In this uncertain time of educating kids, teachers and parents are struggling with how to provide math instruction to kids. One thing that I want to encourage all educators to do, yes, that’s teachers and parents, is to make math visual for the kids.
I’m Christina Tondevold, The Recovering Traditionalist, and today we’re going to take a look at The Importance of Visuals in Math. In our quest to build our math minds, so we can build the math minds of our students.
Watch the video or read the transcript below:
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Watch all the videos in this Fluency Series:
Video 1: Fast Does Not Mean Fluent
Video 2: Helping Kids Learn Their Math Facts
Video 3: Math Experiences That Build Fluency, Not Memorization
Video 4: Students with Math Fluency
Video 5: The Importance of Visuals in Math (This Video)
Video 6: The Root of Math Fluency
**The webinar mentioned in this video is over but get your FREE Fluency starter kit below. Requesting the kit will also sign you up to be notified of any future webinars.**
In reading, we really encourage kids to create a visual image as they’re reading. Like that’s a sign of a good reader, they’re able to comprehend what they’re reading and use it to basically recreate that story in their mind. But in math, kids are pushed into the symbols way too quickly. If you were to ask a random person like not an elementary teacher, to close their eyes and picture nine, most likely the image that they have in their mind is just the digit 9. They don’t have an actual image of a quantity of nine. But if you ask that same person to close their eyes and picture a cat, they actually have an image of a cat and not just c-a-t.
So in this video, I’m going to show you why that visual picture of nine, or any number, is so important. I’m going to hop over to my screen because I want you to be able to see the visuals, not me.
Visualizing Addition
All right, let’s get started. So without a visual, first of all, it just doesn’t give us much about a number. So if I want to know something about 9, without a visual of what 9 looks like, it really doesn’t tell me a whole lot. And then if I had to add 7 to it, then I’m really at a loss at how to do that, except just memorizing a fact.
So when we add in a visual, it can help us really be able to visualize the strategies like this, where we want kids to change the 9 + 7 into thinking about it as man if you just moved one over, it would be 10 + 6. But when we say those things if they don’t have an actual visual to move some over, it really makes no sense.
So we have started to implement visuals like this, using a 10 frame to help kids be able to visualize what 9 looks like, and what 7 looks like and then use that to help them figure out a way to solve what 9 + 7 is. So this idea of just moving one over, becomes a whole lot easier for them to visualize how it becomes 10 + 6 now, when they actually have visuals to use.
The Visual Matters
So we also do need to be careful about the visuals we use because a lot of times we will have kids just count out amounts and then we ask them to add them together.
But without some kind of a system when they count what ends up happening when kids need to count how many here, they will count one by one by one. They end up counting 1, 2, 3, 4, 5, 6 to see how many are in that set. Then they’ll count out the 7 in the other set and then they have to come back and count them all one by one to figure out how many there are.
Instead, if we take those things and put them into a 10 frame, we increase the likelihood…and did you hear that?? We’re increasing the likelihood, it’s not automatic that a kid is absolutely going to see this as 6 instantly without needing to count and 7 on the bottom without needing to count. You’re still going to have kids who will need to count. But you’re increasing the chance, the opportunity for kids to not have to count and that they can build some relationships here that then help them when they go to add.
So if I asked a kid how many total cubes there were in this picture, some kids may still count. But this is what one kid showed me.
We have this on an iPad, and we asked them to figure out how many, and he drew around these, and as he was talking, he said, “Well, if I put the four down here, with the 6 on the top, I know that will give me 10 and I have three leftover, so it makes 13.” Those strategies that we’re wanting kids to be able to do come a little more naturally when they have visuals to help them out.
Here’s another example of a visual, it’s the same thing again, you could count to figure that out, but a lot of kids use this rekenrek and they know that it’s 6 on the top 7 on the bottom without needing to count. But how they then determine the total is again up to them and the visual does matter.
This visual elicited a different strategy from the same kid that I showed you on that last screen. This time when it was set up like this, the kid underlined the 6 at the top and he goes “Well, I know that’s 6” and then drew the line down and he goes “that bottom one has one more. So it’s 6 + 6 + 1 more.”
Here’s another example of a visual, it’s the same thing again, you could count to figure that out, but a lot of kids use this rekenrek and they know that it’s 6 on the top 7 on the bottom without needing to count. But how they then determine the total is again up to them and the visual does matter.
This visual elicited a different strategy from the same kid that I showed you on that last screen. This time when it was set up like this, the kid underlined the 6 at the top and he goes “Well, I know that’s 6” and then drew the line down and he goes “that bottom one has one more. So it’s 6 + 6 + 1 more.”
Visualizing Multiplication
They need that visual of the actual quantities, even as they move into multiplication. 7 x 6 is one of the harder facts, even for adults. And oftentimes, we want to get kids to an easy way to think about multiplying by 7: think about it as multiplying by 5 and then multiplying by 2 and adding those together. That’s an awesome way to multiply anything times 7. But it doesn’t come naturally and a lot of kids don’t know where those numbers came from.
So instead we can include a visual to help them out.
This makes it a little bit more clear of how they can see 7 groups of 6, and how it can be broken up into the 5 groups of 6 on the top, and then the 2 groups of 6 on the bottom, and that if we add those together, it will actually give us the 7 groups of 6. But without these visuals, kids are reliant upon memorization, or they often will go back to counting or skip counting when it comes to multiplication.
Instead, we want to encourage them to create these visual images to help them come up with those derived fact strategies. No matter how hard we try to teach these derived facts strategies to kids, they won’t become second nature to them until they have visuals to tie them to.
So again, if you want more information on this, and information on how to build fluency for your students, I’d love for you to come join me in the free webinar, 3 Keys to Building Elementary Students Math Fluency. I hope that this video helped you build your math mind so you can build the math minds of your students. Have a great day.
**The webinar mentioned in this video is over but get your FREE Fluency starter kit below. Requesting the kit will also sign you up to be notified of any future webinars.**
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