Thursday 14 February 2013

ERROR ANALYSIS - NUMBERS

By Mr Johari
courtesy of Ms Loh KY

Identify the Errors in each of the following solutions as shown by some of the students.
State the nature of errors (conceptual or careless)  and why part of the solution is wrong.

Example 1
Diagnostic Test 2 Q 4 (c)
QA
Nature of errors:  Conceptual
Error:
Line 1   (-1/2)^2 = 1/4
Line 4   (-) x (-) = +


Example 2
Diagnostic Test 2 Q 4 (c)
QB
Nature of errors:  Conceptual
Error: 
Line 2   (-16)(-1/2) = +8
Line 4   (+8) x (-1/2) = -4 incidentally answer right but method wrong therefore 0 mark

Example 3
Diagnostic Test 2 Q 4 (c)
QC
Nature of errors:  Careless
Error: 
Line 2   (-1/2)^2 = 0.25










18 comments:

  1. 1) Diagnostic Test 2 Q 4 (c)
    QD:
    Nature of errors: Careless and conceptual (accordingly)
    Error:
    Line 1 11-9 equals to 2,
    Line 2 -1/2 multiply by -1/2 is 1/4

    2) Diagnostic Test 2 Q 4 (c)
    QE:
    Nature of errors: Conceptual
    Error:
    Line 1 -1/2 x -1/2 is 0.25, or 1/4

    3) Diagnostic Test 2 Q 4 (c)
    QF:
    Nature of errors: Conceptual
    Error:
    Line 1 16(-1/2 x -1/2) does not equal to (16 x -1/2) x (16 x -1/2)

    4) Diagnostic Test 2 Q 4 (d)
    QA:
    Nature of errors: Careless
    Error:
    Line 2 2/12 does not equal to 6. It should be 1/6 instead.

    5) Diagnostic Test 2 Q 4 (d)
    QB:
    Nature of errors: Conceptual
    Error:
    Line 2 1/2 divide by 1/6 does not equal to -1/3. We should change the sign divide to multiplication, and therefore, changing the 1/6 to 6/1. Then, it would be easier to find the answer.

    6) Diagnostic Test 2 Q 4 (d)
    QC:
    Nature of errors: Careless
    Error:
    Line 1 Firstly, 1/2 - 1 should be -1/2. Secondly, 2/3 x 1/4 should be 1/6.

    7) Diagnostic Test 2 Q 4 (d)
    QD:
    Nature of errors: Conceptual
    Error:
    Line 4 The -1/2 should not be flipped when the division sign was being changed to multiplication. Only the second fraction should be flipped.

    8) Diagnostic Test 2 Q 4 (d)
    QE:
    Nature of errors: Conceptual
    Error:
    Line 1 There is no need for the operation to be changed. We can solve the equation 2/3 x 1/4 just like that, without requiring the need to change the operation to division. If you change it to division, you will need to change it back to multiplication to solve it.

    ReplyDelete
  2. wait, nehal i thought only supposed to find one error each? nevermind.
    Diagnostic Test 2 Q 4 (c)
    QD
    nature of error: careless
    error:
    line 1, 2(11-9) equals 2x2 not 2x3.
    line 2 -1/2x-1/2 equals 1/4 not -1.

    ReplyDelete
  3. 1) Diagnostic Test 2 Q 4 (c)
    QD:
    Nature of errors: Careless
    Error:
    Line 1: (11-9)=2, not 3
    Line 2: -1/2 x -1/2 is +1/4

    2) Diagnostic Test 2 Q 4 (c)
    QE:
    Nature of errors: Careless
    Error:
    Line 1: (11-9)=2, not 18; (-1/2)^2 = +0.25 or +1/4

    3) Diagnostic Test 2 Q 4 (c)
    QF:
    Nature of errors: Conceptual then careless
    Error:
    Line 1: Always do the sums in the brackets first;
    2(11-9)=2(2)
    =4;
    -16(-1/2)^2=-16(1/4)
    =-4
    Lines 2&3: (-8)^2 = +64

    4) Diagnostic Test 2 Q 4 (d)
    QA:
    Nature of errors: Careless
    Error:
    Line 2: 2/12=1/6, not 6

