power-up math 12

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PREFACE

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iii

Power-Up Math, a new series applying Singapore Math strategies, is aligned with the Department of Education’s K to 12 Curriculum. The series follows the Concrete-Pictorial-Abstract Approach, which benefits all types of learners in mastering the basic competencies in mathematics. The books in this series use attractive illustrations and pictures, and appropriate tools and manipulatives for learners to have an easier grasp and a better retention of the concepts.

The Power-Up Math Grade 4 textbook is composed of 15 chapters with guided examples and exercises for every lesson. Lessons are presented in a direct and simple manner.

Examples Examples, explained in greater detail, are provided to give emphasis and elaboration on concepts and their applications.

Exercises

Exercises, parallel to each example, allow the learners to practice and reinforce what they have learned. These exercises are categorized into increasing levels of difficulties.

Combined with interesting and real-life situations, this book offers the best possible start of mastering the basics. Learners are expected to learn on their own with less guidance from the teacher.

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Table of Contents

CHAPTER 1 Whole Numbers within 100 000

Lesson 1 Numbers to 100 000 1

Lesson 2 Comparing and Ordering 8

Lesson 3 Rounding Off Numbers 16

Enrichment 22

CHAPTER 2 Number Sense

Lesson 1 Factors 23

Lesson 2 Multiples 29

Lesson 3 Prime Factors 33

Lesson 4 Greatest Common Factor 39

Lesson 5 Least Common Multiple 47

Lesson 6 Word Problems 53

Enrichment 58

CHAPTER 3 Multiplication of Whole Numbers

Lesson 1 Multiplication without Regrouping 59

Lesson 2 Multiplication with Regrouping 66

Lesson 3 Estimating Products 72

Lesson 4 Mental Multiplication 76


Enrichment 86

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CHAPTER 4 Division of Whole Numbers Lesson 1 Division by a 1-Digit Number 87

Lesson 2 Division by a 2-Digit Number 92

Lesson 3 Division by Multiples of 10 and 100 97

Lesson 4 Estimating Quotients 103

Lesson 5 Mental Division 107


Enrichment 120

CHAPTER 5 Order of Operations Lesson 1 The MDAS Rule 121


Enrichment 136

CHAPTER 6 Fractions Lesson 1 Types of Fractions 137

Lesson 2 Comparing and Ordering Fractions 144

Lesson 3 Conversion of Fractions 152

Lesson 4 Simplifying Fractions 157

Lesson 5 Adding and Subtracting Similar

Fractions 161

Lesson 6 Adding and Subtracting Dissimilar

Fractions 164

Lesson 7 Subtracting a Fraction from a

Whole Number 169

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Enrichment 180

CHAPTER 7 Decimals Lesson 1 Tenths, Hundredths and

Thousandths 181

Lesson 2 Comparing and Ordering

Decimals 188

Lesson 3 Rounding Off Decimals 194

Lesson 4 Decimals and Fractions 200

Enrichment 204

CHAPTER 8 Lines and Angles Lesson 1 Parallel and Perpendicular Lines 205

Lesson 2 Angles 209

Enrichment 220

CHAPTER 9 Triangles and Quadrilaterals Lesson 1 Triangles 221

Lesson 2 Quadrilaterals 227

Enrichment 238

CHAPTER 10 Symmetry and Geometric Solids

Lesson 1 Identifying Symmetric Figures 239

Lesson 2 Identifying Lines of Symmetry 246

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Lesson 3 Making Symmetric Figures 252

