Teacher Guide - e- · PDF fileTeacher Guide 6 In collaboration with Dickens Publishing Ltd....

PratomsuksaBased on the Basic EducationCurriculum B.E.2551

TeacherGuide

6In collaboration withDickens Publishing Ltd. (UK)

Mathematics Pratomsuksa 6 – Lesson Plan 1

PPPPPPPPrrrrrrrreeeeeeeeffffffffaaaaaaaacccccccceeeeeeee

The learning of Mathematics imparts many skills that contribute to the

development of the human mind. It trains the learner to think methodically and

rationally, analyse various types of situations, anticipate and plan, make

decisions and solve problems. Mathematics also serves as a tool that facilitates

the gaining of knowledge related to science and technology. Mathematical

skills and knowledge are indeed essential to enhance our standard and quality

of living in the modern area.

The Basic Education Core Curriculum aims to inculcate the following

five key competencies among students:

1. Communication Skill

2. Thinking Skill

3. Problem – Solving Skill

4. Applying Life Skill

5. Technological Application Skill

The learning areas in the study of mathematics are designed to enable

students to acquire mathematical skills and knowledge according to their

utmost potential. The learning areas are as follows:

• Numbers and Operations: numerical concepts and sense of

perception; real number system; properties of real numbers; operation of

numbers; ratio; percentage; problem-solving involving numbers; and

application of numbers in real life.


• Measurement: length; distance; weight; area; volume and capacity;

money and time; measuring units; estimation for measurement; trigonometric

ratio; problem-solving regarding measurement; and application of

measurement in various situations

• Geometry: geometric figures and properties of one-dimensional

geometric figures; visualization of geometric models; geometric theories; and

geometric transformation through translation, reflection and rotation

• Algebra: pattern; relationship; function; sets and their operations;

reasoning; expression; equation; equation system; inequality; graph; arithmetic

order; geometric order; arithmetic series; and geometric series

• Data Analysis and Probability: determining an issue; writing

questions; determining methods of study; study; data collection,

systematization and presentation; central tendency and data distribution; data

analysis and interpretation; opinion polling; probability; application of

statistical knowledge and probability; application of probability in explaining

various situations as well as for facilitating decision-making in real life

• Mathematical Skills and Processes: problem-solving through

diverse methods; reasoning; communication; communication and presentation

of mathematical concepts; linking mathematics with other disciplines; and

attaining ability for creative thinking


Strands and Learning Standards

Strand 1: Numbers and Operations

Standard M1.1: Understanding diverse methods of presenting numbers and

their application in real life

Standard M1.2: Understanding results of operations of numbers,

relationships of operations, and application of operations

for problem-solving

Standard M1.3: Use of estimation in calculation and problem-solving

Standard M1.4: Understanding of numerical system and application of

numerical properties

Strand 2: Measurement

Standard M2.1: Understanding of the basics of measurement; ability to

measure and estimate the size of objects to be measured

Standard M2.2: Solving measurement problems

Strand 3: Geometry

Standard M3.1: Ability to explain and analyse two-dimensional and three-

dimensional geometric figures

Standard M3.2: Ability for visualisation, spatial reasoning and application

of geometric models for problem-solving

Strand 4: Algebra

Standard M4.1: Understanding and ability to analyse pattern, relation and

function

Standard M4.2: Ability to apply algebraic expressions, equations,

inequalities, graphs and other mathematical models to


represent various situations as well as interpretation and

application for problem-solving

Strand 5: Data Analysis and Probability

Standard M5.1: Understanding and ability to apply statistical methodology

for data analysis

Standard M5.2: Application of statistical methodology and knowledge of

probability for valid estimation

Standard M5.3: Application of knowledge of statistics and probability for

decision-making and problem-solving

Strand 6: Mathematical Skills and Processes

Standard M6.1: Capacity for problem-solving, reasoning; communication

and presentation of mathematical concept; linking various

bodies of mathematical knowledge and linking

mathematics with other disciplines; and attaining ability for

creative thinking

For common understanding and correct interpretation, the curriculum

prescribes various codes for learning standards and indicators. One example is

shown below:

M 1.1 Gr 6/2

M Subject area of Mathematics

1.1 First subject area, Standard 1

Gr6/2 Indicator 2 for Grade (Pratomsuksa) 6


Learners’ Quality

•••• Have numerical knowledge, understanding, and sense of cardinal

numbers and zero, fractions, decimals of not more than three places,

percentages, operation of numbers and properties of numbers; can solve

problems involving addition, subtraction multiplication and division of

cardinal numbers, fractions, decimals of not more than three places and

percentages; are aware of validity of the answers reached; and can find

estimates of cardinal numbers and decimals of not more than three places.

•••• Have knowledge and understanding of length, distance, weight, area,

volume, capacity, time, money, direction, diagrams and size of angles; can

measure correctly and appropriately; and can apply knowledge of

measurement for solving problems faced in various situations.

•••• Have knowledge and understanding of characteristics and properties

of triangles, squares, circles, cuboids, cylinders, cones, prisms, pyramids

angles and parallel lines.

•••• Have knowledge and understanding of patterns and can explain their

relationships and solve problems involving patterns; can analyse situations or

problems as well as write linear equations with an unknown that can be

solved.

•••• Can collect data and information and discuss various issues from

pictograms, bar charts, comparative bar charts, pie charts, line graphs and

tables that are availed of for presentation; and can apply knowledge of basic

probability in projecting various possible situations.


•••• Can apply diverse methods for problem-solving, availing of

mathematical and technological knowledge, skills, and processes

appropriately to solve problems faced in various situations; can suitably

provide reasoning for decision-making and appropriately present the

conclusions reached; can use mathematical language and symbols for

communication as well as accurate and appropriate communication and

presentation of mathematical concepts; can link various bodies of

mathematical knowledge and can link mathematical knowledge with other

disciplines; and have attained ability for creative thinking.


YYYYYYYYYYYYeeeeeeeeeeeeaaaaaaaaaaaarrrrrrrrrrrrllllllllllllyyyyyyyyyyyy TTTTTTTTTTTTeeeeeeeeeeeeaaaaaaaaaaaacccccccccccchhhhhhhhhhhhiiiiiiiiiiiinnnnnnnnnnnngggggggggggg PPPPPPPPPPPPllllllllllllaaaaaaaaaaaannnnnnnnnnnn

Mathematics Grade 6 (Pratomsuksa 6)

15 chapters 160 hours

Learning area Duration

(hours)

1. Whole Numbers • Rounding off whole numbers • Combined operations • Solving word problems involving combined

operations

6

2. Equations • Equations • Equation with one unknown • Addition and subtraction properties of equality • Multiplication and division properties of equality • Solving equations using properties of equality • Using equations to solve word problems

11

3. Factors • Factors of whole numbers • Prime factors • Factorization of whole numbers • Highest Common Factor (HCF) • Lowest Common Multiple (LCM) • Using HCF and LCM to solve word problems

14

4. Fractions • Comparing fractions • Ordering fractions • Simplifying fractions • Addition and subtraction of fractions • Multiplication of fractions • Division of fractions • Solving word problems involving fractions • Combined operations on fractions

13


5. Decimals • Three-decimals place numbers • Place values and digit values of digits in decimals • Writing decimals in expanded form • Comparing and ordering decimals • Decimals and fractions • Rounding off decimals

10

6. Addition, Subtraction and Multiplication of Decimals • Addition of decimals • Subtraction of decimals • Multiplication of decimals • Using addition, subtraction and multiplication of

decimals to solve word problems

11

7. Division of Decimals • Dividing decimals by whole numbers • Converting fractions to decimals • Dividing decimals by decimals • Using division to solve word problems • Combined operations on decimals

10

8. Percentage • Finding the percentage of a number out of another • Solving problems involving percentage • Simple interest

15

9. Directions and Diagrams • Directions • Diagram

10

10. Angles and Line Segments • Measuring angles • Drawing angles • Angles of equal sizes • Dividing angles and line segments in half

9

11. Parallel Lines • Corresponding, alternate and interior angles • Determining if two or more lines are parallel lines

7


12. Quadrilaterals • Diagonals of quadrilaterals • Constructing quadrilaterals • Areas of parallelograms and trapeziums • Estimating areas of quadrilaterals • Solving problems involving quadrilaterals

13

13. Circles • Circumference of a circle • Area of a circle

8

14. Three-Dimensional Geometric Shapes and Volume of Cuboid

• Nets • Models of geometric solids • Volume of cuboid

7

15. Statistics and Probability •••• Multiple bar charts •••• Line graphs •••• Pie charts •••• Probability

10

16. Patterns •••• Patterns •••• Solving problems involving patterns

7

Note: The hours needed for each subtopic can be changed when necessary.

The above allocated hours are just a suggestion. Total hours for this subject is

as prescribed in the basic learning time structure, while the learners must attain

the standard as prescribed in the learning standards and indicators.


