Math Department Endeavour Primary School. Purpose of workshop Misconceptions and mistakes by topic: ◦ Whole Numbers (P5) ◦ Fractions (P5 and P6) ◦
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Misconceptions and Common Mistakes made by P5 and P6
pupils – Workshop for ParentsMath Department
Endeavour Primary School
Purpose of workshop Misconceptions and mistakes by topic:
◦Whole Numbers (P5)◦Fractions (P5 and P6)◦Ratio (P5 and P6)◦Percentage (P5 and P6)◦Geometry (P5 and P6)◦Mensuration (P5 and P6)
Workshop Outline
Equip parents with knowledge of common misconceptions and mistakes pupils make.
Help parents to help pupils better. Consistent between what is taught in school
and support from home. Provides a good support structure that can
reduce stress in pupils. If pupils can overcome these
misconceptions, they can fare much better.
Purpose of Workshop
What is a misconception? It is defined as – ‘a view or opinion that is
incorrect because it is based on wrong thinking or understanding.’
Misconception 1: When you divide a number, the answer will be smaller and when you multiply a number, the answer becomes greater.
Misconception 2: When you see the word ‘more’ in the sentence, you always add.
Misconception
WHOLE NUMBERS
1. Writing in numerals or in words
Write in numerals: Three hundred and four thousand and sixty-fiveCorrect answer : 304 065Common mistakes: 300465, 4365
300 + 4000 + 65
Whole Numbers (P5)
Three hundred and four thousand and sixty-five
3 0 4 0 6 5
Write in words:
217 389 vs 217 089
Misconception: can only use ‘and’ once!
2. Order of Operations
Do the following sum:
a) 8 + 3 – 1 = ? b) 8 – 3 + 1 = ?
Ans: 10 and 6
Did you get them right?
Whole Numbers
Now do these:
c) 5 x (8 – 4 ÷ 2) ÷10 =
Is your answer 1 or 3? Or do you get a totally different answer?
Why do pupils get the wrong answer?
B O D M A S
It is not true that you have to follow the order as shown, e.g. D before M and A before S
BODMAS is a misconception
In Primary school, we seldom encounter ‘of’ in the order of operations.Pupils generally only see B, D, M, A, S
Use hierarchy structure
First priority BThen, D M or M D from left to rightLastly, A S or S A from left to right
Let’s try again:5 x (8 – 4 ÷ 2) ÷10
= 5 x (8 – 2) ÷10
= 5 x 6 ÷10
= 30 ÷10
= 3
FRACTIONS
1. Fraction as division
= ?
Pupils work out 8 ÷ 5 instead of 5 ÷ 8. Why?
Misconception: Only a larger number can be divided by a smaller number.
Show counter example: 2 pizzas can be shared with 4 people.
Fractions
8
5
2. Answering ‘Fraction of …’ qns:
John has 7 books, Mary has 5 books.
Express the number of Mary’s books as a fraction of the number of John’s books.
Express the number of John’s books as a fraction of the number of Mary’s books.Pupils may give the first answer as they believe the numerator has to be smaller than the denominator
Fractions
7
5
5
7
Misconception 1: First number is the numerator, second number is the denominator,
Misconception 2: Larger number is the denominator.
Fractions
Consider another question:John has 7 books, Mary has 5 books.
What fraction of the number of Mary’s books is the number of John’s books?
or
Rule: the first number after ‘fraction of’ is the denominator
Fractions
7
5
5
7
3. Multiplication of fractions (cancellation)
x x
What are the common mistakes usually found here?a) Cancellation between 2 numerators or 2
denominatorsb) Double cancellation: 1 denominator with 2
numerators
Fractions
7
22
1
14
2
1
4. Calculator error
Use your calculator to do this:
x 2 = ?
Pupils sometimes did not use mixed number key but used fraction key instead.Pupils who pressed ‘1’ first, then the fraction key to enter half gets a wrong answer. Try doing this?
Fractions
2
11
1) Press the shift button
2) Press the fraction button
5. Dealing with remainder
Compare the two questions:
1) Sarah spent of her money on a bag and of it on a purse.
2) Sarah spent of her money on a bag and of the remainder on a purse.
Tendency to missed out the ‘remainder’.
Fractions
4
1
4
1
4
1
4
1
6. Mrs Tan had kg of flour. She used
of it to make some cookies. How much flour
had she left?
or
Pupils need to be alert on the presence or absence of units.
Fractions
8
72
1
2
1
8
7
2
1
8
7x
RATIO
1. Simplest form
All ratio answers need to be in the simplest form unless specified.
Do not leave ratio in decimal notation.e.g.
3.5 : 4 : 2 = 7 : 8 : 4
Ratio
2. Not alert on ratio requested.
Sam has $34 and Frank has $35.
What is the ratio of Frank’s money to Sam’s money?What is the ratio of Frank’s money to the total amount of money?Tendency to give the ratio answer based on order the numbers appear.
Ratio
3. Answering in the wrong format
The ratio of the number of boys to the number of girls in the school in 2 : 3. What fraction of the total number of pupils are girls?
Pupils answer in ratio instead of fraction.
Ratio
4. Unable to identify standard ratio type
1) The ratio of Ali’s stamps to John’s stamps is 3 : 1. Ali uses 12 stamps and the ratio becomes 3 : 2.
