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- 1. National Institute of Education<br />CHIJ Our Lady of Good Counsel<br />Mentari Books & Marshall Cavendish Education<br />present<br />Teaching <br />Number Sense<br />Dr Yeap Ban Har<br />Marshall Cavendish Institute<br />Singapore<br />Catholic High School (Primary)<br />Keys Grade School, Manila<br />
- 2. develop<br />extend<br />assessment<br />consolidate<br />The Teaching Model<br />
- 3. Place Value<br />Key Concept: The value of digits depends on its place or position.<br />
- 4. Place Value<br />Numbers to 100 – Primary 1<br />Numbers to 1 000 – Primary 2 <br />Numbers to 10 000 – Primary 3 <br />Numbers to 100 000 – Primary 4<br />Numbers to 10 million – Primary 5<br />
- 5. Teaching Place Value<br />Activity 1<br />Combine your sets of digit cards. Shuffle the cards.<br />Take turns to draw one card at a time.<br />Place the card on your place value chart. <br />Once you have placed the card in a position, you cannot change its position anymore.<br />The winner is the one who makes the greatest number.<br />
- 6. Re-groupimg<br />The 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.<br />The idea of regrouping can be incorporated into day-to-day activities such as keeping tally of groups’ points when they paly games. <br />It also teaches graphing skills.<br />
- 7. Score Board<br />
- 8. Score Board<br />
- 9. Score Board<br />
- 10. Multiplication<br />Key Concept: Multiplication as equal groups, arrays, comparison and rate. <br />
- 11. Multiplication<br />Multiplication – Primary 1 <br />2, 3, 4, 5 and 10 Multiplication – Primary 2 <br />6, 7, 8 and 9 Multiplication – Primary 3 <br />2-digit by 1-digit – Primary 3 <br />3-digit by 1-digit – Primary 3<br />4-digit by 1-digit – Primary 4<br />2-digit by 2-digit – Primary 4<br />Multiplication using Calculator – Primary 5<br />
- 12. Teaching Multiplication<br />Demonstration<br />4-digit multiplied by 1-digit<br />2-digit multiplied by 2-digit<br />3-digit multiplied by 2-digit<br />
- 13. Teaching Multiplication<br />Mr Chen sold some oranges.<br />Mr Ding sold 3 times as many oranges as Mr Chen.<br />How many oranges did Mr Ding sell?<br />
- 14. Teaching Multiplication<br />Mr Chen 6 oranges.<br />Mr Ding sold 3 times as many oranges as Mr Chen.<br />How many oranges did Mr Ding sell?<br />
- 15. Teaching Multiplication<br />Mr Chen 76 oranges.<br />Mr Ding sold 3 times as many oranges as Mr Chen.<br />How many oranges did Mr Ding sell?<br />
- 16. Teaching Multiplication<br />Mr Chen 476 oranges.<br />Mr Ding sold 3 times as many oranges as Mr Chen.<br />How many oranges did Mr Ding sell?<br />
- 17. Teaching Multiplication<br />Mr Chen 2476 oranges.<br />Mr Ding sold 3 times as many oranges as Mr Chen.<br />How many oranges did Mr Ding sell?<br />
- 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.<br />expanded<br />condensed<br />
- 19. Discussion<br />There were participants who shared how their students were confused by the condensed form.<br />In the teaching demonstration, the instructor showed how to teach Example 1 using the methodology of Example 4.<br />In his opinion, it is best to teach students the expanded form before the condensed form.<br />If there are students who cannot get the condensed form but are able to do the expanded form, it is alright.<br />
- 20. Consolidating Multiplication<br />Use one set of the digit cards to fill in the five spaces.<br />Make a correct multiplication sentence where a two-digit number multiplied by a 1-digit number gives a 2-digit product.<br />Make as many multiplication sentences as you can.<br />Are the products odd or even?<br />x<br />
- 21. Discussion<br />Why are there so many even products and so few odd products?<br />Participants’ Responses<br />Group H2<br />
- 22.
- 23. My number is 2!<br />The product is 12.<br />National Institute of Education<br />
- 24. Teaching Multiplication<br />Mr Chan stored petrol in 27 containers. Each container contained 2 litres of petrol.<br />Mr Chan stored petrol in 27 barrels. Each barrel contained 30 litres of petrol.<br />Mr Chan stored petrol in 27 barrels. Each barrel contained 32 litres of petrol.<br />
- 25. Problem Solving: Multiplication<br />AB x CD = BA x DC<br />
- 26.
- 27.
- 28.
- 29. Word Problem<br />Carl and Ben had $ altogether.<br />Carl’s share was twice as much as Ben’s.<br />
- 30. Word Problem<br />Carl and Ben had $4686 altogether.<br />Carl’s share was twice as much as Ben’s.<br />
- 31. 4686<br />3000<br />1686<br />1500<br />186<br />180<br />6<br />
- 32.
- 33.
- 34.
- 35.
- 36.
- 37.
- 38.
- 39. Division<br />Key Concept: Division as sharing and grouping. Concept of renaming.<br />
- 40. Division<br />Division – Primary 1 <br />Division without remainder – Primary 2 <br />Division with remainder – Primary 3 <br />2-digit by 1-digit – Primary 3 <br />3-digit by 1-digit – Primary 3<br />4-digit by 1-digit – Primary 4<br />Division and fraction – Primary 5<br />
- 41. Teaching Division<br />6000 sweets were given to the children at a fun fair.<br />Each child received 3 sweets<br />How many children were there at the fun fair?<br />
- 42. Teaching Division<br />6300 sweets were given to the children at a fun fair.<br />Each child received 3 sweets<br />How many children were there at the fun fair?<br />
- 43. Teaching Division<br />6381 sweets were given to the children at a fun fair.<br />Each child received 3 sweets<br />How many children were there at the fun fair?<br />
- 44. Keys Grade School, Manila<br />
- 45. Problem Solving<br />Activity 4<br />Think of a number larger than 10 000 but smaller than 10 million.<br />Jumble its digits up to make another number.<br />Find their difference.<br />Write the difference on a piece of paper. Circle one digit. Add up the rest of the digits.<br />Tell me the sum of the rest of the digits and I will tell you the digit you circled.<br />Example<br />72 167<br />27 671<br />72 167 – 27 671 = 44 496<br />44 496<br />4 + 4 + 4 + 6 = 18<br />Tell me 18.<br />
- 46. Consolidating Order of Operations<br />Use 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.<br />Example: 1, 5, 6 and 9 are given.<br /> 9 + 6 – 5 x 1 = 10<br />
- 47. Further Examples from Textbooks<br />In the textbooks, there are further examples of problem solving. Use what you learn in the workshop to teach this.<br />
- 48. Problem Solving<br />How can you use a calculator where the 4 key is not working to calculate 216 x 14 and 2856 ÷ 14?<br />
- 49.
- 50. Further Examples from Singapore Schools<br />I have included further samples of problems that teachers in Singapore create. Try it yourself after the workshop.<br />
- 51. Word Problem<br />At 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?<br />
- 52. Word Problem<br />Every 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?<br />
- 53. Word Problem<br />Elliot 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?<br />
- 54. Word Problem<br />Elliot 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?<br />
- 55. Word Problem<br />A 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?<br />

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