the basic education core curriculum b.e. 2551 …...the basic education core curriculum b.e. 2551...

The Basic Education Core Curriculum

B.E. 2551 (A.D. 2008)

Mathematics

The Institute for the Promotion of Teaching Science and Technology IPST

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The Mathematics Learning Area

Why study mathematics?

Mathematics plays an important role in the development of the human mind. It inspires

creativity; implants logical and systematic thinking; enables one to make sound and precise

analyses of various situations, all of which in turn leads to accurate predictions, appropriate

planning, optimal problem-solving and decision-making in daily life. Mathematics also serves as a

tool for learning science, technology and other disciplines. Therefore, it can be said that

mathematics proves useful in everyday life; not only does it help improve the quality of life but it

also enables people to live in harmony with others.

What is to be learned in mathematics?

The Mathematics Learning Area aims to have all students continuously learning mathematics in

accordance with their full potential. The following are critical components of a mathematics

program:

o Number and Operations: number concepts and number sense, real number system,

properties of real numbers, number operations, ratio, percentage, problem-solving

involving number and application of numbers in real life

o Measurement: length, distance, weight, area, volume and capacity, money, time,

measurement units, estimation in measurement, trigonometric ratio, problem-solving in

measurement and application of measurement

o Geometry: geometric figures and properties of one-dimensional, two-dimensional and

three-dimensional geometrics figures, visualization, geometric models, theorem of

geometry, geometric transformation (translation, reflection and rotation)

o Algebra: patterns, relations, functions, sets and operations, reasoning, expression,

equation, systems of equations, inequality, graphs, arithmetic sequences, geometric

sequences, arithmetic series, and geometric series

o Data Analysis and Probability: selecting issues, questions and method of study, data

collection, organizing data, presentation of data, measures of central tendency and data

distribution, analyzing and interpreting data, polls, probability, application of statistics

and probability in giving an account of events and assisting in decision-making

The Institute for the Promotion of Teaching Science and Technology

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o Mathematical skills/processes: solving problems using various methods, reasoning,

communication and presentation in mathematics, connecting mathematical ideas to

other concepts in mathematics and to other disciplines

Learning Standards

Strand 1: Numbers and Operations

Students should be able to:

Standard M 1.1: Understand various ways numbers are represented and used in the real world.

Standard M 1.2: Understand the effects of operations on numbers and the relationships among

the operations, and use the number operations in solving problem.

Standard M 1.3: Use estimation in computation and problem-solving.

Standard M 1.4: Understand number systems and apply the properties of numbers.

Strand 2: Measurement


Standard M 2.1: Understand measurement concepts; measure and estimate quantities.

Standard M 2.2: Solve measurement problems.

Strand 3: Geometry


Standard M 3.1: Describe and analyze characteristics and properties of two- and three-

dimensional geometric figures.

Standard M 3.2: Use visualization, spatial reasoning, and geometric models in solving problems.

Strand 4: Algebra


Standard M 4.1: Understand and analyze patterns, relations, and functions.

Standard M 4.2: Use expressions, equations, inequalities, graphs, and other mathematical models

to represent situations; interpret and apply them to solve problems.

Strand 5: Data Analysis and Probability


Standard M 5.1: Understand and use statistical methods to analyze data.

Standard M 5.2: Use statistical methods and probability to make reasonable predictions.

Standard M 5.3: Use statistics and probability concepts in making decisions and solving problems.


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Strand 6: Mathematical Skills and Processes


Standard M 6.1: Solve problems, use reasoning; use mathematical language in communication

and representation, connect mathematical ideas to other mathematical concepts

and to other disciplines, think creatively.

Quality of learners:

Grade 3

After the completion of Grade Three, students should be able to:

o Understand numbers (whole numbers up to 100,000) and operations; develop number sense;

solve problems involving addition, subtraction, multiplication and division; judge the

reasonableness of answers.

o Understand the concepts of length, distance, weight, volume, capacity, time and money; Use

appropriate measurement methods and apply measurement concepts to solve problems.

o Recognize, identify and draw triangles, quadrilaterals, circles and ellipses; recognize and

identify cuboids, spheres, cylinders, points, line segments, rays, lines and angles.

o Complete patterns and describe the relationship in patterns.

o Collect and sort data about oneself and familiar surroundings; read and discuss data from

picture graphs, bar charts.

o Use various methods to solve problems; apply mathematical ideas, skills and processes to solve

problems in various situations; give reasons for decisions and make reasonable conclusions; use

mathematical language and symbols in communication and representation; connect

mathematical ideas to other mathematical concepts and to other disciplines; think creatively.

Grade 6

After the completion of Grade Six, students should be able to:

o Understand numbers (whole numbers, fractions, decimals up to 3 decimal places, percentage)

and operations; develop number sense; understand properties of numbers; solve problems

involving addition, subtraction, multiplication and division of whole numbers, fractions,

decimals up to 3 decimal places, percentage and judge the reasonableness of answers; give

estimation of whole numbers and decimals up to 3 decimal places.


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o Understand the concepts of length, distance, weight, area, volume, capacity, time, money,

direction, map and the size of angles; use appropriate measurement methods and apply

measurement concepts to solve problems.

o Describe characteristics and properties of triangles, quadrilaterals, circle, cuboid, cylinder,

cone, prism, pyramid, angles and parallel lines.

o Complete patterns and describe the relationships in patterns; solve problems involving patterns;

analyze situations or problems; use linear equations with one unknown to represent

situations/problems and solve the equations.

o Collect data; discuss data from picture graphs, bar charts, comparative bar charts, pie charts,

line graphs and tables; use picture graphs, bar charts, comparative bar charts and line graphs to

represent data; apply basic concepts of probability to estimate the possibility of events.

o Use various methods to solve problems; apply mathematical ideas, skills and concepts as well

as technology to solve problems; give reasons for decisions and make reasonable conclusions;

use mathematical language and symbols in communication and representation; connect

mathematical ideas to other mathematical concepts and to other disciplines; think creatively.