Lesson 4 Geometric Solids 258

Enrichment 264

CHAPTER 11 Patterns and Algebra Lesson 1 Identifying Patterns 265

Lesson 2 Completing Number Sentences 271

Enrichment 274

CHAPTER 12 Perimeter Lesson 1 Perimeter of Triangles and

Quadrilaterals 275

Lesson 2 Perimeter of Composite Figures 285


Enrichment 296

CHAPTER 13 Area

Lesson 1 Describing and Estimating Area 297

Lesson 2 Area of Squares and Rectangles 301

Lesson 3 Area of Triangles 305

Lesson 4 Area of Trapezoids 308

Lesson 5 Area of Composite Figures 311


Enrichment 322

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CHAPTER 14 Volume

Lesson 1 Describing Volume 323

Lesson 2 Cubes and Rectangular Prisms 328

Lesson 3 Volume of Rectangular Prisms 333

Enrichment 338

CHAPTER 15 Statistics and Probability

Lesson 1 Tables and Bar Graphs 339

Lesson 2 Interpreting Bar Graphs 346

Lesson 3 Making Simple Predictions 354

Enrichment 360

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Chapter

1

1

Whole Numbers within 100 000

LESSON

1 Numbers to 100 000

seven thousand,eight thousand,

nine thousand,…

The next number is ten thousand.

Let us read the given numbers. What number comes next?

Ten Thousands

Thousands Hundreds Tens Ones

7000

8000

9000

10 000

Ten Thousands


10 000

10 thousands = 1 ten thousand

2

seventy thousand,eighty thousand,

ninety thousand,…

The next number is one hundred thousand.

Let us read the given numbers. What number comes next?

Hundred Thousands

Ten Thousands


70 000

80 000

90 000

100 000

Hundred Thousands

Ten Thousands


100 000

10 ten thousands = 1 hundred thousand

3

Let us show the number 95 846 in the place value chart.

Ten Thousands


9 5 8 4 6

9 ten thousands or 90 000

5 thousandsor 5000

8 hundredsor 800

4 tensor 40

6 onesor 6

95 846 9 5 84 6

ten thousands thousands hundreds

tens o

= + + ++ nnes

= + + + +90 000 5000 800 40 6

95 846

The digit 6 is in the ones place.The value of the digit 6 is 6.The digit 6 stands for 6 ones or 6.

The digit 4 is in the tens place.The value of the digit 4 is 40.The digit 4 stands for 4 tens or 40.

The digit 8 is in the hundreds place.The value of the digit 8 is 800. The digit 8 stands for 8 hundreds or 800.

The digit 5 is in the thousands place.The value of the digit 5 is 5000. The digit 5 stands for 5 thousands or 5000.

The digit 9 is in the ten thousands place.The value of the digit 9 is 90 000.The digit 9 stands for 90 thousands or 90 000.

4

Examples

1 Write the number shown in each place value chart in numerals and in words.

Ten Thousands


34 826

thirty-four thousand, eight hundred twenty-six

Ten Thousands


63 502

sixty-three thousand, five hundred two

Ten Thousands


85 013

eighty-five thousand, thirteen

5

2 Write the following numbers in words.

13 567 = thirteen thousand five hundred sixty-seven

78 209 = seventy-eight thousand two hundred nine

82 017 = eighty-two thousand seventeen

3 Write the following words in numerals.

forty-six thousand ninety-nine = 46 099

eighty-four thousand five hundred = 84 500

sixty-two thousand four hundred seventy-one = 62 471

4 Write the missing numbers or words.

In 72 634, the digit 7 is in the ten thousands place.

In 89 604, the digit 4 is in the ones place.

In 95 073, the digit in the thousands place is 5 .

In 71 476, the value of the digit 4 is 400 .

In 82 351, the digit 5 stands for 5 tens or 50 .

6

Exercises

1 Write the number shown in each place value chart in numerals and in words.

Ten Thousands


Ten Thousands


Ten Thousands


7

2 Write the following numbers in words.

34 705 =

92 185 =

19 206 =

3 Write the following words in numerals.

sixteen thousand ninety-nine =

ninety-five thousand seven hundred =

twenty-two thousand, three hundred seventy-three =

4 Write the missing numbers or words.

In 82 136, the digit is in the ten thousands place.

In 68 439, the digit 9 is in the place.

In 20 874, the digit in the thousands place is .

In 79 453, the value of the digit 7 is .

In 76 548, the digit 6 stands for 6 or .

8

LESSON

2 Comparing and Ordering

Comparing numbers within 100 000

Which number is greater - 89 456

or 56 721?

