9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text

For example, 2 + 2 = 4; 4 + 2 = 6; 6 + 2 = 8 and so on Therefore, the pattern is 2, 4, 6, 8… In this pattern, 2 is the first term, 4 is the second term, 6 is the third term, 8 is the fourth term and so on. Similarly, 18, 20, 22, 24, 26… and 246, 248, 250, 252…. are some more patterns of even numbers. Pattern with odd numbers: The numbers ending with 1, 3, 5, 7 or 9 are called odd numbers. You can make a pattern with odd numbers by adding 2 to the given odd number. For example, 1 + 2 = 3; 3 + 2 = 5; 5 + 2 = 7 and so on. Therefore, the pattern is 1, 3, 5, 7… In this pattern, 1 is the first term, 3 is the second term, 5 is the third term, 7 is the fourth term and so on. Similarly, 27, 29, 31, 33… and 137, 139, 141, 143… are some more patterns of odd numbers. Growing patterns Growing patterns can be found in shapes. Let us see a few examples. Example 2: Complete the following patterns. a) b) c) Solution: a) b) Patterns 12 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 51 1/7/2019 2:17:40 PM

c) In these patterns, we observe that each term has one more basic shape than the previous term. Some patterns have terms increasing by a certain number. We can find this number by subtracting any two consecutive terms. Consider the following patterns. a) 20, 30, 40, 50... b) 100, 200, 300... c) 11, 21, 31, 41... d) 145, 155, 165... e) 246, 346, 446... In pattern a), 40 – 30 = 10 and 30 – 20 = 10. So, the terms increase by 10. Similarly, the terms in c) and d) also increase by 10. In pattern b), 300 – 200 = 100 and 200 – 100 = 100. So, the terms increase by 100. Similarly, the terms in e) also increase by 100. Therefore, we can define the rule of the patterns in a), c) and d) as: increase by 10. The rule of the patterns in b) and e) as: increase by 100. Some patterns can be formed by decreasing the terms by a certain number. Consider the following patterns. a) 820, 720, 620, 520… b) 100, 90, 80, 70… c) 61, 56, 51, 46… d) 165, 155, 145… e) 846, 646, 446… In pattern a), 820 – 720 = 100 and 720 – 620 = 100. So, the terms decrease by 100. Similarly, the terms in e) decrease by 200. In pattern b), 100 – 90 = 10 and 90 – 80 = 10. So, the terms decrease by 10. Similarly, the terms in d) also decrease by 10. In pattern c), 61 – 56 = 5 and 56 – 51 = 5. So, the terms decrease by 5. Therefore, we can define the rule of the pattern in a) as decrease by 100; in pattern e) as decrease by 200; in patterns b) and d) as decrease by 10; in pattern c) as decrease by 5. 13 1/7/2019 2:17:40 PM NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 52

Application We see and use patterns in real life every day. We use ceramic tiles, marble, granite and other such stones for the floors of our houses. Covering a surface with flat shapes like tiles without any gaps or overlaps is called tiling. We see tiling of floors and roofs of buildings and houses. Parking areas have parking tiles laid. Some tiling patterns are as follows. Tiling can also be done using different shaped tiles as shown here. Example 3: Draw the basic shape in the given tiling patterns. a) b) Solution: a) b) Higher Order Thinking Skills (H.O.T.S.) We have seen that patterns in shapes and numbers follow certain rules. Using the rule, we can form the pattern with the given basic shapes. Patterns 14 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 53 1/7/2019 2:17:40 PM

Consider the following examples. 1) Rule: Turn the shape upside down. Basic shape: Pattern: 2) Rule: Turn the shape horizontally to the right and then back vertically. Basic shape: Pattern: 3) Rule: Rotate the shape quarter way to the right. Basic shape: Pattern: Number patterns also follow certain rules. Once the rule is identified, we can continue the given pattern. For example, the rule for a pattern is 'Begin with 1, add 3 and subtract 1 alternately'. The pattern is: 1, 4, 3, 6, 5, 8, 7... Example 4: Complete the given pattern: 8, 16, 24, ____, ____ , _____, ____. Solution: In the given pattern, the first term is 8, the second term is 16 and the third term is 24. This pattern has numbers increasing by 8. So, the next terms of the pattern are: 24 + 8 = 32; 32 + 8 = 40; 40 + 8 = 48; 48 + 8 = 56. So, the rule of this pattern is adding 8. Therefore, the pattern is 8, 16, 24, 32, 40, 48, 56. Try these! Find the rule of the following patterns and write the next terms. a) 12, 24, 36, _____, _____, _____. b) 1+ 2 = 3, 2 + 3 = 5, 3 + 4 = 7, ____________, ____________, ____________. 15 1/7/2019 2:17:40 PM NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 54

Example 5: Form a pattern using the rule, 'Begin with 5 and multiply by 2'. Solution: If the rule is 'Begin with 5 and multiply by 2', the terms in the pattern are: 5, 10, 20, 40... Drill Time Concept 2.1: Patterns in Shapes and Numbers 1) Complete the following patterns. a) ___________ ___________ ___________ ☺☺☻ ☺☺☻ b) ______________ ______________ c) _____________ ____________ d) ____________ ____________ e) ________________ ______________ 2) Fill the blanks with the next two terms of the given patterns. a) 122, 133, 144, ______, ______ b) 303, 304, 305, ______, ______ c) 40, 42, 44, _______, ________ d) 8, 24, 40, ________, ________ e) 35, 30, 25, ________, ________ f) 82, 72, 62, _______, ________ 3) Draw the basic shapes in the given tiling patterns. a) b) c) d) Patterns 16 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 55 1/7/2019 2:17:40 PM

Chapter Numbers 3 Let Us Learn About • writing 4-digit numbers with place value chart. • identifying and forming the greatest and the smallest number. • writing the standard and the expanded forms of the number. • comparing and ordering numbers. Concept 3.1: Count by Thousands Think Farida went to buy one of the toy cars shown. She could not read the price on one of the cars. Can you read the price on ` 1937.00 both the cars and understand what they mean? ` 657.00 Recall We know that 10 ones make a ten. Similarly, 10 tens make a hundred. Let us now count by tens and hundreds as: Counting by 10s: 10, 20, 30, 40, 50, 60, 70, 80 and 90 Counting by 100s: 100, 200, 300, 400, 500, 600, 700, 800 and 900 17 1/7/2019 2:17:40 PM NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 56

When we multiply a digit by the value of its place, we get its place value. Using place values, we can write a number in its expanded form. Let us answer these to revise the concept. a) The number for two hundred and thirty-four is _____________. b) In 857, there are _______ hundreds, _______ tens and _______ ones. c) The expanded form of 444 is _______________________. d) The place value of 9 in 493 is _____________. e) The number name of 255 is _______________________________________. & Remembering and Understanding To know about 4-digit numbers, we count by thousands using boxes. Suppose shows 1. Ten such boxes show a 10. So, = 10 ones = 1 ten Similarly, 10 such strips show 10 tens or 1 hundred. = 10 tens = 1 hundred Numbers 18 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 57 1/7/2019 2:17:40 PM

= 1 hundred = 100 = 2 hundreds = 200 = 3 hundreds = 300 = 4 hundreds = 400 In the same way, we get 5 hundreds = 500, 6 hundreds = 600, 7 hundreds = 700, 8 hundreds = 800 and 9 hundreds = 900. Using a spike abacus and beads of different colours, we represent 999 as shown. 9 blue, 9 green and 9 pink beads on the abacus represent 999. H TO Remove all the beads and Th H T O represent 999 put an orange bead on the represent 1000 next spike. This represents one thousand. We write it as 1000. 1000 is the smallest 4-digit number. Now, we know four places: ones, tens, hundreds and thousands. Let us represent 4732 in the place value chart. 19 1/7/2019 2:17:40 PM NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 58