Grade 9

After the completion of Grade Nine, students should be able to:

o Understand real numbers, ratios, proportions, percentage, and exponentiation with integer

exponent; square roots and cube roots of real numbers; use estimation in number operations and

problem-solving; apply number concepts in everyday life.

o Find the surface area of prisms, cylinders and the volume of prisms, cylinders, pyramids, cones

and spheres; use appropriate measurement methods and units for determining length, area and

volume; apply measurement concepts in everyday life.

o Construct two-dimensional geometric figures using a compass and a straightedge and describe

the construction method; describe characteristics and properties of three-dimensional geometric

figures (prisms, pyramids, cylinders, cones and sphere).

o Understand the properties of congruent triangles and similar triangles, parallel lines, Pythagoras

theorem and its reverse; Use the aforementioned properties in reasoning and problem-solving;

understand and apply geometric transformations (translation, reflection, rotation).

o Visualize and describe two- and three-dimensional geometric shapes.


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o Analyze and describe patterns, the relationships in patterns; analyze mathematical situations/

problems; use one-variable equations, systems of two-variable linear equations, one-variable

linear inequalities and graphs to solve problems.

o Select issues, pose questions, design studies; collect data and select appropriate data

representations.

o Understand measures of central tendency (mean, median and mode) for ungrouped data and

select the appropriate measures; apply the concepts to evaluate statistical information.

o Understand random experiments, events and probability of events; use probability to predict the

likelihood of events and apply the concepts in decision-making.

o Use various methods to solve problems; apply mathematical ideas, skills and processes as well

as technology to solve problems in different contexts; give reasons for decisions and make

reasonable conclusions; precisely use mathematical language and symbols in communication

and representation; connect mathematical ideas to other mathematical concepts and to other

disciplines; think creatively.

Grade 12

After the completion of Grade Twelve, students should be able to:

o Understand real number system, absolute value of a real number, a real number expressed in

radical form and exponentiation with a rational exponent; use appropriate computation to

estimate the value of a real number written in radical expression and exponentiation; apply the

properties of real numbers to solve problems.

o Apply trigonometric ratios to estimate distance and height; solve measurement problems.

o Understand the concepts of sets and operations; apply the Venn-Euler diagram to solve

problems and justify reasoning.

o Understand and apply inductive reasoning and deductive reasoning.

o Understand the concepts of relations and functions; use relations and functions to solve

problems.

o Understand arithmetic sequences, geometric sequences and find the general terms; understand

the sum of the first n terms of arithmetic series, geometric series; use formulae to find the sum

of the first n terms of arithmetic series and the sum of the first n terms of geometric series;

apply the concepts to solve problems.


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o Understand how to solve one-variable equations and inequalities (of up to two degrees); use

graphs of equations, inequalities and functions to solve problems.

o Understand simple polling methods; select appropriate measures of central tendency in accord

with data and purpose; find mean, median, mode, standard deviation and percentile; analyze

data and apply data analysis to decision-making.

o Understand random experiments, events and probability of events; apply probability concepts in

predicting the outcomes of events, making decisions and solving problems.

o Use various methods to solve problems; apply mathematical ideas, skills and processes as well

as technology to solve problems in different contexts; give reasons for decisions and make

reasonable conclusions; precisely use mathematical language and symbols in communication

and representation; connect mathematical ideas to other mathematical concepts and connect

mathematical ideas, principle and processes to other disciplines; think creatively.


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Indicators and Core Content



Standard M 1.1: understand various ways numbers are represented and used in the real world.

Grade Indicators Core Content

1 1. Read and write whole numbers up to

100 in Hindu-Arabic numerals and

Thai numerals to represent

quantities.

• Counting to tell the number of objects

• Writing Hindu-Arabic numerals and Thai

numerals

• Reading numbers represented in Hindu-

Arabic numerals and Thai numerals

• Counting forward by 1s and 2s

• Counting backward by 1s

2. Compare and order whole numbers

up to 100.

• Place value and the value of each digit in

a number

• Using expanded forms to represent numbers

• Comparing numbers by the using the

symbols =, ≠, > and <

• Ordering whole numbers up to five numbers


1,000 in Hindu-Arabic numerals,

Thai numerals and in words to

represent quantities.

• Writing numbers in Hindu-Arabic

numerals, Thai numerals and in words



• Counting forward by 5s, 10s and 100s

• Counting backward by 2s, 10s and 100s

• Even and odd numbers

2. Compare and order whole number

up to 1,000

• Place value, the value of each digit in a

number and the use of 0 as a place holder

• Using expanded forms to represent

numbers

• Comparing numbers by the using the

symbols =, ≠, > and <

• Ordering whole numbers up to five numbers


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100,000 in Hindu-Arabic numerals,

Thai numerals and in words to

represent quantities.

• Writing numbers in Hindu-Arabic

numerals, Thai numerals and in words.



• Counting forward by 3s, 4s, 25s and 50s

• Counting backward by 3s, 4s, 5s, 25s and

50s

2. Compare and order whole numbers

up to 100,000.


number and the use of 0 as a place holder

• Using expanded form to represent

numbers

• Comparing numbers by using the symbols

=, ≠, > and <

• Ordering whole numbers up to five

numbers

4 1. Read and write whole numbers in

Hindu – Arabic numerals, Thai

numerals and in words; read and

write fractions and decimals (one

decimal place).

• Reading and Writing numbers in Hindu-

Arabic numerals, Thai numerals and in

words

• Interpretation of fractions; reading and

writing fractions

• Interpretation of decimals; reading and

writing decimals

2. Compare and order whole numbers,

fractions and decimals with one

decimal place.

