, then get the whole thing wrong because they added a 5000 instead of 50 because they thought their 5 was in the 100s column. Don’t break your teacher’s poor heart because of this error.

The major mistake you want to avoid when setting up your area model is not respecting each digit’s position. Many students, when they’re first learning multi digit multiplication expand 4,368 like this: They write our their number sentences and they’re going through the correct process. The only problem is that they haven’t respected the position.

That 4, that’s no ordinary 4 That 4, that’s no ordinary 4. It’s in the position to the left of the 100s place, the 1,000s. That there’s a 4,000 not a 4. that 3- no ordinary 3- that’s in the 100s place- 300. That 6, that six is in the 10s place, that’s a 60. That 8, well okay, that’s an ordinary 8 but that’s because it’s in the place just to the left of the decimal point, the ones place.

And I hope you’re seeing that multiplying larger numbers isn’t more difficult because of the actual multiplication, it’s because there’s just more to keep track of. So my friends, stay organized- and share your tips for doing so.

LearnZillion Notes: --The “Guided Practice” should include 1 practice problem that targets the skill that was used in the Core Lesson. Use the same vocabulary and process you used in the original lesson to solve this problem. You’ll be making a video in which you solve this question using your tablet and pen, so all you need to do is write the question on this slide.

LearnZillion Notes: --The “Guided Practice” should include 1 practice problem that targets the skill that was used in the Core Lesson. Use the same vocabulary and process you used in the original lesson to solve this problem. You’ll be making a video in which you solve this question using your tablet and pen, so all you need to do is write the question on this slide.

LearnZillion Notes: --On the Extension Activities slide(s) you should describe 2-3 activities written with students as the audience (not teachers). Each extension activity should push the students a bit further with the lesson but in a different application or context. Each activity should be designed to take roughly 20-40 minutes. Teachers will likely display the slide in class and then assign an activity to a student or group for additional practice and differentiation. Ideally, these Extension Activities will be created such that a teacher can differentiate instruction by giving more difficult extension activities to students who have shown mastery of the lesson, and less difficult activities to students who are not yet proficient. --If you need more than one slide to list your extension activities, feel free to copy and paste this slide!

LearnZillion Notes: --On the Extension Activities slide(s) you should describe 2-3 activities written with students as the audience (not teachers). Each extension activity should push the students a bit further with the lesson but in a different application or context. Each activity should be designed to take roughly 20-40 minutes. Teachers will likely display the slide in class and then assign an activity to a student or group for additional practice and differentiation. Ideally, these Extension Activities will be created such that a teacher can differentiate instruction by giving more difficult extension activities to students who have shown mastery of the lesson, and less difficult activities to students who are not yet proficient. --If you need more than one slide to list your extension activities, feel free to copy and paste this slide!

478 = 400 + 70 + 8 A. 478 = 400 + 78 B. 478 = 470 + 8 C. 478 = 478 + 70 + 8 D. LearnZillion Notes: --”Quick Quiz” is an easy way to check for student understanding at the end of a lesson. On this slide, you’ll simply display 2 problems that are similar to the previous examples. That’s it! You won’t be recording a video of this slide and when teachers download the slides, they’ll direct their students through the example on their own so you don’t need to show an answer to the question.

3 275 + 70 5 200 x 3 = 825 70x3= 210 5x3= 15 A. 3 200 + 70 5 200 x 3 = 600 70x3= 210 5x3= 15 B. 3 270 + 5 270 x 3 = 810 5x3= 15 C. 3 200 + 75 200 x 3 = 600 75x3= 225 D. LearnZillion Notes: --”Quick Quiz” is an easy way to check for student understanding at the end of a lesson. On this slide, you’ll simply display 2 problems that are similar to the previous examples. That’s it! You won’t be recording a video of this slide and when teachers download the slides, they’ll direct their students through the example on their own so you don’t need to show an answer to the question.