Bina Bangsa School, Jakarta

y e a p b a n h a r @ g m a i l . c o m

w w w. b a n h a r . b l o g s p o t . c o m

In this short course, we will discuss:

• the basis of counting

• problems based on whole numbers

• teaching and doing problem solving based on everyday situations

• teaching word problems

• one learning theory

Another short course that is relevant for the teaching of whole numbers is Learning

Theories.

y e a p b a n h a r @ g m a i l . c o m

w w w. b a n h a r . b l o g s p o t . c o m

To Count or Not to Count

Count!

The nouns are the same.

We can count.

3 cats + 2 dogs = 5 cats ?!

3 cats + 2 dogs = 5 dogs ?1

3 animals + 2 animals = 5 animals

Problems Using Everyday Things

Problem 1

How many cups are there in this

structure when there are 9 cups in the

lowest layer?

Stack the Cups Problem

Look for a pattern!

Stack the Cups Problem

Big ideas:

• Making connections

• Mathematical modeling – connecting

reality to mathematical concepts

• Creative thinking – fluency, flexibility,

originality, elegance

• Looking for patterns and generalizing

Teaching Using Everyday Things

Are there enough straws?

Are there enough straws?

Are there seven

flowers?

More than seven? By

how many?

How many are there?

Design worksheets based on children’s art work

Everyday situations as:

• As data source

• As learning tool

• As problem

This can be used to facilitate skip counting.

Student scan also be asked to solve a problem – how many

children are there in the room?

Curriculum Structure

Curriculum Structure

Group Activity

When do students learn whatever they learn?

Your group is given a list of topics.

Discuss with your group members when each topic

is introduced and when it is completed in the

Singapore curriculum.

Are there missing topics?

K 1 2 3 4 5 6

Whole Numbers

Cardinal Numbers, Place Value

To

100

To

1000

To

10000

To

100000

To 10

million

Add and Subtract

Multiply

Divide

Factors

Multiples

Combined

Operations

Dienes

play structured practice

Word Problems

Problem 2

Addition – Word Problem

Strategies

• Count all

• Count on

• Make ten

Problem 3

Multiple Operations – Complex

110 g

290 g

Participants of Specialist Certificate Programme may choose to work on some of these.

The portfolio will include about ten entries to showcase your professional ability.

• Write up the solution of the Stack the Cups Problem. One portfolio entry may consists

of a collection of problems discussed in all the modules. Provide different ways of

solving the problems, include the ways discussed in class. Occasionally, problem

extension may be given. Typically one entry consists of about four problems from a

range of topics. You may also look for / design your own problems based on whole

numbers and solve them in different ways.

• Design a learning task based on everyday situation. Provide a photograph of the

everyday situation and a description of the task. Provide the responses that students

may give and what students can learn from this task. See an example of such a

portfolio entry at www.banhar.blogspot.com