2014 K-12
MATH PROGRAM
Find out how Our World of Math can bring joy
to teaching and learning K to 12 Math!
Use this guide to understand
how Vibal Our World of Math
Program was especially developed
for your students. Visit www.
vibalgroup.com for more info.
1
Contents
Vibal Our World of Math Program Advantage ......... 3
The Authors................................................................... 3
Salient Features of Our World of Math Series........... 5
Inquiry-based Advantage............................................ 6
Task-based Advantage................................................. 7
Learner-centered Advantage...................................... 8
Our World of Math Teacher’s Manual........................ 9
Our World of Math N-K-P............................................. 0
Our World of Math Grade 1......................................11
Our World of Math Grade 2......................................12
Our World of Math Grade 3......................................13
Our World of Math Grade 4......................................14
Our World of Math Grade 5......................................15
Our World of Math Grade 6......................................16
Our World of Math Grade 7......................................17
Our World of Math Grade 8......................................18
Our World of Math Grade 9......................................19
Our World of Math Grade 10....................................20
MathEx .........................................................................21
Vsmart Advantage ...............................................22-23
Action Form/ Contact Info.........................................24
Vibal Our World of Math
Program Advantage
Kto12
Our World of Math K to 12 is an all-new series aligned
to the latest K to 12 curriculum being implemented by
the Department of Education. It organizes the key math
concepts into five domains: numbers and number sense,
measurement, patterns and numbers, algebra, geometry,
and probability and statistics. Particularly noteworthy is
its use of the inquiry approach, as well as its progressive
development of higher-order thinking skills.
Our World of Math K to 12 curriculum emphasizes the
spiraling development of concepts and competencies in
ever increasing levels of complexity. Each lesson starts
from the simple, moves to the moderate, and progresses to
a wider and more challenging competency or perspective.
The series aims to make every learner a practical thinker
and problem solver.
The Authors
Grade 1-6
Alicia L. Padua
Head, Research
and Professional
Development and
former Principal,
High School Department
St. Mary’s College
Quezon City
Ricardo M. Crisostomo
Science Teacher
High School
Ateneo de Manila
University
Leona O. Bay
Math Coordinator
Grade School
St. Mary’s College
Quezon City
Juanito D. Yusingco
Math Instructor
Siena College, San Jose
Del Monte City, Bulacan
Mary Lyn U. Dominguez
High School Assistant
Principal for Academic
Affairs-Sciences Don
Bosco Technical College
Mandaluyong City
3
The Authors
Telesforo F. Acopiado, Jr.
Math Teacher
Don Bosco Technical
College Mandaluyong City
Grace U. Yn
Math Teacher
Grade School
Ateneo de Manila
University
Noel M. Menor
Math Coordinator
Grade School
La Salle Green Hills
Niño Jose P. De Guzman
Math Teacher
Grade School
La Salle Green Hills
Roldan G. Tabayoyong
Math Teacher
Marist School
Marikina City
Grade 7-10
Virgie Gayda-Esteves
Math Coordinator
Grade School
Ateneo de Manila
University
Rachelle T. Tang
Chemistry Teacher
Don Bosco Technical
College Mandaluyong
City
Nelson C. Cajandab
Math Teacher
Grade School
La Salle Green Hills
Judy Lim-Gabriel
Retired Math Supervisor
Division of City Schools
Manila
Anita C. Ong
Math Professor
De La Salle University
Taft Avenue, Manila
Alicia L. Padua
Head, Research and
Professional Development
and former Principal,
High School Department
St. Mary’s College
Quezon City
Ricardo M. Crisostomo
Science Teacher
High School
Ateneo de Manila
University
Priscila C. de Sagun
Assistant Schools
Division Superintendent,
DepEd Makati
Julieta G. Bernabe
Math Education
Supervisor of DepEd
Manila Division of City
Schools (1986-1997),
Board Member of the
Mathematics Teachers
Association of the
Philippines (MTAP)
Soledad Jose-Dilao
Facilitator and Resource
Speaker of Seminars
and Conferences on
Mathematics Education,
member of the
Foundation for Upgrading
Standards of Education
(FUSE).