We can compare numbers using the place value chart.

Ten Thousands


8 9 4 5 6

5 6 7 2 1

Compare the ten thousands.8 ten thousands is greater than 5 ten thousands.

So, 89 456 is greater than 56 721.In symbols, 89 456 > 56 721.

CRISMonicaRachel

CRISMonicaRachelCRISMonicaRachelFYI

When comparing numbers, look at the value of each digit starting from the left.

9

Which number is smaller - 34 921

or 38 302?

We can compare numbers using the place value chart.

Ten Thousands


3 4 9 2 1

3 8 3 0 2

Compare the ten thousands.The digits are the same.

Compare the thousands.4 thousands is smaller than 8 thousands.

So, 34 921 is smaller than 38 302.In symbols, 34 921 < 38 302.

CRISMonicaRachel


Two numbers may have the same digits in the same place value. We then compare the next digits.

10

Ordering numbers within 100 000

Arrange the numbers 54 712, 26 934, 71 802, and 93 459 in increasing order.

Ten Thousands


54 712 5 4 7 1 2

26 934 2 6 9 3 4

71 802 7 1 8 0 2

93 459 9 3 4 5 9

First, compare all the digits in the ten thousands place.2 is the smallest. So, 26 934 is the smallest number.

Next, compare the digits in the ten thousands place of the remaining numbers.5 is the smallest. So, 54 712 is second to the smallest number.

Then, compare the digits in the ten thousands place of the two remaining numbers.7 is smaller than 9. So, 71 802 is smaller than 93 459.

Lastly, arrange the numbers in increasing order.26 934, 54 712, 71 802, 93 459

CRISMonicaRachel


Increasing order is an arrangement from the smallest to the greatest.

11

Arrange the numbers 14 695, 86 301, 53 712, and 15 826 in decreasing order.

Ten Thousands


14 695 1 4 6 9 5

86 301 8 6 3 0 1

53 712 5 3 7 1 2

15 826 1 5 8 2 6

First, compare all the digits in the ten thousands place.8 is the greatest. So, 86 301 is the greatest number.

Next, compare the digits in the ten thousands place of the remaining numbers.5 is the greatest. So, 53 712 is second to the greatest number.

Then, compare the digits in the ten thousands place of the two remaining numbers. They are the same. Compare the thousands.5 is greater than 4. So, 15 826 is greater than 14 695.

Lastly, arrange the numbers in decreasing order.86 301, 53 712, 15 826, 14 695

CRISMonicaRachel


Decreasing order is an arrangement from the greatest to the smallest.

12

Examples

1 Compare the numbers by writing greater than or smaller than in the box.

67 134 is greater than 34 091.


46 214 is smaller than 56 327.


11 459 is smaller than 11 746.

2 Compare the following numbers using >, <, or =.

45 612 < 92 672 61 409 < 63 409

33 617 > 33 167 89 156 = 89 156

40 267 = 40 267 43 901 > 43 191

30 433 = 30 433 56 724 > 56 457

21 374 < 21 375 75 682 = 75 682

13

3 Arrange the numbers in increasing order.

25 726, 72 625, 57 218, 67 581

25 726, 57 218, 67 581, 72 625

87 561, 98 651, 65 734, 89 651

65 734, 87 561, 89 651, 98 651

34 891, 48 913, 78 145, 34 709

34 709, 34 891, 48 913, 78 145

4 Arrange the numbers in decreasing order.

35 928, 53 298, 67 137, 41 210

67 137, 53 298, 41 210, 35 928

78 371, 34 012, 43 210, 79 471

79 471, 78 371, 43 210, 34 012

15 672, 51 627, 15 726, 51 276

51 627, 51 276, 15 726, 15 672

14

Exercises

1 Compare the numbers by writing greater than or smaller than in the box.

56 390 is 59 284.

33 126 is 43 712.

28 560 is 20 561.

57 132 is 57 332.

81 619 is 81 629.

