Friday, 23 January 2015

"What's Wrong?" with these Number Line

Question:
Represent the following numbers on a number line: 5, -1/11, π, 0.9

Below are 4 number lines that have "gone wrong".
Do you know what's wrong with these number lines?

Line (1)

Line (2)

Line (3)

Line (4)

Think through before clicking at "Comments" to find out "What's Wrong".

After note (25 Jan 2015, 6 am):
The following groups are awarded additional points (reasons - see the comments to their responses)
Group 1: -
Group 2: 3 + 2 + 4 (Choon Wee) = 9 points
Group 3: -
Group 4: 3 points

Do check out Choon Wee's answers.

1. Line 1 does not have a bit protruding from each end and the numbers should be below the line. He also did not have any dots above the numbers. Line 2 does not have a bit protruding from each end and did not have any dots above the numbers.
Line 3 does not have an arrow where the number line is increasing to. Line 4 drew crosses instead of dots above the numbers and did not have a bit protruding from each end. Yu Min Shen, Group 1

1. Min Shen
Good observation for Q1, Q2 & Q4 - still, one more item is missing from the drawing. What is it?

2. Line 1,2 and 4 did not have any "tails", Lines 1's numbers should be below the line, Lines 1 and 2 did not signify using the dots, lines 3,4 did not have any arrowheads, Lines 4 used crosses instead of dots.
Marcus Tan Gp 4

1. Good observation about the way the line is drawn.
In fact, Lines 1 & 2 have the 'arrows' missed out too.
There's one more "not-to-do" in line 1 that you've not mentioned.

3. All lines did not have arrows and as marcus said, lines1,2,4 don't have any "tails".Like marcus said line 1,2,3 should have black dots to represent the numbers on the number line. And line 4 should not be crossed.

1. Something in Line 1 stood out compared to the rest, and we should not do that when drawing number line.
What is that?

4. Line 1 is wrong because it is terminated, numbers are above the line and there are no dots to represent the mystery numbers
Line 2 is wrong because it is terminated and there are no dots to represent the mystery number
Line 3 is wrong because it has no arrow to represent the continuation of the number line
Line 4 is wrong because it is terminated and the person doing this question should use dots, not crosses, to represent the mystery numbers

1. Clear and precise.
Well done.

>>> 3 points to group 2

5. Line 1 does not have tail, no arrow to represent the increasing order of the numbers, no dots to represent the numbers and the numbers are above the line.
Line 2 does not have a tail, no arrow to represent the increasing order of the number and no dots to represent the numbers.
Line 3 does not have any arrows to represent the increasing order of the numbers.
Line 4 crosses are used to represent the numbers instead of dots, no arrow to represent the increasing order, the line is slightly crooked thus breaking the continuation of the line.

1. Aryan, Group 4

2. Well done!
The explanation is very clear.

>>> 3 points to Group 4

6. Line (1) did not put any dots above the numbers and the numbers were above the line instead of below it. Line (2) had no dots above the number . Line (4) had crosses instead of dots. All lines had no arrows to represent the increasing value of the numbers and lines 1,2 and 4 had no protruding end.

1. Benedict group 2

2. You have pointed out all the areas correctly.
On the other hand, it would be clearer if you were to describe line by line in this case, then the errors that are surfaced for each line is all captured in a sentence.

>>> 2 points to Group 2

7. Line(1) does not have any circles to mark the numbers on the number line, and numbers should be below the line, not above.
Line(2) does not have circles to mark the numbers on the number line as well,
In Line(3), 1/11 is not shown to be negative,as it should.
In Line 4, the markings on the line are not appropriate markings.
And ALL 4 Number Lines do not have the arrowhead drawn at either sides of the line to represent which direction the numbers are increasing/decreasing in.

Sim Choon Wee, Group 2

1. Choon Wee

Good observations!
Apart from the drawing of lines and representation of the answers on the line, you have rightfully pointed out one 'error' that the rest (above) had not mentioned: Though -1/11 has been correctly placed, the negative sign of the number was missing.

>>> 4 points to Group 2

8. Line 1 did not have extending of the vertical lines across the horizontal line and did not have "tails" at the end.
Line 2 did not have "tails" at the end.
Line 3 did not have vertical lines below the dot to represent where the number is.
Line 4 used stars to represent the location of the numbers, when it should have used vertical lines.

Teng Tjin Yao, group 2.

1. Tjin Yao

For lines 1 & 2, you would notice, after improving the line based on what you described, the question is still not answered yet. Do you know why?

For line 3, what do you mean by your sentence?

For line 4, apart from the 'stars' problem, how else can this drawing be improved?

9. Line 1 had the numbers represented above the line, no arrow, or line sticking out on either side.
Line 2 also did not have the line sticking out at either line or an arrow.
Line 3 did not have an arrow, and the dots were on, not above, the line.
Line 4 did not have an arrow, the line did not stick out another side, instead of dots there were crosses and the crosses were on the line.
Hannah, group 3

1. Hannah

For lines 1 & 2, you would notice, after improving the line based on what you described, the question is still not answered yet. Do you know why?

For line 3, yes... the arrow is missing.
Remember, we mentioned in class that, if it is a discrete number, it is fine to place the dot on the number line, though it is a good practice to place the dot above the line.

Observation for Line 4 is correct.

10. 1. Does not have some extra line protruding from the sides and does not have an arrow. The numbers should also be below the line and there are no dots above the numbers.
2. There was no extra line and no arrow, and no dots above the numbers.
3. There are no arrows and the dots should be above numbers, not on the line.
4. No extra line, no arrows, used crosses instead of dots and placed crosses on the line.