1. Lower Primary Mathematics Parents’ Workshop 21 April 2012 Endeavour Primary School Mathematics Department 2012

2. Dear parents, Please ensure that your powerpoint slides are set in the “Notes” format so that you can read the additional notes on each slide. Thank you Mathematics Department

3. Objectives Share how number sense is taught in the classroom How parents can reinforce the children’s learning at home

4. Workshop Outline Whole Numbers Importance of CPA Approach Use of Concrete Materials at home for teaching number facts Multiplication Facts Heuristics & Thinking Skills

5. Whole Numbers P1 & P2 Syllabus Primary 1Primary 2 Number to 10Numbers to 1000 Number BondsMultiplication Tables of 2, 3,4, 5 & 10 Shapes & PatternsUsing Models Ordinal NumbersLength Numbers to 20Mass LengthMoney MassFraction Picture GraphsTime Numbers to 40Volume Multiplication & DivisionGraph DivisionLines & Surfaces Numbers to 100Shapes & Patterns Money

6. Whole Numbers Emphasis on the teaching & learning of whole numbers in lower primary syllabus Learning of later units are built on the understanding of concepts of whole numbers

7. Importance of Number Sense Number sense develops as students understand: -the size of numbers -develop multiple ways of thinking about and representing numbers -use numbers as referents -and develop accurate perceptions about the effects of operations on numbers

8. Importance of Number Sense An attribute of all successful users of Mathematics Developing confidence with numbers and logical skills give a child a real head-start for school & adult life Number sense enables students to understand and express quantities in their world.

9. Understanding Numbers in their World Examples: -whole numbers describe the number of students in a class or the number of days until a special event -Decimal quantities relate to money or metric measures -fractional amounts to describe ingredient measures -percent amounts describing test scores or sale prices

10. How does number sense begin? In early years, children are able to literally see small quantities, develop basic counting skills, and add small amounts. An early sense of number is mostly intuitive, developing through a variety of experiences.

11. Developing Number Sense at Home Home is a great place to start. Having early math conversations with children : – “How many spoons?” – “Which is more?” – “How do you know?” – “What’s one more?” – “Two more?” “One less?” – “How many steps to the door?” – “How long do you think the drive will take?”

12. Talk, talk, talk! These experiences bring math into the lives of children Students approach school with a growing sense of number, and parents and others can build on this

13. Number Bonds 10 46 4 + 6 = 10 40 100 60 40 + 60 = 100

14. Number Bonds 74 + 26 =____ 90 10 100

15. Number Facts Teaching of Number Facts in school Number Bonds Password Game Number Bonds recitation in class Use of 2 sided counters

16. Number Bonds 10 46 Family of Number Sentence 4 + 6 = 10 6 + 4 = 10 10 – 4 = 6 10 – 6 = 4 whole part

17. Misconception of more / less Students often have a misconception of more than and less than

18. More or Less 1. Siti has 10 marbles. Tim has 3 more marbles than Siti. How many marbles does Tim have? 10 + 3 = 13 3 more Tim has _13 marbles.

19. More / Less 2. There are 10 cows on a farm. There are 3 fewer goats than cows. How many goats are there on the farm? 10 – 3 = 7 3 fewer There are 7 goats on the farm.

20. More / Less 3. Dave has 12 toy cars. He has 2 more toy cars than Peter. How many toy cars does Peter have ? Misconception 12 + 2 = 14 Teaching points 1.Dave has 12 toy cars. 2. He --- > Dave 3. Dave has more ---> Peter has less 4. Dave has 2 more --- >Peter has 2 less Answer 12 – 2 = 10 2 more He Dave has 12 toy cars.

21. More / Less 4. May has 15 stamps. She has 3 fewer stamps than Jim. How many stamps does Jim have? Misconception 15 – 3 = 12 Answer 15 + 3 = 18 3 fewer Teaching points 1.May has 15 stamps. 2. She --> May 3. May has fewer -- > Jim has more 4. May has 3 fewer -- > Jim has 3 more May has 15 stamps. She

22. CPA Approach in Mathematics Concrete components include manipulative (for example, linking cubes, Cuisenaire,) measuring tools or other objects the students can handle during the lesson. Pictorial representations include drawings, diagrams, charts, or graphs that are drawn by the students or are provided for the students to read and interpret. Abstract refers to symbolic representations such as numbers or letters that the student writes or interprets to demonstrate understanding of a task.

23. Pictured relationships show visual representations of the concrete manipulative and help students visualize mathematical operations during problem solving. Ultimately, students need to reach that final abstract level by using symbols proficiently. Importance of CPA Approach

24. This CPA approach benefits all students but has been shown to be particularly effective with students who have mathematics difficulties, mainly because it moves gradually from actual objects through pictures and then to symbols. (Jordan, Miller, &Mercer, 1998).

