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.

MaterialsLanguage

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 DoubleStudents can remember the pattern of the doubles in sequence.

1+1=2 4+4=8 7+7=142+2=4 5+5=10 8+8=163+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 Ones 4 2

- 1 5

2 7

3 12

Trade 1 ten into 10 ones.

Strategy for Subtraction

• Cover-upsThis 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 = ?

MultiplicationConcept• 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

Measurement 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 QuotationPartition 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

✿ ✿ ✿ ✿ ✿ ✿ ✿ ✿