    5) Diagnostic Test 2 Q 4 (d)
    QB:
    Nature of errors: Conceptual
    Lines 2&3: -1/2 / 1/6=-1/2 x 6
    =6/2
    =3

    6) Diagnostic Test 2 Q 4 (d)
    QC:
    Nature of errors: Careless
    Error:
    Line 1: 1/2-1=-1/2, not -1 1/2
    2/3 x 1/4=2/12, not 11/12
    Lines 3&4: -18/12 / 11/12=-18/12 x 12/11
    =-18/11
    =-1 7/11

    7) Diagnostic Test 2 Q 4 (d)
    QD:
    Nature of errors: Careless then Conceptual
    Error:
    Line 1: 2/3 x 1/4 is not 1/3 x 1/2
    Line 4: (-1/2) / 1/6=-1/2 x 6
    =-6/2
    =-3

    8) Diagnostic Test 2 Q 4 (d)
    QE:
    Nature of errors: Conceptual
    Error:
    Line 1: 2/3 x 1/4 = 2/12, not 2/3 / 4/1
    Line 2: 2/3 / 4/1 = 2/12, not 0.5/3






    ReplyDelete
  4. Diagnostic Test 2 Q4(c)
    QD
    Nature of errors: Conceptual
    Error
    Line 1:(-(1/2)x(-(1/2))=1/4

    Diagnostic Test 2 Q4(c)
    QE
    Nature of errors: Conceptual
    Error
    Line 1: (-(1/2)^2)=0.25

    Diagnostic Test 2 Q4(c)
    QF
    Nature of errors: Conceptual
    Error
    Line 1: 16(-(1/2))^2=16(0.25)=4

    __________________________________________________

    Diagnostic Test 2 Q4(d)
    QA
    Nature of errors: Careless
    Error
    Line 2: 2/12=1/6

    Diagnostic Test 2 Q4(d)
    QB
    Nature of errors: Careless
    Error
    Line 2:-(1/2)/(1/6)=-(1/2)x6=3

    Diagnostic Test 2 Q4(d)
    QC
    Nature of errors: Careless
    Error
    Line 1: (1/2)-1=-(1/2)

    Diagnostic Test 2 Q4(d)
    QD
    Nature of errors: Conceptual
    Error
    Line 3: (-(1/2))/(1/6)=(-(1/2))x(6/1)=3

    Diagnostic Test 2 Q4(d)
    QE
    Nature of errors:
    Error
    Line 2: (2/3)/(4/1)=(2/3)x(1/4)=1/6

    Pls tell me if there are errors I'll correct them :)

    ReplyDelete
  5. Sorry for replying as a photo as i could not use my LD yesterday so i wrote it down and uploaded it as a picture
    http://postimage.org/image/z4r8u1r3l/ (overview)
    http://postimage.org/image/tvw7w68oh/ (Question 1 )
    http://postimage.org/image/4xu44sz3z/ (Question 2 )

    ReplyDelete
  6. Diagnostic Test 2 Q 4 (c)
    QD
    Nature of errors: Careless
    Error:
    Line 1 2(11-9) = 2x2
    Line 2 (-1/2)(-1/2) = 1/4

    Diagnostic Test 2 Q 4 (c)
    QE
    Nature of errors: Conceptual
    Error:
    Line 1 (1/2)^2 = 0.25

    Diagnostic Test 2 Q 4 (c)
    QF
    Nature of errors: Conceptual
    Error:
    Line 1 16(1/2)^2 = 16 x (1/2)^2 = 16 x 1/4 = 4


    Diagnostic Test 2 Q4(d)
    QA
    Nature of errors: Careless
    Error:
    Line 2: 2/12=1/6

    Diagnostic Test 2 Q4(d)
    QB
    Nature of errors: Conceptual
    Error:
    Line 3 -1/2 / 1/6 = -1/2 x 6/1 = -3

    Diagnostic Test 2 Q4(d)
    QC
    Nature of errors: Careless
    Error:
    Line 1 1/2 - 1 = 1/2
    Line 1 2/3 x 1/4 = 2/12

    Diagnostic Test 2 Q4(d)
    QD
    Nature of errors: Conceptual
    Error:
    (-1/2) / 1/6 = -1/2 x 6/1

