1 / 61

Misconceptions and Common Mistakes made by P5 and P6 pupils – Workshop for Parents

Misconceptions and Common Mistakes made by P5 and P6 pupils – Workshop for Parents. Math Department Endeavour Primary School. Workshop Outline. Purpose of workshop Misconceptions and mistakes by topic: Whole Numbers (P5) Fractions (P5 and P6) Ratio (P5 and P6) Percentage (P5 and P6)

dane
Télécharger la présentation

Misconceptions and Common Mistakes made by P5 and P6 pupils – Workshop for Parents

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Misconceptions and Common Mistakes made by P5 and P6 pupils – Workshop for Parents Math Department Endeavour Primary School

  2. Workshop Outline • 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)

  3. Purpose of Workshop • 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.

  4. Misconception • 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.

  5. WHOLE NUMBERS

  6. Whole Numbers (P5) 1. Writing in numerals or in words Write in numerals: Three hundred and four thousand and sixty-five Correct answer : 304 065 Common mistakes: 300465, 4365 300 + 4000 + 65

  7. 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!

  8. Whole Numbers 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?

  9. 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

  10. 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 B Then,D M or M D from left to right Lastly,A S or S A from left to right

  11. Let’s try again: 5 x (8 – 4 ÷ 2) ÷10 = 5 x (8 – 2) ÷10 = 5 x 6 ÷10 = 30 ÷10 = 3

  12. FRACTIONS

  13. 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.

  14. Fractions 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

  15. Fractions Misconception 1: First number is the numerator, second number is the denominator, Misconception 2: Larger number is the denominator.

  16. 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

  17. Fractions 3. Multiplication of fractions (cancellation) x x What are the common mistakes usually found here? • Cancellation between 2 numerators or 2 denominators • Double cancellation: 1 denominator with 2 numerators

  18. Fractions 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?

  19. 1) Press the shift button 2) Press the fraction button

  20. Fractions 5. Dealing with remainder Compare the two questions: • Sarah spent of her money on a bag and of it on a purse. • Sarah spent of her money on a bag and of the remainder on a purse. Tendency to missed out the ‘remainder’.

  21. Fractions 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.

  22. RATIO

  23. 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

  24. 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.

  25. 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.

  26. Ratio 4. Unable to identify standard ratio type • The ratio of Ali’s stamps to John’s stamps is 3 : 1. Ali uses 12 stamps and the ratio becomes 3 : 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. • 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. 1 Quantity unchanged - John Total remain unchanged Difference is unchanged

  27. Ratio 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 After Ali : John Ali : John 3 : 1 3 : 2 1 Quantity unchanged - John

  28. Ratio Before After Ali : John Ali : John 3 : 1 3 : 2 6 : 2 3u ---- 12 1u ---- 4 4u ---- 4 x 4 = 16 Should have solved for 8u instead of 4u. Good practice: Cancel out the original ratio. Ali – 12 1 Quantity unchanged - John

  29. PERCENTAGE

  30. 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%

  31. Percentage 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.

  32. Percentage 2. Using wrong base MrJahan’s mass was 70kg in 2004. His mass increased to 84 kg in 2014 and reduced after much dieting to 67.2kg in 2016. • What is the percentage increase in his mass in 2014? • What is the percentage decrease in his mass in 2016?

  33. Percentage MrJahan’s mass was 70kg in 2004. His mass increased to 84 kg in 2014 and reduced after much dieting to 67.2kg in 2016. • What is the percentage increase in his mass in 2014? • What is the percentage decrease in his mass in 2016? Increase: 84 – 70 = 14 x 100% = 20% b) Decrease: 84 – 67.2 = 16.8 x 100% = 20% Common mistake: use wrong denominator

  34. GEOMETRY

  35. Geometry 1. Unable to identify parallel lines and angles within

  36. 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.

  37. Geometry 3. Unable to see isosceles triangles within a rhombus By adding the equal lines, pupils can see the isosceles triangles better.

  38. Geometry 4. Wrong naming of type of angles 180° - 23° - 132° = 25° (alternate angle) (vertically opposite angle)

  39. MENSURATION

  40. Mensuration – Area of triangles 1. Forgetting to multiply the half

  41. Mensuration – Area of triangles 2. Not able to identify the correct base and height pair

  42. Mensuration – Area of triangles 2. Not able to identify the correct base and height pair

  43. Mensuration – Area of triangles 3. Difference of areas mistake x 42 x 3

  44. Mensuration – Circles 1. Wrong use of formula Area of circle π x r x r (encouraged)π x r2 Circumference of circle 2 x π x r πx d (encouraged) Encouraged to distinguish the formulas better.

  45. Mensuration – Circles 2. Calculate for a circle instead of part of a circle

  46. Mensuration – Circles 3. Identifying the correct radius and diameter Small semicircle: Radius = 5cm Diameter = 10cm Big quadrant: Radius = 10cm Diameter = 20cm

  47. Mensuration – Circles 4. Incomplete sides when finding perimeter Pupils failed to add the two straight lines.

  48. Mensuration – Circles 4. Incomplete sides when finding perimeter Pupils failed to add the two straight lines.

More Related