Mentari Upper Primary Number Sense

National Institute of Education
CHIJ Our Lady of Good Counsel
Mentari Books & Marshall Cavendish Education
present
Teaching
Number Sense
Dr Yeap Ban Har
Marshall Cavendish Institute
Singapore
Catholic High School (Primary)
Keys Grade School, Manila

develop
extend
assessment
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 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

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
Multiplication using Calculator – Primary 5

Teaching Multiplication
Demonstration
4-digit multiplied by 1-digit

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

Mr Chen 6 oranges.

Mr Chen 76 oranges.

Mr Chen 476 oranges.

Mr Chen 2476 oranges.

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

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’ Responses
Group H2

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

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
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

Keys Grade School, Manila

Problem Solving
Activity 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
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?

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Mentari Upper Primary Number Sense

by Jimmy Keng on Aug 08, 2010

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Mentari Upper Primary Number Sense — Presentation Transcript