Modeling and counting four and five. In this video, we’ll learn how to represent one object by another to help us count four or five objects. Here are some fish. How many are there? We could count the fish by pointing to each one. And as we point to them, we could say each new number. Remember which number we start counting from, one, two, three, four. The last number that we said is the number that there are. There are four fish. And these four fish are neatly in a line.
But we all know fish like swimming around. How many fish are there now? One, two, three, four. Even though they’ve moved, there are still four fish. We counted these objects or fish by pointing at them. Now, let’s have a go at representing a number of objects using cubes.
Count the cats. Show the same number using cubes.
In the picture, we can see a row of cats. And the first thing the question asks us to do is to count them. The question then tells us to show the same number using cubes. How can we make sure that we have the same number of cubes as cats. What if we count each cat. And each time we say a number, we put a cube underneath it, one, two, three, four. We used one cube for each cat. We counted four cubes, so we know there must also be four cats.
Underneath the picture, we can see three groups of cubes. Which one shows us how to represent the number of cats, which we said was four? In the first group, there are one, two cubes. This isn’t the right answer. The next group contains one, two, three cubes. This isn’t the same as four either. Let’s check the last group, one, two, three, four cubes. We counted four cats. To show the same number using cubes, we need to use four cubes. We used cubes to help us answer that question. But we don’t have to use objects. We could use a pencil and paper instead. Let’s have a go.
Count the given oranges. Show the same number by drawing dots.
In this problem, we can see a picture of some oranges. And the first thing we’re told to do is to count them. After we’ve counted them, we’re then told to show the same number by drawing dots. And we can see we’ve got three possible answers to choose from. But we’ll come to those in a moment. To begin with, let’s get counting these oranges. Now we need to make sure that we count each orange only once.
How could we make sure we don’t miss any out and we only count them once? Because these are pictures of oranges, what if we put a counter on top of each picture as we say each number, one, two, three, four, five. There are five oranges. Now we need to show the same number — that’s five — by drawing dots. Let’s count as we go, one, two, three, four, five, five dots to match our five oranges.
Now, which of our three possible answers shows the same number of dots? One, two, there are only three dots in the first group. One, two, three, four, five, there are five dots in the second group. We counted five oranges. To show the same number by drawing dots, we needed to draw five dots. You know another good way to represent numbers up to four and five is using a five frame.
Let’s do that in the next example.
Count the pencils. Color the five frame to show how many there are.
In the picture, we can see a group of pencils. And the first thing we’re told to do in this problem is to count them. We’re then told to color the five frame to show how many pencils there are. And we can see three possible answers. There’re five frames that have been colored in. But which one is correct? You know, five frames like this are a good way to count numbers up to five. Let’s color our own five frame in. Then, we know what to look for in the answer.
To make sure we remember which pencils we’ve counted, let’s move them every time we say a new number. One — we’ve colored one of the squares in our five frame — two, three, four. We’ve counted four pencils. And we’ve colored the five frame to show the number four. Now, which of our three possible answers shows the number four too, just like the one we’ve colored in? Well, one of the five frames we don’t even need to count. We can see that it’s completely colored in. And because it’s a five frame, it shows the number five. We want to show the number four. So this answer is not correct.
What about this five frame? Does this look the same as the one we colored in? One, two, three. This five frame represents the number three, not four. The correct answer must be this one. But let’s just count the squares just to check, one, two, three, four. We colored a five frame to show how many pencils there were. We counted four pencils. And so the correct answer is the one that shows four squares shaded. In that question, we moved the pencils around. They still look a little bit the same, but in a different position.
In our final example, we can have a go at counting objects that are in different positions. Remember those fish at the start of the video.
This card has five dots. Pick another card with five dots. And then, pick another card with five dots.
In this problem, we’re shown a card that has five dots on it. We don’t need to count them. We’re told that it has five dots. Then, there are two parts to our problem. And they’re both very similar. Firstly, we’re shown three tall cards. And we’re told to pick another card that has five dots on it. And the second part of the problem is very similar. We’re shown three more pictures of cards with dots on them. This time, they’re square cards. And instead of the dots being in a line, they’re in different patterns. But the questions are exactly the same. We’re told to pick another card with five dots.
Now, if this here is what five dots look like on a card, it doesn’t look like any of our cards that have got five dots on them. There are no cards that have five dots in a row going across like this. We know we can show the number five in different ways. Let’s use these counters to model the line of five dots on the first card. But all we have to do is to move our counters so they make a tall line of dots, just like those on our first set of cards. There we go.
Now which one of our cards shows a pattern just like this? Let’s count the dots. The first card shows one, two, three, four dots. We’re looking for five dots. So let’s look at our second card, one, two, three, four, five dots. And if we just check our final card, one, two, three, four, five, and there’s still another one. This is too many. This is the card that shows five dots.
Now, let’s count the dots on our second set of cards, one, two, three, four, five. And there’s still one more. This is too many. We have more than five on this card. What about our second card? One, two, three, four. We need five dots. It must be our final card, one, two, three, four, five. There are five dots on the last card. And if we look at the pattern of the dots on this card, we can move our counters to make exactly the same pattern. Our answers show that we can make the number five in different ways.
What have we learned in this video? Well, firstly, we’ve learned to count four or five objects. And although counting from one to five is always the same, we’ve recorded our counting in different ways. Sometimes, we’ve used counters or drawn dots. We’ve also learned how to model four or five objects in different ways too, like using a ten frame. Finally, we’ve learned that often the same number may look different. Think of those dots in the last question.