Thousands (Th) Hundreds (H) Tens (T) Ones (O) 4 7 32 We count by 1000s as 1000 (one thousand), 2000 (two thousand)... till 9000 (nine thousand). The greatest 4-digit number is 9999. Expanded form of 4-digit numbers The form in which a number is written as the sum of the place values of its digits is called its expanded form. Let us now learn to write the expanded form of 4-digit numbers. Example 1: Expand the following numbers. a) 3746 b) 6307 Solution: Write the digits of the given numbers in the place value chart, as shown. Expanded forms: Th H TO a) 3746 = 3000 + 700 + 40 + 6 a) 3 7 46 b) 6307 = 6000 + 300 + 0 + 7 b) 6 3 0 7 Writing number names of 4-digit numbers Observe the expanded form and place value chart for a 4-digit number, 8015. Th H TO Place values 80 15 5 ones = 5 1 tens = 10 0 hundreds = 0 8 thousands = 8000 We can call 8015 as the standard form of the number. Let us look at an example. Example 2: Write the expanded forms and number names of these numbers. a) 1623 b) 3590 Numbers 20 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 59 1/7/2019 2:17:40 PM

Solution: To expand the given numbers, write them in the correct places in the place value chart. Expanded forms: Th H T O a) 1623 = 1000 + 600 + 20 + 3 a) 1 6 2 3 b) 3590 = 3000 + 500 + 90 + 0 b) 3 5 9 0 Writing in words (Number names): a) 1623 = One thousand six hundred and twenty-three b) 3590 = Three thousand five hundred and ninety We can write the standard form of a number from its expanded form. Let us see an example. Example 3: Write the standard form of 3000 + 400 + 60 + 5. Solution: Write the numbers in the place value Th H T O chart in the correct places. Write the 3 46 5 digits one beside the other, starting from the thousands place. 3000 + 400 + 60 + 5 = 3465 So, the standard form of 3000 + 400 + 60 + 5 is written as 3465. Application We can solve a few real-life examples using the knowledge of 4-digit numbers. Example 4: Ram has some money with him as shown. Calculate the amount that Ram has and write it in figures and words. 21 1/7/2019 2:17:40 PM NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 60

Solution: 1 note of ` 2000 = ` 2000 1 note of ` 100 = ` 100 3 notes of ` 10 = ` 30 1 coin of ` 5 = ` 5 So, the amount that Ram has = ` 2000 + ` 100 + ` 30 + ` 5 = ` 2135 In words, ` 2135 is two thousand one hundred and thirty-five rupees. Example 5: The number of students in different schools is given in the table. Read the table and answer the questions that follow. Name of schools Number of students Unique High School 2352 Modern High School 4782 Ideal High School 7245 Talent High School 9423 Concept High School 1281 a) W hat is the number of students in Ideal High School? Write the number in words. b) H ow many students are there in Concept High School? Write the number in words. Solution: a) T he number of students in Ideal High School is 7245. In words, it is seven thousand two hundred and forty-five. b) The number of students in Concept High School is 1281. In words, it is one thousand two hundred and eighty-one. A place value chart helps us to form numbers using given digits. Here is an example. Example 6: A number has 6 in the thousands place and 5 in the hundreds place. It has 1 in the tens place and 4 in the ones place. What is the number? Solution: Write the digits in the place value chart according to Th H T O their places as shown. So, the required number is 6514. 6 5 1 4 Higher Order Thinking Skills (H.O.T.S.) We have learnt the concepts of expanded form and place value chart. Now, we will solve a few examples to identify numbers from the abacus. Numbers 22 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 61 1/7/2019 2:17:40 PM

Example 7: Write the numbers represented by these abacuses. a)   b)   c) Th H T O Th H T O Th H T O Solution: Follow these steps to write the numbers. Step 1: Write the number of beads in each Th H T O Number Step 2: place in the place value chart. a) 1 3 3 2 1332 Put a 0 in the places where there are b) 5 0 3 0 5030 no beads. c) 4 0 3 4 4034 Example 8: Draw beads on the abacus to show the given numbers. a) 3178 b) 6005 c) 4130 Th H T O Solution: Step 1: Follow these steps to show the given numbers. a) 3 1 7 8 Write the digits of the given numbers in the place b) 6 0 0 5 value chart. c) 4 1 3 0 Step 2: Draw the number of beads on each spike of the abacus to show the digit in each place of the number. Th H T O Th H T O Th H T O a) 3178 b) 6005 c) 4130 Concept 3.2: Compare 4-digit Numbers Think Farida has 3506 paper clips and her brother has 3605 paper clips. Farida wants to know who has more paper clips. But the numbers appear to be the same, and she is confused. Can you tell who has more number of paper clips? 23 1/7/2019 2:17:41 PM NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 62

Recall In class 2, we have learnt to compare 3-digit numbers and 2-digit numbers. Let us quickly revise the concept. A 2-digit number is always greater than a 1-digit number. A 3-digit number is always greater than a 2-digit number and a 1-digit number. So, a number with more number of digits is always greater than a number with lesser digits. We use the symbols >, < or = to compare two numbers. & Remembering and Understanding Comparing two 4-digit numbers is similar to comparing two 3-digit numbers. Let us understand the steps to compare through an example. Example 9: Compare: 5382 and 5380 Solution: Follow these steps to compare the given numbers. Steps Solved Solve this Step 1: Compare the number of digits 5382 and 5380 7469 and 7478 Count the number of digits in the given numbers. The number having more number of digits is Both 5382 and greater. 5380 have 4 digits. Step 2: Compare thousands If two numbers have the same number of digits, 5=5 ____ = ____ compare the thousands digits. (If two numbers have an equal number of digits, start comparing 3=3 ____ = ____ from the leftmost digit.) The number with the greater digit in the thousands place is greater. Step 3: Compare hundreds If the digits in the thousands place are the same, compare the digits in the hundreds place. The number with the greater digit in the hundreds place is greater. Numbers 24 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 63 1/7/2019 2:17:41 PM

Steps Solved Solve this 5382 and 5380 7469 and 7478 Step 4: Compare tens 8=8 ____ > ____ If the digits in the hundreds place are also same, So, compare the digits in the tens place. The number with the greater digit in the tens place is greater. ____ > ____ Step 5: Compare ones If the digits in the tens place are also the same, 2>0 compare the digits in the ones place. The So, - number with the greater digit in the ones place is greater. When the ones place are the same, the 5382 > 5380 numbers are equal. Note: Once we can decide a greater/smaller number, the steps that follow need not be carried out. Application We can apply the knowledge of comparing numbers and place value to: 1) arrange numbers in the ascending and descending orders. 2) form the greatest and the smallest numbers using the given digits. Ascending and descending orders Ascending Order: The arrangement of numbers from theTrsmaainllesMt toythBeragrienatest Descending Order: The arrangement of numbers from the greatest to the smallest Example 10: Arrange 4305, 4906, 4005 and 4126 in the ascending and descending orders. Solution: Follow these steps to arrange the given numbers in the ascending and descending orders. Ascending Order Step 1: Compare the digits in the thousands place: All the numbers have 4 in their thousands place. Step 2: Compare the digits in the hundreds place: 4005 – 0 hundreds, 4126 –1 hundred, 4305 – 3 hundreds and 25 1/7/2019 2:17:41 PM NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 64