    Diagnostic Test 2 Q4(d)
    QE
    Nature of errors: Conceptual
    Error:
    Line 1 2/3 x 1/4 does not need to be changed

    ReplyDelete
  7. 1) Diagnostic Test 2 Q4 (c)
    QD
    Nature of errors: Careless
    Error:
    Line 1: (11-9) =2, not 3
    Line 2: -1/2 x -1/2 is +1/4 as negative x negative = positive

    2) Diagnostic Test 2 Q4 (c)
    QE
    Nature of errors: Conceptual
    Error:
    Line 1: -1/2 x -1/2 = +0.25 or +1/4 to negative

    3) Diagnostic Test 2 Q4 (c)
    QF
    Nature of errors: Conceptual
    Error:
    Line 1: 16 x (-1/2)^2 = 4, not -8^2

    4) Diagnostic Test 2 Q4 (d)
    QA
    Nature of errors: Careless
    Error:
    Line 2: the denominator 2/12 in line 1 =1/6, not 6

    5) Diagnostic Test 2 Q4 (d)
    QB
    Nature of errors: Conceptual
    Error:
    Lines 2&3: -1/2/1/6 = -1/2 x 6=3, not 1/3

    6) Diagnostic Test 2 Q4 (d)
    QC
    Nature of errors: Careless
    Error:
    Line 1: -1/2 - 1= 1/2, not -1 1/2; 2/3 x 1/4 = 2/12 or 1/6

    7) Diagnostic Test 2 Q4 (d)
    QD
    Nature of errors: Conceptual
    Error:
    Line 4: When doing the inverted multiplication, the second fraction should be the one that is inverted, not the first. So it's (-1/2) x (6/1)

    8) Diagnostic Test 2 Q4 (d)
    QE
    Nature of errors: Conceptual
    Error:
    Line 1: 2/3 x 1/4 cannot be inverted to division as it does not work that way. So it is 2/12, not 2/3 / 4/1

    ReplyDelete
  8. Diagnostic Test 2 Q4 (C)
    QD
    Nature of errors:Careless
    Error:
    Line 1: 11-9=2
    Line 2: -1/2 x -1/2=1/4

    Diagnostic Test 2 Q4 (C)
    QE
    Error:conceptual
    Error:
    Line 1: -1/2 x -1/2 = 1/4 not-1/4

    Diagnostic Test 2 Q4 (C)
    QF
    Nature of errors: Conceptual
    Error:
    Line 1: 16(1/2)^2=4 not -8^2

    Diagnostic Test 2 Q4 (D)
    QA
    Nature of errors: Careless
    Line 2: 2/12=1/6

    Diagnostic Test 2 Q 4 (D)
    QB
    Nature of errors: Conceptual
    Error:
    Line 2&3: 1/2 /1/6 =-3 not -1/3

    Diagnostic Test 2 Q4 (D)
    QC
    Nature of errors: Careless
    error:
    Line 1: 1/2-1=-1/2 not- 1 and 1/2

    Diagnostic Test 2 Q4 (D)
    QD
    Nature of errors: Conceptual
    Error:
    Line 4: when doing the multiplication the latter fraction is the one that should be inverted.

    Diagnostic Test 2 Q4 (D)
    QE
    Nature of errors: Conceptual
    Error:
    Line 1: 2/3 x 1/4 cannot be changed to 2/3 / 4/1

    ReplyDelete
  9. Diagnostic Test Q4(c)
    QD
    Nature of error: Careless(line 1) and Conceptual Error(Line 2)
    Error: Line 1 (Careless) 11- 9=2
    Line 1 (conceptual) Negative x Negative = Positive. And 1/2 x 1/2 = 1/4

    QE
    Nature of error: Conceptual Error
    Error: Line 1 Negative x Negative = Positive (- 1/2 x -1/2 = 1/4 or 0.25)

    
QF
    Nature of error: Conceptual Error
    Error: Line 1 16(-1/2 x -1/2) is not (16 x -1/2) x (16 x -1/2)


    Diagnostic Test Q4(d)
    QA
    Nature of error: Careless Error

    Error: Line 2 2/3 x 1/4 = 1/6 not 6

    QB
    Nature of error: Conceptual Error

    Error: Line 3 - 1/2 divided by 1/6 = -3 not - 1/3

    QC
    Nature of error: Careless Error
    
Error: Line 1 1/2 - 1 should be -1/2. 2/3 x 1/4 should be 1/6 (He/she did addition)

    QD
    Nature of error: Conceptual Error

    Error: Line 4 -1/2 should not be flipped. Only the second fraction should be flipped when changing division to multiplication.