2 Compare the following numbers using >, <, or =.

99 509 92 571 47 699 27 969

67 340 87 340 11 200 11 200

45 980 45 980 71 309 81 230

52 487 52 847 15 135 15 135

93 716 93 715 25 612 25 700

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3 Arrange the numbers in increasing order.

24 376, 52 298, 14 217, 49 306

76 842, 68 476, 87 726, 76 482

95 213, 97 850, 95 701, 97 834

4 Arrange the numbers in decreasing order.

45 987, 26 451, 70 211, 98 743

65 473, 46 473, 56 743, 46 537

12 378, 21 278, 12 387, 22 871

16

LESSON

3 Rounding Off Numbers

I have ₱12 456. He has ₱16 678. We need to have ₱37 999 to buy

a television.

She has about ₱10 000. I have about ₱20 000.

We have about ₱30 000 altogether. How much more

do we need?

Round off 37 999 to the nearest ten thousand.

30 000 35 000

37 999

40 000

37 999 is between 30 000 and 40 000.It is nearer to 40 000 than to 30 000.

37 999 is 40 000 when rounded off to the nearest ten thousand.We say 37 999 is approximately equal to 40 000. We write 37 999 ≈ 40 000.

40 000 - 30 000 = 10 000They need about ₱10 000 more to buy a television.

CRISMonicaRachel


Rounding off is a method of approximating a number to the nearest place value.

17

Estimate the distance from Jenny's house to the market, to the school, and to the mall.

56 011 m27 025 m 43 521 m

40 000 45 000

43 521

50 000

43 521 is approximately equal to 40 000.43 521 ≈ 40 000The distance from Jenny's house to the market is about 40 000 m.

50 000 55 000

56 011

60 000

56 011 is approximately equal to 60 000.56 011 ≈ 60 000.The distance from Jenny's house to the school is about 60 000 m.

20 000 25 000

27 025

30 000

27 025 is approximately equal to 30 000.27 025 ≈ 30 000The distance from Jenny's house to the mall is about 30 000 km.

18

Examples

1 Round off the following numbers using the number line.

2000 2500

2845

3000

2845 ≈ 3000

70 000 75 000

78 023

80 000

78 023 ≈ 80 000

40 000 45 000

43 024

50 000

43 024 ≈ 40 000

2 Approximate the following numbers by rounding off to the highest place value.

3250 ≈ 3000 4875 ≈ 5000 3564 ≈ 4000

67 502 ≈ 70 000 53 445 ≈ 50 000 85 715 ≈ 90 000

19

3 Mr. Santos has ₱20 000. He wants to buy a mobile phone that costs ₱10 425 and a laptop that costs ₱28 789. What is the estimated cost of the two items? Does Mr. Santos have enough money to buy both items?

First, approximate the prices of the items by rounding them off to the nearest ten thousand.

The cellphone costs ₱10 425 . Its price is about ₱10 000 .

The laptop costs ₱28 789 . Its price is about ₱30 000 .

10 000 + 30 000 = 40 000

The estimated cost of the two items is ₱40 000 .

Mr. Santos does not have enough money to buy both items.

20

Exercises

1 Round off the following numbers using the number line.

6000 6500 7000

6235 ≈

50 000 55 000 60 000

59 430 ≈

90 000 95 000 100 000

96 427 ≈

2 Approximate the following numbers by rounding off to the highest place value.

5901 ≈ 7385 ≈ 3574 ≈

81 950 ≈ 55 326 ≈ 69 814 ≈

21

3 Mrs. Rodriguez has ₱30 000. She wants to buy a washing machine that costs ₱26 501 and a stove that costs ₱12 999. What is the estimated cost of the two items? Does Mrs. Rodriguez have enough money to buy both items?

The washing machine costs . Its price is about .

The stove costs . Its price is about .

+ =

The estimated cost of the two items is .

22

EnrichmentChoose Between

Given each number, write two numbers it is between. Then circle the number in which it is rounded off to. The first item is done for you.

2000 2345 3000 84 920

6794 21 454

9365 27 497

2570 90 984

7746 49 446

power-up math 12

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