Contents. Remember boxes and speech bubbles Important key points and tips. Special Features of Start Up Mathematics 3-5

Transcription

1 Contents 1. Numbers Beyond Roman Numerals Addition 26 Assessment Sheet Subtraction Multiplication Division 69 Assessment Sheet 2 84 Let s Review Fractions Measurement Time 109 Assessment Sheet Money Shapes and Patterns Data Handling 148 Assessment Sheet Let s Review Vedic Mathematics 160 Answers 163 Let s recall... Review exercises Let s Evaluate Chapter-end exercises Remember boxes and speech bubbles Important key points and tips Special Features of Start Up Mathematics 3-5 Solved Examples Quick reference Scratch Your Brain Question based on HOTS Mental Maths Questions to strengthen concepts Assessment Sheets and Let s Review Term-wise evaluation Vedic Mathematics Tricks to sharpen Mathematical Skills

2 1 NUMBERS BEYOND 999 Let s recall... Ten ones (10 ones) = One ten (1 ten) Ten tens (10 tens) = One hundred (1 hundred) 1. Write the number names. (a) 287 (b) 199 (c) 304 (d) Write 26, 87, 19, 145, 52 in ascending order. 3. Write 43, 96, 132, 190, 12, 85 in descending order. 4. Sort out the following into even and odd numbers. 23, 45, 7, 9, 16, 82, 14, 98, 1, 3, 6, 20, 43, 80, 50 Even numbers Odd numbers 5. Put the correct sign >, < or = in the box. (a) (b) (c) 9 16 (d) (e) (f)

3 6. Write in expanded form. (a) 538 = + + (b) 906 = Write the number that comes before. (a) 399 (b) 870 (c) Write the number that comes between. (a) 210,, 212 (b) 589,, 591 (c) 388,, 390 Let s learn further... Ten hundreds (10 hundreds) = One thousand (1 thousand) 9 hundreds + 9 tens + 9 ones = is the greatest 3-digit number. Let s see what happens when we add one more to it. one more 2

4 9 hundreds (900) + 10 tens (100) = 1 thousand (1000) 10 hundreds = 1 thousand So, = 1000 Th H T O Remember We get 1000 which is the smallest 4-digit number. Observe the following pattern. On adding 1 to the largest 1-digit number, we get the smallest 2-digit number = 10 On adding 1 to the largest 2-digit number, we get the smallest 3-digit number = 100 On adding 1 to the largest 3-digit number, we get the smallest 4-digit number = 1000 Counting by Thousands 1000 One thousand 3

5 2000 Two thousand 3000 Three thousand 4000 Four thousand 5000 Five thousand 6000 Six thousand 7000 Seven thousand 4

6 8000 Eight thousand 9000 Nine thousand Ten thousand Numbers and Number Names Let s learn to form 4-digit numbers. Example 1: Represent the given 4-digit numbers in pictorial graphs and write their number names. (a) 1532 (b) 2645 (c) 9783 Solution: (a) (1 thousand) (5 hundreds) (3 tens) (2 ones) = 1532 It is read as one thousand five hundred thirty-two. 5

7 (b) (2 thousands) (6 hundreds) (4 tens) (5 ones) = 2645 It is read as two thousand six hundred forty-five. (c) (9 thousands) (7 hundreds) (8 tens) (3 ones) = 9783 It is read as nine thousand seven hundred eighty-three. We can also form 4-digit numbers using an abacus. Consider a 4-digit number We represent this on an abacus as shown. Remember Th H T O Three thousand two hundred eighty-five 6

8 Example 2: Represent (a) 5064, (b) 7213 and (c) 9989 on the abacus. Solution: (a) 5064 (b) 7213 (c) 9989 Th H T O Th H T O Th H T O EXERCISE Complete the following number grid Observe the pictorial blocks and write the number they represent. (a) = 7

9 (b) = (c) = 3. Draw beads to represent the following numbers on the abacus. (a) 1064 (b) 2731 (c) 5608 Th H T O Th H T O Th H T O (d) 9890 (e) 7342 (f) 4576 Th H T O Th H T O Th H T O 8