Consultants
Rommel S. Quiming
High School Academic
Coordinator of St. Mary’s
College, Quezon City
4
Maricel C. Corpuz
Mathematics area
coordinator, PAASCUStudent Services
chairperson, Math
Teacher of St. Mary’s
College, Quezon City
Michael R. Lee
Year Level Chairman
of Grade 7 of Caloocan
High School,
Math Faculty Member
of Pamantasan ng
Lungsod ng Valenzuela
Ester B. Ogena, Ph.D.
President
Philippine Normal
University
Carmela C. Oracion
Executive Director,
Ateneo Center
for Educational
Development
Ian June L. Garces, Ph.D.
Associate Professor
at the Department of
Mathematics, Ateneo de
Manila University
Salient Features of
Our World of Math Series
✔✔ Supports Understanding by Design (UbD) framework and cooperative learning
✔✔ Follows logically sequenced stages of learning through a conceptual process of
solving routine and non-routine problems
✔✔ Motivates learners to seek and learn new math concepts that are directly or
indirectly applicable to real-life situations
✔✔ Develops higher-order thinking skills (HOTS) through sets
of exercises that are arranged in increasing levels of difficulty
✔✔ Employs the block model approach (in Grades 3 to 6) to help learners solve
situational problems using concrete and practical perspectives
✔✔ Provides enrichment activities with an included CD-ROM for Grades 1 to 6
✔✔ Provides free online support with each book’s companion website for Grades 1
to 10
✔✔ Integrates values via Let’s Connect in Grades 1 to 6, while notes on values are
highlighted in Grades 7 to 10
✔✔ Interactive e-book edition is perfect for school tablets and goes beyond the
print textbook with its animations, rich media, and self-scoring quizzes.
5
Inquiry-based
Lessons are presented with devices that ellicit curiosity
LE
S S ON
1
Reading and Writing
Whole Numbers
Engage lessons open with
real-life situations and
stimulate learners by using
experiences and ideas that
they can easily relate to.
Engage
Numbers can be written and read in many ways for different purposes and situations.
Observe how each of these numbers is written.
s Try
0921-7885006
4 218 586 042 763
11-24-2013
Where do you usually see or use these numbers?
Which one is written in standard form?
1
2 3 Build Your Understanding
Numbers such as 0921-7885006, 11-24-2013, and 712-2722 are examples of a mobile phone
number, a date in the future, and a telephone number. These numbers are used for different purposes
but they do not consider place values.
How about the number 4 218 586 042 763?
Does it consider place values?
How do you read this number?
GRADE SIX 3
CHECK YOUR UNDERSTANDING
Group Work
A.
Read each number and give the period of the underlined digits.
1.
B.
2 305 320 401 203
2.
34 560 780 230 000
3.
40 112 889 245 320
4.
75 280 906 346 501
5.
102 610 891 328 495
Write each number in standard form.
6.
56 trillion, 9 million, 5 thousand
7.
10 trillion, 4 billion, 6 million
8.
780 trillion, 345 million, 2 hundred
9.
631 trillion, 210 billion, 326 million, 85 thousand
10.
987 trillion, 654 billion, 321 million, 123 thousand, 4 hundred
Individual Work
A.
Read each number then give the place value and the value of the digit 8.
Place Value
Example: 7 854 602
B.
C.
Value of the digit 8
hundred thousand
800 000
1.
438 760 931
______________________
______________________
2.
5 386 459 007
______________________
______________________
3.
46 804 747 216
______________________
______________________
4.
372 589 069 444
______________________
______________________
5.
96 872 040 573
______________________
______________________
Build Your Understanding
presents the new lesson
concretely by formalizing
and discussing the derivation
of mathematical concepts
and ideas that can help solve
problems.
Check Your Understanding
exercises, enriches, and
deepens the knowledge and
skills attained in the lesson;
learners can work on these
exercises on their own or in
collaboration with others.
Read each number orally. Then write each number in words.
6.
8 409 523 008
______________________________________________________
7.
35 007 147 056
______________________________________________________
8.
403 750 900 023
9.
5 246 806 077 653
______________________________________________________
10.
70 800 500 275 400
______________________________________________________
______________________________________________________
Write the number in standard form.
_____________ 11.
five hundred twelve million, eighty-six thousand, six hundred forty
_____________ 12.
twelve billion, eight hundred million, eight thousand, seventy-five
_____________ 13.
72 billion, 45 million, 256 thousand, 245
_____________ 14.
506 billion, 3 million, 742
_____________ 15.
8 trillion, 42 billion, 206 million, 7 thousand, 806
6 OUR WORLD OF MATH
Inquiry Questions establishes the relevance of the chapter in
real life.