• Place value, value of each digit in a

number and using 0 as a place holder

• Using expanded form to represent

numbers

• Comparing and ordering whole numbers

• Comparing and ordering like fractions

• Comparing and ordering decimals with

one decimal place


9


5 1. Read and write fractions, mixed

numbers and decimals (up to 2

decimal places).

• Identifying, reading and writing proper

fractions, improper fractions, mixed

numbers and decimals (up to 2 decimal

places)

• Fraction and a whole number equivalent

of a fraction

• Conversion of a whole number to a

fraction

• Conversion of an improper fraction to a

mixed number and vice versa

• Equivalent fractions

• Simplest form of a fraction

2. Compare and order fractions and

decimals (up to 2 decimal places).


whole number and a decimal (up to 2

decimals places)

• Using expanded forms to represent

decimals

• Comparing and ordering decimals (up to

2 decimal places)

• Comparing and ordering related fractions

3. Express a fraction as a decimal and a

percentage; express a percentage as

a fraction and a decimal ; express a

decimal as a fraction and a

percentage.

• Interpretation of percentages; reading and

writing percentages

• Conversion of a fraction whose

denominator is a multiple of 10 or 100 to

a decimal and to a percentage

• Writing percentages as fractions and

decimals

• Writing decimals (up to 2 decimal places) as

fractions and percentages


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6 1. Read and write decimals (up to 3

decimal places).

• Interpretation of decimals (up to 3

decimal places); reading and writing

decimals

2. Compare and order fractions and

decimals (up to 3 decimal places).


whole number and a decimal (3 decimal

places)

• Using expanded forms to represent decimals

• Comparing and ordering decimals (up to

3 decimal places)

• Comparing and ordering fractions

3. Express a decimal as a fraction and

express a fraction as a decimal.

• Writing decimals up to 3 decimal places

as fractions

• Writing fractions whose denominators are

multiples of 10, 100, 1,000 as decimals

7 1. Identify, give examples and compare

positive integers, negative integers,

zero, fractions and decimals

• Positive integers, negative integers, zero,

fractions and decimals

• Comparing integers, fractions and decimals

2. Understand the concepts of

exponentiation with integer

exponent and express numbers using

scientific notation.

• Exponentiation with integer exponent

• Expressing number by using scientific

notation (A × 10n where 1 A < 10 and n

is an integer)

≤

8 1. Express a fraction as a decimal and

express a repeating decimal as a

fraction.

• Fractions and repeating decimals

2. Identify real numbers and give

examples of rational and irrational

numbers.

• Rational and irrational numbers

3. Describe and identify square roots

and a cube root of a real number.

• Square root and cube root of a real

number

4. Apply the concepts of ratio,

proportion and percentage to solve

problem

• Ratio, proportion, percentage and their

application


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9 − −

10-12 1. Express the relationships of numbers

in the real numbers system.

• Real numbers

2. Understand the concepts of absolute

value of a real number.

• Absolute value of a real number

3. Understand the concepts of real

numbers written in exponentiation

with rational exponent and real

numbers written in radical

expression.

• Real numbers written in exponentiation

with rational indices and real numbers

written in radical expressions


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Standard M 1.2: understand the effects of operations on numbers and the relationships among

the operations, and use the number operations in solving problem.


1 1. Add and subtract whole numbers up

to 100; find the answers to 2-step

calculation involving addition and

subtraction; judge the reasonableness

of answers.

• Meaning of addition and use of the

addition symbol +

• Addition without renaming

• Meaning of subtraction and use of the

subtraction symbol –

• Subtraction without renaming

• 2-step calculation involving addition and

subtraction

2. Analyze and solve up to 2-step word

problems involving addition and

subtraction of whole numbers up to

100; judge the reasonableness of

answers.

• Word problems involving addition and

subtraction

• 2-step word problems involving addition

and subtraction

• Creating word problems involving

addition and subtraction

2 1. Add, subtract, multiply and divide

whole numbers up to 1,000; find the

answers to 2-step calculation

involving addition, subtraction,

multiplication and division; judge

the reasonableness of answers.

• Addition and subtraction

• Meaning of multiplication and use of the

multiplication symbol ×

• Multiplication of 1-digit number and up

to 2-digit number

• Meaning of division and use of the

division symbol ÷

• Subtraction without renaming.

• 2-step calculation involving addition,

subtraction, multiplication and division


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2

(cont.)


problems involving addition,

subtraction, multiplication and

division of whole numbers up to

1,000; judge the reasonableness of

answers.

• Word problems involving addition,


• 2-step word problems involving addition,



addition, subtraction, multiplication and

division


whole numbers up to 100,000 ; find

the answers to up to 3-step

calculation involving addition,


division; judge the reasonableness of

answers.


• Multiplication of 1-digit number and up

to 4-digit number

• Multiplication of 2-digit number and 2-

digit number

• Division of up to 4-digit number by a 1-

digit divisor

• Up to 3-step calculation involving


division




division of whole numbers up to

100,000 and judge the

reasonableness of answers

• Word problems involving addition

• Word problems involving subtraction

• Word problems involving multiplication

• Word problems involving division

• Up to 3-Step word problems involving


division



division word problems


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whole numbers; find the answers to

multi-step calculation involving

addition, subtraction, multiplication

and division; judge the



• Multiplication of a 1-digit number and a

more than 4-digit number

• Multiplication of a more than 1-digit

number and a more than 2-digit number

• Division of whole numbers with up to 3-

digit divisor

• Multi-step calculation involving addition,


• Average

2. Analyze and solve multi-step word



division of whole numbers; judge

the reasonableness of answers and

create word problems.

• Word problems involving addition and

subtraction


of a 1-digit number and a more than 4-

digit number


of a more than 1-digit number and a more

than 2-digit number

• Word problems involving division of

whole numbers with up to 3-digit divisor





division

3. Add and Subtract like fractions. • Addition and subtraction of like fractions


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fractions; find the answers to multi-

step calculation involving addition,


division; judge the reasonableness of

answers.

