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International Baccalaureate · PYP 0

Order and Position

⌚ ~82 min ▢ 8 blocks ✓ 33 exercises ➣ Prerequisites : Numbers to 10, Comparing Quantities
I The Number Line
Definition — Number Line
A number line is a straight line with the numbers placed along it in order, one step apart. It helps us see the order of the numbers.
Figure
Numbers get bigger as we move to the right.
Example — Finding a Hidden Number
One number is hidden on the number line. Which one is it?
Figure

We say the numbers in order while pointing at each mark: five, six... The number that comes just after 6 is 7. The hidden number is 7.
Figure

Example — Which Is Bigger?
The numbers \(3\) and \(8\) are marked on the number line. Which one is bigger?
Figure

On the number line, the numbers get bigger as we move to the right. \(8\) is further to the right than \(3\), so \(8\) is bigger than \(3\): we write \(8 > 3\) (read: \(8\) is greater than \(3\)), or \(3 < 8\) (read: \(3\) is less than \(8\)).
Figure
When we count forward (one, two, three…), we also say \(3\) before \(8\): the number we say later is the bigger one.

Method — The Sequence of Numbers up to Thirty
To say the numbers in order after ten:
  • we go on one by one: each number is one more than the number just before it;
  • after ten come eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen;
  • after 19 comes 20, after 29 comes 30 — just as after 9 comes 10: …, seventeen, eighteen, nineteen, twenty, twenty-one, twenty-two, …, twenty-seven, twenty-eight, twenty-nine, thirty.
The number strip shows the numbers from \(1\) to \(30\), ten in each row. We read it row after row: at the end of a row, we go on at the start of the next row (after \(10\) comes \(11\), after \(20\) comes \(21\)). Pointing at each box, we say all the numbers, one by one, up to thirty.
Figure
To count backward, we go back one step each time, as at the start of a race: \(10\), \(9\), \(8\), \(7\), \(6\), \(5\), \(4\), \(3\), \(2\), \(1\), \(0\) — go!
Figure
Skills to practice
  • Finding Numbers with Dots
  • Finding Numbers without Dots
  • Comparing with the Number Line
  • Continuing the Sequence up to Thirty
  • Counting Backward
II Position in a Line

Five children are waiting in a line for the slide. The dot and the arrow show where the line starts.
Figure
Who is first? Who is last?

We count the children from the starting dot: one, two, three, four, five.
Figure
The child we count first is the first one: nobody is in front. The child we count last is the last one: nobody is behind.


Definition — The Position of an Object
In a line, the position of an object is its place when we count from the start. The dot shows where we start, and the arrow shows which way we go.
Figure
The object we reach first is in position 1, the next one is in position 2, and so on. The object at the end of the line is the last one. When the line has several objects, the one just before the last is the second to last.
Method — Finding the Position
To find the position of an object in a line:
  1. look for the dot: it shows where we start;
  2. count the objects one by one, following the arrow;
  3. stop on the object we are asked about: the last number we said is its position.
The Position Depends on the Start and the Direction
The same object is not always in the same position: it depends on where the line starts and which way we go.
Figure
Counting from the dot on the left, the framed lemon is in position 2: it is the second.
Figure
Counting from the dot on the right — we start at the other end, so we also go the other way — the same lemon is in position 4: it is the fourth. Before saying a position, we always look at where we start and which way we go.
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Skills to practice
  • Finding the Position
  • Finding the Position from the Other End
III Going further
Skills to practice
  • Finding Positions in Pictures
  • Quiz