There are LOTS of different visuals you can show kids, but there are two in particular that are extremely powerful. In this video I talk about them and how they connect to visuals early on in math and even later in mathematics.
Learn to LOVE Teaching Math
The stickers on the unifix cubes to move from cubes to number path is SO simple, yet SO GENIUS!!!! Love it!
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In this video you noted that students need to recognize that bar models and number lines for example represent the same thing. When I’m using 10-frames and Rekenreks with my students, I have often wondered if they understand that these 2 different models really represent the same thing too. I’m not sure how to help them connect these two ideas. Any ideas??
I’m so glad you are thinking about this. So once kiddos get comfortable with a particular representation then I like to encourage the connections between that and another representation. So, take activities where you normally would just use one representation and now use two. For example, let’s say you are doing a Quick Images thing with ten frames, you flashed an amount and you ask the kids “How many did you see?”…instead flash the amount with the ten frame and then have them make that amount using their rekenrek. Anytime you can show it with one representation and have the kiddos show the other representation will help build this. Make sure you are asking questions like “So how are these two the same? How are they different?”
So, am I doing a dis-service to students when they are drawing their amounts in a ten-frame format? For example: If Jack has 4 marbles and he gets four more, they will draw five circle on top, then three circles on the bottom.
I don’t think it’s a ‘dis-service’ but I would want the child to see the original 4 and 4 that connect with the problem. If the child creates that ten frame drawing and can tell you “here’s the 4 he had and here’s the 4 he got” then no worries. But my guess is that if they weren’t taught to fill a ten frame with the top row first, they would most likely put the 4 in the top row and then the 4 he got in the bottom row.
Once again, awesome information! I especially like your explanation regarding the importance of equivalent fractions represented on a number line. It certainly is more “black and white” than showing it as sets. My fourth grade RtI students struggle with this concept. Playing Marilyn Burns “Uncover 2” fraction game has also helped solidify this concept as well.