Conquering Place Value: Strategies to Help Students Thrive (EP8)

Conquering Place Value: Strategies to Help Students Thrive

Hey there, and welcome to another episode of Elementary Math Chat!

Today’s episode is my first content-specific episode, and we’re going to talk all about place value. We’re going to go through the most challenging lessons in that unit, and I’ll share my favorite teaching tips that helped my students overcome these challenging concepts along with a few activities you can do in your whole group lesson, as well as in small groups.

My focus will mainly be on fourth and fifth grade concepts since I believe third grade embeds their place value skills mainly within addition and subtraction. Except for rounding, I know that one is taught in isolation, and I will be talking a lot about rounding today.

Before we get into specifics, I want to talk about why I believe so many students struggle with place value. I actually have a theory about this, and I think it’s because it is always taught at the very beginning of the year.

Think about the beginning of the year from the perspective of a student. They are on information overload, and then on top of that, you probably don’t have your small groups up and running. I mean, I know I didn’t those first few lessons, and so they’re not getting the attention from you that they normally would.

And then from the teacher’s perspective, I always found place value challenging to teach because every single lesson had more than one skill embedded. It just felt like a lot of content to cover at the beginning of the year, when I was still trying to teach beginning of the year procedures and also still trying to get to know my students. S,o that’s my theory as to why I believe it’s so challenging for both students and teachers.

So, let’s get into the ways that we can help our students with these challenging concepts, and I’m going to start by talking about place value relationships. This is a huge focus for fourth and fifth grade, and it’s hard to jump into this lesson without building up to it. So, I broke this lesson down into two separate days.

On the first day I focused on reading large numbers and placing commas in the correct spot, along with value versus place value. I did find it helpful to start with reading numbers because a lot of students struggle with this. It’s a big leap from third grade where they don’t go past the thousands place to then go up to the millions place in fourth grade.

It can be a little boring to read numbers over and over, but you can make it a lot more interesting and exciting with what I call big number fun facts. Here’s one you can use about McDonald’s that I think your students will enjoy.

Did you know that McDonald’s sells roughly 4.1 million Happy Meals every single day? Now you’ll want to change that 4.1 million to be a number that’s close to 4.1 million, but you want it to be a seven-digit number because that’ll be the number that you practice reading. So, you could say McDonald’s sells 4,076,382 Happy Meals a day. They’re still practicing reading the large number, but they’re also learning a fun fact along the way.

Here’s another one you can use. Did you know that one acre of land may have anywhere from 50,000 to 1 million worms underground? So again, create a number in between and practice reading that number along with the fun fact.

Here’s one more fun fact you can use. Did you know that the average person has about 100,000 hairs growing on their heads? So, create a number close to 100,000 and practice reading that number. Isn’t this so much better than just reading random seven-digit numbers? You know, our students fourth and fifth graders, they’re not used to working with numbers this large. So, I like that it puts these large numbers into context.

As far as reading the numbers go, your students will struggle the most reading the thousands period within a large number. They seem to be able to start the number okay and end it, but they do get lost in the middle. It’s like they don’t make the connection that those three digits are read just like any other three-digit number.

One thing I did that helped with this was I put a box around one section of the number at a time, and I guess you call it the period of a number. I just think that’s a weird way of saying a group of three digits. But anyway, I would put it around those groups of three digits, and then I would move it down the number as we pronounced it, and that helped them see that they were only reading three digits at a time. 

I always told them If you can read a three-digit number, you can read a nine-digit number or an eight-digit number. So, that’s something you can try if you also have students struggle to read large numbers.

Let’s move on to value and place value. They will confuse the two topics. They’re so similar, but yet a little bit different. So, I recommend using a place value chart, as well as place value discs. These work well because they are labeled with the value of the digit, so they’re very visual for students. Once you’ve modeled the number, it’s super easy to see the difference between value and place value, and then you can practice writing both.

If you’re a fifth grade teacher, they do have place value discs with decimals on them. I had these but I never used them in fourth grade. I think they’re just better for fifth grade. They go all the way to the thousandths place. So, I think they would come in handy for you.