• Addition and subtraction of related

fractions

• Multiplication of a fraction and a whole

number

• Multiplication of fractions

• Division of a fraction by a whole number

• Division of a fraction by a fraction


subtraction and multiplication of fractions

2. Add, subtract, multiply and divide

decimals whose quotients are up to 2

decimal places; find the answers to

multi-step calculation involving


and division; judge the


• Addition and subtraction of up to 2-digit

decimals

• Multiplication of an up to decimal (2

decimal places) and a whole number

• Multiplication of a 1-digit decimal and

a 1-digit decimal


subtraction and multiplication of decimals




division of whole numbers,

fractions, decimals and percentage;

judge the reasonableness of answers

and create word problem involving


and division of whole numbers.

• 1-Step and multi-step word problems


multiplication and division of whole

numbers

• Word problems involving unitary method

• Creating 1-Step and multi-step word

problems involving addition, subtraction,


numbers


subtraction, multiplication and division of

fractions

• Multi-step word problems involving

addition subtraction and multiplication of

fractions


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• Solving and creating word problems

involving addition, subtraction and

multiplication of decimals

• Percentage word problems in various

contexts including profit, loss, discount

and sell price


fractions, mixed numbers and

decimals; find the answers to multi-

step calculation involving addition,


division and judge the


• Addition, subtraction, multiplication and

division of fractions


division of mixed numbers



fractions and mixed numbers


division of decimals whose answers are

up to 3 decimal places



decimals whose answers are up to 3

decimal places




division of whole numbers,

fractions, mixed numbers, decimals

and percentage; judge the

reasonableness of answers and

create word problem involving


and division of whole numbers.

• 1-step and multi-step word problems



numbers

• Creating 1-step and multi-step word

problems involving addition, subtraction,


numbers



multiplication and division of fractions



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multiplication and division of decimals

• creating 1-step and multi-step word

problems involving multiplication and

division of decimals

• Percentage word problems in various

contexts including profit, loss, discount,

sell price, product cost and interest


integers; apply the concepts to solve

problem; judge the reasonableness

of answers ; describe the effects of

adding, subtracting, multiplying, and

dividing integers ; identify the

relationship between addition and


division of integers.


division of integers

• Word problems involving integers

2. Add, subtract, multiply and divide

fractions and integers as well as apply

the concepts to solve problem; judge

the reasonableness of answers; describe

the effects of adding, subtracting,

multiplying, and dividing integers;

identify the relationship between

addition and subtraction, multiplication

and division of fractions and decimals.


division of fractions and decimals

• Word problems involving fractions and

decimals

3. Describe the effects of

exponentiation operations with

integers, fractions and decimals

• Exponentiation with integer exponent

4. Multiply and divide two quantities

with exponents where they have the

same base and integer exponents.

• Multiplication and division of quantities

with exponents where they have the same

base and integer exponents


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8 1. Find square roots and cube roots of

integers by factorization and apply

to solve problem; judge the


• Finding square roots and cube roots of

integers by factorization and its

application

2. Describe the effects of computing

square roots and cube roots of

integers, fractions, decimals;

describe the relationship between

exponentiation and the nth roots of

real number.

• Square roots and cube roots of real

numbers

9 − −

10-12 1. Understand the meaning and find the

result of addition, subtraction,

multiplication and division of real

numbers, real numbers written in

exponentiation with rational

exponents and real numbers written

in radical expressions.


division of real numbers


division of real numbers written in

exponentiation with rational exponent and

real numbers written in radical

expressions


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Standard M 1.3: use estimation in computation and problem-solving.


1 − −

2 − −

3 − −

4 − −

5 1. Estimate whole numbers to the

nearest ten, hundred and thousand

and apply the concept to solve

problems.

• Estimation of whole numbers to the

nearest ten, hundred and thousand

6 1. Estimate whole numbers to the

nearest ten thousands, hundred

thousands, million and apply the

concept to solve problems.

• Estimation of whole numbers to the

nearest ten thousands, hundred thousands

and million

2. Estimate decimals up to 3 decimal

places.

• Estimation of decimals to 1 decimals and

2 decimals places

7 1. Appropriately use estimation in

various situations including judging

the reasonableness of results from

numeral computation.

• Estimation and its application

8 1. Estimate square roots and cube roots

of real numbers and apply the

concept to solve problems; judge the


• Square roots and cube roots of real

numbers and their application

9 − −

10-12 1. Estimate the value of real numbers

written in radical expression and

exponentiation by using appropriate

computation.

• Estimation of real numbers written in

radical expression and exponentiation


20



Standard M 1.4: understand number systems and apply the properties of numbers.


1 − −

2 − −

3 − −

4 − −

5 − −

6 1. Use commutative, associative and

distributive properties in calculation.

• Addition and multiplication



2. Find the highest common factor

(H.C.F) and the lowest common

multiple (L.C.M.) of whole

numbers.

• Factors, prime numbers and prime factors

• Finding highest common factors

• Finding lowest common multiples

7 1. Apply concepts and properties of

integers to solve problems.

• Highest common factors and lowest

common multiples of whole numbers and

their application

• Application of concepts and properties of

integers

8 2. Identify the relationships among

real, rational and irrational numbers

• Rational and irrational numbers

9 − −

10 - 12 1. Understand real numbers addition

and multiplication properties,

equalities, inequalities and apply the

concept to solve problems.

• Properties of real numbers and their

applications


21



Standard M 2.1: understand measurement concepts, measure and estimate quantities.


1 1. Measure length, weight, volume and

capacity in non-standard units.

• Comparing lengths (taller, shorter, longer,

equal length, equal height)

• Measurement of length in non-standard units

• Comparing weights (heavier, lighter, equal

weight)

• Measurement of weight in non-standard

units

• Comparing volumes/capacities (greater

volume, smaller volume, equal volume,

greater capacity, smaller capacity, equal

capacity)

• Measurement of volume/capacity in non-

standard units

2. Tell time of the day, the number of

days in a week and the name of days

in a week.