IIIIIIIIIIIInnnnnnnnnnnnddddddddddddiiiiiiiiiiiiccccccccccccaaaaaaaaaaaattttttttttttoooooooooooorrrrrrrrrrrrssssssssssss aaaaaaaaaaaannnnnnnnnnnndddddddddddd LLLLLLLLLLLLeeeeeeeeeeeeaaaaaaaaaaaarrrrrrrrrrrrnnnnnnnnnnnniiiiiiiiiiiinnnnnnnnnnnngggggggggggg AAAAAAAAAAAArrrrrrrrrrrreeeeeeeeeeeeaaaaaaaaaaaassssssssssss

CCCCCCCCCCCChhhhhhhhhhhhaaaaaaaaaaaapppppppppppptttttttttttteeeeeeeeeeeerrrrrrrrrrrr 111111111111 WWWWWWWWWWWWhhhhhhhhhhhhoooooooooooolllllllllllleeeeeeeeeeee NNNNNNNNNNNNuuuuuuuuuuuummmmmmmmmmmmbbbbbbbbbbbbeeeeeeeeeeeerrrrrrrrrrrrssssssssssss ((((((((((((666666666666 hhhhhhhhhhhhoooooooooooouuuuuuuuuuuurrrrrrrrrrrrssssssssssss))))))))))))

Indicator Learning Area

M1.2 Gr6/2 Analyse and show method of

finding answers to problems and mix-problems

of cardinal numbers, fractions mixed numbers,

decimals and percentages, as well as be aware

of validity of the answers, and can construct

problems involving cardinal numbers.

M1.4 Gr6/1 Use communicative, associative

and distributive properties in calculation.

•••• Combined operations

•••• Solving word problems

involving combined

operations

M1.3 Gr6/1 Make approximate estimates of

various integers of cardinal numbers, which can

be applied.

•••• Rounding off whole

numbers

LLL eeeaaarrr nnniii nnnggg OOObbbjjj eeecccttt iii vvveeesss

Students will be taught to:

1. Understand how to round off whole numbers.

2. Perform combined operations.

LLL eeeaaarrr nnniii nnnggg OOOuuuttt cccooommmeeesss

Students will be able to:

1. Round off whole numbers.


3. Solve word problems involving combined operations


LLL eeeaaarrr nnniii nnnggg AAArrr eeeaaasss

•••• Rounding off whole numbers

•••• Combined operations

•••• Solving word problems involving combined operations

TTTeeeaaaccchhhiii nnnggg aaannnddd LLL eeeaaarrr nnniii nnnggg AAAcccttt iii vvviii ttt iii eeesss

1st – 2nd hours (Rounding Off Whole Numbers)

1. Guide students to always look at the digit on the right of the place value

to which the number is to be rounded off, when they are going to round

off numbers.

2. Use the examples on pages 2 and 3 to guide students to round off

numbers.

3. Ask students to try Practice on page 3. Discuss the answers with them.

4. Have students work on Exercises A to C on pages 2 and 3 of the

workbook as their homework.

3rd hour (Combined Operations)

1. Help students to recall the commutative property, the associative

property and the distributive property. Use the examples on pages 4 and

5.

2. Remind students to do the operations in the brackets, follow by the

multiplication and division, and then addition and subtraction when they

are performing combined operations.

3. Refer to the example on pages 5 and 6.


5. Have students work on Exercises D to F on pages 3 and 4 of the



4th hour (Solving Word Problems Involving Combined Operations)

1. Use the example on page 7 to guide students to solve word problems

involving combined operations.


3. Have students work on Exercise G on pages 5 and 6 of the workbook as

their homework.

5th – 6th hours (Conclusion)

1. To test students’ understanding of this chapter, have them try Test

Yourself on page 9. Discuss the answers with them.

2. Have students work on Mastery Practice on pages 7 to 9 of the


EEEmmmppphhhaaasssiii zzzeeeddd CCChhhaaarrr aaacccttteeerrr iii sssttt iii cccsss:::

1. Thinking skill

2. Problem-solving skill

3. Analysing skill

LLL eeeaaarrr nnniii nnnggg MMM aaattteeerrr iii aaalll sss:::

•••• Primary Education Smart Textbook Mathematics P6

•••• Primary Education Smart Workbook Mathematics P6


LLLLLLLLeeeeeeeeaaaaaaaarrrrrrrrnnnnnnnniiiiiiiinnnnnnnngggggggg OOOOOOOOuuuuuuuuttttttttccccccccoooooooommmmmmmmeeeeeeee FFFFFFFFoooooooorrrrrrrrmmmmmmmm

Name-Surname: ............................................................................. No. ..................................

Pratomsuksa: .................................................................................... Date: ................................

Chapter 1 Whole Numbers

Explanation: Summary of learning outcomes

Feeling after learning this

chapter:

...........................................................

...........................................................

...........................................................

...........................................................

Contents that you need teacher

to explain further:

...............................................................

...............................................................

...............................................................

..............................................................

Knowledge gained from this

chapter:

...............................................................

...............................................................

...............................................................

...............................................................

Application of knowledge from

this chapter on your daily life:

...............................................................

................................................................

................................................................

................................................................

Contents that you like the

most in this chapter (give your

reason):

...........................................................

...........................................................

...........................................................

...........................................................

Exercises that you like and want

to be selected as the

outstanding work:

...............................................................

...............................................................

...............................................................

...............................................................

Chapter 1

Whole Numbers



CCCCCCCCCCCChhhhhhhhhhhhaaaaaaaaaaaapppppppppppptttttttttttteeeeeeeeeeeerrrrrrrrrrrr 222222222222 EEEEEEEEEEEEqqqqqqqqqqqquuuuuuuuuuuuaaaaaaaaaaaattttttttttttiiiiiiiiiiiioooooooooooonnnnnnnnnnnnssssssssssss ((((((((((((111111111111111111111111 hhhhhhhhhhhhoooooooooooouuuuuuuuuuuurrrrrrrrrrrrssssssssssss))))))))))))


M4.2 Gr6/1 Write an equation based on a

situation or problem, solve the equation and

check the answer.

•••• Equations

•••• Equations with one

unknown

•••• Addition and subtraction

properties of equality

•••• Multiplication and division


•••• Solving equations using


•••• Using equations to solve

word problems



1. Understand the concept of equations.

2. Solve word problems involving equations.



1. Determine true and false equations.

2. Identify equations with an unknown.

3. Know the addition, subtraction, multiplication and division properties of

equality.

4. Solve problems and word problems involving equations.



•••• Equations

•••• Equations with one unknown

•••• Addition and subtraction properties of equality

•••• Multiplication and division properties of equality

•••• Solving equations using properties of equality

•••• Using equations to solve word problems


1st - 2nd hours (Equations)

1. Introduce equations to students. Equations have the equal sign (=).

2. Use the examples on page 11 to explain further.


4. Have students work on Exercise A on page 11 of the workbook as their

homework.

5. There are true and false equations. A true equation has the same value

on both sides of the equal sign. A false equation has two different values

on both sides of the equal sign.

6. Refer to page 12 to explain.


8. Have students work on Exercise B on page 11 of the workbook as their

homework.

3rd hour (Equation with One Unknown)

1. Explain what an unknown is in Mathematics. We usually use a letter to

represent an unknown. When an unknown is used in an equation, the

equation is known as an equation with one unknown. Refer to page 13.


2. We can solve these equations. Use the examples on page 14 to guide

students on how to solve the equations.


4. Have students work on Exercise C on page 12 of the workbook as their

homework.

4th hour (Addition and Subtraction Properties of Equality)

1. The values on both sides of the equal sign in a true equation are the

same. Therefore when we add the same number to both sides, the

equation remains true.

2. What happens when we subtract the same number from both sides of a

true equation? Write an equation on the board and ask a student to do it.

The equation remains true.

3. Use the example on page 15.


5th hour (Multiplication and Division Properties of Equality)

1. When we multiply or divide both sides of a true equation by the same

number, the equation remains true.

2. Use the examples on page 16.


4. Have students work on Exercise D on page 12 of the workbook as their

homework.

6th – 7th hours (Solving Equations Using Properties of Equality)

1. We can use the addition and subtraction properties of equality to solve

problems.

2. Use the examples on pages 17 and 18 to guide students to solve them.


3. Always substitute the answer back into the equation to check if the

answer is correct.


5. For multiplication and division problems, we can use the multiplication

and division properties of equation to solve them.

6. Refer to the examples on page 19.


8. Have students work on Exercise E on page 13 of the workbook as their

homework.

8th – 9th hours (Using Equations to Solve Word Problems)

1. When solving word problems, always analyse the problems and write

the equations before solving them. Remember to check the answers by

substitute the answers into the equations.

2. Refer to the examples on pages 20 and 21 to guide students to solve

word problems.


4. Have students work on Exercises F and G on pages 14 to 16 of the





2. Have students work on Mastery Practice on pages 17 and 18 of the




1. Thinking skill


3. Analysing skill






Name-Surname: ............................................................................. No. ..................................


Chapter 2 Equations



chapter:

...........................................................

...........................................................

...........................................................

...........................................................


to explain further:

...............................................................

...............................................................

...............................................................

..............................................................


chapter:

...............................................................

...............................................................

...............................................................