If you teach third grade, these discs will be helpful when you teach addition strategies because you can model the expanded form of the number with these discs. So, lots of different ways you can use them. I think they’re a must-have manipulative for upper elementary teachers.

So again, on day one I covered reading large numbers, placing commas in the correct spot, and value versus place value. The next day I covered place value relationships where one position is 10 times greater than the position to its right.

I began this lesson with a number talk, and that number talk focused on looking at the patterns in the value of a digit when you move it down the place value chart. They learn about patterns of multiplying by 10 in third grade, so I was just trying to help them connect the dots.

So, let’s say we were doing the number talk and we started with two. We would have 2, 20, 200, 2000, 20,000, etc. written on the board. Right away, they’re going to notice that there’s an extra zero that’s added on to each number.

So, then I asked them to think about what number we must have multiplied by that added that extra zero to the end. And they’re like, wait, I know this from third grade. Anytime you multiply by 10, you just add a zero to the end, and that will lead you into the discussion about multiplying by 10 and how our place value positions have that 10 times greater relationships.

Once they’ve discovered the patterns, then it’s much easier for them to identify the place value relationships within those large numbers, and that’s where you can take this next. It does seem like an easy concept. But since it’s brand new to fourth graders, it is going to take them some time to catch on. You just have to keep practicing with it.

I also found it helpful to teach them the word adjacent because those are the positions that have the 10 times greater relationship. If that word doesn’t make sense to them, then try using the word neighbor. I always told them the digits had to be twins. They had to be the same digit, and they had to be neighbors right next to each other.

I also recommend using a place value chart as you teach this lesson, as well as having students write the equations. So. let’s say you’re identifying that the four in the hundreds place is 10 times greater than the four in the tens place. You would write 400 = 10 x 40. It’s so hard for them in the beginning to have the 400 first. They’re so used to having 40 x 10 = 400, or 10 x 40. So practicing, that’s going to help reinforce this new way of thinking.

It also prepares them for multiplicative comparisons that come in the next unit. So, as you identify those 10 times greater relationships, it’s helpful to have them write the equation that matches as well.

Now, fifth graders are going to be aware of these patterns. But some will struggle when it comes to fractional relationships, like saying 50 is 1/10 of 500. You can simplify this process by starting with the phrase 10 times less, because that’s more like what they learned in fourth grade. So, you would say 50 is 10 times less than 500 and then move towards saying 50 is 1/10 of 500.

It’ll take them some time to get used to thinking about 10 times less and writing that smaller number first. So, get them comfortable with that and then incorporate the fractions.

The second place value skill I want to talk about today is rounding. This is a tough one I know. No matter what grade do you teach, you will have students who struggle with rounding. This is another skill I taught over the course of two days.

On the first day, I focused heavily on number lines, and I also kept my numbers to five digits or less. You’ll hear me talk a lot in the future about work mats, and I used one for rounding that made a big difference in this lesson. This is a free work mat that I offer, and I will have that linked in the show notes for you.

The work mat has a place value chart on it along with a number line, and these are two must-haves when it comes to rounding. It also has a spinner on it to make it more engaging, and this is great if you want to use it for a small group activity because they love anything that has a spinner on it. But you can also use this in your whole group lesson.

The biggest struggle they have is when they have to round in the middle of the number, specifically the thousands period. You can help them with this by having them solve a simpler problem first. Let’s say they are rounding a seven-digit number to the thousands place. Have them underline the thousands place and then put a box around the last four digits.

So, instead of focusing on a seven-digit number and where that would round to, they’re now thinking about a four-digit number and where that would round to. And again, they’re doing all of this on the work mat that has the place value chart and the number line, and these visuals will help them see that.

Once they’ve determined, for example, that 3,789 rounds up to 4000, they write down the numbers to the left, and just like that they have their rounded number. I will put a link to a reel that I did on Instagram that shows this in action in case you’re having a hard time following along.