25. Number Bonds ( CPA) 5 whole 3 2 part

26. Use of concrete materials for teaching Whole Numbers Normal household items such as : Beans Lego blocks ice-cream sticks straws buttons, etc. Poker cards

27. Importance of Knowing Multiplication Facts an essential part of the children's primary education building blocks for other math topics taught in school

28. Importance of Knowing Multiplication Facts applied in higher learning such as division, long multiplication, fractions & algebra. students who have not memorized the times tables will find these levels of math much more difficult than they need to be students who have not mastered their tables will very often fall behind in math and begin to loose confidence.

29. What is more important, memorization or understanding? It's not one or the other, it's both! A child must understand and memorize the facts.

30. Importance of Knowing Multiplication Facts At P3, pupils will be able to carry out Multiplication procedure and Division Procedure. At P4, pupils will need to use their multiplication facts into learning of Factors and Multiples, Fractions.

31. Multiplication Facts Skip – counting Password Game Multiplication Song Charts Multiplication Card Games

33. Helping your Child Memorize the Times Tables 1.Make sure there is understanding. 2.Explain why it is important. 3.Demonstrate what fast recall is. 4.Involve your child in the goal setting process. 5.Use a chart to monitor progress.

34. Helping your Child Memorize the Times Tables 6. Provide encouragement along the way. 7. Acknowledge their success. 8. Spend quality time together practicing. 9. And most importantly: Have fun!

35. Thinking Skills in P6 PSLE Specimen Paper - MCQ Lily spent 4 days making paper dolls for her friends. Each day, she managed to make 2 paper dolls more than the day before. She made a total of 24 paper dolls. How many paper dolls did she make on the last day?

36. Thinking Skills in P6 PSLE Specimen Paper Hassan had 5 tins of marbles. At first, each of the tins contained the same number of marbles. He took 18 marbles from each tin. After that, the total number of marbles left in the 5 tins was equal to the total number of marbles in 2of the tins at first. What was the number of marbles in each tin at first?

37. HEURISTICSP1P2P3P4P5P6 Making a Drawing / ModelsXXXXXX Looking for a PatternXXXXXX Act It OutXX Make a List / table XXXX Working Backwards XXXX Guess and Check XXX Using Before-After Concept XX Making Supposition XX* Restate the problem Simplify the problem Solve part of the problem Thinking Skills P1P2P3P4P5P6 Analysing Parts and WholesXXXXXX ComparingXXXXXX Identifying patterns and relationships XXXXX Deduction XXX Induction XX Spatial Visualisation X Total no of skills46791011

38. Why does my child require Thinking Skills ? Part of Assessment includes ‘Thinking Skills’ Requirements based on Mathematics Framework

39. Math Framework Mathematical Problem Solving C M A S P oncepts rocesses kills ttitudes etacognition Numerical, Algebraic Geometrical, Statistical Numerical calculation Algebraic manipulation Spatial visualisation Data analysis Measurement Estimation Use of Mathematical tools Thinking Skills Heuristics Modeling Applications reasoning, communication and connections Monitoring of one’s own thinking Self-regulation of learning Beliefs Interest Appreciation Confidence Perseverance

40. Challenges due to Paper format Paper 1 to be completed within 50 minutes (30 questions – less than 2 minutes/qn) Paper 2 – focuses on thinking skills as well as heuristics Culture shock in P5 for pupils

41. Our move in preparing your child Mathematics Department - a progressive approach Adoption of a Spiral Approach – Skills and Number Facts moving back continuously Focusing on Heuristics from lower primary levels – Act It Out, Draw a Diagram & Look for a Pattern

42. There are 4 girls and 4 boys in a group. The teacher wants 2 children to be the group leaders, a girl and a boy. How many different pairs can he choose from? Act It Out B1 B2 B3 B4 G1 G2 G3 G4 16 pairs

43. The picture below is made up of 13 toothpicks. Rearrange 4 toothpicks so that the picture shows one square above 3 squares. SOLUTION Act It Out

44. Study the pattern below. Draw the next pattern in the sequence. Look for a Pattern ?

45. What is the missing number? 3 8 6 5 ? 4 9 1 7 17 8 Look for a Pattern

46. 2 kg of grapes cost $5. How many kilograms of grapes can I buy with $20? Draw a Diagram $ 20 = 4 groups of $5 $ 20 $ 5 2 kg ? 4 × 2 kg = 8 kg

47. Some children are in a queue for ice cream. Sally is the fourth child from the front and fifth from the end of the queue. How many children are there in the queue? End Front Draw a Diagram

48. Thank You