power-up math 12
TRANSCRIPT
ExercisesExamples
LESSON
PREFACE
ExercisesExamples
LESSON
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
Lesson 5 Word Problems 80
Enrichment 86
ExercisesExamples
LESSON Exercises
Examples
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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
Lesson 6 Word Problems 113
Enrichment 120
CHAPTER 5 Order of Operations Lesson 1 The MDAS Rule 121
Lesson 2 Word Problems 130
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
ExercisesExamples
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ExercisesExamples
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Lesson 8 Word Problems 173
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
Lesson 3 Word Problems 291
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
Lesson 6 Word Problems 316
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
ExercisesExamples
LESSON
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
Thousands Hundreds Tens Ones
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
Thousands Hundreds Tens Ones
70 000
80 000
90 000
100 000
Hundred Thousands
Ten Thousands
Thousands Hundreds Tens Ones
100 000
10 ten thousands = 1 hundred thousand
3
Let us show the number 95 846 in the place value chart.
Ten Thousands
Thousands Hundreds Tens Ones
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
Thousands Hundreds Tens Ones
34 826
thirty-four thousand, eight hundred twenty-six
Ten Thousands
Thousands Hundreds Tens Ones
63 502
sixty-three thousand, five hundred two
Ten Thousands
Thousands Hundreds Tens Ones
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
Thousands Hundreds Tens Ones
Ten Thousands
Thousands Hundreds Tens Ones
Ten Thousands
Thousands Hundreds Tens Ones
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
Thousands Hundreds Tens Ones
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
Thousands Hundreds Tens Ones
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
CRISMonicaRachelCRISMonicaRachelFYI
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
Thousands Hundreds Tens Ones
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
CRISMonicaRachelCRISMonicaRachelFYI
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
Thousands Hundreds Tens Ones
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
CRISMonicaRachelCRISMonicaRachelFYI
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.
92 478 is greater than 81 449.
46 214 is smaller than 56 327.
79 561 is greater than 78 250.
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
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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
CRISMonicaRachelCRISMonicaRachelFYI
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.
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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 .