4906 – 9 hundreds So, 4005 < 4126 < 4305 < 4906 Step 3: Arranging the numbers in ascending order: 4005, 4126, 4305, 4906 Descending Order Step 1: Compare the digits in the thousands place: All the numbers have 4 in their thousands place. Step 2: Compare the digits in the hundreds place: 4005 – 0 hundreds, 4126 – 1 hundred, 4305 – 3 hundreds and 4906 – 9 hundreds So, 4906 > 4305 > 4126 > 4005 Step 3: Arranging the numbers in descending order: 4906, 4305, 4126, 4005 Simpler way! The descending order of numbers is just the reverse of their ascending order. Forming the greatest and the smallest 4-digits numbers Let us learn to form the greatest and the smallest 4-digit numbers. Look at the following examples. Example 11: Form the greatest and the smallest 4-digit number using 4, 3, 7 and 5 (without repeating the digits). Solution: The given digits are 4, 3, 7 and 5. The steps to find the greatest 4-digit number are given below. Step 1: Arrange the digits in descending order as 7 > 5 > 4 > 3. Step 2: Place the digits in the place value chart from left to right. So, the greatest 4-digit number formed is 7543. Th H T O The steps to find the smallest 4-digit number are given 7543 below. Step 1: Arrange the digits in ascending order as Th H T O 3 < 4 < 5 < 7. 34 5 7 Step 2: Place the digits in the place value chart from left to right. So, the smallest 4-digit number formed is 3457. Numbers 26 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 65 1/7/2019 2:17:41 PM

Example 12: Form the smallest 4-digit number using 4, 1, 0 and 6 (without repeating the digits). Solution: The given digits are 4, 1, 0 and 6. Step 1: Arrange the digits in ascending order as 0 < 1 < 4 < 6. Step 2: Place the digits in the place value chart from left to Th H T O right. But the number formed is 0146 or 146. 01 4 6 It is a 3-digit number. In such cases, we interchange the first two digits in Th H T O the place value chart. 10 4 6 So, the smallest 4-digit number formed is 1046. Example 13: Form the smallest and the largest 4-digit numbers using 4, 0, 8 and 6 (with repeating the digits). Solution: The given digits are 4, 0, 8 and 6. Follow the steps to form the smallest 4-digit number. Step 1: Find the smallest digit. 0 is the smallest of the given digits. (But a number cannot begin with 0.) Step 2: If the smallest digit is ‘0’, find the next smallest digit, which is 4. Write ‘4’ in the thousands place. Write ‘0’ in the rest of the places. Therefore, the smallest 4-digit number is 4000. Note: If the smallest of the given digits is not ‘0’, repeat the smallest digit four times to form the smallest number. Now, let us form the largest 4-digit number from the given digits. Step 1: The largest of the given digits is 8. Step 2: Repeat the digit four times to form the largest 4-digit number. Therefore, the largest 4-digit number that can be formed is 8888. Higher Order Thinking Skills (H.O.T.S.) Let us see a few real-life examples where we use the comparison of 4-digit numbers. Example 14: 4538 people visited an exhibition on Saturday and 3980 people visited it on Sunday. On which day did fewer people visit the exhibition? 27 1/7/2019 2:17:41 PM NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 66

Solution: Number of people who visited the exhibition on Saturday = 4538 Number of people who visited the exhibition on Sunday = 3980 Comparing both the numbers using the place value chart, Th H T O Th H T O 4 53 8 3 98 0 4 > 3 or in other words, 3 < 4 So, 3980 < 4538. Therefore, fewer people visited the exhibition on Sunday. Example 15: Razia arranged the numbers 7123, 2789, 2876 and 4200 in the ascending order as 2876, 2789, 4200, 7123. Reena arranged them as 2789, 2876, 4200, 7123. Who arranged them correctly? Why? Solution: Reena’s arrangement is correct. Reason: Comparing the hundreds place of the smaller of the given numbers, 7 hundreds < 8 hundreds. So, 2789 is the smallest number. Drill Time Concept 3.1: Count by Thousands 1) Write the numbers in the place value chart. a) 1451 b) 8311 c) 9810 d) 1000 e) 7613 2) Write the numbers in their expanded forms. a) 8712 b) 6867 c) 1905 d) 4000 e) 9819 3) Write the number names of the following numbers: a) 9125 b) 5321 c) 3100 d) 1900 e) 7619 4) Form 4-digit numbers from the following: a) 4 in the thousands place, 3 in the hundreds place, 0 in the tens place and 2 in the ones place b) 9 in the thousands place, 1 in the hundreds place, 4 in the tens place and 0 in the ones place Numbers 28 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 67 1/7/2019 2:17:41 PM

c) 5 in the thousands place, 4 in the hundreds place, 9 in the tens place and 7 in the ones place d) 8 in the thousands place, 2 in the hundreds place, 6 in the tens place and 5 in the ones place e) 1 in the thousands place, 2 in the hundreds place, 3 in the tens place and 4 in the ones place 5) Word problems a) The number of people in different rows in a football stadium is as given: Row 1: 2345 Row 2: 6298 Row 3: 7918 Row 4: 8917 Row 5: 1118 (A) What is the number of people in Row 1? Write the number in words. (B) How many people are there in Row 4? Write the number in words. b) R am has a note of ` 2000, a note of ` 500, a note of ` 20 and a coin of ` 2. How much money does he have? Write the amount in figures and words. Concept 3.2: Compare 4-digit Numbers 6) Compare the following numbers using <, > or =. a) 8710, 9821 b) 1689, 1000 c) 4100, 4100 d) 2221, 2222 e) 6137, 6237 7) Arrange the numbers in ascending and descending orders. a) 4109, 5103, 1205, 5420 b) 7611, 7610, 7609, 7605 c) 9996, 8996, 1996, 4996 d) 5234, 6213, 1344, 5161 e) 4234, 6135, 4243, 6524 8) Form the greatest and the smallest numbers using: a) 3, 5, 9, 2 b) 1, 5, 9, 4 c) 7, 4, 1, 8 d) 9, 1, 3, 5 e) 8, 2, 3, 4 9) Word problems a) 5 426 people visited a museum on a Friday and 3825 people visited it on the following Sunday. On which day did fewer people visit the museum? b) A shopkeeper sold 1105 milk chocolates and 2671 white chocolates. Which type of chocolates did he sell more? 29 1/7/2019 2:17:41 PM NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 68

Chapter Addition 4 Let Us Learn About • adding numbers with and without regrouping. • rounding off numbers to the nearest tens. • estimating the sum by adding mentally. Concept 4.1: Estimate the Sum of Two Numbers Think Farida has ` 450 with her. She wants to buy a toy car for ` 285 and a toy train for ` 150. Do you think she has enough money to buy the toys? Recall We have learnt addition of 2-digit and 3-digit numbers. Here is a quick recap of the steps. Step 1: Place the numbers one below the other, according to their places. Step 2: Start adding from the ones place. Step 3: Regroup the sum and carry it forward to the next place, if necessary. Step 4: Write the answer. NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 69 30 1/7/2019 2:17:41 PM

