Rivervale Primary School Maths Workshop for P4 to P6 Parents. 10 February 2018, Saturday a.m.

Transcription

1 Rivervale Primary School Maths Workshop for P4 to P6 Parents 10 February 2018, Saturday a.m.

2 MATHS ASSESSMENT, EXAM PAPER FORMAT AND APPROACH TO WORD PROBLEMS

3 Assessments: Formative (Assessment for Learning, AfL): Gather feedback about how pupils have learnt, e.g. multiplication of fractions Teacher to reinforce concepts, skills to close any learning gap / stretch pupils learning Workbooks and worksheets

4 Assessments: Summative (Assessment of Learning, AoL): Measure pupil achievement at a particular point in time Covers a range of topics, concepts and skills Used for banding, promotion, awards Exams

5 Assessments: P4 Subject-based Banding: Choice to take a combination of standard or foundation subjects Recognise pupils different learning abilities and provide greater flexibility to concentrate on the subjects they are good at Details:

6 2018 Assessments: P4, P5: 2 Semestral Assessments (Terms 2, 4) P6: 1 Continual Assessment (Term 1) 1 Semestral Assessment (Term 2) 1 Preliminary Exam (Term 3)

7 Achievement Bands, Grades / Mark Range: P4: Band Mark Range Below 50 P5, P6: Grade Mark Range A* A B C D E U (Ungraded) Below 20

8 P4 Exam Format: 1 h 45 min, 100 marks Section A (MCQ): Section B (SAQ): Section C (LAQ): 15 2-marks 15 2-marks 11 3/4/5-marks

9 P5P6 Exam Format: Paper 1: 1 hour paper, 45 marks (calculator not allowed) Booklet A (MCQ): Booklet B (SAQ): 10 1-mark and 5 2-marks 5 1-mark and 10 2-marks Paper 2: 1 h 30 min paper, 55 marks (calculator allowed) SAQ: 5 2-marks LAQ: 12 3/4/5-marks rs.pdf

10 Presentation of solutions: 1) Arrows for Percentage and Rate Use arrows to express workings when doing questions involving percentage and rate. Percentage: Wrong Right 100% = % 20 1% = = % = = 10 1% = % = 10

11 Presentation of solutions: 1) Arrows for Percentage and Rate Use arrows to express workings when doing questions involving percentage and rate. Rate: Wrong Right 20 min = 80 bottles 20 min 80 bottles 1 min = = 4 bottles 8 min = 8 4 = 32 bottles 1 min = 4 bottles 8 min 8 4 = 32 bottles

12 Presentation of solutions: 2) Equal sign for unitary method Use equal signs when doing questions involving units. Wrong Right 15 units units = 75 1 unit = 5 7 units 7 5 = 35 1 unit = = 5 7 units = 7 5 = 35

13 WHOLE SCHOOL APPROACH TO SOLVING WORD PROBLEMS: FORSTEN S 7 STEPS Step 1: Read the entire problem Step 2: Rewrite the question in sentence form, leaving space for the answer Step 3: Determine who (underline) and/or what (circle) is involved in the problem Step 4: Choose a suitable strategy Step 5: If model drawing is used, chunk the problem, adjust the unit bars and fill in the question mark Step 6: Correctly compute and solve the problem Step 7: Write and check that the answer makes sense

14 P4 & P5 HEURISTICS

15 Guess & Check (Trial & Error)

16 Step 1: Read the problem P4 Example Step 3: Determine who/what is involved 1) Karen had 20 coins, which consisted of fifty-cent and twenty-cent coins. She had a total of $8.20. How many fifty-cent coins did she have? Step 4: Choose a strategy Step 5: Chunk the problem Step 6: Compute and solve No. of 50-cent coins x 50 = x 50 = x 50 = x 50 = 700 No. of 20-cent coins x 20 = x 20 = x 20 = x 20 = 120 FIXED F + T = = = = = 20 TARGET Total = $8.20 Check / x $5 + $2 = $7 x $ $1.80 = $7.30 x $ $1.40 = $7.90 x $7 + $1.20 = $8.20 Step 2: Rewrite the questions Step 7: Write and check answer Ans: 14 fifty-cent coins

17 Step 1: Read the problem Step 3: Determine who/what is involved 4) In a class of 40 students, each boy received 4 sweets and each girl received 3 sweets from their teacher. Given that the teacher distributed 143 sweets, find the number of boys in the class. Step 4: Choose a strategy Step 5: Chunk the problem Step 6: Compute and solve No. of boys (4 sweets) x 4 = x 4 = x 4 = 92 No. of girls (3 sweets) x 3 = x 3 = x 3 = 51 FIXED B + G = = = = 40 P4 Example TARGET Total sweets = 143 Check / x = 140 x = 141 x = 143 Step 2: Rewrite the questions Step 7: Write and check answer Ans: 23 boys