...............................................................



...............................................................

................................................................

................................................................

................................................................



reason):

...........................................................

...........................................................

...........................................................

...........................................................



outstanding work:

...............................................................

...............................................................

...............................................................

...............................................................

Chapter 2

Equations



CCCCCCCCCCCChhhhhhhhhhhhaaaaaaaaaaaapppppppppppptttttttttttteeeeeeeeeeeerrrrrrrrrrrr 333333333333 FFFFFFFFFFFFaaaaaaaaaaaaccccccccccccttttttttttttoooooooooooorrrrrrrrrrrrssssssssssss ((((((((((((111111111111444444444444 hhhhhhhhhhhhoooooooooooouuuuuuuuuuuurrrrrrrrrrrrssssssssssss))))))))))))


M1.4 Gr6/2 Find highest common factor

(H.C.F.) and lowest common multiples

(L.C.M.) of cardinal numbers.

• Factors of whole numbers

• Prime factors

• Factorization of whole

numbers

• Highest Common Factor

• Lowest Common

Multiple

• Using HCF and LCM to

solve word problems



1. Understand the concept of factors of whole numbers.

2. Understand the characteristics and use the knowledge of prime factors

of whole numbers.

3. Understand the characteristics and use the knowledge of the Highest

Common Factor (HCF).

4. Understand the characteristics and use the knowledge of the Lowest

Common Multiple (LCM).



1. Determine the factors of whole numbers.

2. Identify characteristics of prime numbers.


3. Identify prime factors from a list of factors.

4. Find prime factors of whole numbers.

5. Find common factors of two and three whole numbers.

6. Determine whether a number is a common factor of two and three given

whole numbers.

7. Find the HCF of two and three given numbers.

8. Find common multiples of two or three whole numbers.

9. Determine whether a number is the common multiple of two or three

given whole numbers.

10. Find the LCM of two or three given numbers.

11. Use HCF and LCM to solve word problems.


• Factors of whole numbers

• Prime factors

• Factorization of whole numbers

• Highest Common Factor

• Lowest Common Multiple

• Using HCF and LCM to solve word problems


1st – 2nd hours (Factors of Whole Numbers)

1. Explain what a factor is in Mathematics. Write the number 90 on the

board and ask them if 9 is a factor of 90. Try with other numbers.

2. Refer to page 24.


4. Write the number 15 on the board and ask students to list all the factors

for 15. Try with other numbers.




homework.

7. We can use factors to find products too. Refer to the example on page

26. Use it to explain to students.



homework.

10. We can use factors to find quotients too. Refer to the example on page

27.



homework.

3rd – 4th hours (Prime Factors)

1. A prime number can be divided, without remainder, only by itself and

by 1. This number has only 2 factors – that is 1 and itself. Zero and 1 are

not considered as prime numbers.

2. Use the examples on page 27 to explain prime numbers. In order to

prove if a number is a prime number, try to divide by 2 and see if you

can get a whole number. If you can, then the number is not a prime

number. Next try divide by prime numbers – 3, 5, 7, 11…. If it is a

prime number, you should not get a whole number as the quotient.

3. Ask students to list all the prime numbers between 2 and 20.


5. Have students work on Exercises D and E on pages 22 and 23 of the



6. Prime factors are factors of a whole number that are prime numbers too.

We can get the prime factors of a whole number by listing all the factors

and then determine the prime numbers.

7. Use the example on page 29 to guide students.


9. Have students work on Exercise F on page 23 of the workbook as their

homework.

5th – 7th hours (Factorization of Whole Numbers)

1. Finding the prime factorization of a whole number is finding the prime

numbers that multiply together to make that whole number. Use the

example on page 30 to explain.

2. Have students work on Exercises G and H on pages 24 and 25 of the


3. We can find the prime factorization using division. Refer to page 31.

Always divide using the smallest prime numbers that divide it.

4. Have students work on Exercise I on page 25 of the workbook as their

homework.

5. We can find prime factorization using a factor tree. Refer to page 32 to

explain.


8th – 9th hours (Highest Common Factor (HCF))

1. Common factors of two or more whole numbers are the factors for the

numbers. Use the example on page 33.

2. The highest common factor of two or more whole numbers is the

greatest common factor of the number. We can find the highest common

factor using three methods – by listing all the factors, by prime

factorization and by division algorithm.


3. Use the examples on pages 33 to 35 to guide students to find the highest

common factor.

4. Write four numbers on the board and ask three students to find the

highest common factor using the three different methods.


6. Have students work on Exercises J to L on pages 25 to 27 of the


10th – 11th hours (Lowest Common Multiple (LCM))

1. Multiples of a whole numbers are the products of the number and

another whole number. Ask students to list multiples of 7, 9 and 11.

2. The common multiples of two or more whole numbers are the multiples

of both numbers. Ask students to list the common multiples of 2 and 3.

3. Use the examples on page 36 to explain.

4. Have students work on Exercise M on page 28 of the workbook as their

homework.

5. The lowest common multiple (LCM) of two or more whole numbers is

the common multiple with the least value.

6. We can find LCM by three methods – by listing the multiples, by prime

factorization and by division algorithm.

7. Use the examples on pages 36 to 38 to guide students to find LCM.


9. Have students work on Exercises N to O on pages 28 and 29 of the


12th hours (Using HCF and LCM to Solve Word Problems)

1. Use the examples on pages 39 and 40 to help students solve word

problems.


2. Guide students when to use HCF and LCM to solve word problems

refereeing to the Math Tips on page 40.


4. Have students work on Exercise P on pages 30 and 31 of the workbook

as their homework.







1. Thinking skill


3. Analysing skill






Name-Surname: ............................................................................. No. ..................................


Chapter 3 Factors



chapter:

...........................................................

...........................................................

...........................................................

...........................................................


to explain further:

...............................................................

...............................................................

...............................................................

..............................................................


chapter:

...............................................................

...............................................................

...............................................................

...............................................................



...............................................................

................................................................

................................................................

................................................................



reason):

...........................................................

...........................................................

...........................................................

...........................................................



outstanding work:

...............................................................

...............................................................

...............................................................

...............................................................

Chapter 3

Factors



CCCCCCCCCCCChhhhhhhhhhhhaaaaaaaaaaaapppppppppppptttttttttttteeeeeeeeeeeerrrrrrrrrrrr 444444444444 FFFFFFFFFFFFrrrrrrrrrrrraaaaaaaaaaaaccccccccccccttttttttttttiiiiiiiiiiiioooooooooooonnnnnnnnnnnnssssssssssss ((((((((((((111111111111333333333333 hhhhhhhhhhhhoooooooooooouuuuuuuuuuuurrrrrrrrrrrrssssssssssss))))))))))))


M1.1 Gr6/2 Compare and arrange sequence of fractions and decimals with not more than 3 places.

•••• Comparing fractions •••• Ordering fractions •••• Simplifying fractions

M1.2 Gr6/1 Add, subtract, multiply, divide and mix addition, subtraction, multiplication and division of fractions, mixed numbers and decimals, as well as be aware of validity of the answers.

•••• Addition and subtraction of fractions

•••• Multiplication of fractions •••• Division of fractions

M1.2 Gr6/2 Analyse and show method of finding answers to problems and mix-problems of cardinal numbers, fractions mixed numbers, decimals and percentages, as well as be aware of validity of the answers, and can construct problems involving cardinal numbers.

•••• Solving word problems involving fractions

•••• Combined operations of fractions



1. Compare fractions.

2. Order fractions.

3. Simplify fractions.

4. Understand the concept of addition and subtraction of fractions to solve

problems.

5. Understand the concept of multiplication and division of fractions to

solve problems.




1. Use LCM to find equivalent fractions to compare.

2. Use LCM to find equivalent fractions to order.

3. Use HCF to simplify fractions.

4. Perform addition and subtraction involving

a. fractions with different denominators

b. mixed numbers

c. combined operations on fractions and mixed numbers

5. Perform multiplications involving

a. mixed numbers

b. three fractions

6. Perform division involving mixed numbers.

7. Solve word problems involving fractions.



•••• Comparing fractions

•••• Ordering fractions

•••• Simplifying fractions

•••• Addition and subtraction of fractions

•••• Multiplying fractions

•••• Division of fractions

•••• Solving word problems involving fractions

•••• Combined operations of fractions



1st hour (Comparing Fractions)

1. When we compare fractions with different numerators and

denominators, we should equalize the denominators first. We can do so

by finding the LCM for the denominators. Then, the fraction with

greater numerator is the greater fraction.

2. Use the example on page 44 to guide students to compare. You may use

the tips given on page 44.


4. Have students work on Exercises A and B on page 36 of the workbook

as their homework.

2nd hour (Ordering Fractions)

1. When we want to arrange a set of fractions in an order, we need to

compare them first. These fractions should be converted into equivalents

fractions with the same denominator. Use LCM to look for the same

denominator.

2. Use the example on pages 45 and 46 to guide students to compare.


4. Have students work on Exercises C and D on pages 37 and 38 of the


3rd hour (Simplifying Fractions)

1. When simplifying a fraction, we can divide the numerator and

denominator with their HCF.