& Remembering and Understanding Many a times, knowing the exact number may not be needed. When we say there are about 50 students in class, we mean that the number is close to 50. Numbers which are close to the exact number can be rounded off. Rounding off numbers is also known as estimation. If the digit in the ones place is equal to or greater than 5, we round off the number to the closest multiple of ten, greater than the given number. Let us now learn to round off or estimate the given numbers. Rounding to the nearest 10 Observe the number line given. The numbers on it are written in tens. 12 is between 10 and 20 and is closer (12) (28) (35) (49) to 10. So, we round off 12 down to 10. 0 10 20 30 40 50 35 is exactly in between 30 and 40. So, we round it off up to 40. Let us now learn a step-wise procedure to round off numbers to the nearest 10. Example 1: Round off the following numbers to the nearest 10. a) 86 b) 42 Solution: Let us round off the given numbers using a step-wise procedure. Steps Solved Solve these 86 42 57 25 63 Step 1: Observe the digit in the ones place 86 42 57 25 63 of the number. Step 2: If the digit in 6>5 2 < 5 ____ > 5 ____ = 5 ____ < 5 the ones place is 4 or less, round the number 86 is 42 is ____ is ____ is ____ is down to the previous rounded rounded rounded rounded rounded ten. up to 90 down to 40 up to ____ up to ____ down to If it is 5 or more, round the number up, to the ____ next tens. 31 1/7/2019 2:17:41 PM NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 70

Rounding off numbers is used to estimate the sum of two 2-digit and 3-digit numbers. Let us understand this through an example. Example 2: Estimate the sum of: a) 64 and 15 b) 83 and 18 Solution: a) 64 + 15 Rounding off 64 to the nearest tens gives 60 (as 4 < 5). R ounding off 15 to the nearest tens gives 20 (as 5 = 5). So, the required sum is 60 + 20 = 80. b) 83 + 18 Rounding off 83 to the nearest tens gives 80 (as 3 < 5). Rounding off 18 to the nearest tens gives 20 (as 8 > 5). So, the required sum is 80 + 20 = 100. Example 3: Estimate the sum in the following: a) 245 and 337 b) 483 and 165 Solution: a) 245 + 337 R ounding off 245 to the nearest tens gives 250 (as 5 = 5). Rounding off 337 to the nearest tens gives 340 (as 7 > 5). So, the required sum is 250 + 340 = 590. b) 483 + 165 R ounding off 483 to the nearest tens gives 480 (as 3 < 5). Rounding off 165 to the nearest tens gives 170 (as 5 = 5). So, the required sum is 480 + 170 = 650. Application Here are a few examples where the estimation of the sum can be useful. Example 4: Arun wants to distribute sweets among students in the two sections of his class. In Section A, there are 43 students and in Section B, there are 36 students. Estimate the number of sweets that Arun should take to the class. Addition 32 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 71 1/7/2019 2:17:41 PM

Solution: Number of students in Section A = 43 Rounding off 43 to the nearest tens, we get 40. Number of students in Section B = 36 Rounding off 36 to the nearest tens, we get 40. Their sum is 40 + 40 = 80. Therefore, Arun should take about 80 sweets to the class. Example 5: Raj buys vegetables for ` 63 and fruits for ` 25. Estimate the amount he should pay to the shopkeeper. Solution: Amount spent on vegetables = ` 63 63 rounded to the nearest tens is 60. Amount spent on fruits = ` 25 25 rounded to the nearest tens is 30. Total amount to be paid = ` 60 + ` 30 = ` 90 HigShoe, rROajrsdheour lTdhpinakyinagboSukti`lls90(Hto.Oth.Te.Ssh.)opkeeper. Observe a few more situations where estimation of sum is used. Example 6: There are 416 walnut trees in a park. The park workers plant 574 more walnut trees. Estimate the number of walnut trees in the park after the workers finish planting. Solution: Number of trees in the park = 416 Rounding off 416 to the nearest tens, we get 420. Number of more trees the workers plant = 574 Rounding off 574 to the nearest tens, we get 570. Their sum is 420 + 570 = 990. Therefore, the park will have about 990 walnut trees after the workers finish planting. Example 7: Ramya has 26 cookies and 34 toffees. Renu has 42 cookies and 13 toffees. Estimate the total number of cookies and toffees. 33 1/7/2019 2:17:41 PM NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 72

Solution: Number of cookies with Ramya = 26 Number of toffees with her = 34 Rounding off 26 and 34 to the nearest tens, we get 30 and 30 respectively. Number of cookies with Renu = 42 Number of toffees with her = 13 Rounding off 42 and 13 to the nearest tens, we get 40 and 10 respectively. So, the sum of cookies = 30 + 40 = 70 Sum of toffees = 30 + 10 = 40 Therefore, they have 70 cookies and 40 toffees altogether. Concept 4.2: Add 3-digit and 4-digit Numbers Think Farida’s father bought her a shirt for ` 335 and a skirt for ` 806. Farida wants to find how much her father had spent in all. How do you think she can find that? Recall We can add 2-digit or 3-digit numbers by writing them one below the other. This method of addition is called vertical addition. Let us revise the earlier concept and solve the following. a) 22 + 31 = _________ b) 42 + 52 = _________ c) 82 + 11 = _________ d) 101 + 111 = _________ e) 100 + 200 = _________ f) 122 + 132 = _________ Addition 34 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 73 1/7/2019 2:17:41 PM

& Remembering and Understanding Let us now understand the addition of two 3-digit numbers with regrouping. We will also learn to add two 4-digit numbers. Add 3-digit numbers with regrouping Sometimes, the sum of the digits in a place is more than 9. In such cases, we need to regroup the sum. We then carry forward the digit to the next place. Example 8: Add 245 and 578. Solution: Arrange the numbers one below the other. Regroup if the sum of the digits is more than 9. Step 1: Add the ones. Solved Step 3: Add the hundreds. H TO Step 2: Add the tens. H TO 1 11 245 H TO 245 11 +578 245 +578 3 +578 823 23 H TO Solve these H TO H TO 823 171 +197 390 +219 +121 Add 4-digit numbers without regrouping Adding two 4-digit numbers is similar to adding two 3-digit numbers. Let us understand this through an example. Example 9: Add 1352 and 3603. Solution: Arrange the numbers one below the other. 35 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 74 1/7/2019 2:17:41 PM

Solved Step 1: Add the ones. Step 2: Add the tens. Th H T O Th H T O 135 2 135 2 +3 6 0 3 +3 6 0 3 5 55 Step 3: Add the hundreds. Step 4: Add the thousands. Th H T O Th H T O 135 2 13 5 2 +3 6 0 3 +3 6 0 3 955 49 5 5 Solve these Th H T O Th H T O Th H T O 41 9 0 20 0 2 11 1 1 +2 0 0 0 +3 0 0 3 +2 2 2 2 Add 4-digit numbers with regrouping We regroup the sum when it is equal to or more than 10. Example 10: Add 1456 and 1546. Solution: Arrange the numbers one below the other. Add and regroup, if necessary. Solved Step 1: Add the ones. Step 2: Add the tens. Th H T O Th H T O 1 11 1456 1456 +1 5 4 6 +1 5 4 6 2 02 Addition 36 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 75 1/7/2019 2:17:41 PM

Solved Step 3: Add the hundreds. Step 4: Add the thousands. Th H T O Th H T O 111 111 1456 1456 +1 5 4 6 +1 5 4 6 002 3002 Th H T O Solve these O Th H T O Th H T 175 8 459 2 +5 6 6 2 267 8 +1 4 5 6 +1 3 3 2 Application Look at a few examples where we use addition of 3-digit and 4-digit numbers. Example 11: Vinod had some stamps out of which he gave 278 stamps to his brother. Vinod now has 536 stamps left with him. How many stamps did he have in the beginning? H TO Solution: Number of stamps Vinod has now = 536 11 Number of stamps he gave his brother = 278 5 36 Number of stamps Vinod had in the +2 78 beginning = 536 + 278 = 814 8 14 Therefore, Vinod had 814 stamps in the beginning. 37 1/7/2019 2:17:41 PM NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 76