10 4. Write the numbers represented on the abacus. (a) (b) (c) Th H T O Th H T O Th H T O (d) (e) (f) Th H T O Th H T O Th H T O 5. Write the number names. (a) 3463 = (b) 7018 = (c) 9920 = (d) 5409 = (e) 6999 = Place Value and Face Value We know that the place value of a digit depends on its place or position in a number, while the face value of a digit is the value of the digit itself. Example 3: Write the place value and face value of digits in Solution: 8632 = 8 thousands + 6 hundreds + 3 tens + 2 ones The place value of 8 in 8632 is 8000 and its face value is 8. The place value of 6 in 8632 is 600 and its face value is 6. The place value of 3 in 8632 is 30 and its face value is 3. The place value of 2 in 8632 is 2 and its face value is 2. Mental Maths What is the place value and face value of 7 in 4706 and in 7821? 9

11 Expanded Form Example 4: Write 9516 in expanded form. Solution: 9516 = = 9 Th + 5 H + 1 T + 6 O Expanded form of a number is the sum of the place values of its digits. Short form Expanded form EXERCISE Fill in the boxes. (a) 3623 = Th + H + T + O (b) 4780 = Th + H + T + O (c) 6095 = Th + H + T + O (d) 9909 = Th + H + T + O 2. Write the number names in your notebooks. Then write their numbers. (a) 5 Th + 3 H + 7 T + 1 O = (c) 4 Th + 9 H + 2 T + 4 O = (e) 7 Th + 0 H + 1 T + 8 O = (b) 6 Th + 8 H + 0 T + 2 O = (d) 8 Th + 6 H + 5 T + 9 O = (f) 3 Th + 5 H + 0 T + 3 O = 3. Write in expanded form. (a) 1827 = (b) 9869 = (c) 8053 = (d) 5899 = Write in short form. (a) = (c) = (b) = (d) = 10

12 5. Write the place value and face value of each circled digit of the given numbers in the table. Number Place Value Face Value 6. Complete the sequence. (a) 2035,,,, 2039, (b) 3210,,,,, 3215 (c) 5995,,, 5998,, (d) 9788,,,, 9792, Comparison of Numbers While comparing two numbers, we must remember the following points: The number which is ahead in counting is the bigger number. If two numbers have different number of digits, then the number with more digits is always greater. Example 5: Compare the numbers 2685 and 798. Solution: The number of digits in 2685 = 4 and in 798 = 3. Since, 4 > 3, therefore, 2685 > 798. If two numbers have the same number of digits, then always start comparing from the leftmost digit, i.e., the digit at the thousands place in both the numbers. Example 6: Compare the numbers 2982 and Solution: The digit at the thousands place in 2982 is 2 and in 3105 is 3. Since, 3 > 2, therefore, 3105 > If the digits at the thousands place are same, then compare the digits at the hundreds place. Example 7: Compare the numbers 4861 and Solution: The digit at the thousands place in both the numbers is 4. So we move ahead. The digit at the hundreds place in 4861 is 8 and in 4539 is 5. Since 8 > 5, therefore, 4861 > If the digits at the thousands and hundreds place are same, then compare the digits at the tens place. 11

13 Example 8: Compare the numbers 4861 and Solution: In both the numbers, the digit at the thousands place is 4 and at the hundreds place is 8. The digit at the tens place in 4861 is 6 and in 4875 is 7. Since 7 > 6, therefore, 4875 > If the digits at the thousands, hundreds and tens place are same, then compare the digits at the ones place. Example 9: Compare the numbers 4861 and Solution: In both the numbers, the digits at the thousands place is 4, the hundreds place is 8 and the tens place is 6. The digit at the ones place in 4861 is 1 and in 4865 is 5. Since 5 > 1, therefore, 4865 > If all the digits in both the numbers are same then the numbers are equal and we use the sign =. Mental Maths Which of these is greater? (a) (b) (c) (d) Before, After and Between The numbers which follow one after the other are called consecutive numbers. For example, 1316, 1317, 1318, 1319, 1320 are consecutive numbers. Consecutive numbers can also be written backwards. For example, 1320, 1319, 1318, 1317, 1316 A number one less than a given number comes just before it and is called its predecessor. A number one more than a given number comes just after it and is called its successor. Consider a 4-digit number Its predecessor = = 5862 and its successor = =