• Time of the day (day, night, morning, late

morning, noon, afternoon, evening)

• Number and the names of days in a week

2 1. Measure length in meter and

centimeter and compare lengths

within the same unit.

• Measurement of length (meter, centimeter)

• Comparing lengths (same unit)

2. Measure weight in kilogram and

kheed* and compare weights within

the same unit.

• Measurement of weight (kilogram, kheed)

• Comparing weights (same unit)

3. Measure volume/capacity in liter

and compare volumes/capacities.

• Finding volume/capacity (liter)

• Comparing volume/capacity (liter)

2 4. Tell the amount of money from the • Denomination of coins and notes

* Thai customary unit 10 kheeds = 1 kilogram


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(cont.) given set of notes and coins. • Comparing the denomination of coins and

notes

• Telling the amount of money (baht,

satang**.)

5. Tell time from the clock face (to 5

minutes).

• Telling time from the clock face (to 5

minutes)

6. Tell day, month and year from a

calendar.

• Calendar reading and the months in a year

3 1. Measure length in meter, centimeter

and millimeter; select appropriate

measurement tools and compare

lengths.

• Measurement of length (meter, centimeter,

millimeter)

• Selecting appropriate measurement tools

(meter stick, ruler, body tape measure, tape

measure)

• Comparing lengths

• Estimation of length (meter, centimeter)

2. Measure weight in kilogram, gram

and kheed; select appropriate


weights.

• Measurement of weight (kilogram, gram,

kheed)

• Selecting appropriate measurement tools

(spring scales, bathroom scales, balance

scales and field scales)

• Comparing weights

• Estimation of weight (kilogram)

3. Measure volume/capacity in liter,

milliliter; select appropriate


volumes/capacities within the same

unit

• Finding volume/capacity (liter, milliliter)

• Selecting appropriate measurement tool

(tang***, liter, measuring spoons, measuring

cups, graduated cylinder, fuel jug)

• Comparing volumes/capacities (liter)

** In Thai currency 100 satang = 1 baht *** Thai customary unit 1 tang = 20 liters


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3

(cont.)

4. Tell time from the clock face (to 5

minutes); read and write time.

• Telling time from the clock face (to 5

minutes)

• Reading and writing time

5. Describe the relationships among

length units, weight units and time

units.

• The relationships among length units

(millimeter and centimeter; centimeter and

meter)

• The relationships among weight units

(kilogram and kheed, kheed and gram,

kilogram and gram)

• The relationships among time units (minute

and hour; hour and day; day and week; day

and month; month and year; day and year)

6. Read and write the amount of money

using decimal notation.

• Reading and writing the amount of money

using decimal notation

4 1. Describe the relationships among

length units, weight units,

volume/capacity units and time

units.

• The relationships among length units

(centimeter and millimeter; meter and

centimeter; kilometer and meter; waa****

and meter)

• The relationships among weight units (gram

and kilogram; kilogram and metric ton;

kheed and gram)

• The relationships among volume/capacity

units (milliliter and cubic centimeter;

milliliter and liter; cubic centimeter and

liter)

• The relationships among time units (second

and minute; minute and hour; hour and day;

day and week; day and month; week and

year; month and year; day and year)

**** Thai customary unit of length 1 waa = 2 meters


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2. Find the area of a rectangle. • Finding the area in square units and square

centimeters

• Find the area of a rectangle

3. Tell time from the clock face; read

and write time using ‘.’ and find the

duration of a time interval.

• Telling time from the clock face

• Reading and writing time using ‘.’

• Finding the duration of a time interval

4. Estimate length, weight,

volume/capacity

• Estimation of length (meter, centimeter,

waa)

• Estimation of weight (kilogram, kheed)

• Estimation of volume/capacity (liter)

5 1. Describe the relationships among

volume/capacity units.

• The relationships among volume/capacity

units (cubic centimeter, cubic meter)

2. Find the perimeter of quadrilaterals

and triangles.

• Perimeter of a quadrilateral

• Perimeter of a triangle

3. Find the area of a rectangle and a

triangle.

• Finding the area of a rectangle

• Finding the area of a triangle

4. Measure angles. • Measurement of angles using a protractor

• Measurement of reflex angles

5. Finding the volume/capacity of a

cuboid.

• Finding volume/capacity in cubic units,

cubic centimeters and cubic meters

• Use of a formula to find the volume/capacity of

a cuboid

6 1. Describe route or tell a location by

specifying the directions and the

actual distance from diagrams, maps

and plans.

• Directions

• Telling location by specifying directions

• Map scales

• Maps and plans reading

2. Find the area of a quadrilateral. • Finding the area of a quadrilateral by using

the side lengths

• Finding the area of a quadrilateral by using

the diagonal lengths

3. Find the circumference and the area

of a circle.

• Finding the circumference of a circle

• Finding the area of a circle


25


7 − −

8 1. Compare length units, area units

within the same system and across

the system; select appropriate

measurement tools.

• Finding length and area and its application

• Selecting measurement tools to find length

and area

2. Give close estimation of time,

distance, area, and volume/capacity

and describe strategies for

estimation.

• Estimation of time, distance, area, volume,

weight and theirs application

3. Appropriately use estimation in

measurement in various contexts.

9 1. Find the surface area of prisms and

cylinders.

• Surface area of prisms and cylinders

2. Find the volume of prisms,

cylinders, pyramids, cones and

spheres.

• Volume of prisms, cylinders, pyramids,

cones and spheres

3. Compare volume/capacity units

within the same system or across the

systems.

• Comparing volume/capacity units within the

same system or across the systems

4. Appropriate use of estimation in

measurement in different contexts.

• Estimation in measurement

10-12 1. Use trigonometric ratios to estimate

distance and height.

• Trigonometric ratios and its applications


26



Standard M 2.2: solve measurement problems.