Engage lesson openers
provide problem situations−
these serve as springboard
for the learners to simulate
experiences and ideas that
would relate to the new
lesson.
Learning Objective
statement gives an overview
on what you must learn from
each lesson.
6
Task-based
Plenty of activities and tasks
Chapter
1
Share What You Know
Questions at the beginning
of each chapter elicit prior
knowledge and encourage
students to learn more in
upcoming discussions.
WHOLE NUMBERS
Exponents are also useful when writing powers of ten. Numerical expressions such as 100,
101, 102, and so on are called powers of 10.
In this chapter, you will
learn the following:
1
2
3
A power of 10 equals the number 10 multiplied by itself for a given number of times.
Study this example.
Reading and Writing
Whole Numbers
Exponents
100 000 = 10 × 10 × 10 × 10 × 10
Writing Numbers in
Expanded Notations
4
5
6
7
There are five zeros in 100 000, so 10 is multiplied by itself 5 times.
Thus, to write 100 000 in exponential form or notation we have,
Scientific Notation
10 × 10 × 10 × 10 × 10 = 100 000 = 105.
Rounding Off Numbers
Writing Sets and Set
Notations
Let’s
Operations on Sets
1. How can you describe one
billion to someone who has
no idea of the size of this
number?
Do you see the relationship between the exponent in a power of 10 and the number of zeros
in the standard form of the number?
We read numbers in exponential form as follows:
100 is read as “ten to the zeroth power.”
101 is read as “ten to the first power.”
102 is read as “ten to the second power” or “ten squared.”
At present, our country has a population
of approximately a hundred million people. The
government spends billions and trillions of pesos every
year for the basic services, infrastructures, and other
needs of the people.
2. How large is a trillion?
103 is read as “ten to the third power” or “ten cubed.”
2 OUR WORLD OF MATH
104 is read as “ten to the fourth power.”
Let’s Say
Study the following examples.
1. 53 written in standard form is 125 since 53 = 5 × 5 × 5 = 125
2.
Let’s Say
In the place value chart, notice that the digits are grouped into sets of three digits. Each group
of three digits is called period. The words units, thousands, millions, billions, and trillions are called
periods in our numeration system.
In the number 24 607 112 874 007, the digit 6 is in the hundred billions place and its value
is 600 000 000 000 or 6 hundred billions.
It is read as “twenty-four trillion, six hundred seven billion, one hundred twelve million, eight
hundred seventy-four thousand, seven.”
Likewise, the digit 7 in the billions place, has a value of 7 000 000 000 or 7 billions.
The digit 0 has no value but it is used as a place holder.
The place value of the digit 0, between 6 and 7 is ten billions. Its value is 0.
Let’s Try gives learners
exercises to work on their
own to determine the extent
of knowledge and skills they
have internalized.
Let’s Try
A.
B.
hundred thousands place?
___________
millions place?
___________
3.
ten billions place?
4.
hundred millions place?
___________
5.
billions place?
___________
___________
Read the number words. Then write each number in standard form.
6.
twenty million, seven hundred sixty-five thousand, eighty-three ____________
7.
fifteen billion, four hundred five million, seventy-six thousand, five hundred
fifty-four ___________
8.
nine trillion, one hundred five billion, two hundred fifty-one million, four hundred
twenty-eight thousand, eighty-five ______________
4.
1 000 000 written in exponential form is 106
Let’s Try
A.
2.
34 written in standard form is 81 since 34 = 3 × 3 × 3 × 3 = 81
10 × 10 × 10 × 10 written in exponential form is 104
1 000 000 = 10 × 10 × 10 × 10 × 10 × 10 = 106
In the number 76 073 588 421, what digit is in the:
1.
3.
B.
Write the following in exponential form and give the result in standard form.
1.
6×6×6×6×6
2.
8×8×8×8
3.
12 × 12 × 12
4.
5×5×5×5
5.
7×7×7
Write each exponential form in standard form.
1.
107 = _________
2.
33 = _________
3.
72 = __________
4.
18 = __________
REMEMBER KEY IDEAS
•
•
•
Chapter Review contains
answers to Share What You
Know as well as the Summary
of Key Ideas contained in the
lesson, as well as properties
and mathematical procedures
learned within the chapter.