2) The ratio of Ali’s stamps to John’s stamps is 3 : 1. After Ali gave John 12 stamps, the ratio becomes 2 : 1.
3) The ratio of Ali’s stamps to John’s stamps is 3 : 1. If they both buy 12 stamps each, the ratio becomes 2 : 1.
Ratio
1 Quantity unchanged - John
Total remain unchanged
Difference is unchanged
5. Using wrong original ratio
E.g. The ratio of Ali’s stamps to John’s stamps is 3 : 1. Ali uses 12 stamps and the ratio becomes 3 : 2. How many stamps do they have altogether in the beginning?
Before AfterAli : John Ali : John 3 : 1 3 : 2
Ratio
1 Quantity unchanged - John
Before AfterAli : John Ali : John 3 : 1 3 : 2 6 : 2
3u ---- 121u ---- 44u ---- 4 x 4 = 16 Should have solved for 8u instead of 4u. Good practice: Cancel out the original ratio.
Ratio
1 Quantity unchanged - JohnAli – 12
PERCENTAGE
1. Wrong mathematical sentence
Do this: Change to percentage
a) b)
Method 1 is to convert denominator to 100.Method 2 is to multiply fraction with 100%
Percentage
25
12
8
7
Method 2 is to multiply fraction with 100%
x 100 = 48% (incorrect statement)
x 100% = 48% (Correct statement)
However, try doing both using the calculator. What do you notice? When using calculator, do not press the % key.
Percentage
25
12
25
12
2. Using wrong base
Mr Jahan’s mass was 70kg in 2004. His mass increased to 84 kg in 2014 and reduced after much dieting to 67.2kg in 2016.
a) What is the percentage increase in his mass in 2014?
b) What is the percentage decrease in his mass in 2016?
Percentage
Mr Jahan’s mass was 70kg in 2004. His mass increased to 84 kg in 2014 and reduced after much dieting to 67.2kg in 2016.a) What is the
percentage increase in his mass in 2014?
b) What is the percentage decrease in his mass in 2016?
Percentage
a) Increase: 84 – 70 = 14
x 100% = 20%
b) Decrease: 84 – 67.2 = 16.8
x 100% = 20%
Common mistake: use wrong denominator
70
14
84
8.16
GEOMETRY
1. Unable to identify parallel lines and angles within
Geometry
2. Not labeling angles
180° – 132° = 48°48° – 23° = 25°180° – 90° – 25° =65°132° – 65° = 67°
No way of knowing what the working done are for.
Geometry
3. Unable to see isosceles triangles within a rhombus
By adding the equal lines, pupils can see the isosceles triangles better.
Geometry
4. Wrong naming of type of angles
180° - 23° - 132° = 25°(alternate angle)(vertically opposite angle)
Geometry
MENSURATION
1. Forgetting to multiply the half
Mensuration – Area of triangles
2. Not able to identify the correct base and height pair
Mensuration – Area of triangles
2. Not able to identify the correct base and height pair
Mensuration – Area of triangles
3. Difference of areas mistake
x 42 x 3
Mensuration – Area of triangles
2
1
1. Wrong use of formula Area of circleπ x r x r (encouraged) π x r2
Circumference of circle 2 x π x r π x d (encouraged)
Encouraged to distinguish the formulas better.
Mensuration – Circles
2. Calculate for a circle instead of part of a circle
Mensuration – Circles
3. Identifying the correct radius and diameter
Mensuration – Circles
Small semicircle:Radius = 5cmDiameter = 10cm
Big quadrant:Radius = 10cmDiameter = 20cm
4. Incomplete sides when finding perimeter
Pupils failed to add the two straight lines.
Mensuration – Circles
4. Incomplete sides when finding perimeter
Mensuration – Circles
Pupils failed to add the two straight lines.
5. Mathematically wrong statement
Correct: 2u 60 or 2u = 60
Incorrect: 2 60 2 = 60
Mensuration – Circles
Statement says area of circle but pupils calculated for a quadrant instead.
Missing π in the working answer
6. Doing things the hard way
Mensuration – Circles
Find area of quadrantAnswer x 2
Find area of square – Area of quadrantAnswer x 2
Add both answers
Shortcut:Area of square x 2
6. Doing things the hard way
Mensuration – Circles
Shortcut: Area of square – Area of semicircle
Can you see it?
7. The value of pi
Usually, we use 4 values of pi
1) 3.142) In terms of π3) Calculator value4)
Mensuration – Circles
7
22
Pupils must use the value of π as mentioned in the question.
Some pupils used the wrong value.
Mensuration – Circles
What is the value of π in the calculator?
3.141592654
So how do pupils use this value?
Imagine needing to find perimeter of quadrant
Pupils tend to round off first and that will result in inaccurate answer.
Pupils are advised to use the symbol π until the last step, then press the value of π into the final answer.
Mensuration – Circles
When pupils do not get the marks they are supposed to get, there are usually 3 reasons:
a) Do not understand the question.
b) I understand but I do not know how to do.
c) I understand and I know how to do but I am not alert and careless.
In Summary
Common mistakes made in exams may cause pupils to lose enough marks to cause a drop of 1 grade and in some cases, even two grades.
In Summary
The End
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