Oridinal Numbers: 0.5
Supporting materials
Indicator of Progress
At this level students can name the relative position of an object in a small ordered collection (e.g. of toys), using ordinal numbers such as first, second, fifth, eighth, etc. They are also able to recognise and describe in which order the participants finish a game. Students will recognise that in some activities there may be a single winner, in other activities recognition may be given to those who come first, second or third. They understand that order is dependent on which object/event is identified as the starting point, so distinguish 'third from the door' from 'third from the window' etc. The contexts are spatial (e.g. lining up), temporal (e.g. the second hour of the day) and personal (e.g. I came first).
Using ordinal number words is closely tied to understanding the concepts on which objects or events are being ordered, i.e. comparing heights, comparing volumes, comparing times, comparing areas etc.
Before achieving this, students will be able to recognise whether they win or lose a game or race. They will be able to identify first and last (e.g. of a line of students) but will not be able to identify who is fourth in line or describe the position of the person who is third in line, especially when the starting point is not intuitive.
Later, students will be able to interpret and use ordinal numbers to describe more complex situations, such as “At play, I am going to be the second fairy in the third row” and “I will be the fifth person standing on the left of Ms Callea.”
Illustration 1: “I win so you lose”
When young children play simple games they are often heard to say: “I win” or “You lose”. When playing card games like Snap children realise that whoever has the largest number of pairs will be the winner. In board games like Snakes and Ladders the winner is the first person to reach 100. They may be able to recognise that some players 'nearly won' because they were 'close.'
Progress will be evident when students can describe positions such as first (the winner), second, third, etc and not just as winning and losing or first and last.
Illustration 2: First in line can become last in line
Children who have attained this indicator of progress know that ordinal numbers depend on the starting point. If children make a line at the door, the child closest to the door is first, the next is second etc. However if the teacher stands at the other end of the line the child nearest the door will become the last in the line. A student who is sent to the back of the line will become the last child.
Illustration 3: Links to the Mathematics Online Interview
Examples of the types of tasks that would be illustrative of ordinal counting aligned from the Mathematics Online Interview:
- Question II (f) - First year of schooling detour - Location/Pattern/Ordinal Number
Teaching Strategies
Students will have difficulties with ordinal numbers unless they can count forwards fluently by ones. Being able to count backwards will also help.
When working with ordinal numbers the focus needs to be on developing the connections between:
- the known counting numbers
- the new vocabulary of ordinal numbers (first, second, third …) and
- the short written representation (1st, 2nd, 3rd …).
After the irregular vocabulary for ‘first’ and ‘second’ the later ordinals follow the number names regularly (e.g. ninth, tenth, eleventh).
Activity 1: Incidental Classroom Activities highlights the types of occasions when teachers can emphasise ordinal numbers.
Activity 2: Toy Line Up is an activity that focuses on the importance of deciding on starting and finishing positions.
Activity 3: Races is a mathematics activity in a physical education context where teachers can use the ordinal numbers in a real-life context.
Activity 4: Visualising order encourages students to use order names flexibly up and down the number sequence.
Activity 1: Incidental Classroom Activities
When students are participating in classroom activities such as lining up at the door or going to their tables, teachers can emphasise the ordinal language. For example: “The students in Blue Group can go to their table first”, “John can line up at the door first and Mary can be second”, “The children in Red group were first to be ready for lunch.”
Do not confine instructions to ‘first’, but include lots of other ordinals. Teachers can list groups in order of completing tasks. For example, “Blue group finished first, Red group were second, Yellow group were third, and Orange group were fourth.” Teachers should look for such opportunities to use ordinal numbers beyond the well-known first, second and third.
In teaching this vocabulary, teachers should also note that most of the ordinal number names have a strong relationship to their cardinal number counterparts (e.g. sixth and six) and should give extra emphasis to the ‘-th’ sound that distinguishes most cardinal numbers. There are, however, some irregular names, which include the three commonly used ones: first (one), second (two), and third (three), with fifth (five) being another mismatch. Teachers will need to make the connection between these pairs of words and highlight the regular names in the rest of the collection.
The final ‘-th’ sound is common in English, but not common in many other languages. Consequently, children from some language backgrounds will find this ‘-th’ sound especially hard to hear.
Activity 2: Toy Line Up
The teacher lines up a row of plastic teddies and points to the nearest teddy saying “This is the first teddy”. Then the teacher points to the next teddy and says: “This is the second teddy” and continues for the third teddy.
Now choose 3 more teddies and put them in a row. The teacher identifies the first teddy and then asks student to show the second and third teddies. Repeat with other coloured teddies and other sets of two or three bears. Orient the lines in different directions, and vary the choice of which end of the line is designated as the first position.
Once children are confident with the first three ordinal numbers (first, second and third) then use larger sets of teddies to introduce other ordinal numbers from fourth to tenth. Children can say the ordinal names together, whilst pointing at each teddy: “first, second, third, fourth, fifth …”
Once children are confident with the ordinal numbers ‘first’ to ‘tenth’ where the start of the ordered set has been identified, the teacher can indicate the third teddy and ask students to identify from which end of the line she is counting. Be alert to ambiguous cases such as having the teacher identify the third teddy in a set of five and asking students to identify which teddy is first. This can actually lead to a good discussion about the fact that there are two possible answers. The teacher could then point to an appropriate teddy and say “What if I ALSO told you that THIS teddy is the fourth one”, leading students to deduce which of the two possibilities is correct.
Activity 3: Races
Young children love races. Vary the types of activity so that all children have a chance to be a place getter - first, second, third. For example:
- Running
- Skipping
- Hopping
- Walking heel to toe
- Egg and spoon race
- Three-legged race
- Wheel-barrow race
The teacher can also devise other activities that rely less on sporting prowess, such as collecting something that starts with a B, picking up the most blocks, sitting down on the mat after putting your books away, putting your hand up after spotting a hidden object and so on.
The idea here is not just to have fun, good though that is. When the purpose is to use and reinforce knowledge of ordinal number, make sure that children identify, say and possibly record the places (fourth, 4th, etc) and link them to the associated cardinal number (4). Questions similar to those in Activity 3 could also be used.
Activity 4: Visualising order
Using a long line of teddies (or other objects) facing forwards, the teacher can ask questions such as those below.
Note: To begin with students can answer with their eyes open, looking at the objects. Then they can attempt the task with their eyes closed, which forces more advanced strategies.
Questions can be pitched to different degrees of difficulty, depending on students’ facility with number.
- Which teddy is behind this one (pointing at the third)? (Answer: the fourth)
Ask: How do we know it is the fourth? (i) count from the front, or (ii) say “first, second, third, fourth” or (iii) know that 4 comes after 3 etc.
- Which teddy is behind the fifth? (Answer: the sixth)
Ask: How do we know it is the sixth? (i) count from the front, or (ii) say “first, second, third, fourth, ..” or (iii) know that 6 comes after 5 etc.
- Which teddy is two behind this one (pointing at the fifth)? (Answer: the seventh)
- Which teddy is in front of the tenth one? (Answer: the ninth)
Now there are 6 teddies. Which one is last / second last / third last? (Answer: sixth / fifth / fourth).