    QE
    Nature of error: Conceptual Error
    Error: Line 1 2/3 x 1/4 = 2/12, not 2/3 / 4/1
    Line 2 2/3 / 4/1 = 2/12, not 0.5/3

    ReplyDelete
  10. Diagnostic Test Q4(c)
    QD
    Nature of error: Careless(line 1) and Conceptual(Line 2)
    Error: Line 1 (Careless) 11- 9=2
    Line 1 (conceptual) Negative x Negative = Positive. And 1/2 x 1/2 = 1/4

    QE
    Nature of error: Conceptual
    Error: Line 1 Negative x Negative = Positive (- 1/2 x -1/2 = 1/4 or 0.25)

    
QF
    Nature of Error: Conceptual
    Error: Line 1 16(-1/2 x -1/2) is not (16 x -1/2) x (16 x -1/2)


    Diagnostic Test Q4(d)
    QA
    Nature of error: Careless
    Error: Line 2 2/3 x 1/4 = 1/6 not 6

    QB
    Nature of error: Conceptual
    Error: Line 3 - 1/2 divided by 1/6 = -3 not - 1/3

    QC
    Nature of error: Careless
    
Error: Line 1 1/2 - 1 should be -1/2. 2/3 x 1/4 should be 1/6 (He/she did addition)

    QD
    Nature of error: Conceptual
    Error: Line 4 -1/2 should not be flipped. Only the second fraction should be flipped when changing division to multiplication.

    QE
    Nature of error: Conceptual
    Error: Line 1 2/3 x 1/4 = 2/12, not 2/3 / 4/1
    Line 2 2/3 / 4/1 = 2/12, not 0.5/3

    ReplyDelete
  11. Diagnostic Test 2 Q 4 (c)
    QD
    nature of error: careless
    error:
    line 1, 2(11-9) equals 2x2 not 2x3.
    line 2 -1/2x-1/2 equals 1/4 not -1.

    diagnostic test 2 Q 4 (c)
    QE
    nature of error: conceptual
    line 1 he thought that 2(11-9) equals 2x11 - 2x9.


    Diagnostic test 2 Q (c)
    QF
    nature of error: conceptual
    line 1 he thought 2(11-9) equals multiplying both numbers in the brackets by 2 then minus them. and also 16x(-1/2)^2 does not equal (16x -1/2)^2.

    diagnostic test 2 Q (d)
    QA
    nature of error: conceptual
    line 2 1/12 equals 1/6 not 6.

    diagnostic test @ Q (d)
    QB
    nature of error: conceptual
    line 3 1/2 divided by 1/6 equals 3 not 1/3.

    diagnostic test Q (d)
    QC
    nature of error: conceptual
    line 1, he just added -1 to 1/2 instead of substracting 1 from 1/2
    nature of error: careless
    line 1 he got 11/12 from 1/2x2/3. it is actually 1/12.
    line 4 the answer is actually 18/11 not 7/12

    diagnostic test Q (d)
    QD
    nature of error: conceptual
    line 1 he he divided 2/3 by 2 and multiplied 1/4 by 2.

    ReplyDelete
  12. Diagnostic Test 2 Q 4 (c)
    QD
    Nature of errors: Careless
    Error:
    Line 1 11-9 = 2, not 3
    -½ x -½ = ¼ , not -1.