18 2 units 1 unit 2) In a farm, there are twice as many chickens as horses. Given that there are 288 legs altogether, how many chickens are there in the farm? No. of horses (1unit) x 4 = x 4 = 120 No. of chickens (2 units) x 2 = x 2 = 120 TARGET Total legs = 288 P5 Example Guess & Check Check / x = 160 x = 240 x x 4 = x 2 = = chickens Ans:

19 P5 Example Unit x Value 2 units 1 unit 2) In a farm, there are twice as many chickens as horses. Given that there are 288 legs altogether, how many chickens are there in the farm? No. of animals No. of Total unit (units) x legs (legs) chickens 2 units x 2 4 leg units horse 1 unit x 4 4 leg units total units = 4 units + 4 units = 8 units 8 units = unit = = (horses) 36 2 units = 36 x 2 = 72 There are. 72 chickens

20 Model Drawing / Summary (Before & After Concept)

21 P4 Example (Model Drawing) 4 units 1 unit 1 part 1 part 1) Imran had 4 times as much money as Lucy. After Imran had given Lucy $210, they had an equal amount of money left. How much did each of them have at first? Before: After: I 4u 210 I 1p L 1u +210 L 1p Before After I L I L 1u 4 units 3 units units = 210 = unit = = 140 (L) I at 1st = 140 = x 4 Ans: Imran: $ 560 Lucy: $ 140

22 P4 Example (Compressed Model) 4 units 1 unit 1 part 1 part 1) Imran had 4 times as much money as Lucy. After Imran had given Lucy $210, they had an equal amount of money left. How much did each of them have at first? Before: After: I 4u 210 I 1p L 1u +210 L 1p I L 1u 1unit 4units units 3 units = 210 = unit = 420 = 140 (L) 3 I at 1st = 140 = x 4 Ans: Imran: $ 560 Lucy: $ 140

23 P5 Example (Summary) 1) On an MRT, the ratio of the number of male to the number of female passengers was 2 : 7. After 12 male passenger alighted, the ratio become 1 : 4. How many passengers were there on the trains at first? Summary Before: M : F 2u : 7u 12 After: 1u : 4u x4 x7 M : F 8u : 28u 12 7u :28u total units (b4)= 8units+ 28units = 36units 36units = 12 x 36 = 432 in units = 8units 7units = 1unit 1unit = 12 Ans: 432 passengers

24 P6 SHARING

25 Heuristics Draw a diagram/model Identifying patterns Act it out Guess-and-Check Before and After Supposition method Whole School Approach to solving word problems: Forsten s 7 steps

26 What to revise? Revise with skill Use files to find out areas of improvement How to revise? Cover solution and redo on rough paper When to revise? Constant revision Plan a schedule and stick to it Where to revise? Conducive environment

27 2017 PSLE Paper 2 Q10 Jess needs 200 pieces of ribbons, each of length 110 cm, to decorate a room for a party. Ribbon is sold in rolls of 25 m each, What is the least number of rolls of ribbons that Jess needs to buy? Wrong solution Total length needed: = m = 2500 cm No. of pieces: = Correct solution 25m = 2500cm Number of ribbons per roll: Number of rolls:

28 2015 PSLE Paper 1 Q6 Which of the following is likely to be the total mass of 8 one-dollar coins? 6 g about 6 paper clips 60 g about a tennis ball 600 g about a basketball 6000 g slightly heavier than a 5-kg bag of rice

29 2014 PSLE Paper 2 Q16a Wrong solution $8 x $10 x 0.8 = $ $8 = $15.20 Correct solution $10 x $8 x 0.8 = $9 + $6.40 = $15.40

30 2016 PSLE Paper 1 Q28 A trapezium T is drawn by joining dots on a square grid below with four straight lines. In the same way, a) Draw a rectangle with twice the area of T. Label the rectangle R. b) Draw a parallelogram with the same perimeter as T. Label the parallelogram P. Observe that trapezium T has 2 slanted sides and 8 straight sides. T Observe that area of trapezium T is 8 unit squares. Area of Rectangle R: 8 x 2 = 16 R R P

31 Tips For Answering PSLE Questions 1) Be calm and attempt questions systematically 2) Think flexibly and divergently 3) Do not always narrow down to a method of solution

32 Tips For Answering PSLE Questions 4) Don t skip too many questions --- attempt all the questions 5) Check your work, NOT just read 6) Complete the whole PSLE Mathematics book

33 COMMON MISCONCEPTIONS

34 P4 Misconceptions Fractions Problem Solving

35 Fractions Fractions are added together by adding the numerators together then adding the denominators together. Example + = + = 9 1 1

36 Fractions + = + =

37 Problem Solving 2 vases and 3 plates cost $1421. The cost of 1 plate is half the cost of 1 vase. What is the cost of 1 vase?