Extended Tasks require
students to demonstrate the
transfer of learning, while the
Chapter Test contains both
objective and comprehensive
tests to evaluate learning;
Problem Solving deepens
learners’ abilities and skills
in tackling real-life word
problems.
The digits in a number are separated into groups of three. Each
group, separated by a comma or a space is called period.
Each digit of a number occupies a different position or place
value. Its value depends on its place in the number.
To read any whole number, read the names of the periods occupied
by the digits except the units period.
GRADE SIX 9
GRADE SIX 5
ANSWERS TO SHARE WHAT YOU KNOW
1.
You can think about numbers in many different ways. A billion is equal to one thousand times
one million. This means that there are one thousand millions in one billion. A billion when written in standard form is 1 followed by nine zeros.
2.
A trillion is in the fifth period of the numeration system. There are 1 000 billions in one trillion. A trillion
is equal to one million times one million. It is written in standard form as 1 followed by 12 zeros.
•
The digits in a number are separated into groups of three. Each group of three digits is called
period.
•
Each digit occupies a specific position or place value. Its value depends on its place in the
number.
•
To read a whole number, read the names of the periods except the units period. The word
and is not used in reading and writing whole numbers.
SUMMARY OF KEY IDEAS
•
The exponent tells how many times the base is to be multiplied by itself.
•
Any nonzero number with a zero exponent is equal to 1 and the number raised to the exponent
1 is equal to the number itself.
•
A number can be written in expanded notation by using the value of its digits, the place values
of its digits, and the powers of ten.
•
A number is in scientific notation when it is written as the product of a number between 1 and
10 and a power of 10.
•
To round off whole numbers, first determine the round off place. Then look at the digit to the
right side of the round off place. If the digit is 5 or more, add 1 to the digit in the round off
place, otherwise retain the digit in the round off place. Replace all the digits to its right with
zeros.
•
A set is a well-defined collection of objects. The objects in a set are called members or elements.
•
Braces { } are used to enclose the elements of a set. The symbol ∈ reads “is an element of”
and ∉ is its negation.
Let’s Say features illustrative examples that contain graphics,
conceptual, and procedural approaches to help students
work out the step-by-step solutions to mathematical and
situational problems.
base → 54 ← exponent
•
A set can be described by using the description method and roster or listing method.
•
The union of two or more sets is the set of all elements which belong to both sets. A ∪ B is
read as “the union of set A and B” or “A union B.”
•
The intersection of two or more sets is the set of all elements that are common to both sets.
A ∩ B is read as “the intersection of set A and B” or “A intersection B.”
•
The Venn diagram is a pictorial representation of the union and intersection of two or more
sets.
34 OUR WORLD OF MATH
7
Learner-centered
Lessons are developed around the learner
REMEMBER KEY IDEAS
•
WWW
A number in exponential form has a base and an exponent.
The base is the repeated factor. The exponent tells the
number of times the base is to be multiplied by itself.
Any nonzero number with a zero exponent is equal to 1.
Any number raised to the exponent 1 is equal to the
number itself.
The number of zeros found after the digit 1 in a power of
10 corresponds to the exponent of 10.
•
•
•
Visit i-learn.vibalpublishing.com and click the
link to a fun game about
writing exponents.
CHECK YOUR UNDERSTANDING
Remember Key Ideas
summarizes at a glance the
ideas, concepts, definitions,
properties, and procedures
discussed in the lesson.
Group Work
A.
B.
Write each in exponential form.
1.
5 × 5 × 5 = ____________
2.
4 × 4 × 4 × 4 × 4 = ____________
3.
8 × 8 × 8 × 8 = ____________
4.
7 × 7 × 7 × 7 × 7 × 7 = ____________
5.
1 × 1 × 1 × 1 × 1 × 1 × 1 × 1 = ____________
Write each in standard form.
6.
8.
35 = ___________
7.
25 = ___________
43 = ___________
9.
10.
106 = ___________
11.
109 = ____________
12.
1010 = ____________
13.
107 = ____________
14.
10 = ____________
15.
108 = ____________
4
74 = ___________
Individual Work
A.
Write each in exponential form.
1.
3 × 3 × 3 × 3 × 3 = _______________
2.
10 × 10 × 10 × 10 × 10 × 10 = _______________
3.
100 × 100 × 100 = _______________
4.
10 000 000 = _______________
5.
100 000 000 000 = _______________
10 OUR WORLD OF MATH
EXTEND YOUR UNDERSTANDING
A.