2. Use the example on page 47 to explain.



homework.


4th – 5th hours (Addition and Subtraction of Fractions)

1. When we add or subtract fractions with different denominators, we need

to equalize the denominators first. We can use LCM to find the common

denominator.

2. Use the examples on pages 48 and 49 to guide students to add and

subtract.

3. When we add or subtract mixed numbers, we need to change them into

improper fractions first. Then find equivalent improper fractions that

have same denominator before adding or subtracting.

4. Use the examples on pages 49 and 50 to guide them.


6. When performing any combined operations, we should always perform

the operations in the brackets.



9. Have students work on Exercise F on pages 38 to 39 of the workbook as

their homework.

6th – 7th hours (Multiplication of Fractions)

1. When we multiply mixed numbers, always convert the mixed numbers

into improper numbers before multiplying.



4. This is the same when we multiply three fractions.


6. Have students work on Exercise G on page 40 of the workbook as their

homework.


8th – 9th hours (Division of Fractions)

1. When we divide mixed numbers, we should convert them into improper

fractions first. Always remember to change the sign ÷ to × and the

divisor to its reciprocal. Then, only we multiply them.


3. Write a few division problems involving mixed numbers on the board

for the students to solve.


5. Have students work on Exercise H on page 41 of the workbook as their

homework.

10th hour (Solving Word Problems Involving Fractions)

1. Use the example on page 55 to guide students on how to solve word

problems involving fractions.



homework.

11th hour (Combined Operations of Fractions)

1. When we perform combined operations, remember to perform those in

the brackets first.

2. Use the examples on page 56 to guide them.


4. Have students work on Exercise J on page 43 of the workbook as their

homework.

5. Always remember when solving word problems involving combined

operations of fractions, we should analyse the question first and write

the number sentence. Refer to the example on page 57.



7. Have students work on Exercise K on page 44 of the workbook as their

homework.



Yourself on pages 59 and 60. Discuss the answers with them.




1. Thinking skill


3. Analysing skill






Name-Surname: ............................................................................. No. ..................................


Chapter 4 Fractions



chapter:

...........................................................

...........................................................

...........................................................

...........................................................


to explain further:

...............................................................

...............................................................

...............................................................

..............................................................


chapter:

...............................................................

...............................................................

...............................................................

...............................................................



...............................................................

................................................................

................................................................

................................................................



reason):

...........................................................

...........................................................

...........................................................

...........................................................



outstanding work:

...............................................................

...............................................................

...............................................................

...............................................................

Chapter 4

Fractions



CCCCCCCCCCCChhhhhhhhhhhhaaaaaaaaaaaapppppppppppptttttttttttteeeeeeeeeeeerrrrrrrrrrrr 555555555555 DDDDDDDDDDDDeeeeeeeeeeeecccccccccccciiiiiiiiiiiimmmmmmmmmmmmaaaaaaaaaaaallllllllllllssssssssssss ((((((((((((111111111111000000000000 hhhhhhhhhhhhoooooooooooouuuuuuuuuuuurrrrrrrrrrrrssssssssssss))))))))))))


M1.1 Gr6/1 Write and read decimals with not more than 3 places.

•••• Three-decimal place numbers

•••• Place values and digit values of digits in decimals

•••• Writing decimals in expanded form

M1.1 Gr6/2 Compare and arrange sequence of fractions and decimals with not more than 3 places.

•••• Comparing and ordering decimals

M1.1 Gr6/3 Write decimals in the form of fractions and write fraction in form of decimal.

•••• Decimals and fractions

M1.3 Gr6/2 Make estimates of decimals of not more than 3 places.

•••• Rounding off decimals



1. Read and write decimals.

2. Understand the concept of place value and value of each digit in

decimals.

3. Understand the relationship between decimals and fractions.




1. Read and write decimals to thousandths.

2. State the place value and the value of each digit in a decimal.

3. Write decimals in expanded forms.

4. Compare the values of two given decimals.

5. Arrange decimals in order.

6. Represent decimals in fractions and vice versa.

7. Round off decimals.


•••• Three-decimal place numbers

•••• Place values and digit values of digits in decimals

•••• Writing decimals in expanded form

•••• Comparing and ordering decimals

•••• Decimals and fractions

•••• Rounding off decimals


1st hour (Three-Decimal Place Numbers)

1. Guide students on how to read and write three-decimal place numbers.

Explain that a three-decimal place number can be represented by a

fraction with 1000 as its denominator.


3. Write a few three-decimal place numbers on the board as ask students to

read and write them in words.

4. Ask students to try Question 1 in Practice on page 64. Discuss the

answers with them.



as their homework.

2nd hour (Place Values and Digit Values of Digits in Decimals)

1. Guide students to understand the place values and digit values of the

digits in a three-decimal place number. Use the example on page 63.

2. Write a few three-decimal place numbers and ask students to state the

place values and digit values of the digits.

3. Refer to the example on page 91.


answers with them.

3rd hour (Writing Decimals in Expanded Form & Comparing and

Ordering Decimals)

1. Use the example on page 64 to show students on how to write decimals

in expanded form.


answers with them.


homework.

4. When we compare two decimals, always compare the whole number

parts first. If they are similar, then compare the digits in the tenths,

hundredths and thousandths. Refer to page 65.


6. Use the examples on page 66 to guide students to order decimals.


8. Have students work on Exercises D and E on page 50 of the workbook

as their homework.


4th – 7th hours (Decimals and Fractions)

1. We can easily convert a decimal into a fraction by analyzing the number

of decimal place the decimal has. If the decimal has 2 decimal places

such as 12.89, then the fraction will have 100 as its denominator and its

fraction is 12100

89 . If the decimal has three-decimal place such as 0.108,

then the fraction has 1000 as its denominator and its fraction is 1000

108 .




homework.

5. It is easy to convert fractions with 10, 100 and 1000 as their

denominators into decimals. Refer to the example on page 68.


7. However, if the fractions or mixed numbers do not have 10, 100 or 1000

as their denominators, we will have to change to them into fractions

with those denominators before converting into decimals.

8. Use the examples on pages 69 and 70.



homework.

8th hour (Rounding Off Decimals)

1. When rounding off decimals, always look at the digit on the right of the

digit that will be rounded. Refer to pages 71 to 74.


3. Have students work on Exercises H on page 51 of the workbook as their

homework.








1. Thinking skill


3. Analysing skill






Name-Surname: ............................................................................. No. ..................................


Chapter 5 Decimals



chapter:

...........................................................

...........................................................

...........................................................

...........................................................


to explain further:

...............................................................

...............................................................

...............................................................

..............................................................


chapter:

...............................................................

...............................................................

...............................................................

...............................................................



...............................................................

................................................................

................................................................

................................................................



reason):

...........................................................

...........................................................

...........................................................

...........................................................



outstanding work:

...............................................................

...............................................................

...............................................................

...............................................................

Chapter 5

Decimals



CCCCCCCCCCCChhhhhhhhhhhhaaaaaaaaaaaapppppppppppptttttttttttteeeeeeeeeeeerrrrrrrrrrrr 666666666666 AAAAAAAAAAAAddddddddddddddddddddddddiiiiiiiiiiiittttttttttttiiiiiiiiiiiioooooooooooonnnnnnnnnnnn,,,,,,,,,,,, SSSSSSSSSSSSuuuuuuuuuuuubbbbbbbbbbbbttttttttttttrrrrrrrrrrrraaaaaaaaaaaaccccccccccccttttttttttttiiiiiiiiiiiioooooooooooonnnnnnnnnnnn aaaaaaaaaaaannnnnnnnnnnndddddddddddd MMMMMMMMMMMMuuuuuuuuuuuullllllllllllttttttttttttiiiiiiiiiiiipppppppppppplllllllllllliiiiiiiiiiiiccccccccccccaaaaaaaaaaaattttttttttttiiiiiiiiiiiioooooooooooonnnnnnnnnnnn

ooooooooooooffffffffffff DDDDDDDDDDDDeeeeeeeeeeeecccccccccccciiiiiiiiiiiimmmmmmmmmmmmaaaaaaaaaaaallllllllllllssssssssssss ((((((((((((111111111111111111111111 hhhhhhhhhhhhoooooooooooouuuuuuuuuuuurrrrrrrrrrrrssssssssssss))))))))))))


M1.2 Gr6/1 Add, subtract, multiply, divide

and mix addition, subtraction, multiplication

and division of fractions, mixed numbers and

decimals, as well as be aware of validity of

the answers.

•••• Addition of decimals

•••• Subtraction of decimals

•••• Multiplication of

decimals


finding answers to problems and mix-

problems of cardinal numbers, fractions

mixed numbers, decimals and percentages, as

well as be aware of validity of the answers,

and can construct problems involving cardinal

numbers.

•••• Using addition,

subtraction and

multiplication of

decimals to solve word

problems



1. Understand the concept of addition and subtraction of decimals to solve

problems.

