I always want to try to give some free information for all elementary teachers whether or not you take the online course. If you have been around for a while, you know that I believe that number sense is one of the key missing pieces for a lot of our students. Whether it’s in elementary or any grade level, the teachers that I talk to always say it’s the missing piece.

Watch the video or read the transcript below:

Here are links to products/activities mentioned in this vlog. (Some may be affiliate links which just means that if you do purchase using my link, the company you purchased from sends me some money. Find more info HERE about that.)

• Blank Fraction Tiles from ETA Hand2Mind (no longer available)
• Number Sense Routines in Grades 3-5 by Jessica Shumway

The Number Sense courses have been reworked and are now called The Flexibility Formula

Key Take-Away #1: Provide Experiences

My first top tip is provide experiences for your students. Let’s say that we are working on multiplication and I want my students to learn 4 x 5. There are many of us, who just learned 4 x 5 = 20. That’s it. Learn it, memorize, know it. Unfortunately for those of us who learned that way, if you were like me, we made no connections. We made no connections to other multiplication facts. We made no connections to our own real life.

The first thing I want you to do is provide experiences. Let’s say we’re working on multiplication. Here’s a little picture of where you could. If you’re you’re passing out papers, you can give it as a scenario. Make it into a math problem in everyday scenarios.

“If each kid at your table gets five pieces of paper, and there’s four kids at the table, how many pieces did your table get?”

Now you may have some kids who are sitting there counting one by one by one. They want to count every single piece of paper. That’s where kids start.

But you might also get some kids who will see some different groupings. And that’s one of the powerful situations is you have them talk about what they’re noticing in that situation. But, that wouldn’t come out if we just gave them four times five.

Let’s take a look at this picture again.

We might have some kids who will see like splitting it in half, and they know one group of five and another group of five will give them 10, and then they can just double that. They’re starting to build this cool relationship of when they are doing four groups of something, that’s like having two groups of something, and then we can double it to make the four groups of whatever we are needing.

You might have another kid who just sees the groups of five and has basically skipped counting by fives. All of these are viable strategies for doing multiplication but they may not have come out if we didn’t provide experiences for kids to see the multiplication in action.

Again, my first top tip is to provide experiences. Help your students see mathematical concepts in their everyday lives.

Key Take-Away #2: Use Manipulatives and Visuals

Now my second tip is to be providing lots of chances for kids to work with manipulatives and visuals. This is often known as the C-R-A continuum. It stands for Concrete to Representational to Abstract. Often times we jump straight to the abstract which is just symbols on a piece of paper. But, for our upper grades kids there is a lot of new stuff that they’re learning. They’re learning multiplication, they’re learning with fractions and they don’t have the number sense yet of those numbers to really be able to jump straight into operations.

We have to start with concrete materials. Let them physically see and feel these numbers. What does 1/3 look like, feel like? All of those things. It’s not just “⅓” on a piece of paper. You want to start out with doing things concretely. Here’s an image of using fraction tiles.

These are blank fraction tiles. These are one of my favorite tools, because it does not tell you the amount that each fraction is worth. The only reason that the yellow is a fourth is because it takes four of them to fill up the red one. It’s a fourth because the red is a whole. If the red wasn’t the whole, then that yellow one would be worth something more. It’s really cool. It doesn’t tell the kids that is a fourth. They have to figure out which one is the fourth based upon what the whole is.

Then when they start to go to add fractional amounts together. We’ve talked about it, I want them to model it, then they might start to put those two pieces together and they’ll put the 1/3 and the 1/4 together. But they still aren’t sure how much it is. The cool part about doing it with these tiles is they start to notice and wonder things like, “Man that looks a little bit bigger than a half. Does that make sense that it would be bigger than a half? Why should it be bigger than a half?”

There’s all this number sense that can happen just by giving them concrete materials. They’re not jumping straight to the answer because they can’t figure out the answer yet. They have to use the concrete manipulatives to help them because it’s not there yet and most of them can’t jump straight to “just get common denominators.” They need to understand why we need common denominators. The concrete materials help us out. They start to realize that if they had a different size, that could maybe tell how far along the whole it was. They start discovering that we need to find a fractional amount that could go all the way by using that same unit.

They got all of the same unit going across but then they’ve got to figure out what to call those units? What are the black ones called? How many of them did I use?

Being able to do things concretely helps kids move along and eventually get them to the abstract of just being able to add 1/3 and 1/4, and be able to find common denominators. But the concrete and the representations (the pictures) that they will draw along the way, things like this, help kids understand the abstract procedure of finding common denominators and then adding those together.

Alright, my second tip again is to start with concrete, move to having them do drawings, doing representations and then we move to the abstract concept of just the symbols and procedures that we are working on.

Key Take-Away #3: Develop a Daily Routine

Alright, tip number three is to make a point of doing things daily. Develop a number sense routine every single day. Whether that is providing a real life experience for your students every single day, or whether it’s having some kind of manipulative or visual every single day, you have to make this be part of your daily routine. Otherwise it’s going to go by the wayside. Textbooks assume that kids have these things and they’re not built into the lessons.

If you don’t make a point of doing it, just like everything, we get wrapped up into the daily things, we gotta get this done, we gotta get this done. You have to make a point of it being there every single day. It can be woven into your math time through everyday experiences, through using manipulatives and the visuals or you could have designated daily routines.

I would encourage you to check out Jessica Shumway’s book Number Sense Routines. There is one for grades 3-5 that just came out recently, and it’s fabulous.

Typically routines are done separately. Sometimes it can be part of your math time. Sometimes it’s just when you have five or 10 minutes that you have extra in your schedule.

As you’re planning things out this year, if you see that you have this five minute little block right here, then pick a number sense routine. There’s things like counting circles, doing a number talk, the book is full of activities and ideas that you can use to create that daily number sense routine.

Now if you want easy access to these three tips that I just gave you, click down below. There’s a little cheat sheet that will give you the links and the visuals that I use in this post for you to have easy access to, once you’ve kind of gone from here we tend to forget it. Print it off, have it there on your desk, somewhere where you can find it and look at it quickly.

Now, go help your students catch some number sense, and I hope that this has helped you build your math mind, so you can go build the math minds of your students.

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