14 predecessor is between 5862 and 5864 successor Ordering of Numbers Comparison of two or more numbers becomes easy if we arrange the numbers in a sequence. This sequence can be from smaller to bigger or from bigger to smaller. Writing numbers in order from smaller to bigger is called ascending order and from bigger to smaller is called descending order. 6089, 6190, 7191, 8792 are in ascending order. 9791, 8790, 7787, 4688 are in descending order. Mental Maths Is 4271, 4281, 4396, 4402 an ascending or descending sequence? EXERCISE Put the correct sign <, > or =. (a) (b) (c) (d) (e) (f) Arrange the following in ascending order. (a) 3285, 4061, 298, 3469,,, (b) 1892, 1982, 1289, 1189,,, (c) 9099, 9909, 9990, 999,,, (d) 6341, 6143, 6431, 6314,,, 3. Arrange the following in descending order. (a) 7649, 7496, 7549, 7459,,, (b) 8291, 8192, 8091, 8129,,, (c) 1123, 1312, 1213, 1321,,, (d) 4523, 5619, 4807, 5032,,, 4. Write the number that comes between the given numbers. (a) 698,, 700 (b) 4039,, 4041 (c) 1287,, 1289 (d) 8500,,

15 5. Write the predecessor and successor of the given numbers. Predecessor Number Successor (a) 889 (b) 2341 (c) 7038 (d) Choose and write the largest number from the given numbers. (a) 3124, 2689, 708, 4925, 4259 (b) 1987, 2000, 2999, 2001, 399 (c) 6023, 6203, 6302, 6320, 6032 (d) 9989, 9819, 9899, 9879, 9897 Forming 4-digit Numbers We can form numbers using the given digits by arranging them in different order. For example, using the digits 6, 3, 8 and 1, the greatest 4-digit number that can be formed is 8631 and the smallest 4-digit number that can be formed is To form the greatest 4-digit number, arrange the given digits in descending order. 2. To form the smallest 4-digit number, arrange the given digits in ascending order. Example 10: Write the greatest and the smallest 4-digit number using the digits 2, 9, 0 and 5. Solution: The greatest 4-digit number is (on arranging the digits in descending order) The smallest 4-digit number is (on arranging the digits in ascending order) Note that the smallest 4-digit number is 2059 and not 0259 as 0 in the beginning of a number has no value. Skip Counting You have already learnt skip counting in 2 s, 3 s, 5 s and 10 s in the previous class. Now let s learn skip counting in 100 s and 1000 s. Remember 14

16 Skip count in 100 s means skipping 100 places (digits at the tens and ones places remain the same). For example, 7108, 7208, 7308, 7408, 7508 Skip count in 1000 s means skipping 1000 places (digits at the hundreds, tens and ones places remain the same). For example, 2845, 3845, 4845, 5845, 6845, 7845 More Than and Less Than Consider the number To find a number 2 more than 8135, we add 2 to 8135, i.e., = To find a number 3 less than 8135, we subtract 3 from 8135, i.e., = You need not add or subtract every time. You can also observe the pattern and find the number. Mental Maths What is 10 more than 90? What is 10 less than 50? EXERCISE Build the greatest and the smallest number with the given digits, using each digit only once. Digits Greatest Number Smallest Number (a) 3, 8, 2, 1 (b) 5, 6, 0, 3 (c) 9, 5, 8, 7 (d) 0, 2, 4, 6 2. Skip count in 100 s and complete the pattern. (a) 4531, 4631,,,, (b) 5287, 5387,,,, (c) 1872, 1972,,,, (d) 6594, 6694,,,, 15

