How to Differentiate and Scaffold Math Centers Part 3 (EP12)

How to Differentiate and Scaffold Math Centers (Part 3)

Hey there, and welcome to another episode of Elementary Math Chat. Today’s episode is the third and final episode in this series about differentiating and scaffolding math centers. We have certainly covered a lot in this series. 

But you know what, I think this part might be your favorite because today I’ll be sharing specific examples of scaffolded and differentiated question sets, and I’ll be doing this for third, fourth and fifth grade.

So, if you teach a different grade level, I think you’ll still find some of these ideas applicable because a lot of these skills are taught over the course of several grades. So, I really think there’s a little bit in this episode for everyone.

Before we get started, I want to let you know that there is a free guide you can download in the show notes. It includes all of the examples that I’ll be talking through today, and it also includes information from the last two episodes as well. So, I think this will be a really great resource for you to have moving forward, and it’s free. So, you can’t ask for anything better.

So, let’s get started with third grade. Now you’re gonna hear me refer to these questions as red, yellow, or green, and if you listened to last week’s episode, you might remember that these colors matched a traffic light self-assessment that I gave my students. So, red questions are for my strugglers, yellow are for those right on track, and green are my challenge questions.

The standard I chose in third grade is to determine the unknown number in a multiplication or division equation relating three whole numbers within 100. An example of this could be 9 times n equals 45, or a division example would be 25 divided by n equals 5, and they have to solve for that unknown number.

I always plan my red level first. So, let’s go ahead and start at red. This is where you’re going to give them more support. So, you could provide them a multiplication chart or just some sort of math facts reference page, and this could be your scaffolded support.

When you’re choosing questions for this level, I would keep it pretty basic. So, have them start off with multiplication, since that’s a little bit easier, and then move towards solving for an unknown in division. There’s your differentiation piece.

So, whenever they come to you and they are at a red level, they’re getting a little more support, their numbers might be a little easier, but they’re still working with that standard.

All right, let’s move up to yellow. In your yellow level, they should not have a multiplication chart. So, you’re going to remove that support, which remember is the goal of scaffolding. We want to take it away as they get better and become more proficient. And then questions at this level should include both multiplication and division because that is the expectation for this standard.

And then finally, for your green level, these questions should include both multiplication and division, and they also can include four numbers instead of three. So, adding that extra number is going to make this a little more challenging for them.

In fact, if you look at this example in the handout, you can see how I took the exact same question and made small adjustments to the level of support and then also the level of rigor to create these three sets of questions.

For example, I took the problem 9 x n = 45, and I changed it to 3 x n x 3 = 45. Same skill just a little more challenging.

The second third-grade standard we’re going to look at is adding and subtracting within 1000 using strategies based on place value. Once again, starting at your red level, you could provide a place value chart to help them line up their numbers. That’s going to be your scaffolded support.

And by the way, I used a place value chart all the time, not just when teaching place value. I used it for rounding, adding and subtracting, multiplying and dividing. It is a really helpful resource because a lot of our strategies are based on place value, so make sure you have a really good place value chart.

Now going back to your red questions, you’ll want these problems to only be written vertically since that is a little bit easier. But remember, we never want them to stay red. But by giving them the supports in the red level, they are likely to move up to yellow pretty quickly.

So, for your yellow questions, these should be written both vertically and horizontally, and you’ll also want to include zeros. So, this level is a little more challenging. They’re gonna have to rewrite the horizontal problems on their own, and they’re gonna have to subtract when there are zeros involved. But that’s the third-grade expectation. So, those are perfect for yellow questions.

And then finally, for your green level, you can present the original problem in either word form or expanded form. My example in the handout has them subtract the value of 400 + 70 + 5 from the value of 3000 + 40 + 6. So, they first have to change the expanded form back to standard form, and then they have to know how to write the larger number on top.

You can also extend this to four-digit numbers, I think both of these are great ways to differentiate this skill. So, that takes care of third grade.

Let’s move on to fourth grade. I’m going to start with the multiplication standard, and I chose specifically the partial product method with one-digit multiplication for this example. This is a tough skill for them at first. So, you’ll notice that I have a little more support in the red level than I normally do, and I even have support within the yellow level.