1 − −

2 1. Solve measurement problems

involving lengths, weights,

volumes/capacities and money.

• Word problems involving lengths

(addition, subtraction)

• Word problems involving weights


• Word problems involving

volumes/capacities (addition, subtraction,

multiplication, division)

• Word problems involving money

(addition, subtraction, in baht only)








• Word problems involving

volumes/capacities (addition, subtraction)



• Word problems involving time

2. Read and write simple home

accounts.

• Reading and writing simple home

accounts

3. Read and write records of activities

with time specified.

• Reading and writing records of activities

with time specified






• Word problems involving volume/capacity


• Word problems involving time

2. Write simple home accounts. • Writing simple home accounts


27


3. Read and write records of activities

with time specified.

• Reading and writing records of activities

with time specified

• Timetable reading

5 1. Solve problems involving the area

and the perimeter of a rectangle and

a triangle.

• Word problems involving the area of a

rectangle and a triangle

• Word problems involving the perimeter of

a rectangle and a triangle

6 1. Solve problems involving the area

and the perimeter of a quadrilateral

and a circle.

• Estimating the area of a quadrilateral.

• Word problems involving the perimeter

and the area of a quadrilateral

• Word problems involving the

circumference and the area of a circle

2. Solve problems involving the

volume/capacity of a cuboid.

• Word problems involving the

volume/capacity of a cuboid

3. Draw a map specifying location and

a route map.

• Drawing a map to specify locations

• Drawing a route map

• Drawing a rough map

7 − −

8 1. Apply length and area concepts to

solve problems in various contexts.

• Application of length and area concepts to

solve problems

9 1. Apply area, surface area and volume

concepts to solve problems in

various contexts.

• Application of area, surface area and

volume concepts to solve problems

10-12 1. Solve word problems involving

distance and height by using

trigonometric ratios.

• Word problems involving distances and

heights


28

Strand 3: Geometry


Standard M 3.1: describe and analyze characteristics and properties of two – and three –

dimensional geometric figures.


1 1. Recognize triangles, quadrilaterals,

circles and ellipses.

• Triangles, quadrilaterals, circles and

ellipses

2 1. Identify triangles, quadrilaterals,

circles and ellipses.

• Triangles, quadrilaterals, circles and

ellipses

2. Identify cuboids, spheres and

cylinders.

• Cuboids, spheres and cylinders

3. Distinguish between a rectangle and

a cuboid; a circle and sphere.

• Two- and three-dimensional geometric

shapes

3 1. Identify two-dimensional shapes in

three-dimensional objects.

• Circles, ellipse, triangles, quadrilaterals,

pentagons, hexagons, octagons

2. Identify symmetric figures. • Symmetric figures

3. Specify name of given points, lines,

rays, line segments, and angles; use

notations to represent point, lines,

rays, line segments and angles.

• Points, lines, rays, line segments,

intersections, angles and notations

4 1. Identify the type of angles; specify

name and components of an angle

and use notations to represent

angles.

• Components of an angle

• Angles name and notations

• Type of angles (right angles, acute angles,

obtuse angles)

2. Identify parallel lines/line segments

and use notation to represent parallel

lines.

• Parallel lines and notation

3. Specify the components of a circle. • Components of a circle (centre, radius,

diameter and circumference)

4. Identify rectangles in objects and

distinguish between a square and an

oblong rectangle.

• Rectangles

• Squares and oblong rectangles


29


5. Identify symmetric figures and

specify the number of symmetrical

lines.

• Symmetric figures

5 1. Describe and classify three-

dimensional geometric shapes.

• Spheres, cylinders, cones, prisms and

pyramids

2. Describe and classify quadrilaterals;

describe the relationships among

types of quadrilaterals.

• Squares, rectangles, rhombus,

parallelograms, trapeziums, kites

3. Describe and classify triangles;

specify the components of a triangle

and describe the relationships among

types of triangles.

• Classification of triangles according to

sides

• Classification of triangles according to

angles

• Components of a triangle

• Interior angles of a triangle

6 1. Identify two-dimensional geometric

shapes in three-dimensional

geometric shapes.

• Components of three-dimensional

geometric shapes (cuboids, spheres,

cylinders, cones, prisms and pyramids).

2. Describe properties of diagonals of

quadrilaterals.

• Properties of diagonals of quadrilaterals

3. Identify parallel lines. • Identifying parallel lines from the size of

alternate angles

• Identifying parallel lines from two interior

angles on same side of a transversal (the

sum of the angles size is 180 degrees)

7 1. Construct geometric shapes and

describe basic geometric

construction.

• Basic geometric constructions (using a

compass and a straightedge)

1) Constructing a line segment with

the same length as a given line

segment

2) Bisecting a line segment

3) Constructing an angle with the

same side of a given angle


30


4) Bisecting an angle

5) Constructing a perpendicular line

from a point to a given line

6) Constructing perpendicular lines

from a point on a given line

2. Construct two-dimensional

geometric figures by basic geometric

construction.

• Constructing two-dimensional geometric

figures by using basic geometric

construction (using a compass and a

straightedge)

3. Investigate, observe and make

conjecture about geometric

properties.

• Geometric properties which require

investigation, observation and conjecture,

for example, the side of the opposite

angles formed by the intersection of two

line segments, the angle formed by the

intersection of diagonals of a quadrilateral

4. Describe three-dimensional shapes

in two-dimensional representations.

• Two-dimensional representations of

three-dimensional shapes

5. Identify front view, side view and

top view images of 3-dimensional

shapes.

• Front view, side view and top view

images of three-dimensional shapes

6. Draw or build three-dimensional

shapes made from cubes given front

view, side view and top view

images.

• Drawing or building three-dimensional

shapes made from cubes given front view,

side view and top view images

8 − −

9 1. Describe characteristics and

properties of prisms, cylinders,

cones and spheres.