17 3. Skip count in 1000 s and complete the pattern. (a) 1045, 2045,,,, (b) 3986, 4986,,,, (c) 2105, 3105,,,, (d) 4999, 5999,,,, 4. Match the following. Column A Column B (a) 4 more than 2096 (i) 3999 (b) 10 more than 8285 (ii) 7785 (c) 1 less than 4000 (iii) 2100 (d) 10 less than 9989 (iv) 3075 (e) 100 more than 7685 (v) 8295 (f) 100 less than 3175 (vi) 5940 (g) 1000 more than 5893 (vii) 6893 (h) 1000 less than 6940 (viii) 9979 Rounding Off Numbers Hey friends, can you guess the number of ice creams in the cart? Hmm... about 50 or 60! When we are not sure of the exact number, we use the word about. It gives a rough estimation of the number. We can also say that the number has been rounded off. We can round off a number to the nearest 10, 100 or Rounding off to the nearest 10 To round off a number to the nearest ten, look at the digit in the ones place. If the digit in the ones place is 4 or less, then place a zero in the ones place and let the digit in the tens place remain as it is. If the digit in the ones place is 5 or more, then place a zero in the ones place. Also add 1 to the digit in the tens place.

18 Example 11: Round off (a) 43, (b) 87 and (c) 65 to the nearest 10. Solution: (a) 43 is rounded off to 40 since the digit in the ones place is 3 which is less than 4. (b) 87 is rounded off to 90 since the digit in Mental Maths the ones place is 7 which is more than 5. Round off to the nearest 10. (c) 65 is rounded off to 70 since the digit in (a) 68 (b) 82 the ones place is 5. Rounding off to the nearest 100 To round off a number to the nearest hundred, look at the digit in the tens place. If the digit in the tens place is 4 or less, then place zeroes in the tens and ones place. The digit in the hundreds place remains the same. If the digit in the tens place is 5 or more, then place zeroes in the tens and ones place. Add 1 to the digit in the hundreds place. Example 12: Round off (a) 243 and (b) 1887 to the nearest 100. Solution: (a) 243 is rounded off to 200 because the digit at the tens place is 4. (b) 1887 is rounded off to 1900 because the digit at the tens place is 8. (c) 94 (d) 55 Mental Maths Round off to the nearest 100. (a) 497 (b) 8383 Rounding off to the nearest 1000 (c) 216 (d) 3541 To round off a number to the nearest thousand, look at the digit in the hundreds place. If the digit in the hundreds place is 4 or less, then place zeroes in the digits at the hundreds, tens and ones place. Keep the digit in the thousands place as it is. If the digit in the hundreds place is 5 or more, then place zeroes in the digits at the hundreds, tens and ones place. Also, add 1 to the digit in the thousands place. Example 13: Round off (a) 6253 and (b) 7923 to the nearest Solution: (a) 6253 is rounded off to 6000 as the digit in the hundreds place is 2. (b) 7923 is rounded off to 8000 as the digit in the hundreds place is 9. Mental Maths Round off to the nearest (a) 7249 (b) 1621 (c) 5913 (d) 8469 Even and Odd Numbers You have already studied that numbers in which we can form pairs are called even numbers and numbers in which we cannot form pairs are odd numbers. For example, 238, 1746, 3280, 7632 are even numbers and 413, 685, 7981, 9377 are odd numbers. 17

19 To decide whether a given number is even or odd, we look at the ones place. If the digit in the ones place is 0, 2, 4, 6 or 8, then the number is an even number. If the digit in the ones place is 1, 3, 5, 7 or 9, then the number is an odd number. EXERCISE Round off the following numbers to the nearest 10. (a) 63 (b) 922 (c) Round off the following numbers to the nearest 100. (a) 586 (b) 354 (c) Round off the following numbers to the nearest (a) 6119 (b) 7999 (c) Match the following. Number Rounded off to the nearest 10 (a) 94 (i) 50 (b) 11 (ii) 100 (c) 46 (iii) 70 (d) 68 (iv) 10 (e) 95 (v) Separate and write the even and odd numbers into their respective boxes Even numbers Odd numbers LET S EVALUATE 1. Observe the pictorial blocks and write the numbers they represent. (a) = 18