Example 12: Ajit collected ` 2683 and Radhika collected ` 3790 for donating to a nursing home. What is the total money Th H T O collected? Solution: Amount collected by Ajit = ` 2683 11 Amount collected by Radhika = ` 3790 2 6 83 Total amount collected for the donation +3 7 9 0 =` 2683 + ` 3790 = ` 6473 6 4 73 Example 13: The number of Class 3 students in Heena’s school is 236. The number of Class 3 students in Veena’s school is 289. How many total number of students were present in Class 3 of both the school? Solution: Number of students in Heena’s school = 236 Number of students present in Veena’s school = 289 Total number of students present in Class 3 of both the schools = 236 + 289 = 525 Higher Order Thinking Skills (H.O.T.S.) Let us see a few more examples on the addition of 4-digit numbers. Example 14: Three pieces of ribbon of lengths 2134 cm, 1185 cm and 3207 cm are cut from a long ribbon. What was the total length of the ribbon before the pieces were cut? Solution: The pieces of ribbon are 2134 cm, 1185 cm Th H T O and 3207 cm long. 11 Length of the ribbon before the pieces were 2134 cut = 2134 cm + 1185 cm + 3207 cm +1 1 8 5 Therefore, the ribbon was 6526 cm long before + 3 2 0 7 6526 the pieces were cut. Example 15: Payal, Eesha and Suma have 1284, 7523 and 5215 stamps respectively. Frame an addition problem. Solution: An addition problem contains words such as - in all, total, altogether and so on. So, the question can be ‘‘Payal, Eesha and Suma have 1284, 7523 and 5215 stamps respectively. How many stamps do they have altogether?” Addition 38 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 77 1/7/2019 2:17:41 PM

Concept 4.3: Add 2-digit Numbers Mentally Think Farida had 18 colour pencils. Her sister gave her 71 more. Farida wanted to calculate the total number of pencils mentally. Do you know how Farida could do? Recall We have already learnt to add two 1-digit numbers mentally. To do so, we keep the larger number in mind and add the smaller one to it. Let us answer the questions to revise the concept. a) 5 + 4 = ________ [ ] (A) 5 (B) 4 (C) 1 (D) 9 b) 3 + 3 = ________ [ ] (A) 3 (B) 6 (C) 0 (D) 5 c) 1 + 4 = ________ [ ] (A) 3 (B) 4 (C) 6 (D) 5 d) 5 + 0 = ________ Train My Brain [ ] (A) 4 (B) 5 (C) 0 (D) 6 e) 6 + 3 = ________ [ ] (A) 4 (B) 6 (C) 3 (D) 9 & Remembering and Understanding Let us now learn to add two 2-digit numbers mentally, through these examples. Add 2-digit numbers mentally without regrouping Example 16: Add mentally: 53 and 65 Solution: To add the given numbers mentally, follow these steps: 39 1/7/2019 2:17:41 PM NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 78

Steps Solved Solve this 53 and 65 38 and 41 Step 1: Add the digits in the ones place of the two 3+5=8 _____ + _____ = _____ numbers mentally. Step 2: Add the digits in the The digits in the tens The digits in the tens place of tens place of the two numbers place of the two the two numbers are ___ and mentally. To mentally add numbers are 5 and 6. ____. Keep ____ in your mind, two 1-digit numbers, keep the Keep 6 in your mind, count ___ forward as ____, larger number in mind and the count 5 forward as 7, ____and ____. smaller on the fingers. 8, 9, 10 and 11. ____ + ____ = ___ 5 + 6 = 11 Step 3: Write sum of the digits So, 53 + 65 = 118. So, 38 + 41 = ___. obtained in step 1 and sum of the digits obtained in step 2 together. This is the sum of the given numbers. Add 2-digit numbers mentally with regrouping Example 17: Add mentally: 29 and 56 Solution: To add the given numbers mentally follow these steps. Steps Solved 29 and 56 Solve this 83 and 47 Step 1: Regroup the two 29 = 20 + 9 83 = ___ + ____ given numbers as tens and 56 = 50 + 6 47 = ___ + ____ ones mentally. ____ + ____ = ____ Step 2: Add the ones of the 9 + 6 = 15 ____ + ____ = ____ two numbers mentally. ____ + ___ = ____ Step 3: Add the tens of the 20 + 50 = 70 two numbers mentally. So, 83 + 47 = ___. Step 4: Add the sums from 70 + 15 steps 2 and 3 mentally = 70 + 10 + 5 (regroup if needed). = 85 So, 29 + 56 = 85. Step 5: Write the sum of the given numbers. Addition 40 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 79 1/7/2019 2:17:41 PM

Application We have seen how easy it is to add two 2-digit numbers mentally. Let us see some real-life situations in which mental addition of 2-digit numbers is useful. Example 18: Suraj has 34 sheets and Kamal has 27 sheets of paper. How many sheets of paper do they have in all? Solve mentally. Solution: Number of sheets of paper Suraj has = 34 Number of sheets of paper Kamal has = 27 Total number of sheets they have together = 34 + 27 Regrouping the given numbers in tens and ones and adding, we get 30 + 4 + 20 + 7 To add two 1-digit numbers mentally, keep the larger number in mind and add the smaller one to it. Add tens and ones accordingly. = 50 + 11 = 50 + 10 + 1 (Regroup and add) = 60 + 1 = 61 Therefore, Suraj and Kamal have 61 sheets of paper. Example 19: Vivek has 49 bags and Shyam has 29 bags. How many bags do they have in total? Solve mentally. Solution: Number of bags Vivek has = 49 Number of bags Shyam has = 29 Total number of bags they have together = 49 + 29 Regrouping the given numbers in tens and ones and adding, we get 40 + 9 + 20 + 9 To add two 1-digit numbers, keep the larger number in mind and add the smaller one to it. Add tens and ones accordingly. = 40 + 20 + 18 = 60 + 10 + 8 (Regroup and add) = 70 + 8 = 78 So, they have 78 bags in total. 41 1/7/2019 2:17:41 PM NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 80

Higher Order Thinking Skills (H.O.T.S.) We have seen mental addition of two 2-digit numbers. Let us now see a few examples to add three 2-digit numbers mentally. Example 20: Add mentally: 25, 37 and 19 Solution: To add the given numbers mentally follow these steps. Steps Solved Solve this 25, 37 and 19 40, 29 and 54 Step 1: Regroup the three given 25 = 20 + 5 40 = ___ + ____ numbers as tens and ones mentally. 37 = 30 + 7 29 = ___ + ____ 19 = 10 + 9 54 = ____+____ Step 2: Add the tens mentally. 20 + 30 + 10 = 60 ____ + ____+ ____ = ____ Step 3: Add the ones mentally. 5 + 7 + 9 = 21 ____+___ + ____ = ____ Step 4: Add the sums from steps 2 60 + 21 ____ + ___ = ____ and 3 mentally, regroup again if = 60 + 20 + 1 = 81 needed. So, 25 + 37 + 19 = 81. So, 40 + 29 + 54 = ___. Step 5: Write the sum of the given numbers. Drill Time Concept 4.1: Estimate the Sum of Two Numbers 1) Estimate the sum of the following: a) 211 and 115 b) 549 and 120 c) 385 and 190 d) 222 and 524 e) 672 and 189 Addition 42 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 81 1/7/2019 2:17:41 PM