Numbers can be named and written in several ways. Look at the following examples.
46 hundreds = 4 600
840 000 = 84 ten thousands
500 000 000 = 50 ten millions
Write another number that represents each given value.
B.
1.
456 hundreds
2.
708 hundred thousands = ______________________ millions
3.
62 ten billions
= ______________________ thousands
= ______________________ hundred thousands
4.
16 billions
= ______________________ millions
5.
8 trillions
= ______________________ hundred millions
Answer the following:
6.
7.
8.
How many tens are there in
a.
16 000?
_____________
b.
23 730 000?
_____________
c.
700?
_____________
d.
339 400?
_____________
How many ten thousands are there in
a.
300 000?
_____________
b.
6 500 000?
_____________
c.
35 000 000 000?
d.
65 000?
_____________
_____________
How many millions are there in
a.
9 000 000?
_____________
b.
124 000 000 000? _____________
Think About This
Extend Your Understanding
contains exercises and
activities that further enrich
and challenge learners to
be much better problem
solvers by involving them in
deeper analysis, synthesis,
and reflection on the lesson
while developing the learners’
critical and higher-order
thinking skills.
Determine the value of the following. Write each number in standard form.
1. 46 ten millions more than 8 millions
2. 18 hundred millions less than 27 billions
GRADE SIX 7
Answer to Inquiry Question provides a possible answer(s)
to the inquiry question found at the beginning of the
chapter.
8
Check Your Understanding
exercises to enrich and
deepen the knowledge and
skills attained in the lesson;
learners can work on these
exercises on their own or in
collaboration with others.
Our World of Math Teacher’s
Manual and Resource Materials
The accompanying Teacher’s Manuals are organized with
the three stages of UbD design in mind, namely, identifying
desired outcomes, products, and performances; assessment
with rubrics that identify the criteria and performance
indicators; and learner-centered and activity-laden
instructional plans. Each manual lists authentic tasks that are
specified for learners, complete with strategies for developing
higher-order skills.
Our World of Math Teacher’s Manual guides teachers in their day-to-day classroom
instruction. It assists teachers in making the teaching- learning process more
engaging and meaningful through the following features:
✔✔ Introduction gives a brief description of the content of each lesson found in the
chapter.
✔✔ Instructional Design outlines the three teaching-learning stages based on the
Understanding by Design (UbD) framework
✔✔ Desired Results highlight Established Learning Concepts, Acquisition, Makemeaning, and Transfer Goals.
✔✔ Assessments provide Performance Task, Rubric, and Other Evidences.
✔✔ Learning Activities initiate review, explore prior knowledge, motivation and all
other activities for acquisition, meaning-making, and transfer of learning.
✔✔ Activities integrate values, technology, and connections with other disciplines.
9
Our World of Math
N, Pre-K, K
Our World of Math for Nursery, Pre-K, and Kinder levels offer
complementary math activity books for early childhood:
✔✔ Give learners in Nursery, Kinder, and Preparatory a head start in the world
of numbers
✔✔ Provide preschoolers activities toward appreciation of basic
mathematical concepts
✔✔ Develop a genuine interest in math toward understanding of fundamental math
principles
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Grade 1
Chapter 1 Understanding Sets and Whole
Numbers
inquiry question: Write the largest possible odd number using the digits
3, 1, and 7.
Lesson 1 Identifying and Classifying Sets (1.NNS.2)
Lesson 2 Comparing Sets (1.NNS.2)
Lesson 3 Ordering Sets (1.NNS.7)
Lesson 4 Reading and Writing Numbers from 0 to 10 (1.NNS.1)
Lesson 5 Counting More than 10 (1.NNS.2)
Lesson 6 Place Value of Two-Digit and Three-Digit Numbers (1.NNS.10)
Lesson 7 Comparing Numbers (1.NNS.12)
Lesson 8 Ordering Numbers (1.NNS.13)
Lesson 9 Ordinal Numbers (1.NNS.15)
Chapter 2 Addition of Whole
Numbers
Chapter 3 Subtraction of Whole
Numbers
Chapter 8 Geometry
Chapter 9 Measurements
Chapter 10 Reading Graphs
Chapter 4 Multiplication of Whole
Numbers
Chapter 5 Division of Whole Numbers
Chapter 6 Money
Chapter 7 Fractions
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Chapter 1 Understanding Sets
and Whole Numbers
Chapter 2 Addition of Whole
Numbers
Chapter 3 Subtraction of Whole
Numbers
Grade 2
Chapter 7 Geometry
Chapter 8 Measurement
Chapter 9 Pattern Recognition
Chapter 5 Division of Whole Numbers
Chapter 6 Fractions
Chapter 4 Multiplication of
Whole Numbers
inquiry question: Aling Ising bought 9 boxes of bottled
water. Each box contains 24 small bottles. How many bottles did
Aling Ising buy in all?