    Diagnostic Test 2 Q 4 (c)
    QE
    Nature of errors: Conceptual and Careless
    Error:
    Line 1 (-½ ) x (-½ ) = 0.25, not -0.25
    2(11-9) = 4

    Diagnostic Test 2 Q 4 (c)
    QF
    Nature of errors: Careless
    Error
    Line 1 2(11-9) = 4
    16(-½) ^2 is not equal to (16 x -½ )^2

    Diagnostic Test 2 Q 4 (d)
    QA
    Nature of errors: Careless
    Error:
    Line 2 2/12 = ⅙ , not 6

    Diagnostic Test 2 Q 4 (d)
    QB
    Nature of errors: Conceptual
    Error:
    Line 3 -½ / ⅙ = -3, not ⅓

    Diagnostic Test 2 Q 4 (d)
    QC
    Nature of errors: Conceptual
    Error:
    Line 1 1/2 - 1 = -½, not -1½ . 2/3 x ¼ = ⅙ , not 11/12

    Diagnostic Test 2 Q 4 (d)
    QD
    Nature of errors: Conceptual
    Error:
    Line 4 - ½ should not be flipped, ⅙ should.

    Diagnostic Test 2 Q 4 (d)
    QE
    Nature of errors: Conceptual
    Error:
    Line 1 To multiply a fraction, the 2nd fraction should not be flipped and the multiplication operation (x) should not be turned into a division operation (/). In this case, ¼ should not be flipped.

    ReplyDelete
  13. 1) Diagnostic Test 2 Q 4 (c)
    QD:
    Nature of errors: Careless and conceptual (accordingly)
    Error:
    Line 1 11-9 equals to 2,
    Line 2 -1/2 multiply by -1/2 is 1/4

    2) Diagnostic Test 2 Q 4 (c)
    QE:
    Nature of errors: Careless
    Error:
    Line 1: (11-9)=2, not 18; (-1/2)^2 = +0.25 or +1/4

    Diagnostic Test 2 Q4(c)
    QF
    Nature of errors: Conceptual
    Error
    Line 1: 16(-(1/2))^2=16(0.25)=4

    Diagnostic Test 2 Q4(d)
    QA
    Nature of errors: Careless
    Error:
    Line 2: 2/12=1/6

    5) Diagnostic Test 2 Q4 (d)
    QB
    Nature of errors: Conceptual
    Error:
    Lines 2&3: -1/2/1/6 = -1/2 x 6=3, not 1/3

    Diagnostic Test 2 Q4 (D)
    QC
    Nature of errors: Careless
    error:
    Line 1: 1/2-1=-1/2 not- 1 and 1/2

    Diagnostic Test 2 Q4 (d)
    QD
    Nature of errors: Conceptual
    Error:
    Line 4 - ½ should not be flipped, ⅙ should.

    Diagnostic Test 2 Q4 (d)
    QE
    Nature of error: Conceptual
    Error:
    Line 1 2/3 x 1/4 = 2/12, not 2/3 / 4/1
    Line 2 2/3 / 4/1 = 2/12, not 0.5/3

    ReplyDelete
  14. Diagnostic test 2 Q4(c)
    QA
    Nature of error:conceptual
    Line 1 (-1/2)^2=1/4 not -1/4
    Nature of error:careless and conceptual
    Line4 -12x(-1/4)=3 not-120

    Diagnostic test 2 Q 4(c)
    Nature of error
    QB
    Nature of errors:conceptual
    Line 2:16x (-1/2)=-8 not 8

    Diagnostic test 2 Q 4(c)
    QC
    Nature of errors:careless
    Line2 (-1/2)^2=1/4 not 2.5

    Diagnostic test 2 Q 4(c)
    QD
    Nature of error:careless
    Line1 11-9=2 not 3
    Nature of error:conceptual
    -1/2 x -1/2=1/4 not -1

    Diagnostic test 2 Q 4(c)
    QE
    Nature of error:careless and conceptual, according to order
    Line1 2=2 not 22, 11-9=2 not18

    Diagnostic test 2 Q 4(c)
    QF
    Nature of error: conceptual
    Line1 16(-1/2)^2 =(-8)^2 not [16x-1/2]^2
    Line3 (-8)^2=64 not-64

    Diagnostic test 2 Q 4(d)
    QA
    Nature of error:conceptual
    Line2 2/12 = 2/6 not 6

    Diagnostic test 2 Q 4(d)
    QB
    Nature of error:conceptual
    Line3 -(1/2)/(1/3)=-3 not -1/3