2) Word problems a) Susan has 46 red roses and Mukesh has 22 yellow roses. Estimate the total number of roses. b) Rakesh has 67 pencils and Mona has 43 pencils. Estimate the number of pencils both of them have in all. Concept 4.2: Add 3-digit and 4-digit Numbers 3) Add 3-digit numbers with regrouping. a) 481 + 129 b) 119 + 291 c) 288 + 288 d) 346 + 260 e) 690 + 110 4) Add 4-digit numbers without regrouping. a) 1234 + 1234 b) 1000 + 2000 c) 4110 + 1332 d) 5281 + 1110 e) 7100 +1190 5) Add 4-digit numbers with regrouping. a) 5671 + 1430 b) 3478 + 2811 c) 4356 + 1753 d) 2765 + 1342 e) 4901 + 2222 6) Word problems a) T here are 142 people riding in Train A and 469 people in Train B. How many people rode in both the trains altogether? b) A li scored 272 points in one level of a computer game. His friend, Jenny, scored 538 points in the next level. What is their total score in both the levels? Concept 4.3: Add 2-digit Numbers Mentally 7) Add 2-digit numbers mentally without regrouping. a) 31 and 22 b) 22 and 42 c) 45 and 51 d) 11 and 34 e) 32 and 61 8) Add 2-digit numbers mentally with regrouping. a) 45 and 47 b) 25 and 56 c) 12 and 19 d) 27 and 35 e) 17 and 37 43 1/7/2019 2:17:41 PM NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 82

Chapter Subtraction 5 Let Us Learn About • Subtracting 3-digit numbers with regrouping. • Subtracting 4-digit numbers with and without regrouping. • rounding off numbers. • estimating the difference between numbers. • subtracting two numbers mentally. Concept 5.1: Estimate the Difference between Two Numbers Think Farida had ` 450 with her. She wanted to buy a toy car for ` 185 and a toy train for ` 150. How much money will remain with Farida after buying the toys? Recall We know that in some situations where we do not need the exact number, we use estimation. Estimation can be done by rounding off numbers to a given place. Let us answer these to revise the concept of rounding off to the nearest 10. a) 87 = ______ b) 53 = ______ c) 65 = ______ d) 42 = ______ e) 33 = ______ & Remembering and Understanding Estimation is finding a number that is close enough to the right answer. Rounding off numbers can be used to estimate the difference between two 2-digit numbers and between two 3-digit numbers. NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 83 44 1/7/2019 2:17:42 PM

Let us understand this through examples. Example 1: Estimate the difference: a) 69 – 15 b) 86 – 12 Solution: a) 69 – 15 Rounding off 69 to the nearest tens gives 70 (as 9 > 5) and rounding off 15 to the nearest tens, gives 20 (as 5 = 5). So, the required difference is 70 – 20 = 50. b) 86 – 12 R ounding off 86 to the nearest tens gives 90 (as 6 > 5) and rounding off 12 to the nearest tens, gives 10 (as 2 < 5). So, the required estimated difference is 90 – 10 = 80. Example 2: Estimate the difference: a) 593 – 217 b) 806 – 124 Solution: a) 593 – 217 R ounding off 593 to the nearest tens gives 590 (as 3 < 5) and rounding off 217 to the nearest tens, gives 220 (as 7 > 5). So, the required estimated difference is 590 – 220 = 370. b) 806 – 124 R ounding off 806 to the nearest tens gives 810 (as 6 > 5) and rounding off 124 to the nearest tens, gives 120 (as 4 < 5). So, the required estimated difference is 810 – 120 = 690. Application Estimation of differences can be used in real-life situations. Let us see a few examples. Example 3: Parul has 83 pencils. She gives 32 pencils to her sister. Estimate the number of pencils that remain with Parul. Solution: Number of pencils Parul has = 83 83 rounded off to the nearest tens is 80 (since 3 < 5). Number of pencils given to Parul’s sister = 32 32 rounded off to the nearest 10 is 30 (since 2 < 5). 45 1/7/2019 2:17:42 PM NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 84

So, the estimated number of pencils left with Parul = 80 − 30 = 50 Therefore, Parul has about 50 pencils. Example 4: Ram has 94 sweets. He distributes 46 sweets among his friends. About how many sweets remain with Ram? Solution: Number of sweets Ram has = 94 94 rounded off to the nearest tens is 90 (since 4 < 5). Number of sweets distributed among Ram's friends = 46 46 rounded off to the nearest tens is 50 (since 6 > 5). So, the estimated number of sweets left with Ram = 90 − 50 = 40 Therefore, Ram has about 40 sweets. Higher Order Thinking Skills (H.O.T.S.) In some situations, we may need to carry out both addition and subtraction. In such cases, we need to identify which operation is to be carried out first. Example 5: In a school, there are 976 students. Of them, 325 are from the pre-primary section, 416 are from the primary section, and the rest are from high school. How many high school students are there in the school? Solution: Total number of students = 976 HTO Number of students from the pre-primary section = 325 1 Number of students from the primary section = 416 Total number of students in pre-primary and primary 325 school sections = 325 + 416 = 741 +4 1 6 741 Number of students in high school = Total number of HTO students – Number of students in pre-primary and 9 7 6 primary school sections = 976 – 741 = 235 −7 4 1 Therefore, there are 235 high school students. 235 Subtraction 46 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 85 1/7/2019 2:17:42 PM

Concept 5.2: Subtract 3-digit and 4-digit Numbers Think The given grid shows the number of men and women in Farida’s town in the years 2017 and 2018. Years 2017 2018 How can Farida find out how may more Men 2254 2187 men than women lived in her town in the Women 2041 2073 two years. Recall Recall that we can subtract numbers by writing the smaller number below the greater number. A 2-digit number can be subtracted from a larger 2-digit number or a 3-digit number. Similarly, a 3-digit number can be subtracted from a larger 3-digit number. Let us answer these to revise the concept. a) 15 – 0 = _________ b) 37 – 36 = _________ c) 93 – 93 = _________ f) 50 – 45 = _________ d) 18 – 5 = _________ e) 47 – 1 = _________ & Remembering and Understanding We have learnt how to subtract two 3-digit numbers without regrouping. Let us now learn how to subtract them with regrouping. Subtract 3-digit numbers with regrouping When a larger number is to be subtracted from a smaller number, we regroup the next higher place and borrow. And, we always start subtracting from the ones place. Let us understand this with an example. Example 6: Subtract 427 from 586. Solution: To subtract, write the smaller number below the larger number. 47 1/7/2019 2:17:42 PM NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 86

Step 1: Subtract the ones. But, 6 – 7 is Solved Step 3: Subtract the not possible as 6 < 7. So, regroup the hundreds. digits in the tens place. Step 2: Subtract the tens. 8 tens = 7 tens + 1 tens. Borrow 1 ten to the ones place. Reduce the tens by 1 ten. Now subtract 7 ones from 16 ones. H TO H TO H TO 7 16 7 16 5 5 7 16 –4 8\\ 6\\ 5 \\8 \\6 –4 \\8 \\6 27 –4 2 7 1 9 59 27 59 H TO Solve these H TO H TO 6 23 5 52 4 53 – 3 76 – 2 63 – 2 64 Subtract 4-digit numbers without regrouping Subtracting a 4-digit number from a larger 4-digit number is similar to subtracting a 3-digit number from a larger 3-digit number. The following examples help you understand this better. Example 7: Subtract: 5032 from 7689 Solution: To subtract, write the smaller number below the larger number. Step 1: Subtract the ones. Solved Step 2: Subtract the tens. Th H T O O 76 8 9 Th H T 9 −50 3 2 768 2 7 −503 7 5 Subtraction 48 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 87 1/7/2019 2:17:42 PM