Lesson 1 Understanding the Properties of Multiplication
Lesson 2 Multiplying 1- to 2-Digit Numbers by 1-Digit Numbers without Regrouping
Lesson 3 Multiplying Numbers by 10, 100, and 1 000
Lesson 4 Multiplying 1- to 2-Digit Numbers by 1-Digit Numbers with Regrouping
Lesson 5 Solving One- to Two-Step Word Problems
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Chapter 1 Whole Numbers
Chapter 2 Addition of Whole
Numbers
Grade 3
Chapter 3 Subtraction of Whole
Numbers
Chapter 4 Multiplication of Whole
Numbers
Chapter 7 Fractions
inquiry question: When adding or subtracting like
fractions, do you add or subtract the denominators in the same
way that you add or subtract the numerators?
Lesson 1 Understanding Concepts of Fractions
Lesson 2 Identifying Kinds of Fractions
Lesson 3 Identifying Equivalent Fractions
Lesson 4 Comparing and Ordering Fractions
Lesson 5 Expressing Fractions in Simplest Form
Lesson 6 Solving for the Fractional Part of a Number
Lesson 7 Adding and Subtracting Like Fractions and Mixed Numbers
Chapter 5 Division of Whole
Numbers
Chapter 10 Measurement
Chapter 11 Maps and Graphs
Chapter 6 Number Relations
Chapter 8 Decimals and Money
Chapter 9 Geometry
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Grade 4
Chapter 1 Whole Numbers
Chapter 2 Operations on Whole
Numbers
Chapter 3 Decimals
Chapter 4 Number Theory
Chapter 5 Fractions
Chapter 6 Ratio and Proportion
Chapter 7 Geometry
Chapter 8 Measurement and Graphs
inquiry question: How can you use your knowledge of place value, special products, and
special quotients to convert units of measure?
Lesson 1 Measures of Length
Lesson 2 Measures of Mass
Lesson 3 Bar Graphs (4.SP.2, 4.SP.3, 4.SP.4)
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Grade 5
Chapter 1 Whole Numbers
Chapter 8 Measurement
Chapter 2 Operations on Whole
Numbers
Chapter 9 Introduction to Graphs
Chapter 3 Number Relations
Chapter 4 Fractions
Chapter 5 Decimals
Chapter 7 Geometry
Chapter 6 Ratio, Proportion, and Percent
inquiry question: If you have P1,000,000, what percent of the amount
can you share to the poor? Why?
Lesson 1 Computing for Ratio and Rates
Lesson 2 Understanding Proportion
Lesson 3 Solving Direct Proportion
Lesson 4 Solving Indirect Proportion
Lesson 5 Applying Partitive Proportion
Lesson 6 Understanding Percent and Its Relation to Fractions and Decimals
Lesson 7 Finding Base, Percentage, and Rate
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Chapter 1 Whole Numbers
Chapter 7 Geometry
Chapter 2 Operations on Whole
Numbers
Chapter 8 Measurement and Graphs
Chapter 3 Number Relations
Chapter 4 Understanding Decimals
Chapter 6 Ratio and Proportion
Chapter 5 Understanding
Fractions
inquiry question: Do you agree that if you multiply two
proper fractions, the product is greater than 1?
Lesson 1 Concept of Fraction
Lesson 2 Equivalent Fractions and Fractions in
Simplest Forms
Lesson 3 Adding Fractions and Mixed Numbers
Lesson 4 Subtracting Fractions and Mixed Numbers
Lesson 5 Multiplying Fractions and Mixed Numbers
Lesson 6 Dividing Fractions and Mixed Numbers
16
Grade 6
Chapter 9 Probability and Statistics
Chapter 10 Introduction to Algebra
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Grade 7
Chapter 1 Exploring The Real Number
System
Chapter 3 Introducing The Language
Of Algebra
Chapter 4 Solving Linear Equations
And Inequalities In One Variable
Chapter 5 Exploring The Language Of
Geometry
Chapter 6 Identifying Geometric
Shapes
Chapter 7 Describing Data Through
Statistical Measures
Chapter 2 Doing Measurements
inquiry question: Write a letter to your teacher explaining what you
understand about measuring length and what needs to be clarified.