2. Understand the concept of multiplication of decimals to solve problems.



1. Add three-decimal place numbers.

2. Add three decimals.


3. Subtract three-decimal place numbers.

4. Multiply three-decimal place numbers by whole numbers.

5. Multiply decimals by decimals.

6. Use addition, subtraction and multiplication of decimals to solve word

problems.


•••• Addition of decimals

•••• Subtraction of decimals

•••• Multiplication of decimals

•••• Using addition, subtraction and multiplication of decimals to solve

word problems


1st – 2nd hours (Addition of Decimals)

1. Adding two three-decimal place numbers is just like any addition of two

two-decimal numbers. We need to align the digits by their place values

before adding.

2. Refer to page 77 to guide them to add.


4. Have students work on Exercises A and B on pages 55 and 56 of the


5. It is the same when we add up three decimals. Make sure all the digits

are aligned according to their place values.



homework.


3rd – 4th hours (Subtraction of Decimals)

1. When comes to subtraction of decimals, we have to align the digits

based on their place value too before subtracting.

2. Use the examples on page 79 to guide students.

3. Write a few subtraction problems involving decimals on the board and

have students solve them.


5. Have students work on Exercise D on page 57 of the workbook as their

homework.

5th – 7th hours (Multiplication of Decimals)

1. Helps students to recall what multiplication means.

2. We can multiply decimals by whole numbers using different method -

by repeated addition, by converting the decimals into fractions first

before multiply and by multiplying as if they are whole numbers.

3. Use the examples on pages 80 and 81 to guide them.

4. When we multiply decimals by 10, 100 or 1000, we move the decimal

point to the right by 1, 2 or 3 places respectively.



7. Use the examples on pages 82 and 83 to guide students to multiple

decimals by multiples of 10, 100 and 1000.

8. Use the examples on page 83 to guide students to multiple decimals of 3

or less decimal places by whole numbers.


10. When we multiply decimals by decimals, we need to extra caution with

the positioning of the decimal point in the product.

11. You may use the examples on page 84 to explain.



13. Have students work on Exercises E and F on pages 58 and 59 of the


8th – 9th hours (Using Addition, Subtraction and Multiplication of

Decimals to Solve Word Problems)

1. We can use addition, subtraction and multiplication to solve word

problems involving decimals.

2. Refer to the example on page 85 to guide students.


4. Have students work on Exercise G on pages 60 and 61 of the workbook

as their homework.







1. Thinking skill


3. Analysing skill






Name-Surname: ............................................................................. No. ..................................


Chapter 6 Addition, Subtraction and Multiplication of Decimals



chapter:

...........................................................

...........................................................

...........................................................

...........................................................


to explain further:

...............................................................

...............................................................

...............................................................

..............................................................


chapter:

...............................................................

...............................................................

...............................................................

...............................................................



...............................................................

................................................................

................................................................

................................................................



reason):

...........................................................

...........................................................

...........................................................

...........................................................



outstanding work:

...............................................................

...............................................................

...............................................................

...............................................................

Chapter 6

Addition, Subtraction

and Multiplication of

Decimals



CCCCCCCCCCCChhhhhhhhhhhhaaaaaaaaaaaapppppppppppptttttttttttteeeeeeeeeeeerrrrrrrrrrrr 777777777777 DDDDDDDDDDDDiiiiiiiiiiiivvvvvvvvvvvviiiiiiiiiiiissssssssssssiiiiiiiiiiiioooooooooooonnnnnnnnnnnn ooooooooooooffffffffffff DDDDDDDDDDDDeeeeeeeeeeeecccccccccccciiiiiiiiiiiimmmmmmmmmmmmaaaaaaaaaaaallllllllllllssssssssssss ((((((((((((111111111111000000000000 hhhhhhhhhhhhoooooooooooouuuuuuuuuuuurrrrrrrrrrrrssssssssssss))))))))))))


M1.2 Gr6/1 Add, subtract, multiply, divide and mix addition, subtraction, multiplication and division of fractions, mixed numbers and decimals, as well as be aware of validity of the answers.

•••• Dividing decimals by whole numbers

•••• Converting fractions to decimals

•••• Dividing decimals by decimals

M1.2 Gr6/2 Analyse and show method of finding answers to problems and mix-problems of cardinal numbers, fractions mixed numbers, decimals and percentages, as well as be aware of validity of the answers, and can construct problems involving cardinal numbers.

•••• Using division of decimals to solve word problems

•••• Combined operations of decimals



1. Understand the concept of division of decimals to solve problems.



1. Divide decimals by whole numbers.

2. Convert fraction to decimals by dividing.

3. Divide decimals by decimals.

4. Use division of decimals to solve word problems

5. Perform combined operation of decimals.



•••• Dividing decimals by whole numbers

•••• Converting fractions to decimals

•••• Dividing decimals by decimals

•••• Using division of decimals to solve word problems

•••• Combined operations of decimals


1st – 2nd hours (Dividing Decimals by Whole Numbers)

1. We can divide decimals by converting the decimals into fractions first.

Then we divide the fractions. Remember to change the sign ÷ into × and

the divisor into its reciprocal. Refer to page 89.

2. We can also divide decimals using long division. Always align the

decimal points of the dividend and the quotient.

3. Refer to pages 90 and 91.


5. Have students work on Exercise A on pages 54 and 66 of the workbook

as their homework.

6. For some numbers when divided by another number, the quotients we

get might be repeating decimals or non-terminating decimals. Then, we

need to round off the quotient.

7. Use the examples on pages 92 to 93 to explain.



homework.

3rd hour (Converting Fractions to Decimals)

1. When we convert a fraction into a decimal, we can divide its numerator

by its denominator.





homework.

4th – 5th hours (Dividing Decimals by Decimals)

1. When we divide a decimal by a decimal, we can convert them into

fractions with denominators of 10, 100 or 1000 before dividing.

2. We can also convert the decimals into fractions and then multiply both

the numerator and denominator with 10, 100 or 1000 to make the

denominator a whole number before dividing.


4. Write a few division problems involving decimals on the board and have

students solve them.


6. Have students work on Exercise D on pages 69 and 70 of the workbook

as their homework.

6th hour (Using Division of Decimal to Solve Word Problems)

1. Whenever we need to solve any word problem, always analyze the

problem and write the number sentence before solving it.




homework.


7th – 8th hours (Combined Operations of Decimals)

1. Always do the operation in the brackets first for any combined

operations. We can always round up the numbers to check if the answers

obtained are reasonable.

2. Use the example on pages 97 and 98.



homework.

5. We can also use combined operation to solve word problems.


7. Ask students to try Practice on page 100. Discuss the answers with

them.


homework.







1. Thinking skill


3. Analysing skill






Name-Surname: ............................................................................. No. ..................................


Chapter 7 Division of Decimals



chapter:

...........................................................

...........................................................

...........................................................

...........................................................


to explain further:

...............................................................

...............................................................

...............................................................

..............................................................


chapter:

...............................................................

...............................................................

...............................................................

...............................................................



...............................................................

................................................................

................................................................

................................................................



reason):

...........................................................

...........................................................

...........................................................

...........................................................



outstanding work:

...............................................................

...............................................................

...............................................................

...............................................................

Chapter 7

Division of

Decimals



CCCCCCCCCCCChhhhhhhhhhhhaaaaaaaaaaaapppppppppppptttttttttttteeeeeeeeeeeerrrrrrrrrrrr 888888888888 PPPPPPPPPPPPeeeeeeeeeeeerrrrrrrrrrrrcccccccccccceeeeeeeeeeeennnnnnnnnnnnttttttttttttaaaaaaaaaaaaggggggggggggeeeeeeeeeeee ((((((((((((111111111111555555555555 hhhhhhhhhhhhoooooooooooouuuuuuuuuuuurrrrrrrrrrrrssssssssssss))))))))))))



finding answers to problems and mix-

problems of cardinal numbers, fractions

mixed numbers, decimals and percentages,

as well as be aware of validity of the

answers, and can construct problems

involving cardinal numbers.

•••• Finding the percentage of a

number out of another

•••• Solving problems involving

percentage

•••• Simple interest



1. Perform computation and solve problems involving percentages.



1. Find the percentage of a number out of another.

2. Solve problems involving percentage.

3. Solve problems involving simple interest.


•••• Finding the percentage of a number out of another

•••• Solving problems involving percentage

•••• Simple interest



1st – 2nd hours (Finding the Percentage of a Number Out of Another)

1. If a student gets 80 marks out of the full marks of 100, what is the mark

obtained in percentage? We will convert the known terms into a fraction

with 80 as the numerator and 100 as the denominator and multiply this

fraction with 100%.



them.

4. Have students work on Exercises A to D on pages 77 to 79 of the


3rd – 11th hours (Solving Problems Involving Percentage)

1. Students need to understand the meaning of a percentage of profit and a

percentage of loss. These percentages are based on the cost price, not

the selling price. Refer to the notes on page 104.

2. Refer to the examples on pages 105 to 106 to find the selling price using

the cost price. There are a few methods to solve them and the

understanding of the whole concept is essential.


them.

4. We can find the cost price using the selling price and the percentage of

loss and profit.