Step 3: Subtract the hundreds. Step 4: Subtract the thousands. Th H T O Th H T O 7689 7 68 9 −5032 − 5 03 2 2 65 7 657 Th H T O Solve these Th H T O 2879 8000 –2137 Th H T O –2000 4789 –2475 Subtract 4-digit numbers with regrouping In subtraction of 4-digit numbers, we can regroup the digits in thousands, hundreds and tens places. Let us see an example. Example 8: What is the difference 7437 and 4868? Solution: Write the smaller number below the larger number. Steps Solved Solve these Step 1: Subtract the ones. Th H T O Th H T O But, 7 − 8 is not possible as 1654 74 2 17 −1 2 4 6 7 < 8. So, regroup the tens digit, −4 8 3. 3 tens = 2 tens + 1 ten. Borrow 3\\ \\7 1 ten to the ones place. 6 8 9 Step 2: Subtract the tens. But, Th H TO 12 2 − 6 is not possible as 2 < 6. 7 So, regroup the hundreds digit, −4 3 \\2 17 4. 4 hundreds = 3 hundreds + 4\\ 3\\ \\7 1 hundred. Borrow 1 hundred to 868 the tens place. 69 49 1/7/2019 2:17:42 PM NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 88

Step 3: Subtract the hundreds. Th H T O Th H T O But, 3 − 8 is not possible. So, 13 12 regroup the thousands digit, 5674 7. 7 thousands = 6 thousands + 6 \\3 \\2 17 −2 3 8 2 1 thousand. Borrow 1 thousand to the hundreds place. \\7 4\\ 3\\ \\7 −4 8 6 8 569 Step 4: Subtract the thousands. Th H T O Th H T O 13 12 7468 6 \\3 \\2 17 −4 8 3 7 \\7 4\\ 3\\ \\7 −4 8 6 8 2569 Application Subtraction of 3-digit numbers is very often used in real life. Here are a few examples. Example 9: Sonu bought 375 marbles. He gave 135 marbles to his brother. How many marbles are left with him? Solution: Total number of marbles Sonu bought = 375 HT O Number of marbles given to Sonu’s brother = 135 37 5 Number of marbles left with him = 375 – 135 = 240 −1 3 5 Therefore, 240 marbles are left with Sonu. 240 Example 10: Vinod had 536 stamps. He gave some stamps to his brother and then Vinod was left with 278 stamps. How many stamps did Vinod give his Solution: brother? H TO Total number of stamps Vinod had = 536 12 Number of stamps Vinod had after giving some 4 2\\ 16 to his brother = 278 \\5 \\3 \\6 −278 Number of stamps he gave his brother = 258 536 – 278 = 258 Therefore, Vinod gave 258 stamps to his brother. Subtraction 50 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 89 1/7/2019 2:17:42 PM

We can use subtraction of 4-digit numbers in real-life situations. Let us see some examples. Example 11: Mohan’s uncle stays 8630 m away from Mohan’s house. Mohan travelled 6212 m of the distance. What is the distance yet to Th H T O Solution: be covered by Mohan to reach his uncle’s house? 2⁄ 1⁄0 Distance between Mohan’s house and his uncle’s 8 630 house = 8630 m − 6 212 Distance travelled by Mohan = 6212 m 2 418 Remaining distance Mohan has to travel = 8630 m – 6212 m = 2418 m Therefore, Mohan has to travel 2418 m more to reach his uncle’s house. Example 12: A rope is 6436 cm long. A 3235 cm long piece is cut from it. How much of the rope is left? Solution: Length of the rope = 6436 cm Th H T O 6436 Length of the piece cut = 3235 cm −3 2 3 5 The length of the remaining piece of rope 3201 = 6436 cm – 3235 cm = 3201 cm Therefore, 3201 cm of the rope is left. Higher Order Thinking Skills (H.O.T.S.) We can check the correctness of a subtraction problem using addition. Consider an example. b) 145 from 364. Example 13: Subtract: a) 27 from 36 Solution: a) 36 – 27 b) 364 – 145 TO HT O 2 16 5 14 \\3 \\6 3 \\6 4\\ −2 7 −1 4 5 9 21 9 We can write 36 = 27 + 9 364 – 145 = 219 We can write 364 = 145 + 219 51 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 90 1/7/2019 2:17:42 PM

We can conclude that to check if the subtraction is correct, we add the subtrahend (the number being subtracted) and the difference. If this sum is the same as the minuend (the number from which a number is subtracted), the subtraction is correct. Framing word problems Let us consider these subtraction facts. a) 37 – 14 = 23 b) 37 – 23 = 14 We can try to frame some interesting situations and problems using these subtraction facts. a) O f the 37 students in class, 14 are in the green house. How many students are in the red house? b) 37 children are playing on the ground. 23 of them are playing football. How many are playing basketball? Similarly, we can frame some interesting problems using subtraction facts of 3-digit numbers. Let us see an example. Example 14: Frame a word problem using: a) 706 – 234 = 472 b) 461 − 110 = 351 Solution: A few possible word problems are: a) In a school, there are 706 students. 234 students were absent on Monday. How many students were present? b) 461 people booked the train for a trip to Goa. 110 people cancelled the trip. How many people went on the trip? Concept 5.3: Subtract 2-digit Numbers Mentally Think Farida had 19 pens. She gave 12 pens to her sister. Can you find the number of pens remaining with Farida without using a paper and a pencil? Recall Recall that to subtract two 1-digit numbers mentally, we keep the larger number in mind and subtract the smaller one from it. Subtraction 52 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 91 1/7/2019 2:17:42 PM

Let us answer these to revise the concept. [] a) 5 – 4 = ________ [] (A) 5 (B) 4 (C) 1 (D) 9 [] b) 3 – 3 = ________ [] (A) 3 (B) 6 (C) 0 (D) 5 [] c) 4 – 1 = ________ (A) 3 (B) 4 (C) 6 (D) 8 d) 5 – 0 = ________ (A) 4 (B) 5 (C) 0 (D) 6 e) 6 – 3 = ________ (A) 4 (B) 6 (C) 3 (D) 9 & Remembering and Understanding We have learnt to subtract 1-digit numbers mentally. Let us understand subtraction of 2-digit numbers mentally through an example. Subtract 2-digit numbers mentally without regrouping Example 15: Subtract mentally: 52 from 76 Solution: Follow these steps to subtract mentally. Steps Solved Solve this n 52 from 76 35 from 69 Step 1: Subtract mentally 6 – 2 = 4 ______ – ______ = the digits in the ones place of the two numbers. Step 2: Subtract mentally The digits in the tens place The digits in the tens place of the digits in the tens place of the two numbers are 7 the two numbers are _______ of the two numbers. and 5. and _______. So, imagine that 7 fingers So, imagine that _____ fingers are open. Then imagine are open. closing 5 of them. Then imagine closing ___ of 7–5=2 them. ____– ____ = ___ 53 1/7/2019 2:17:42 PM NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 92