What I like about it is that even though it’s a seven-digit number, they can still use a number line to help them determine where to round to. They would just write the simpler number on the number line instead of the larger number.

Now, it’s also important to put these rounded numbers in context, just like when we read those large numbers and put those into context. I would look into your textbook for that because they typically have a lot of word problems with rounding, and that’ll help put this all into context.

What I would do sometimes is take snippets of the word problems from the book, or I just typed them out on my slides, and then I used the work mat to solve them. I always found the book’s lessons were a little too guided and sometimes hard to follow when I was introducing a skill. 

So, I either had my students use a work mat, a dry erase board, or their math notebook for the lesson instead of working out of the book. In the end, we would usually complete a set of practice problems in their workbook. So, we did use it quite often, but just not for the lesson.

So again, day one was heavily focused on number lines. Then on day two, I introduced the rounding rules, and this time I went up to the millions place. I wanted them to feel comfortable rounding to any place value position along with kind of reverse thinking. If I gave them a number that was already rounded, they should be able to identify numbers that would round to that number.

Again, your textbook is a great resource for these types of word problems. But you can also look up examples yourself. Here’s an example of a question you could use about a Taylor Swift concert. About 70,000 fans attended a Taylor Swift concert on Saturday. Which three numbers could the exact attendance be? Then give them a list of five to six numbers to choose from.

Here’s another example you could use. The 1996 Summer Olympics in Atlanta had an attendance of about 5,320,000 people. What three numbers could the exact attendance be? And then again, give them five to six numbers to choose from. It seems like both district and state testing asked a lot of questions like this. So, you want to make sure to include those types of questions in your lessons.

As far as the other lessons in your place value unit, like three forms of a number, and comparing and ordering numbers, I feel like you can just spend one day on those lessons. They are pretty straightforward and easy to teach in one day.

Let’s move on to small group activities. Small groups are my favorite because this is often where the aha moments are made. One of my favorite tools to use for small groups is place value dice. What’s neat about these dice is they are labeled with the values of the number all the way up to the millions place, and there are some really great low prep and engaging activities you can do with these dice.

One activity you can do is to have them roll the place value dice and then put the number in standard form. So, they’re going from expanded form to standard form. As an extension, you can then have them write it in word form. So, that’s a great math center when you get to that lesson on three forms of a number.

Another simple small group activity involves that rounding mat I spoke about earlier, but if you combine it with the place value dice, they get that extra practice of going from expanded form to standard form for every single example. So, they would roll their number in expanded form, they would write it on the mat in standard form, and then they would spin the spinner to determine where they round to.

So far, I’ve mentioned quite a few resources for small groups and math centers. But if you need resources for your whole group lesson, I recently converted all of my lessons from SMART notebook that I used when I was in the classroom to PowerPoint so I can easily share them with other teachers. 

That was one of the first things I worked on when I left the classroom because I know so many teachers want to use resources beyond the textbook, but they just don’t have the time to create them on their own.

Now, the good news is that these PowerPoints are editable, so you can make any changes to the text that you need to. You can also add a BrainPOP video in there, or a workbook page. You can really make them your own.

There is also a non-editable version that you’ll receive, and that would be a really good one to send your sub since it is ready to teach. All you need to do is send them the PowerPoint. If you’re interested in checking out these PowerPoints, they will be linked in the show notes along with everything else that I discussed today. So, make sure you check those out.

All right, well, let’s go ahead and wrap up with today’s teaching tip of the week. Today’s tip is another one for your parent newsletter.

Whenever you begin to run low on a school supply, put this in your newsletter. I sent my newsletters out on Fridays, and anytime I put this in my newsletter, I often had what I needed by Monday. Just let them know what you’re running low on, maybe it’s glue sticks or dry erase markers, and that you would be so grateful for their donations. Most of the time they’re out shopping on the weekend anyway, so it’s a convenient time for them to grab a few extra things for your classroom.

Well, that is all for today’s episode. Thank you so much for joining me. Have a great week, and I will see you next Tuesday.