I actually made a whole set of task cards with these three levels that I’m about to describe, and I will have those linked in the show notes if you want to take a look at them. And again, they include both scaffolded and differentiated supports between those three levels.

The first level I used for my red questions, and they are written within a place value chart. That’s going to help them line up their digits because that is an extremely important part of this strategy. And then they also have color-coded boxes for the partial products. So, this is going to help them know where to write the digits, and how many digits each partial product will be, and that’s really helpful because often in this strategy, they either leave off zero or they have too many zeros. So, the color-coded boxes are really helpful for that.

Also, in this first level, the multiplication facts are very basic. I did not want them to spend two to three minutes trying to figure out what eight times seven was. So, I used pretty basic multiplication facts. You can see in the handout that the task card I used for the red example is 13 x 46, nothing really over five or six in this red level. So, there’s my differentiation.

The second level of task cards is what I used for my yellow questions. These questions still do have the place value chart there to help them line up their numbers just like the red level did, but they don’t have the color-coded boxes. So, they still have a little guidance just because this is a pretty challenging strategy, but they don’t have any of the color-coded boxes, and then the multiplication facts are also a little more challenging.

The third level of these task cards is what I used for my green questions, and these questions don’t have a place value chart. They don’t have any color-coded boxes. They’re pretty much on their own, and they do include more challenging multiplication facts, like sixes, sevens, eights, and nines. So, that also made this level a little more challenging.

So, throughout these three levels, I am scaffolding with the support of the place value chart and the boxes, and then differentiating based on the difficulty of the multiplication facts.

For the next fourth-grade example, I chose the long division standard, and I’m going to use the standard algorithm for this example. You’ll notice these levels are very similar to the multiplication standard I just talked about. But instead of task cards, I used a long division work mat, and that helped me to scaffold and differentiate these questions.

I love work mats. I’m probably going to talk about them all the time on this podcast. They are such a great way to provide extra support, and so you’ll notice this work mat has three different levels of support.

The work mats for the red level include a place value chart, and they also have guided boxes to help them know where the numbers go. I mean, that’s kind of half the battle when you’re doing long division. So, those boxes are going to help with that.

Also in this level, when you create your problems, you want to make sure the division facts are very basic. So, my example in the handout is 89 divided by 3, so very simple.

The work mats for my yellow level still include a place value chart to help with alignment, but it does not have any guided boxes. You’ll also want to make sure these problems don’t always have a digit in the first place of the quotient. And then of course make sure your division facts are a little more challenging. So, include some of those trickier facts like 56 divided by 7, or 42 divided by 6. My example for this in the handout is 357 divided by 6, so a little more challenging than that first example.

And then finally, in green, no guidance is needed. They don’t need a work mat. They don’t need a place value chart. They can solve these all on their own.

But if you want to provide them with a few challenges in this green level, you can have students create and solve a division problem with certain requirements. I mentioned this in last week’s episode. For example, you can have them create and solve a four-digit by one-digit division problem that has an estimate of 700. However, each digit in the division problem must be unique. That means they can’t use something like 2800 divided by 5 equals 700. That’s way too easy.

So, they’ll have to think about estimation first, and then they’ll create a division problem that would get 700. You can even say that 700 has to be an overestimate, or 700 has to be an underestimate. That kind of takes it to a new level.

Another fun challenge you can do with your green level, or really, you can do this with anyone. But it’s called the loooooonnnnnggggg division challenge, and it sounds like exactly what it is. Your kids will love this, and the best part is that all you need to do is give them either computer paper or graph paper. Let them choose which one they want to use, and the goal for them is to create the longest division problem possible. The longer the better.

When I did this, we started out just doing this as a classroom challenge, and then we hung them in the hallway. And once we hung them up, then it turned into this entire fourth-grade challenge. We’d be walking down the hallway, and they’d look at each other’s problems, and they were like, whoa, wait a minute. Look at hers! She has one that’s five pages long. I guess I gotta take mine home and add to it so I can get 10 pages!

And the thing is, they would do that. They would come back with these gigantic long division problems. Some of them even worked on these during indoor recess if that tells you anything. 

Another thing I like about this is it will motivate students to learn long division because they’ll see how much fun the others are having with it, and they’ll want to join in and participate too. So, I really think you can make this available to anybody.