5. Refer to the examples on pages 107and 108.


them.

7. Have students work on Exercise E and F on pages 80 and 81 of the



8. Explain the meaning of discount. Discount is usually presented by

percentage.

9. Refer to pages 109 and 110 for explanation.


them.


homework.

12. We can find profit, loss or discount percentage with the provided

information.

13. Use the examples on pages 111 and 112 to guide students.


them.


homework.

16. Sometimes there could be more than one transactions. Refer to the

examples on pages 113 and 114.


them.


homework.

12th – 13th hours (Simple Interest)

1. Explain what interest is. What are the factors that affect the amount of

interest gained or imposed? What is simple interest? Refer to the text on

pages 115 and 116.

2. We can calculate the interest for a year by multiplying the interest rate

by the amount. Refer to the examples on pages 116 and 117.


them.


4. We can also find the interest for a period less than a year. Refer to the

example on page 118.


them.

6. Have students work on Exercise J on page 85 of the workbook as their

homework.







1. Thinking skill


3. Analysing skill






Name-Surname: ............................................................................. No. ..................................


Chapter 8 Percentage



chapter:

...........................................................

...........................................................

...........................................................

...........................................................


to explain further:

...............................................................

...............................................................

...............................................................

..............................................................


chapter:

...............................................................

...............................................................

...............................................................

...............................................................



...............................................................

................................................................

................................................................

................................................................



reason):

...........................................................

...........................................................

...........................................................

...........................................................



outstanding work:

...............................................................

...............................................................

...............................................................

...............................................................

Chapter 8

Percentage



CCCCCCCCCCCChhhhhhhhhhhhaaaaaaaaaaaapppppppppppptttttttttttteeeeeeeeeeeerrrrrrrrrrrr 999999999999 DDDDDDDDDDDDiiiiiiiiiiiirrrrrrrrrrrreeeeeeeeeeeeccccccccccccttttttttttttiiiiiiiiiiiioooooooooooonnnnnnnnnnnnssssssssssss aaaaaaaaaaaannnnnnnnnnnndddddddddddd DDDDDDDDDDDDiiiiiiiiiiiiaaaaaaaaaaaaggggggggggggrrrrrrrrrrrraaaaaaaaaaaammmmmmmmmmmmssssssssssss ((((((((((((111111111111000000000000 hhhhhhhhhhhhoooooooooooouuuuuuuuuuuurrrrrrrrrrrrssssssssssss))))))))))))


M2.1 Gr6/1 Explain a route or indicate

positions of various objects by specifying

direction and real distance from pictures,

maps and diagrams.

M2.2 Gr6/3 Draw diagrams showing

positions of various objects and diagrams

showing travel routes.

•••• Directions

•••• Diagrams



1. Understand the cardinal and ordinal directions.

2. Understand route or position shown from pictures, maps and diagrams.



1. State and the cardinal and ordinal directions.

2. Describe locations using directions.

3. Find the actual measurements or measurements in pictures, maps and

diagrams based on the given scale.

4. Read given diagrams.

5. Draw diagrams based on given information.



•••• Directions

•••• Diagrams


1st – 4th hours (Directions)

1. Explain the four cardinal directions – North, South, East and West. You

may use a compass to show the directions. Guide students to realise the

sizes of angles between the directions.

2. Explain also the four ordinal directions – North-east, South-east, South-

west and North-west. Guide students to realise the sizes of angles

between the directions.


as their homework.

4. We can use these directions to describe locations. Use the example on

page 123.


them.

6. Have students work on Exercises C to E on pages 96 and 97 of the


5th – 8th hours (Diagrams)

1. Explain the meaning of scale. A scale is used to indicate the relative size

of drawn image compared to the size of the original object. Be careful

with the sizes.

2. Refer to the examples shown on pages 124 and 125.


them.



homework.

5. When we read diagrams or maps, we should be able to identify the sizes

and locations of the objects and direction indicated on them.

6. Use the example on page 126 to guide students to read a diagram.


them.

8. Have students work on Exercise G on pages 98 and 99 of the workbook

as their homework.

9. When we want to draw a diagram, we need to know the actual size of

the object and the suitable scale for the diagram.

10. Refer to the example shown on pages 128 and 129.


them.

12. We can draw a diagram of a journey using scale.



them.

15. We can also draw a summarized diagram. See page 132.


them.


homework.








1. Thinking skill


3. Analysing skill




•••• Compass



Name-Surname: ............................................................................. No. ..................................


Chapter 9 Directions and Diagrams



chapter:

...........................................................

...........................................................

...........................................................

...........................................................


to explain further:

...............................................................

...............................................................

...............................................................

..............................................................


chapter:

...............................................................

...............................................................

...............................................................

...............................................................



...............................................................

................................................................

................................................................

................................................................



reason):

...........................................................

...........................................................

...........................................................

...........................................................



outstanding work:

...............................................................

...............................................................

...............................................................

...............................................................

Chapter 9

Directions and

Diagrams



CCCCCCCCCCCChhhhhhhhhhhhaaaaaaaaaaaapppppppppppptttttttttttteeeeeeeeeeeerrrrrrrrrrrr 111111111111000000000000 AAAAAAAAAAAAnnnnnnnnnnnngggggggggggglllllllllllleeeeeeeeeeeessssssssssss aaaaaaaaaaaannnnnnnnnnnndddddddddddd LLLLLLLLLLLLiiiiiiiiiiiinnnnnnnnnnnneeeeeeeeeeeessssssssssss SSSSSSSSSSSSeeeeeeeeeeeeggggggggggggmmmmmmmmmmmmeeeeeeeeeeeennnnnnnnnnnnttttttttttttssssssssssss ((((((((((((999999999999 hhhhhhhhhhhhoooooooooooouuuuuuuuuuuurrrrrrrrrrrrssssssssssss))))))))))))


-

•••• Measuring angles

•••• Drawing angles

•••• Angles of equal sizes

•••• Dividing angles and line

segments in half



1. Measure and draw angles.

2. Divide angles and line segments in half



1. Measure angles using a protractor.

2. Draw angles using a protractor and a ruler.

3. Identify angles of equal size.

4. Divide angles and line segments in half.


•••• Measuring angles

•••• Drawing angles

•••• Angles of equal sizes

•••• Dividing angles and line segments in half



1st – 2nd hours (Measuring Angles)

1. We use a protractor to measure angles.

2. Use the examples on page 135 to guide students on how to measure the

angles.


them.


homework.

3rd – 4th hours (Drawing Angles)

1. Use the examples on pages 136 and 137 to guide students on how to

draw angles using a protractor.

2. Ask students to draw a few angles with the given sizes.


them.


homework.

5th hour (Angles of Equal Sizes)

1. We can use a protractor to identify the angles of same sizes.



them.


homework.


6th – 7th hours (Dividing Angles and Line Segments in Half)

1. We can divide angles into halves using a protractor. We measure the

angle and determine the halved size of the angle. Then we draw a line to

halve the angle.


3. We can also use a compass to do so. Refer to the example on page 140.


them.

5. Have students work on Exercises D and E on page 106 of the workbook

as their homework.

6. We can also halve a line segment using a ruler or a compass. Refer to

pages 141 and 142.


them.


homework.







1. Thinking skill


3. Analysing skill





•••• A pair of compasses

•••• Protractor



Name-Surname: ............................................................................. No. ..................................


Chapter 10 Angles and Line Segments



chapter:

...........................................................

...........................................................

...........................................................

...........................................................


to explain further:

...............................................................

...............................................................

...............................................................

..............................................................


chapter:

...............................................................

...............................................................

...............................................................

...............................................................



...............................................................

................................................................

................................................................

................................................................



reason):

...........................................................

...........................................................

...........................................................

...........................................................



outstanding work:

...............................................................

...............................................................

...............................................................

...............................................................

Chapter 10

Angles and Line

Segments



CCCCCCCCCCCChhhhhhhhhhhhaaaaaaaaaaaapppppppppppptttttttttttteeeeeeeeeeeerrrrrrrrrrrr 111111111111111111111111 PPPPPPPPPPPPaaaaaaaaaaaarrrrrrrrrrrraaaaaaaaaaaalllllllllllllllllllllllleeeeeeeeeeeellllllllllll LLLLLLLLLLLLiiiiiiiiiiiinnnnnnnnnnnneeeeeeeeeeeessssssssssss ((((((((((((777777777777 hhhhhhhhhhhhoooooooooooouuuuuuuuuuuurrrrrrrrrrrrssssssssssss))))))))))))


M3.1 Gr6/3 Identify which pair of straight

lines is parallel.

•••• Corresponding, alternate

and interior angles

•••• Determine if two or

more lines are parallel

lines



1. Understand the properties of angles associated with transversal lines.



1. Determine the properties of angles associated with transversal lines –

corresponding angles, alternate angles and interior angles.

2. Determine if two or more lines are parallel lines.


•••• Corresponding, alternate and interior angles

•••• Determine if two or more lines are parallel lines


1st – 3rd hours (Corresponding, Alternate and Interior Angles)

1. Explain what a transversal line is. There are 8 angles formed on

transversal line that pass through two other lines. However when a


transversal line passes through two parallel lines, we can classify the

angles into corresponding angles, alternate angles and interior angles.