Steps Solved Solve this 52 from 76 35 from 69 Step 3: Write the difference obtained in So, 76 – 52 = 24. So, 69 – 35 = ____. steps 1 and 2 together as the difference of the given numbers. Sometimes regrouping is necessary in subtraction. Let us see an example to understand this. Subtract 2-digit numbers mentally with regrouping Example 16: Subtract mentally: 29 from 56 Solution: Follow these steps to subtract mentally. Steps Solved Solve this 29 from 56 46 from 83 83 = ___ + ____ Step 1: Regroup the two 29 = 20 + 9 46 = ___ + ____ given numbers as tens and 56 = 50 + 6 ones. Regroup the sum if it is equal to or more than 10. Step 2: Check if the ones 6 – 9 is not possible. So, ____ – ____ is possible (True/ can be subtracted. If not, regroup the tens. False). If it is true, subtract. If it regroup the tens. is false, regroup. Add 10 ones to 6 to get Add ten ones to ones and 16 and subtract 1 ten Add 10 ones to ___ to get reduce 1 ten from tens. from 5 tens to get 4 tens. ____ and subtract 1 ten from ____ tens to get ____ tens. Step 3: Subtract the ones of 16 – 9 = 7 ____ – ____ = ____ the two numbers mentally. Step 4: Subtract the tens of 4 tens – 2 tens = 2 tens ____ – ____ = ____ the two numbers mentally. ____ – ___ = ____ Step 5: Write the answers So, 56 – 29 = 27. from steps 3 and 4 together as the difference. Subtraction 54 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 93 1/7/2019 2:17:42 PM

Application We have seen that it is easy to subtract two 2-digit numbers mentally. In some real-life situations, we use mental subtraction of numbers. Let us see a few examples. Example 17: Manoj has 64 notebooks. He sold 45 notebooks. How many notebooks are left with him? Solve mentally. Solution: Number of notebooks Manoj has = 64 Number of notebooks he sold = 45 The number of notebooks remaining with him = 64 – 45 = 19 Therefore, Manoj has 19 notebooks left with him. Example 18: Alisha went to school for 49 days in Term I and 65 days in Term II. For how many more days did Alisha go to school in the Term II than in the Term I? Solve mentally. Solution: Number of days Alisha went to school in Term I = 49 Number of days she went to school in Term II = 65 Difference in number of days = 65 – 49 = 16 Therefore, Alisha went to school 16 days more in Term II than in Term I. Higher Order Thinking Skills (H.O.T.S.) We have seen mental subtraction of two 2-digit numbers. Let us now see a real-life example where we might have to add and subtract numbers mentally. Example 19: Renu had ` 80. She bought guavas for ` 25 and bananas for ` 17. Calculate mentally the money that Renu has to pay the fruit seller. Also calculate mentally the money left with her. Solution: Total money Renu had = ` 80 Money she spent on guavas = ` 25 Money she spent on bananas = ` 17 To find the money she has to give the fruit seller, Renu has to add the prices of guavas and bananas. That is, ` 25 + ` 17 = ` 42. 55 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 94 1/7/2019 2:17:42 PM

To find the money remaining with her, Renu has to subtract this sum from the total money she had. So, ` 80 – ` 42 = ` 38. Therefore, ` 38 is left with Renu. Drill Time Concept 5.1: Estimate the Difference between Two Numbers 1) Estimate these differences: a) 65 – 15 b) 48 – 16 c) 67 – 32 d) 896 – 432 e) 679 – 387 2) Word problems a) In a class, there are 562 students. Of them, 118 are from the red group, 321 are from the green group, and the rest are from the blue group. How many students are in the blue group? b) Sneha has 77 balloons. She gives 42 balloons to her sister. About how many balloons remain with Sneha? Concept 5.2: Subtract 3-digit and 4-digit Numbers 3) Subtract 3-digit numbers with regrouping. a) 254 – 173 b) 678 – 619 c) 147 – 129 d) 781 – 682 e) 356 – 177 4) Subtract 4-digit numbers without regrouping. a) 2341 – 1230 b) 7632 – 5120 c) 9763 – 2311 d) 7629 – 1318 e) 7589 – 1268 5) Subtract 4-digit numbers with regrouping. a) 7632 – 1843 b) 4391 – 2482 c) 9843 – 7943 d) 8325 – 5436 e) 6893 – 3940 Subtraction 56 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 95 1/7/2019 2:17:42 PM

6) Word problems a) A stick is 8745 cm long. A 4313 cm long piece is cut from it. What part of the stick is remaining? b) Raj stays 5786 m away from Matin’s house. Raj travelled 3825 m of the distance. What is the distance yet to be covered by Raj to reach Matin’s house? Concept 5.3: Subtract 2-digit Numbers Mentally 7) Subtract 2-digit numbers mentally without regrouping. a) 43 from 84 b) 24 from 76 c) 52 from 87 d) 34 from 75 e) 14 from 38 8) Subtract 2-digit numbers mentally with regrouping. a) 42 from 81 b) 28 from 84 c) 11 from 20 d) 23 from 51 e) 76 from 81 9) Word problems a) Rehmat has 48 pencils. He has used 29 pencils. How many pencils are left with him? b) Sam travelled for 23 km on Day 1 and 76 km on Day 2. How much more distance (in km) did Sam travel on Day 2 than on Day 1? 57 1/7/2019 2:17:42 PM NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 96

EVS−I (Science) Textbook Features Let Us Learn About Think Contains the list of learning objectives to Introduces the concept/subtopic and be achieved in the lesson arouses curiosity among students Understanding Remembering Explains the aspects in detail that form Introduces new concepts to build on the basis of the concept the prerequisite knowledge/skills required Includes elements to ensure that students to understand and apply the objective are engaged throughout of the topic Application Amazing Facts Connects the concept to real-life Fascinating facts and trivia related to situations by enabling students to apply the concept what has been learnt through the practice questions Higher Order Thinking Skills (H.O.T.S.) Encourages students to extend the concept learnt to advanced application scenarios Inside the Lab Provides for hands-on experience with creating, designing and implementing something innovative and useful NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 97 1/7/2019 2:17:42 PM

EVS−I (Science) Contents Class 3 1 My Hobbies�������������������������������������������������������������������������������������������������������� 1 2 Family as First School���������������������������������������������������������������������������������������� 5 3 Organ Systems��������������������������������������������������������������������������������������������������� 8 4 Skeletal System������������������������������������������������������������������������������������������������ 11 5 Way around Our Neighbourhood������������������������������������������������������������������ 15 6 Forms of Water������������������������������������������������������������������������������������������������� 18 Inside the Lab – A�������������������������������������������������������������������������������������������������� 22 Activity A1: Salt from Seawater Activity A2: Create Your Compass NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 98 1/7/2019 2:17:42 PM

Lesson My Hobbies 1 Let Us Learn About R hobbies and their types. U how hobbies are useful to us. A choosing a hobby as a job. H my parents’ hobbies. Think Sam likes to watch movies in his free time. His sister likes photography. They enjoy doing these activities. What are such activities, other than your studies, called? Remembering You go to school every day to learn new things. You play with your friends at school. What do you do after school? At home, you do homework, watch TV, play and help your parents. How do you spend your free time on Sundays and holidays? NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 99 different types of activities 1 1/7/2019 2:17:42 PM

Some of the activities that you may enjoy doing are shown below. Guess what they are. They are called hobbies. Hobbies are the activities that we do for relaxation when we have free time. There are different types of hobbies. They are shown in the chart given below: Types of hobbies sports outdoor arts collection making and coins games recreation painting stamps scrapbook leaves making football birdwatching singing feathers knitting stargazing reading and pottery badminton cooking writing cricket gardening dancing video games travelling photography yoga trekking running mountaineering swimming adventure sports 2 1/7/2019 2:17:43 PM NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 100