Mentari Upper Primary Number Sense

CHIJ Our Lady of Good Counsel

National Institute of Education

Catholic High School (Primary)

Keys Grade School, Manila

Mentari Books & Marshall Cavendish Education

present

Teaching Number Sense

Dr Yeap Ban Har

Marshall Cavendish InstituteSingapore

assessment

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consolidate The Teaching

Model

Place Value

Key Concept: The value of digits depends on its place or position.

Place Value

• Numbers to 100 – Primary 1• Numbers to 1 000 – Primary 2 • Numbers to 10 000 – Primary 3 • Numbers to 100 000 – Primary 4• Numbers to 10 million – Primary 5

Teaching Place Value

Activity 1• Combine 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.

Re-groupimg

• 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.

• 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.

Score Board= 10

7 8 4

5 6 4 8 6

9

A1 A2 B1 B2 C1 C2 D1 D2 E1 E2

Score Board

6 1 6

1 5

6 2 2

6

F1 F2 G1 G2 H1 H2 I1 I2 J1 J2

Score Board

8 5 8

2

6

K1 K2 L1 L2 M1 M2

Multiplication

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

Multiplication

• Multiplication – 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 3• 4-digit by 1-digit – Primary 4• 2-digit by 2-digit – Primary 4• Multiplication using Calculator – Primary 5

Teaching Multiplication

Demonstration• 4-digit multiplied by 1-digit• 2-digit multiplied by 2-digit• 3-digit multiplied by 2-digit

Teaching Multiplication

• Mr Chen sold some oranges.• Mr Ding sold 3 times as many oranges as Mr

Chen.• How many oranges did Mr Ding sell?

Teaching Multiplication

• Mr Chen 6 oranges.• Mr Ding sold 3 times as many oranges as Mr

Chen.• How many oranges did Mr Ding sell?

Teaching Multiplication

• Mr Chen 76 oranges.• Mr Ding sold 3 times as many oranges as Mr

Chen.• How many oranges did Mr Ding sell?

Teaching Multiplication

• Mr Chen 476 oranges.• Mr Ding sold 3 times as many oranges as Mr

Chen.• How many oranges did Mr Ding sell?

Teaching Multiplication

• Mr Chen 2476 oranges.• Mr Ding sold 3 times as many oranges as Mr

Chen.• How many oranges did Mr Ding sell?

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

condensed

expanded

Discussion

• There 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.

Consolidating Multiplication• Use 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

Discussion

• Why are there so many even products and so few odd products?

Participants’ ResponsesGroup H2

National Institute of Education

The product is 12.

My number is 2!

Teaching Multiplication

• Mr 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.

Problem Solving: Multiplication

AB x CD = BA x DC

Word Problem

• Carl and Ben had $ altogether.

• Carl’s share was twice as much as Ben’s.

Word Problem

• Carl and Ben had $4686 altogether.

• Carl’s share was twice as much as Ben’s.

4686

3000 1686

1500 186

180 6

Division

Key Concept: Division as sharing and grouping. Concept of renaming.

Division

• Division – 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 3• 4-digit by 1-digit – Primary 4• Division and fraction – Primary 5

Teaching Division

• 6000 sweets were given to the children at a fun fair.

• Each child received 3 sweets• How many children were there at the fun fair?

Teaching Division

• 6300 sweets were given to the children at a fun fair.

• Each child received 3 sweets• How many children were there at the fun fair?

Teaching Division

• 6381 sweets were given to the children at a fun fair.

• Each child received 3 sweets• How many children were there at the fun fair?

Keys Grade School, Manila

Problem SolvingActivity 4• Think 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.

Example

• 72 167

• 27 671

• 72 167 – 27 671 = 44 496

• 44 496

• 4 + 4 + 4 + 6 = 18

• Tell me 18.

Consolidating Order of Operations

• 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.

• Example: 1, 5, 6 and 9 are given.9 + 6 – 5 x 1 = 10

FURTHER EXAMPLES FROM TEXTBOOKS

In the textbooks, there are further examples of problem solving. Use what you learn in the workshop to teach this.

Problem Solving

• How can you use a calculator where the 4 key is not working to calculate 216 x 14 and 2856 ÷ 14?

FURTHER EXAMPLES FROM SINGAPORE SCHOOLS

I have included further samples of problems that teachers in Singapore create. Try it yourself after the workshop.

Word Problem

• 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?

Word Problem

• 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?

Word Problem

• 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?

Word Problem

• 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?

Word Problem

• 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?