Core Concepts

Skills

Strategies

4 levels of Mathematics Languages

Languages Descriptions

Student’s

Language

By this level/ stage, teacher is using students’ language or

familiar objects for introduces and teaches students.

For example: apples, cars, books and so on.

Materials

Language

By this level/ stage, teacher is using concrete materials such

as counters, MAB blocks, Unifix Blocks.

Mathematics

Language

This level/ stage, teacher is using proper mathematics

language such as three, two, one, ….

Symbolic

Language

This level/ stage, teacher is using symbolic to teach students.

For example: 1,2,3…+, -, ,

Addition

Strategies:

1. Counting up (count on) is most easy way of

addition. It is a way to add small number into

bigger number.

For example: 3+2= ?

Then count up two from 3; 4,5.

Addition Strategies

2. Use Double

Students can remember the pattern of the

doubles in sequence.

1+1=2 4+4=8 7+7=14

2+2=4 5+5=10 8+8=16

3+3=6 6+6=12 9+9=18

If 2+1+2+1= 2+2+1+1

= 4 +2

= 6

4 Levels of Mathematics Languages

Children

Language

Alice has 4 books and Melody has 3 books , put all

books together on the table.

How many books on the table?

Materials

Language

There are 4 counters put 3 more counters make 7

counters altogether.

Mathematics

Language

Four add three equal seven

Symbolic

Language

4 + 3= 7

Subtraction

• Skill : Decomposition (Jamieson-Proctor, 2012)

Tens Ones4 2

- 1 5

2 7

3 12

Trade 1 ten

into 10 ones.

Strategy for Subtraction

• Cover-ups

This strategy is just like ‘take away’ skill.

For Example:

Alice has 3 cupcakes and rabbit take away one cupcake

from her. How many cupcakes does Alice has?

3 – 1 = ?

Multiplication

Concept

• Multiplication is repeated addition of some equal

set or group (Jamieson-Proctor, 2012).

For example:

Alice has 4 boxes of cupcakes and each box has 2

cupcakes. How many cupcakes does she has

altogether?

Answer : 4 X 2 = 2+2+2+2

= 8

Set Model

2+ 2+2 = 3X2

Array Model This model is used on measure area. For example: The length of a square is 2 cm and the width is 2 cm. What is the area of the square?

2 X2 = 4 cm

Measuremen

t Model

I bought 2 ribbons each 3 meters long. How many meters did I buy?

2X3 = 3+3= 6 meters

Combination

Model

I have 2 different patterns shirts and 3 different patterns of pants. How many outfits can I make?

2 X3 = 3+3=6

4 types of Multiplication Models (Jamieson-Proctor, 2012)

2 cms

2 cms

4 Levels of Mathematics Languages

Language Stage Materials Stage Language Stage Recording Stage

Student

Language

Concrete Materials such

as apples, balls .

Altogether, how many No symbols, children

draw pictures only

Materials

Language

Substituted objects.

E.g: unifix blocks,

counters

Add repeatedly, how

many, altogether

No symbols, children

draw pictures only

Mathematics

Language

Substituted objects.

E.g: unifix blocks,

counters

Multiply, multiplication,

euals

No symbols, children

draw pictures only

Symbolic

Language

- multiply 2 X 3 =

4 X 3=

Division

Concept

• Division is separating an amount into equals groups (Jamieson-Proctor, 2012).

• There are two ways to do the separation process : partition and quotation

Teaching sequences

• Use Student’s language (1st level of Mathematics language)

• Introduce: Teacher use concrete materials students are familiar with to

demonstrate the concept, whole class activity, oral activity.

• Models: Visual and verbal

• How : Teacher use familiar object to help student to make connection about the

concept of division is to separate the total amounts into equals groups. Division

is the inverse of multiplication.

Partition and Quotation

Partition Quotation

Partition is sharing objects into groups

equally and see how many there are in

the group.

12 3 = ？

Quotation is repeated subtraction

where a small quantity. To find the

number of groups needed to divide up

the total.

I have 8 flowers, give 2 flowers to each

friend. How many friends can I give to?

1 group of 3

2 group of 3

3 group of 3

4 group of 3