38 Step 1 2 vases and 3 plates cost $1421. $1421?

39 Step 2 The cost of 1 plate is half the cost of 1 vase. Plate Vase The cost of 2 = The cost of 1

40 Step 3 What is the cost of 1 vase? Vase Plate 7 units = $ unit = $ = $203 2 units = $203 2 = $406 $1421 Vase Plate A vase costs $406.

41 P5 Misconceptions Order of operations Triangles Fractions

42 Order of operations The rules 1. Work inside the brackets first 2. Multiply and divide, left to right 3. Add and subtract, left to right (20 5) x = 15 x = = 36 Left to right rule: = = 12 5 x 4 10 = = 2

43 Order of operations Some common mistakes: 15 5 x = 10 x = = 26 (36 15) x 2 = = x = = = 11 (36 15) x 2 = 21 x 2 = 42

44 Height Triangles Difficulty naming the related height A B C Base D

45 Height Triangles Base / Height Base / Height Base

46 Triangles Difficulty naming the related height P Height Q Base R Extension line S

47 Triangles Area of triangle ABC = 1 2 x 5 cm x 5 cm = 12.5 cm 2 Area of triangle ABC = 1 2 x 5 cm x 7 cm = 17.5 cm 2

48 Fractions 300 people attended a party. After 1 hour, 1 of the people 3 left the party. After another hour, 3 of the remaining 10 people left the party. How many people were left at the party in the end? Language issues 3/10 of the remaining people left the party people were left at the party

49 Fractions 300 people attended a party. After 1 hour, 1 of the people 3 left the party. After another hour, 3 of the remaining 10 people left the party. How many people were left at the party in the end? Only removed the group that Mistake #1: left after 2 hours = = x 3 = 60 No. of people that were left at the party = = 240 (incorrect)

50 Fractions 300 people attended a party. After 1 hour, 1 of the people 3 left the party. After another hour, 3 of the remaining 10 people left the party. How many people were left at the party in the end? Mistake #2: = x 300 = 190

51 Fractions 300 people attended a party. After 1 hour, 1 of the people 3 left the party. After another hour, 3 of the remaining 10 people left the party. How many people were left at the party in the end? Correct solution 15 units = unit = = 20 7 units = 20 x 7 = Remaining Alternative solution 2 3 x 7 10 = units = unit = = 20 7 units = 20 x 7 = 140 Left (1 st ) Left (2 nd )?

52 Fractions 300 people attended a party. After 1 hour, 1 of the people 3 left the party. After another hour, 3 of the remaining 10 people left the party. How many people were left at the party in the end? 2 nd Alternative Solution: 1 st hour : 1 3 left the party (which is 100 people ) 2 nd hour: 3 10 of the remaining people left the party (which is 60 people) No. of people left behind at the party = = 140 (Ans)

53 P6 Misconceptions Algebra Wrong Use of Notation

54 Algebra 2014 PSLE Paper 2 Q2 Three boys collected plastic bottles for recycling. Jaya collected 2m bottles which was half as many as what Kai collected. Kai collected 7 bottles more than Lat. How many bottles did they collect altogether? Give your answer in terms of m in the simplest form. Common mistake: J: 2m K: m L: m 7 Total: 2m + m + m 7 = 4m - 7

55 2014 PSLE Paper 2 Q2 Three boys collected plastic bottles for recycling. Jaya collected 2m bottles which was half as many as what Kai collected. Kai collected 7 bottles more than Lat. How many bottles did they collect altogether? Give your answer in terms of m in the simplest form. Solution J: 2m K: 2m 2 = 4m L: 4m 7 Total: 2m + 4m + 4m 7 = 10m - 7 J K L 2m 2m 2m 7

56 Wrong Use of Notation Wrong mathematical statements Wrong use of equal and approximation signs 2 = of the books = 40 Express 3 7 as a percentage, correct to 1 decimal place. 3 7 = 42.9% %