Now, if you do plan on hanging these up in your hallway, I recommend just capping it out once it hits the ground. Otherwise, you’re gonna have loose papers just hanging everywhere and it can look a little sloppy. I say that because one year we did that, and it was just a mess. It was a beautiful mess, but it was a mess.

All right, let’s move on to fifth grade. The first example I have is for evaluating expressions using the order of operations. So, your red questions can have a guided template or a work mat to help get them started, and you’ll also want the PEMDAS rules written out. So, what does the P stand for? What does the E stand for, and so on.

As far as the difficulty level, you’ll want to make your expression pretty basic. So, just two to three steps in this first level.

For yellow questions, you’ll still want to use the PEMDAS acronym, so make sure it’s visible. But you don’t need to list out what the acronym means. They can interpret what that means on their own. So, that would be your scaffolded support. And then for the differentiation, you’ll want your expressions to be three to four steps and also include brackets since that is the expectation for fifth grade.

I don’t believe they need to do exponents within the order of operations. You’ll have to correct me if I’m wrong, but I could not find any examples in fifth grade with exponents. All of that was in sixth grade. So, you’ll notice I have exponents in my green level.

So, let’s talk about green. There are a few ways you can differentiate this skill. One way is to have the expression presented in words. When I taught fifth grade, this was one of our standards. Changing the word form back to standard form within these expressions, and it was pretty challenging for them. So, I think they’ll really enjoy this challenge of changing the word form back into standard form and then evaluating the expression.

Now here’s a little tip for you. You can actually type the expression into chat GPT and it’ll translate it for you. I had to play around with it a little bit. What ended up working was giving them the prompt, write this expression in word form, and then I copied and pasted the expression at the end of the prompt.

My example in the handout is twelve more than the quotient of fifteen minus nine (that was in parentheses) and three. So, the 15 minus nine they would do first to get six, and then they would find the quotient of six and three, which would be two. And then 12 more than that would be 14. So, that’s really challenging and that takes the difficulty up a notch for sure.

Another way to differentiate is to include exponents like I mentioned before, and you’ll want these problems to be at least four steps. Four or five steps I think is good for green. And then I think this goes without saying, but in this green level, the PEMDAS acronym is not visible. They won’t need it. They’ll know how to interpret it and use it.

Let’s look at another fifth-grade standard. This one is comparing decimals to the thousandths place. I think the tricky thing with this standard is when the decimals are different lengths, like when one goes to the tenths place, and one goes to the thousandths place.

So, for red questions, you’ll want to make sure that these have the same number of digits, and you can also provide a place value chart for support.

For yellow questions, you won’t need a place value chart, and you also want to provide examples where the decimals are not the same number of digits. For example, have them compare 6.5 to 6.375. It’s also a little bit harder if these decimals are written horizontally. So, I would recommend doing that in this yellow level.

For green questions, the comparison statement can be written in different forms. So, you can write one decimal in expanded form, and then the other in word form, and they have to change them back to standard form before they compare.

You can also extend this to compare three or more decimals, which leads me to my next idea. You can give them scores from a sporting event and have them put those scores in order from first place to third place.

What’s neat about this idea is they’ll have to consider when you want a lower score, like in swimming or other racing events, and when you would want a higher score, like in gymnastics or figure skating. I love that these questions tie in that real-world connection, and it also gives them a little bit of challenge.

All right, well, that was my final example for today. Hopefully, these examples got your wheels turning as to how you can create scaffolded and differentiated question sets. And again, even if you don’t teach third, fourth or fifth grade, I think a lot of these examples that we went through you can also apply to your own grade level.

So, let’s go ahead and wrap up with today’s teaching tip of the week. This one is another techy tip that I have found to be extremely helpful, because sometimes I close a tab too soon, or sometimes it’s by complete accident. But if you do that there is absolutely no need to panic. So, here’s what you do.

Go to the tab bar at the top of your screen, and you’ll see a plus sign there. Now normally, when you click on that plus sign, it will open a new tab. But this time, you’re going to right-click on it. And when you do that, you’ll see an option that says reopen closed tab. So, if you click on that, it will restore the tab that you just closed. So, the next time you accidentally close the tab, there is no need to panic.

All right. Well, that is all for today’s episode. I hope you’ve enjoyed it. Have a great week, and I will see you next Tuesday.