• Characteristics and properties of prisms,

pyramids, cylinders, cones and spheres

10-12 − −


31

Strand 3: Geometry


Standard M 3.2: use visualization, spatial reasoning, and geometric models in solving problems.


1 − −

2 1. Draw two-dimensional geometric

shapes by using templates.

• Drawing triangles, quadrilaterals, circles

and ellipses by using templates

3 1. Draw two-dimensional geometric

shapes from different perspectives.

• Drawing two-dimensional geometric

shapes

2. Identify geometric shapes in

surroundings.

• Two-dimensional geometric shapes

4 1. Use geometric shapes to create

patterns and designs.

• Using geometric shapes to create patterns

and designs

5 1. Draw angles by using a protractor. • Types of angles

2. Draw rectangles, triangles and

circles.

• Drawing a rectangle

• Drawing a triangle

• Drawing a circle

3. Draw parallel lines by using ruler

and set squares.

• Drawing parallel lines through a given

point by using ruler and set squares

6 1. Make cuboids, cones, prisms and

pyramids from nets or two-

dimensional geometric shapes.

• Nets of three-dimensional geometric

shapes (cuboids, spheres, cylinders,

cones, prisms and pyramids)

• Making three-dimensional geometric

shapes

2. Draw quadrilaterals. • Drawing quadrilaterals when given

lengths and angles or when given the

length of diagonals

7 − −


32


8 1. Apply the properties of congruent

triangles and the properties of

parallel lines in reasoning and

problem-solving.

• A pair of equal sides and a pair of equal

angles of two congruent triangles

• Conditions for two triangles to be

congruent: side-angle-side; angle-side-

angle; side-side-side and angle-angle-side

• Properties of parallel lines

• Application of the properties of congruent

triangles and the properties of parallel line

in reasoning and problem-solving

2. Apply Pythagorean theorem and the

reverse in reasoning and problem-

solving.

• Pythagorean theorem and the reverse and

their application

3. Understand and apply geometric

transformations (translation,

reflection, rotation).

• Translation, reflection, rotation and their

application

4. Identify the images from translation,

reflection and rotation and describe

the geometric transformation when

given the initial and the result

images.

• Translation, reflection, rotation and their

application

9 1. Apply the properties of similar

triangles in reasoning and problem-

solving.

• Properties of similar triangles and their

application

10-12 − −


33

Strand 4: Algebra


Standard M 4.1: understand and analyze patterns, relations, and functions.


1 1. Complete number patterns whose

numbers increase by 1s, 2s and

number patterns that decrease by 1s

and describe the relationships in

patterns.

• Number patterns whose numbers increase

by 1s, 2s

• Number patterns whose numbers decrease

by 1s

2. Complete patterns according to one

of the following attributes: shape,

size, color and describe the

relationships in patterns.

• Patterns with one of the following

attributes: shape, size, color


numbers increase by 5s, 10s, 100s

and number patterns whose numbers

decrease by 2s, 10s, 100s; describe

the relationships in patterns.

• Number patterns whose number increase

by 5s, 10s, 100s

• Number patterns whose number decrease

by 2s, 10s, 100s

2. Complete patterns according to one

of the following attribute: shape,

size, color and describe the


• Patterns with one of the following



numbers increase by 3s, 4s, 25s, 50s,

number patterns whose numbers

decrease by 3s, 4s, 5s, 25s, 50s and

repeating number patterns; describe

the relationships in patterns.


by 3s, 4s, 25s, 50s

• Number patterns whose numbers decrease

by 3s, 4s, 5s, 25s, 50s

• Repeating number patterns

2. Complete patterns according to two

of the following attributes: shape,

size, color.

• Patterns with two of the following



34



numbers increase or decrease by

equal amount.


or decrease by equal amount

2. Complete patterns and describe the


• Patterns with two or more attributes

5 1. Complete number patterns and

describe the relationships in

patterns.

• Number patterns

6 1. Solve problems involving patterns. • Problems involving patterns

7 1. Analyze and describe the


• Relationships in patterns

8 − −

9 − −

10-12 1. Understand the concepts of set and

set operations.

• Sets and set operations

2. Understand and apply inductive and

deductive reasoning.

• Inductive and deductive reasoning

3. Understand the concepts of relations

and functions; express relations and

functions in various forms such as

tables, graphs and equations.

• Relations and functions

• Graphs of relations and functions

4. Understand the meaning of

sequences and find the general term

of a finite sequence.

• Sequence and the general term of a finite

sequence

5. Understand the meaning of

arithmetic sequences; find the

missing terms in arithmetic and

geometric sequences and apply the

concepts.

• Arithmetic and geometric sequences


35

Strand 4: Algebra


Standard M 4.2: use expressions, equations, inequalities, graphs, or other mathematical models to

represent situations, interpret and apply them to solve problems.


1 − −

2 − −

3 − −

4 − −

5 − −

6 1. Write equations to represent given

situations or problems; solve the

equations and check the answers.

• Linear equations with one unknown

• Solving equations by using addition-,

subtraction-, multiplication- and division-

property of equality

• Solving word problems by using

equations

7 1. Solve simple one-variable linear

equations.

• One-variable linear equations

2. Write linear equations to represent

simple situations or problems.

• Writing linear equations to represent

situations or problems

3. Solve word problems involving

simple one-variable linear equation;

judge the reasonableness of answers.

• Word problems involving one-variable

linear equations

4. Draw graphs on a coordinate plane

to represent the relationship of two

quantities.

• Graphs on a coordinate plane

5. Read and interpret graphs on a

coordinate plane.

8 1. Solve word problems involving one-

variable linear equation; judge the


• Word problems involving one-variable

linear equations


36


8

(cont.)

2. Find the coordinate of a point and

describe the result image of a

geometric shape that has undergone

translation, reflection and rotation in

a coordinate plane.

