The document is a teaching guide from the National Institute of Education focusing on mathematics instruction for primary students, covering key concepts such as place value, multiplication, and division. It includes teaching methodologies, example problems, and activities to enhance students' understanding of numbers and operations. The guide emphasizes the importance of regrouping in multiplication and problem-solving strategies across various mathematical scenarios.

1. National Institute of EducationCHIJ Our Lady of Good CounselMentari Books & Marshall Cavendish EducationpresentTeaching Number SenseDr Yeap Ban HarMarshall Cavendish InstituteSingaporeCatholic High School (Primary)Keys Grade School, Manila

2. developextendassessmentconsolidateThe Teaching Model

3. Place ValueKey Concept: The value of digits depends on its place or position.

4. Place ValueNumbers to 100 – Primary 1Numbers to 1 000 – Primary 2 Numbers to 10 000 – Primary 3 Numbers to 100 000 – Primary 4Numbers to 10 million – Primary 5

5. Teaching Place ValueActivity 1Combine your sets of digit cards. Shuffle the cards.Take turns to draw one card at a time.Place the card on your place value chart. Once you have placed the card in a position, you cannot change its position anymore.The winner is the one who makes the greatest number.

6. Re-groupimgThe idea of regrouping is central in large number operations. For example, in 39 x 6, one regroup 39 as 30 and 9 before performing the multiplication.The idea of regrouping can be incorporated into day-to-day activities such as keeping tally of groups’ points when they paly games. It also teaches graphing skills.

7. Score Board

8. Score Board

9. Score Board

10. MultiplicationKey Concept: Multiplication as equal groups, arrays, comparison and rate.

11. MultiplicationMultiplication – Primary 1 2, 3, 4, 5 and 10 Multiplication – Primary 2 6, 7, 8 and 9 Multiplication – Primary 3 2-digit by 1-digit – Primary 3 3-digit by 1-digit – Primary 34-digit by 1-digit – Primary 42-digit by 2-digit – Primary 4Multiplication using Calculator – Primary 5

12. Teaching MultiplicationDemonstration4-digit multiplied by 1-digit2-digit multiplied by 2-digit3-digit multiplied by 2-digit

13. Teaching MultiplicationMr Chen sold some oranges.Mr Ding sold 3 times as many oranges as Mr Chen.How many oranges did Mr Ding sell?

14. Teaching MultiplicationMr Chen 6 oranges.Mr Ding sold 3 times as many oranges as Mr Chen.How many oranges did Mr Ding sell?

15. Teaching MultiplicationMr Chen 76 oranges.Mr Ding sold 3 times as many oranges as Mr Chen.How many oranges did Mr Ding sell?

16. Teaching MultiplicationMr Chen 476 oranges.Mr Ding sold 3 times as many oranges as Mr Chen.How many oranges did Mr Ding sell?

17. Teaching MultiplicationMr Chen 2476 oranges.Mr Ding sold 3 times as many oranges as Mr Chen.How many oranges did Mr Ding sell?

18. There was a discussion on how to teach this page and if it is better to do the expanded form before the condensed form.expandedcondensed

19. DiscussionThere were participants who shared how their students were confused by the condensed form.In the teaching demonstration, the instructor showed how to teach Example 1 using the methodology of Example 4.In his opinion, it is best to teach students the expanded form before the condensed form.If there are students who cannot get the condensed form but are able to do the expanded form, it is alright.

20. Consolidating MultiplicationUse one set of the digit cards to fill in the five spaces.Make a correct multiplication sentence where a two-digit number multiplied by a 1-digit number gives a 2-digit product.Make as many multiplication sentences as you can.Are the products odd or even?x

21. DiscussionWhy are there so many even products and so few odd products?Participants’ ResponsesGroup H2

23. My number is 2!The product is 12.National Institute of Education

24. Teaching MultiplicationMr Chan stored petrol in 27 containers. Each container contained 2 litres of petrol.Mr Chan stored petrol in 27 barrels. Each barrel contained 30 litres of petrol.Mr Chan stored petrol in 27 barrels. Each barrel contained 32 litres of petrol.

25. Problem Solving: MultiplicationAB x CD = BA x DC

29. Word ProblemCarl and Ben had $ altogether.Carl’s share was twice as much as Ben’s.

30. Word ProblemCarl and Ben had $4686 altogether.Carl’s share was twice as much as Ben’s.

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39. DivisionKey Concept: Division as sharing and grouping. Concept of renaming.

40. DivisionDivision – Primary 1 Division without remainder – Primary 2 Division with remainder – Primary 3 2-digit by 1-digit – Primary 3 3-digit by 1-digit – Primary 34-digit by 1-digit – Primary 4Division and fraction – Primary 5

41. Teaching Division6000 sweets were given to the children at a fun fair.Each child received 3 sweetsHow many children were there at the fun fair?

42. Teaching Division6300 sweets were given to the children at a fun fair.Each child received 3 sweetsHow many children were there at the fun fair?

43. Teaching Division6381 sweets were given to the children at a fun fair.Each child received 3 sweetsHow many children were there at the fun fair?

44. Keys Grade School, Manila

45. Problem SolvingActivity 4Think of a number larger than 10 000 but smaller than 10 million.Jumble its digits up to make another number.Find their difference.Write the difference on a piece of paper. Circle one digit. Add up the rest of the digits.Tell me the sum of the rest of the digits and I will tell you the digit you circled.Example72 16727 67172 167 – 27 671 = 44 49644 4964 + 4 + 4 + 6 = 18Tell me 18.

46. Consolidating Order of OperationsUse the four given numbers and any of the four basic operations and at most one pair of brackets to make a number sentence that has a value of 10.Example: 1, 5, 6 and 9 are given. 9 + 6 – 5 x 1 = 10

47. Further Examples from TextbooksIn the textbooks, there are further examples of problem solving. Use what you learn in the workshop to teach this.

48. Problem SolvingHow can you use a calculator where the 4 key is not working to calculate 216 x 14 and 2856 ÷ 14?

50. Further Examples from Singapore SchoolsI have included further samples of problems that teachers in Singapore create. Try it yourself after the workshop.

51. Word ProblemAt first Shop A had 156 kg of rice and Shop B had 72 kg of rice. After each shop sold the same quantity of rice, the amount of rice that Shop A had was 4 times that of Shop B. How many kilograms of rice did Shop A sell?

52. Word ProblemEvery minute Machine A prints 12 pages more than Machine B. Machine A and Machine B together print a total of 528 pages in 3 minutes. At this rate, how many pages does Machine B print in 1 minute?

53. Word ProblemElliot was asked to number the pages of a book. When he had numbered the last page, he had written a total of 1089 digits. How many pages were in the book?

54. Word ProblemElliot was asked to number the pages of a book. When he had numbered the last page, he had written a total of 1089 digits. How many pages were in the book?

55. Word ProblemA transport company delivered 5 000 flower pots to a florist. It charged $3 for every flower pot safely delivered, but had to pay the florist $15 for every flower pot broken. If the florist paid a total of $14 784 for the delivery, how many flower pots were broken?