Rekenreks 2

Hello there mathematicians, I hope you're having a delightful day today. You will need a pencil, your workbook or some paper, your imagination, your rekenrek and also these ten-frame cards. If you don't have these ones exactly, that's ok.

You can use other cards like it as long as you have the numbers represented on a ten-frame from zero through to twenty. If you don't have them yet, it's ok, we can start together and then later when we come to the game, you can go get those things. Ok, so you might have a rekenrek that you made at home or at school. It might look like this. It might look like something different. Today they help us.

We're going to use a rekenrek that's similar to that one but we made it on the computer. Ok, so mathematicians over to you to start thinking about what do you notice when we start playing with our rekenrek's today? Here we go. How many beads do I have? Two and how could I describe them? Yes, one way I could describe them is one and one. Is there another way I could describe two?

Uh-huh as double one. Two is double one. Ok. What about now? How many can you see? Four, and how can I describe four? Four is... You say it, four is... Oh yeah, some of you said two and two. Is there another way that I could describe four? Four is... Uh-huh double two. Ok, what about now? Yes, there are six and six is three and three. But I can also describe six as, yes double three. So I think we might have a working definition of the word double. A double describes two collections that have the same quantity; 'cause there's three at the top. That's one collection and three at the bottom. That's my second collection.

Let's see if that definition stays. How many beads are there now altogether? There are eight and I can see eight as four and four and that means there is four at the top and four at the bottom, which means eight is double. Eight is in fact double four.

Yeah, ok, what about now? Yes, you can see the pattern, ten and ten is five and five. Five at the top and five at the bottom. They are my two collections and they both have the same quantity. So I can describe five and five as double five which is ten. Aha ok, what about now? I have nine and nine is five and four. Ah, and I do have double four. Can you see that? And one more.I could also say double five and one less. But it's no longer a double, is it because there's not the same exact same, exact same amount in both collections. One has five, and one has four, or yeah, one has five and one had five and one was taken away to leave four. So it no longer is a double. Now I can think about this as an almost double. We call that an near double 'cause near double is almost a double.

It's like there's a little double in there and it's hiding. There's just one more or one less than a double. Yeah, ok, 'cause we can see that double four and one more. And we could also see the double five and one less. Ah, let's see. What about this one? How many beads are there now? Yes, there's the seven. And I can see the double three hiding in there. Double three and one more. And I can also imagine, yes, now I would have double four and one less.

Aha. ok, what about this one? Can you make this one on your rekenrek? Make the same so it matches. And how many beads are there that we have? Eleven and how could we describe eleven? Aha, it's double five and one more. What's another way that we could describe it as a double, or in relationship to a double? Aha! Double six and one less, 'cause you can imagine that other dot if it was there that bead and then it going away, ok.

You know when we were doing this I think I noticed something. Let's see if you noticed it too. That when we describe doubles we can describe them in one way, like ten is double five. That's one way. Eight is double four. But when we're talking about near doubles, we can describe them in two ways. Look, seven is double three and one more. Or, it's double four and one less.

Ah ha, nine. Yes, double four and one more. Double five and one less.

Ok, so here's our challenge today mathematicians. This is where you need your ten-frame cards. You need them cut up and in a pile and you need your rekenrek. And we're going to turn over a card on our pile and what quantity does that card represent?

Seven, yes, I can see five at the top and two on the bottom and seven is five and two. And now I'm, you're going to have to think about representing seven on your ten-frame as either on your rekenrek as either a double or a near double. Can you make it now on your rekenrek? Make a collection of seven as a double or near double. Ok, let's do it together.

So we know there's seven. And we might move across four because double four is eight. And get rid of one to be seven. Seven is a near double. You can make double four and take one away. Oh, you made it a different way. Yes, you could see the double three hiding in there and the one more to make seven. So we could also describe it as seven is a near double and you can double three and add one more.

Ok, move your beads back across. Let's turn over our next card. Oh, what quantity do we have here? One whole ten-frame and two more. And one, ten and two we rename. Yes, as twelve. Ok, can you can you make twelve on your rekenrek and represent it as either a double or a near double? Ah yes, let's have a look together. Did you have double six? Yes, twelve is a double. It is double six.

Ok, let's try one more together, ready? What quantity does this represent? Uh-huh it is nine 'cause there's one less than ten which is nine. Alright, and can we make nine as a double or near double on your rekenrek? Ah ha, did you think about it like this? Nine is double four and one more. Oh, you thought about it as nine is double, double five and take one away. Yeah, so again there were two ways to describe a near double.

Alright, mathematicians over to you to continue playing this game.

So what's some of the mathematics here? So a double is when there are two collections that have the same quantity. So double five and double three. A near double is almost a double. There's a double hiding in the number, you just need one more or one less. And you can describe near doubles in two ways. That's cool, isn't it? You can describe it like, seven as double three and one more. You could also describe it as double four and one less. What are two ways to describe nine, as a near double? Are you imagining? Good strategy, or you might even be making it on your rekenrek. That's a good strategy too. Yes, double four and one more or double five and one less. Ok, mathematicians until the next time we gather. Have a great day.