How many, and which place
Five shapes stand in a line: a circle, a square, a triangle, a rectangle and a hexagon. Count them and you get 5. That number says how many shapes there are.
A different kind of number says where each shape stands. Counting from the left, the circle is first, the square is second, the triangle is third, the rectangle is fourth and the hexagon is fifth. First, second and third are ordinal numbers: each one names a place in the line.
Counting from the left, each shape has its place under it. The triangle is 3rd.
A place, not an amount
"The triangle is third" does not mean there are 3 triangles, or 3 shapes. It means that when you count along the line from the left, the triangle is the one you reach when you say 3. There is still only 1 triangle, and still 5 shapes.
The place also tells you how many shapes come before it. The triangle is third, so 2 shapes come before it: the circle and the square. The triangle is one of the first three, but it does not come before itself, so there are 2, not 3.
Start from the end that is named
A place depends on where you start counting. Counting from the left, the square is second. Counting from the right, the hexagon is first, the rectangle is second, the triangle is third, and the square is fourth.
So always check which end the question starts from. The shape at that end is first, never zero.
The same line counted from the right: the hexagon is 1st, and the square is 4th.
1st from the left is 5th from the right: 0 before it, 4 after it, and 0 + 1 + 4 = 5
Find the shape that is 4th from the right
The places above the line count from the left, and the places below count from the right. The shapes before the marked one, the marked one and the shapes after it always make 5.
The short way to write them
Each place has a short written form: the number, then the last two letters of its word. First is written 1st, second is 2nd, third is 3rd and fourth is 4th.
From fifth to tenth, every word ends in th, so the short forms do too: 5th, 6th, 7th, 8th, 9th and 10th. Only the first three places have their own endings.
Worked example: A Child's Place in a Line of Six
Question There are 6 children in a line for the slide. Mei is 3rd in the line. (a) How many children are in front of Mei? (b) How many children are behind Mei?
1.Draw 6 children in a line. Write 1st, 2nd, 3rd, 4th, 5th and 6th under them, from the front.
There are 6 children in a line. The places are 1st, 2nd, 3rd, 4th, 5th and 6th from the front. 2.Mei is the 3rd child. Color her in.
Mei is the 3rd child in the line. 3.(a) Count the children in front of Mei: 1, 2. There are 2 children in front of Mei.
(a) Count the children in front of Mei: 1, 2. There are 2 children in front of Mei. 4.(b) Count the children behind Mei: 1, 2, 3. There are 3 children behind Mei.
(b) Count the children behind Mei: 1, 2, 3. There are 3 children behind Mei.
Answer: (a) 2 children; (b) 3 children
Common mistakes
- Saying 3 children are in front of Mei because she is 3rd. Mei is one of the first three children, so only 2 children are in front of her.
- Counting Mei with the children behind her and saying 4. Mei is not behind herself, so start counting at the 4th child.
Worked example: A Line of Five Counted from the Front and from the Back
Question There are 5 children in a line. From the front they are Ali, Ben, Mei, Sam and Eva. (a) Ali is 1st from the front. What is Ali's place from the back? (b) Who is 2nd from the back?
1.Draw the 5 children in a line. Ali is at the front and Eva is at the back.
There are 5 children in a line. Ali is at the front and Eva is at the back. 2.Count places from the back. Eva is 1st, Sam is 2nd, Mei is 3rd, Ben is 4th and Ali is 5th.
Count places from the back: Eva is 1st, Sam is 2nd, Mei is 3rd, Ben is 4th and Ali is 5th. 3.(a) Ali is 5th from the back. The first child from the front is the last child from the back.
(a) Ali is 1st from the front and 5th from the back. 4.(b) Sam is 2nd from the back. From the front, Sam is 4th.
(b) Sam is 2nd from the back. From the front, Sam is 4th.
Answer: (a) 5th from the back; (b) Sam, who is 4th from the front
Common mistakes
- Saying Ben is 2nd from the back. Ben is 2nd from the front, and the question asks for the place from the back, so start counting at Eva.
- Starting the count from the back at 0, so that Sam is 1st. The child at the very back is 1st from the back, just as the child at the very front is 1st from the front.