    Diagnostic test 2 Q 4(d)
    QC
    Nature of error:careless
    Line 1 (1/2 -1)/[(2/3)x(1/40]=(-1/2)/(1/6) not (-1 (1/2))/(11/12)

    Diagnostic test 2 Q 4(d)
    QD
    Nature of error:careless
    Line1 2/3=2/3 not 1/3 and 1/4=1/4 not/1/2
    Nature of error:conceptual
    Line 4 1/6 should be switched not 1/2

    Diagnostic test 2 Q 4(d)
    QE
    Nature of errors:conceptual
    Line 3 (0.5)/(0.5/3)=3 not-1/3

    ReplyDelete
  15. Diagnostic Test 2 Q 4(c)
    QA
    Nature of errors: Conceptual
    Line 1: 2x2-16(1/4) not (-1/4)

    Diagnostic Test 2 Q 4(c)
    QB
    Nature of errors: Conceptual
    Line 3: -16(-1/2)=+8 not -8

    Diagnostic Test 2 Q 4(c)
    QC
    Nature of errors: Careless
    Line 2: -16(-1/2)^2= -16x0.25 not 2.5

    Diagnostic Test 2 Q 4(c)
    QD
    Nature of errors: Careless
    Line 1: 2(11-9)=2x2 not 2x3

    Diagnostic Test 2 Q 4(c)
    QE
    Nature of errors: Conceptual
    Line 1: (1/2)^2=0.25 not -0.25

    Diagnostic Test 2 Q 4(c)
    QF
    Nature of errors: Conceptual
    Line 1: -16(-1/2)^2=-16(0.25) not (16x-1/2^2)

    Diagnostic Test 2 Q 4(d)
    QA
    Nature of errors: Careless
    Line 2: (-1/2)/(2/12)= (-1/2)/(1/6) not (-1/2)/6

    Diagnostic Test 2 Q 4(d)
    QB
    Nature of errors: Careless
    Line 3: (-1/2)/ (1/6)= -3 not -1/3

    Diagnostic Test 2 Q 4(d)
    QC
    Nature of errors: Careless
    Line 1:(1/2)-1/(2/3 x1/4) = -1/2/(1/6) not (-1(1/2)/(11/12)

    Diagnostic Test 2 Q 4(d)
    QD
    Nature of errors: Careless
    Line 1: 2/3=2/3 not 1/3 and 1/4=1/4 not 1/2
    Nature of errors: Conceptual
    Line 4: 1/6 should be switched not 1/2

    Diagnostic Test 2 Q 4(d)
    QE
    Nature of errors: Conceptual
    Line 3 : (0.5)/(0.5/3)=3 not1/3

    ReplyDelete
  16. 1) Diagnostic Test 2 Q 4 (c)
    QD:
    Nature of errors: Careless
    Error:
    Line 1: (11-9)=2.
    Line 2: -1/2 x -1/2 is 1/4

    2) Diagnostic Test 2 Q 4 (c)
    QE:
    Nature of errors: Careless
    Error:
    Line 1: (11-9)=2,

    3) Diagnostic Test 2 Q4 (c)
    QF
    Nature of errors: Conceptual
    Error:
    Line 1: 16 x (-1/2)^2 = 4,

    4) Diagnostic Test 2 Q4 (d)
    QA
    Nature of errors: Careless
    Error:
    Line 2: the denominator 2/12 in line 1 =1/6

    5) Diagnostic Test 2 Q4 (d)
    QB
    Nature of errors: Conceptual
    Error:
    Lines 2&3: -1/2/1/6 = -1/2 x 6=3

    6)Diagnostic Test 2 Q4 (D)
    QC
    Nature of errors: Careless
    error:
    Line 1: 1/2-1=-1/2

    7)Diagnostic Test 2 Q4 (d)
    QD
    Nature of errors: Conceptual
    Error:
    Line 4 - ½ should not be flipped, ⅙ should.

    8)Diagnostic Test 2 Q4 (d)
    QE
    Nature of error: Conceptual
    Error:
    Line 1 2/3 x 1/4 = 2/12, not 2/3 / 4/1
    Line 2 2/3 / 4/1 = 2/12, not 0.5/3

    ReplyDelete