Math Department Endeavour Primary School. Purpose of workshop Misconceptions and mistakes by topic: ◦ Whole Numbers (P5) ◦ Fractions (P5 and P6) ◦

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


2. Not able to identify the correct base and height pair


3. Difference of areas mistake

x 42 x 3


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


3. Identifying the correct radius and diameter


Small semicircle:Radius = 5cmDiameter = 10cm

Big quadrant:Radius = 10cmDiameter = 20cm

4. Incomplete sides when finding perimeter

Pupils failed to add the two straight lines.


4. Incomplete sides when finding perimeter


Pupils failed to add the two straight lines.

5. Mathematically wrong statement

Correct: 2u 60 or 2u = 60

Incorrect: 2 60 2 = 60


Statement says area of circle but pupils calculated for a quadrant instead.

Missing π in the working answer

6. Doing things the hard way


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


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)


7

22

Pupils must use the value of π as mentioned in the question.

Some pupils used the wrong value.


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.


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

Math Department Endeavour Primary School. Purpose of workshop Misconceptions and mistakes by topic: ◦ Whole Numbers (P5) ◦ Fractions (P5 and P6) ◦

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