• Translation, reflection and rotation of a

geometric shape on a coordinate plane

9 1. Apply the concept of one-variable

linear inequality to solve problems;

judge the reasonableness of answers.

• One-variable linear inequality and its

application

2. Draw graphs to represent a linear

relationship of two quantities.

• Graphs represent a linear relationship of

two quantities

3. Draw graphs of two-variable linear

inequalities.

• Graphs of two-variable linear inequalities

4. Read and interpret graphs of a

system of two-variable linear

equations and other graphs.

• Graphs of a system of two-variable linear

equations

• Other graphs

5. Solve a system of two-variable

linear equations and apply the

concept to solve problems; judge the


• Systems of two-variable linear equations

and applications

10-12 1. Draw Venn-Euler diagrams to

represent sets and apply the concept

to solve problems.

• Venn-Euler diagrams

2. Justify reasoning by using Venn-

Euler diagrams.

• Reasoning

3. Solve one-variable equations and

inequalities of up to 2 degrees.

• One-variable equations and inequalities of

up to 2 degrees

4. Use relations and functions to

represent situations or problems and

apply the concepts to solve problems.

• Relations and functions

5. Use graphs of equations,

inequalities, functions to solve

problems.

• Graphs of equations, inequalities,

functions and their applications


37


10-12

(cont.)

6. Understand the meaning of sum of

the first n terms of arithmetic series

and geometric series; use formulae

to find sum of the first n terms of

arithmetic series and geometric

series and apply the concepts.

• Arithmetic series and geometric series


38



Standard M 5.1: understand and use statistical methods to analyze data.


1 − −

2 − −

3 1. Collect and sort data about oneself

and familiar surroundings.

• Collecting and sorting data about oneself

and familiar surroundings

2. Read simple picture graphs and bar

charts.

• Reading picture graphs and bar charts

4 1. Collect and sort data. • Collecting and sorting data

2. Read picture graphs, bar charts and

tables.

• Reading picture graphs

• Reading bar charts

• Reading tables

3. Make picture graphs and bar charts. • Making picture graphs and bar charts

5 1. Make bar charts with the numerical

data axis rescaled.

• Collecting and sorting data

• Making bar charts with the numerical data

axis rescaled

2. Read comparative bar charts. • Reading comparative bar charts

6 1. Read line graphs and pie charts. • Reading line graphs and pie charts

2. Make comparative bar charts and

line graphs.

• Making comparative bar charts and line

graphs

7 − −

8 1. Read pie charts and use pie charts to

represent data.

• Pie charts

9 1. Select issues and questions from

various problems or situations as

well as appropriate methods for

study and data collection.

• Data collection


39


2. Find arithmetic mean, median and

mode of ungrouped data and select

appropriate measure of central

tendency.

• Measures of central tendency and their

applications

3. Select appropriate representation of

data

• Representation of data

4. Read, interpret and analyze data • Data analysis

10 - 12 1. Understand simple polling method. • Polling

2. Find arithmetic mean, median,

mode, standard deviation and

percentiles.

• Measures of central tendency

• Measures of data distribution

• Find the ranking of data


40



Standard M 5.2: use statistical methods and probability to make reasonable predictions.


1 − −

2 − −

3 − −

4 − −

5 1. Describe events using the following

terms: certain, possible, impossible.

• Estimating the possibility of events

6 1. Describe events using the words that

have the same meaning as the following

terms: certain, possible, impossible.

• Estimating the possibility of events

7 1. Identify the event which is more

likely to occur from a given set of

events.

• Likelihood of events

8 1. From a given set of events, identify

events that are certain, impossible

and events which are more likely to

occur.

• Likelihood of events

9 1. Find the probability of events from

random experiments with equally

likely possible outcomes and apply

the concepts of probability in

making reasonable predictions.

• Random experiments and events

• Probability of events

• Application of probability concepts in

making prediction

10-12 1. Use poll results to make predictions

in given situations.

• Polls

2. Describe random experiments,

probability of events and use the

results to make predictions in given

situations.

• Basic combinatorics

• Random experiments

• Sample space

• Events



41



Standard M 5.3: use statistics and probability concepts in making decisions and solving problems.


1 − −

2 − −

3 − −

4 − −

5 − −

6 − −

7 − −

8 − −

9 1. Apply statistic and probability in

various decision-making situations.

• Application of statistic and probability in

decision-making

2. Discuss errors which may arise in

statistical representation. −

10-12 1. Use information and statistics to aid

decision-making.

• Statistics and information

2. Apply probability concepts in

decision-making and problem-

solving.



42

Strand 6: Mathematical Skills and Processes


Standard M 6.1: solve problems, use reasoning; use mathematical language in communication and

representation, connect mathematical ideas to other mathematical concepts and

to other disciplines, think creatively.


1 – 3 1. Use various methods in solving

problems. −

2. Appropriately use mathematical

concepts and mathematical

processes to solve problems in

various contexts.

−

3. Use reasoning in decision-making

and make reasonable conclusion. −

4. Properly use mathematical language

and symbols in communication and

representation.

−

5. Connect mathematical ideas to other

mathematical concepts and to other

disciplines.

−

6. Think creatively. −

4 – 6 1. Use various methods in solving

problems.

−




various contexts.

−


and make reasonable conclusion.

−

4. Accurately use mathematical

language and symbols in

communication and representation.

−


43



mathematical concepts and to other

disciplines.

−


7– 9 1. Use various methods in solving

problems.

−




various contexts.

−



−

4. Precisely use mathematical language


representation.

−


mathematical concepts and connect

mathematical concepts, principles

and processes to other disciplines.

−


10-12 1. Use various methods in solving

problems.

−


concepts, mathematical processes

and technology to solve problems in

various contexts.

−



−

4. Precisely use mathematical language


representation.

−


44



mathematical concepts and connect

mathematical concepts, principles

and processes to other disciplines.

−



the basic education core curriculum b.e. 2551 …...the basic education core curriculum b.e. 2551...

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