Lesson 1 History of Measurement (7.M.2)
Lesson 2 Measuring Length (7.M.3, 7.M.4)
Lesson 3 Measuring Mass (7.M.3, 7.M.4)
Lesson 4 Measuring Volume and Capacity (7.M.3, 7.M.4)
Lesson 5 Measuring Temperature (7.M.3, 7.M.4)
Lesson 6 Measuring Time (7.M.3, 7.M.4)
Lesson 7 Measuring Angle (7.M.3, 7.M.4)
Lesson 8 Comparing Quantities Using Ratio (7.M.4)
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Grade 8
Chapter
9 Proving
Congruence Of
Chapter 2 Manipulating Rational Expression Triangles
And Equations
Chapter 11
Identifying
Chapter 3 Simplifying Expressions With
Quadrilaterals
Integral Exponents
Chapter 1 Finding Special Products And
Factoring
Chapter 4 Understanding Relations And
Functions
Chapter 5 Exploring Linear Functions
Chapter 12
Describing Data
Through Statistical
Measures
Chapter 6 Graphing Two Variables In Linear
Equations And Inequalities
Chapter 7 Defining And Solving Systems Of
Linear Equations And Inequalities
Chapter 8 Using Logic in Geometry
Chapter 10: Recognizing Parallel
Lines And Their Implications
inquiry question: If line is parallel to line b and line b is parallel
to line c, is line a parallel to line c? If yes, give a real-life situation to
demonstrate the concept.
Lesson 1 Parallel Lines and Transversals
Lesson 2 Properties of Parallel Lines
Lesson 3 Conditions for Parallel Lines
18
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Chapter 1 Solving Quadratic Equations
Chapter 2 Graphing Quadratic Functions
Chapter 3 Solving Equations Involving
Rational Expressions
Grade 9
Chapter 7 Highlighting The Special
Properties Of Right Triangles
Chapter 9 Solving Problems Related To
Triangle Trigonometry
Chapter 4 Analyzing Variation
Chapter 5 Manipulating Rational
Exponents And Radicals
Chapter 6 Recognizing Similarities Of
Geometric Figures
Chapter 8 Identifying
Parallelograms And Kites
inquiry question: If the median of a trapezoid has length
3.5 cm, what are the possible integral lengths for the two bases?
Lesson 1 Kinds of Quadrilaterals (9.G.8)
Lesson 2 Parallelogram and Its Properties (9.G.9)
Lesson 3 Tests for Parallelograms (9.G.19)
Lesson 4 Special Parallelogram and Kites (9.G.11)
Lesson 5 Trapezoid and Its Properties (9.G.12)
19
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Grade 10
Chapter 1 Searching Patterns
in Sequences
INQUIRY question: What other pattern do you observe
about the terms of a Fibonacci sequence? Make a research
on this.
Lesson 1 Patterns, Sequences, and Series
Lesson 2 Geometric Sequence and Series
Lesson 3 Harmonic and other sequences and series
Chapter 2 Graphing Polynomial Functions
Chapter 3 Delving Into Circles
Chapter 4 Exploring Plane Coordinate
Chapter 5 Counting the Number of
Arrangements
Chapter 6 Quantifying Chances
Chapter 7 Locating the Position of an
Object in a Data
20
MathEx
SD Magazines are supplementary reading and activity
materials for the major subjects in elementary and high
school level, the content of each magazine adheres to the
prescribed curriculum for the subject.
MATH Ex is a supplementary magazine for mathematics published by SD
Publications, a subsidiary of Vibal Group. As an activity-oriented supplementary
reading material for mathematics, it provides learners with fun, varied, and
interesting exercises and problem sets that help them understand and master
math concepts and skills.
Math Idol
spotlights math
personalities
Chat About Math
clarifies math
concepts by giving
light discussions and
visualizations
Math Teasers
give interesting
background of math
concepts or principles
developed by
mathematicians
Ride on These
provides hands-on
activities or exercises
Go This Way
presents practical math
problem-solving tips
and tricks
21
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