2. Refer to pages 145 and 146.

3. Draw a transversal line passing through two parallel lines on the board.

Ask students to identify the angles. Which angles are similar? Which

two angles have the sum of 180o?

4. Use the examples on page 147 to guide students to find the sizes of the

angles on the transversal line that passes through two parallel lines.


them.

6. Have students work on Exercises A to D on pages 112 to 113 of the


4th – 5th hours (Determine If Two or More Lines Are Parallel Lines)

1. We can determine if two or more lines are parallel lines by checking the

sizes of the angles formed by the transversal line.

2. Students have to be clear of the characteristics of the angles formed by a

transversal lines passing through the parallel lines.



them.

5. Have students work on Exercises E and F on pages 114 and 115 of the









1. Thinking skill


3. Analysing skill







Name-Surname: ............................................................................. No. ..................................


Chapter 11 Parallel Lines



chapter:

...........................................................

...........................................................

...........................................................

...........................................................


to explain further:

...............................................................

...............................................................

...............................................................

..............................................................


chapter:

...............................................................

...............................................................

...............................................................

...............................................................



...............................................................

................................................................

................................................................

................................................................



reason):

...........................................................

...........................................................

...........................................................

...........................................................



outstanding work:

...............................................................

...............................................................

...............................................................

...............................................................

Chapter 11

Parallel Lines



CCCCCCCCCCCChhhhhhhhhhhhaaaaaaaaaaaapppppppppppptttttttttttteeeeeeeeeeeerrrrrrrrrrrr 111111111111222222222222 QQQQQQQQQQQQuuuuuuuuuuuuaaaaaaaaaaaaddddddddddddrrrrrrrrrrrriiiiiiiiiiiillllllllllllaaaaaaaaaaaatttttttttttteeeeeeeeeeeerrrrrrrrrrrraaaaaaaaaaaallllllllllllssssssssssss ((((((((((((111111111111333333333333 hhhhhhhhhhhhoooooooooooouuuuuuuuuuuurrrrrrrrrrrrssssssssssss))))))))))))


M2.1 Gr6/2 Find the area of quadrilateral.

•••• Areas of parallelograms

and trapeziums

•••• Estimating areas of

quadrilaterals

M2.2 Gr6/1 Solve problems involving area

and perimeter of quadrilaterals and circles.

•••• Solving problems

involving quadrilaterals

M3.1 Gr6/2 Identify characteristics of

diagonals in various kinds of quadrilaterals.

•••• Diagonals of

quadrilaterals

M3.2 Gr6/2 Construct various kinds of

quadrilaterals.

•••• Constructing

quadrilaterals



1. Identify and use geometric properties of quadrilateral to solve problems.

2. Understand the concept of areas of parallelograms and trapezium to

solve problems.



1. Identify types of quadrilaterals.

2. Construct quadrilaterals using a protractor and a ruler.

3. Identify the heights of parallelograms and trapeziums.

4. Find the areas of parallelograms and trapeziums.


5. Find the areas of figures made up of triangles, trapeziums,

parallelograms or rectangles.

6. Estimate areas of quadrilaterals.

7. Solve problems involving quadrilaterals.


•••• Diagonals of quadrilaterals

•••• Constructing quadrilaterals

•••• Areas of parallelograms and trapeziums

•••• Estimating areas of quadrilaterals

•••• Solving problems involving quadrilaterals


1st – 2nd hours (Diagonals of Quadrilaterals)

1. A diagonal is a line joining two non-consecutive vertices of a

quadrilateral. Refer to page 153 for the property of the diagonals in

some quadrilaterals.


them.


homework.

3rd – 5th hours (Constructing Quadrilaterals)

1. We can construct a quadrilateral when given the lengths of the sides and

the sizes of the angles.

2. Use the examples on pages 154 to 156 to guide students.

3. We can also construct a quadrilateral when given the lengths of its

diagonals.




them.

6. Have students work on Exercise B on pages 119 and 120 of the


6th – 8th hours (Areas of Parallelograms and Trapeziums)

1. Refer to page 159 for the explanation on how the formula for areas of

parallelogram and trapezium are obtained.

2. Use the examples on pages 160 and 161 to guide students on how to

find the areas of parallelograms and trapeziums.


them.

4. Have students work on Exercises C and D on pages 120 and 121 of the


9th hour (Estimating Areas of Quadrilaterals)

1. Use the example on page 163 to guide students to estimate the areas of

quadrilaterals.


them.

10th – 11th hours (Solving Problems Involving quadrilaterals)

1. Use the examples on pages 164 to 166 to guide students to solve word

problems involving quadrilaterals.


them.


homework.








1. Thinking skill


3. Analysing skill





•••• A pair of compasses



Name-Surname: ............................................................................. No. ..................................


Chapter 12 Quadrilaterals



chapter:

...........................................................

...........................................................

...........................................................

...........................................................


to explain further:

...............................................................

...............................................................

...............................................................

..............................................................


chapter:

...............................................................

...............................................................

...............................................................

...............................................................



...............................................................

................................................................

................................................................

................................................................



reason):

...........................................................

...........................................................

...........................................................

...........................................................



outstanding work:

...............................................................

...............................................................

...............................................................

...............................................................

Chapter 12

Quadrilaterals



CCCCCCCCCCCChhhhhhhhhhhhaaaaaaaaaaaapppppppppppptttttttttttteeeeeeeeeeeerrrrrrrrrrrr 111111111111333333333333 CCCCCCCCCCCCiiiiiiiiiiiirrrrrrrrrrrrcccccccccccclllllllllllleeeeeeeeeeeessssssssssss ((((((((((((777777777777 hhhhhhhhhhhhoooooooooooouuuuuuuuuuuurrrrrrrrrrrrssssssssssss))))))))))))


M2.1 Gr6/3 Find the circumference and area of circles.

M2.2 Gr6/1 Solve problems involving area and perimeter of quadrilaterals and circles.

•••• Circumference of a circle

•••• Area of a circle



1. Understand the concept of circumference of a circle to solve problems.

2. Understand the concept of area of a circle to solve problems.



1. Find the circumference of a circle.

2. Find the area of a circle.


•••• Circumference of a circle

•••• Area of a circle


1st – 2nd hours (Circumference of A Circle)

1. Refer to page 170 on how to obtain the formula for the circumference of

a circle. Pi (π) is a constant number and has a value of about

3.14159265358979323846.

2. Use the examples on page 171 to guide students on how to use the pi.


3. Ask students to try Practice on pages 171 and 172. Discuss the answers

with them.



3rd – 5th hours (Area of A Circle)

1. Use the information on pages 172 and 173to understand how the

formula for the area of a circle is obtained.

2. Use the example on page 173 to guide students to find the area of a

circle.


them.

4. Have students work on Exercises C to E on pages 127 to 129 of the








1. Thinking skill


3. Analysing skill


1. Primary Education Smart Textbook Mathematics P6

2. Primary Education Smart Workbook Mathematics P6



Name-Surname: ............................................................................. No. ..................................


Chapter 13 Circles



chapter:

...........................................................

...........................................................

...........................................................

...........................................................


to explain further:

...............................................................

...............................................................

...............................................................

..............................................................


chapter:

...............................................................

...............................................................

...............................................................

...............................................................



...............................................................

................................................................

................................................................

................................................................



reason):

...........................................................

...........................................................

...........................................................

...........................................................



outstanding work:

...............................................................

...............................................................

...............................................................

...............................................................

Chapter 13

Circles



CCCCCCCCCCCChhhhhhhhhhhhaaaaaaaaaaaapppppppppppptttttttttttteeeeeeeeeeeerrrrrrrrrrrr 111111111111444444444444 TTTTTTTTTTTThhhhhhhhhhhhrrrrrrrrrrrreeeeeeeeeeeeeeeeeeeeeeee------------DDDDDDDDDDDDiiiiiiiiiiiimmmmmmmmmmmmeeeeeeeeeeeennnnnnnnnnnnssssssssssssiiiiiiiiiiiioooooooooooonnnnnnnnnnnnaaaaaaaaaaaallllllllllll GGGGGGGGGGGGeeeeeeeeeeeeoooooooooooommmmmmmmmmmmeeeeeeeeeeeettttttttttttrrrrrrrrrrrriiiiiiiiiiiicccccccccccc SSSSSSSSSSSShhhhhhhhhhhhaaaaaaaaaaaappppppppppppeeeeeeeeeeeessssssssssss

aaaaaaaaaaaannnnnnnnnnnndddddddddddd VVVVVVVVVVVVoooooooooooolllllllllllluuuuuuuuuuuummmmmmmmmmmmeeeeeeeeeeee ooooooooooooffffffffffff aaaaaaaaaaaa CCCCCCCCCCCCuuuuuuuuuuuubbbbbbbbbbbbooooooooooooiiiiiiiiiiiidddddddddddd ((((((((((((777777777777 hhhhhhhhhhhhoooooooooooouuuuuuuuuuuurrrrrrrrrrrrssssssssssss))))))))))))


M2.2 Gr6/2 Solve problems involving volume and capacity of cuboids.