20 (b) + + = 2. Draw beads to represent the numbers given in the boxes. (a) (b) (c) Th H T O Th H T O Th H T O Write the number names of the numbers represented on the abacus. (a) (b) Th H T O Th H T O 4. Fill in the boxes. (a) 7982 = Th + H + T + O (b) 2805 = Th + H + T + O (c) (d) = 6 Th + 0 H + 1 T + 9 O = 8 Th + 9 H + 2 T + 7 O 19

21 5. Write in expanded form. (a) 4208 = (b) 8976 = (c) 1635 = Write the place value of the circled digit in the given numbers. (a) (b) Write five consecutive numbers for the given numbers. (a) 3186,,,,, (b) 9247,,,,, 8. Put the correct sign <, > or =. (a) (b) (c) (d) (e) (f) Arrange 5624, 5426, 4571, 6245, 6345, 6340 in ascending order.,,,,, 10. Arrange 1843, 1934, 1624, 1857, 1846, 1924 in descending order.,,,,, 11. Colour the largest number blue and the smallest number pink. (a) (b) Write True or False. (a) The predecessor of 2090 is (b) 4896 is an even number. (c) The successor of 7819 is (d) 2437 lies in between 2435 and (e) 62 rounded off to its nearest 10 is 70. (f) In words 9038 is written as nine thousand thirty-eight. 20

22 13. Write five numbers backward from the given numbers. (a) 5643,,,,, (b) 9289,,,,, 14. There are 2015 students in a school. Write the number of students in words. 15. A school X has 1986 students and another school Y has 1896 students. Which school has more students? 16. There were 163 people in a party. What is the rough estimate of the number of people in the party? 17. In a game, Rima picked up four digits from a bowl containing digits from 0 to 9. The digits she picked up were 3, 5, 6 and 8. What is the greatest number that Rima could make using these digits? 18. Choose the correct answer. (a) The place value of 7 in 8375 is: (i) 700 (ii) 7000 (iii) 70 (b) 8503 is greater than: (i) 9846 (ii) 8502 (iii) 8508 (c) The greatest 4-digit number formed using 4, 5, 3, 0 is: (i) 5430 (ii) 5304 (iii) 5403 (d) The smallest 4-digit number formed using 9, 7, 2, 0 is: (i) 0972 (ii) 2079 (iii) 2097 (e) 6 less than 9442 is: (i) 9346 (ii) 9446 (iii) 9436 SCRATCH YOUR BRAIN (HOTS) 1. What is the difference between the largest 3-digit number and the smallest 2-digit number? stands for RANK, 5128 stands for STUN and 9073 stands for CAKE. What do the following numbers stand for? (a) 5904 (b) 1248 (c) 1307 (d)

23 Colour and Learn Colour the smallest 4-digit number green. 2. Colour the largest 4-digit number orange. 3. Colour the numbers which are the predecessors of the following numbers red. (a) 5370 (b) Colour the numbers which are the successors of the following numbers yellow. (a) 2891 (b) Colour the even numbers pink. 6. Colour the odd numbers purple. MATHS LAB ACTIVITY 1. Cut a big cardboard in the shape of a circle. 2. Now cut 10 small circles of different coloured sheets of paper and mark them as 0, 1, 2, 3, 4, 5, 6, 7, 8, Paste these small numbered circles on the cardboard in a mixed order. 4. Hang the cardboard on the wall. 5. Each child should come one by one and hit the cardboard with a small plastic ball four times. 6. Each time the child hits a digit he/she should note it down. Thus every child will have 4 digits. 7. Using the 4 digits each child should form the following and write their number names. (a) the greatest 4-digit number (b) the smallest 4-digit number (c) as many 4-digit numbers as possible 22