•••• Volume of cuboid

M3.1 Gr6/1 Identify kinds of two-dimensional geometric figures that are components of three-dimensional geometric figures.

M3.2 Gr6/1 Create cuboids, cylinders, cones, prisms and pyramids from nets of three-dimensional geometric figures or two-dimensional geometric figures given.

•••• Nets

•••• Models of geometric solids



1. Understand the concept of net.

2. Understand the concepts of volumes of cuboid to solve problems.



1. Draw nets for cubes, cuboids, prisms, pyramids, cylinders and cones.

2. State the types of solids given the nets.

3. Construct models of geometrics given the nets.


•••• Nets

•••• Models of geometric solids

•••• Volume of a cuboid



1st – 2nd hours (Nets)


workbook as their homework. This is to refresh their memory on 3-D

shapes.

2. Ask students to bring any boxes to school. Ask them to open up the

boxes and lay them flat on the table. Those open-up boxes are the nets

of the boxes.

3. Use page 177 to explain.

4. Ask students to imagine the nets for a cylinder, pyramid, cone, prism,

square and cuboid. Compare with the nets on pages 177 and 178.

5. We can imagine the 3-D solid shapes we will get from folded nets.



them.

8. Have students work on Exercises C and D on pages 134 to 136 of the


3rd hour (Models of Geometric Solids)

1. Refer to page 180 to fold nets into models of geometric solids.

4th – 5th hours (Volume of a Cuboid)

1. To find the volume of cuboid, we need to multiply the length, width and

height of the cuboid.

2. Refer to pages 181 and 182 to guide students to find the volumes of

cuboids.


them.


4. Have students work on Exercises E and F on page 136 and 137 of the








1. Thinking skill


3. Analysing skill






Name-Surname: ............................................................................. No. ..................................


Chapter 14 Three-Dimensional Geometric Shapes and Volume of a

Cuboid



chapter:

...........................................................

...........................................................

...........................................................

...........................................................


to explain further:

...............................................................

...............................................................

...............................................................

..............................................................


chapter:

...............................................................

...............................................................

...............................................................

...............................................................



...............................................................

................................................................

................................................................

................................................................



reason):

...........................................................

...........................................................

...........................................................

...........................................................



outstanding work:

...............................................................

...............................................................

...............................................................

...............................................................

Chapter 14

Three-Dimensional

Geometric Shapes and

Volume of a Cuboid



CCCCCCCCCCCChhhhhhhhhhhhaaaaaaaaaaaapppppppppppptttttttttttteeeeeeeeeeeerrrrrrrrrrrr 111111111111555555555555 SSSSSSSSSSSSttttttttttttaaaaaaaaaaaattttttttttttiiiiiiiiiiiissssssssssssttttttttttttiiiiiiiiiiiiccccccccccccssssssssssss aaaaaaaaaaaannnnnnnnnnnndddddddddddd PPPPPPPPPPPPrrrrrrrrrrrroooooooooooobbbbbbbbbbbbaaaaaaaaaaaabbbbbbbbbbbbiiiiiiiiiiiilllllllllllliiiiiiiiiiiittttttttttttyyyyyyyyyyyy ((((((((((((111111111111000000000000 hhhhhhhhhhhhoooooooooooouuuuuuuuuuuurrrrrrrrrrrrssssssssssss))))))))))))


M5.1 Gr6/1 Read data from line graphs and

pie-charts.

M5.1 Gr6/2 Draw comparative bar charts and

line graphs.

M5.2 Gr6/1 Explain events by using terms

with similar meaning to:

- will definitely happen;

- may or may not happen;

- will definitely not happen.

•••• Multiple bar charts

•••• Line graphs

•••• Pie charts

•••• Probability



1. Represent and interpret data from multiple bar charts, line graphs and

pie charts.

2. Understand and use the concept of probability to solve problems.



1. Construct multiple bar charts.

2. Extract data from multiple bar charts.

3. Solve problems involving multiple bar charts.

4. Construct line charts.

5. Extract data from line charts.

6. Solve problems involving line charts.


7. Construct pie charts.

8. Extract data from pie charts.

9. Solve problems involving pie charts.

10. Solve problems involving probability.


•••• Multiple bar charts

•••• Line graphs

•••• Pie charts

•••• Probability


1st – 2nd hours (Multiple Bar Charts)

1. Guide students on how to construct multiple bar charts from the

information given and to extract information from multiple bar charts.



them.

4. Have students work on Exercises A and B on pages 143 to 145 of the


3rd – 4th hours (Line Graphs)

1. Guide students on how to construct line graphs from the information

given and to extract information from line graphs.



them.

4. Have students work on Exercises C and D on pages 146 to 148 of the



5th – 6th hours (Pie Charts)

1. Guide students on how to extract information from pie charts.


3. Ask students to try Practice on pages 192 and 193. Discuss the answers

with them.

4. Have students work on Exercise E on pages 149 to 150 of the workbook

as their homework.

7th – 8th hours (Probability)

1. In any event, there are a few outcomes. For example, in a story telling

with four contestants, a contestant may get the first place, the second

place, the third place or the fourth place. If the contestant does not

remember his story, he may most probably get the fourth place. If he is

well prepared and confident, he might get the first place. Probability is

how likely for something to happen.

2. Probability can be shown using a scale. Refer to page 194.

3. Use the example on page 195 to guide students to answer questions

involving probability.


them.


homework.








1. Thinking skill


3. Analysing skill






Name-Surname: ............................................................................. No. ..................................


Chapter 15 Statistics and Probability



chapter:

...........................................................

...........................................................

...........................................................

...........................................................


to explain further:

...............................................................

...............................................................

...............................................................

..............................................................


chapter:

...............................................................

...............................................................

...............................................................

...............................................................



...............................................................

................................................................

................................................................

................................................................



reason):

...........................................................

...........................................................

...........................................................

...........................................................



outstanding work:

...............................................................

...............................................................

...............................................................

...............................................................

Chapter 15

Statistics and

Probability



CCCCCCCCCCCChhhhhhhhhhhhaaaaaaaaaaaapppppppppppptttttttttttteeeeeeeeeeeerrrrrrrrrrrr 111111111111666666666666 PPPPPPPPPPPPaaaaaaaaaaaatttttttttttttttttttttttteeeeeeeeeeeerrrrrrrrrrrrnnnnnnnnnnnnssssssssssss ((((((((((((777777777777 hhhhhhhhhhhhoooooooooooouuuuuuuuuuuurrrrrrrrrrrrssssssssssss))))))))))))


M4.1 Gr6/1 Solve problems involving pattern. •••• Patterns •••• Solving problems

involving patterns



1. Recognise and extend patterns.

2. Solve problems involving patterns.



1. Describe the pattern given.

2. Extend the pattern given.

3. Solve problems involving patterns.


•••• Patterns

•••• Solving problems involving patterns


1st – 3rd hours (Patterns)

1. When a set of object produces a repeating pattern, the pattern is known

as geometric pattern.



them.


4. Have students work on Exercises A and C on pages 154 and 155 of the


5. When a set of numbers produces a repeating pattern, the pattern is

known as number pattern.

6. Use the example on pages 200 to 202.


them.

8. Have students work on Exercises B and D on pages 155 and 156 of the


4th – 5th hours (Solving Problems Involving Patterns)

1. Use the example on page 203 to guide students to solve word problems

involving patterns.


homework.







1. Thinking skill


3. Analysing skill






Name-Surname: ............................................................................. No. ..................................


Chapter 16 Patterns



chapter:

...........................................................

...........................................................

...........................................................

...........................................................


to explain further:

...............................................................

...............................................................

...............................................................

..............................................................


chapter:

...............................................................

...............................................................

...............................................................

...............................................................



...............................................................

................................................................

................................................................

................................................................



reason):

...........................................................

...........................................................

...........................................................

...........................................................



outstanding work:

...............................................................

...............................................................

...............................................................

...............................................................

Chapter 16

Patterns


You may use Term Test 1 on pages 88 to 93 of the workbook to test students’

understanding after learning the first 6 chapters and also Term Test 2 on pages

160 to 166 for all the chapters learnt.

Notes: Strand 6: Mathematical Skills and Processes are inculcated in all the

chapters appearing in the textbook and workbooks of Primary Education Plus

Series. Through them, students will learn to:

� Apply diverse methods for problem-solving.

� Appropriately apply mathematical knowledge, skills and processes

for problem-solving in various situations

� Suitably provide reasoning for decision-making and appropriately

present the conclusions reached.

� Accurately use mathematical language and symbols for

communication of concepts and presentation.

� Link various bodies of mathematical knowledge, and link

mathematics with other disciplines.

� Attain ability for creative thinking.

Date post:	06-Feb-2018
Category:	Documents
Upload:	phungkhanh
View:	220 times
Download:	5 times

Teacher Guide - e- · PDF fileTeacher Guide 6 In collaboration with Dickens Publishing Ltd....

Documents