1. This material is made freely available at www.njctl.org and is intended for the non-commercial use of students and teachers. These materials may not be used for any commercial purpose without the written permission of the owners. NJCTL maintains its website for the convenience of teachers who wish to make their work available to other teachers, participate in a virtual professional learning community, and/or provide access to course materials to parents, students and others. Click to go to website: www.njctl.org New Jersey Center for Teaching and Learning Progressive Mathematics Initiative

2. 4th Grade Number Sense & Algebraic Concepts www.njctl.org 2012-07-17

3. Setting the PowerPoint View Use Normal View for the Interactive Elements To use the interactive elements in this presentation, do not select the Slide Show view. Instead, select Normal view and follow these steps to set the view as large as possible: On the View menu, select Normal. Close the Slides tab on the left. In the upper right corner next to the Help button, click the ^ to minimize the ribbon at the top of the screen. On the View menu, confirm that Ruler is deselected. On the View tab, click Fit to Window. Use Slide Show View to Administer Assessment Items To administer the numbered assessment items in this presentation, use the Slide Show view. (See Slide 13 for an example.)

4. Table of Contents Read and Represent Multi-Digit Numbers Patterns Round Numbers Compare numbers Click on a topic to go to that section. Order Numbers

5. Read & Represent Multi-Digit Numbers Click to return to the table of contents

6. Read Multi-digit Numbers Words to Remember Whole numbers: The numbers 0, 1, 2, 3, 4, 5, 6, 7...... Even : Odd: Even numbers make pairs. Odd numbers have one left over.

7. Fill in the chart with 8 odd and 8 even numbers ODD EVEN

8. Counting by Ones and Tens Goal: Count and group objects in ones and tens Materials: apples, counters, index cards Step 1 Step 2 Step 4 Step 3 Count to 25 by ones using the apples (see next page) Regroup the apples into piles of 10. Separate the 25 apples into two groups of 10 and one group of 5. Replace each pile of 10 apples with one counter. Draw the new model showing 2 counters and 5 apples. Replace the new model with a number. Remember that each counter equals 10. Two counters and five apples equals 20 + 5, or 25.

10. Students Groups Form groups of 4-5 students. Each student should have piles of macaroni, counters, and 4-5 index cards. Each student writes a whole number under 25 on each of the 4-5 cards. Students switch cards, models the numbers with macaroni, and then with counters, and check each other's work.

11. 3 dimes +5 pennies 30 + 5 equals 35 cents Money Two-digit numbers can be represented with dimes and pennies

12. 4 dimes represents 6 pennies represents 40 6 40 + 6 = 46 cents

13. There are 4 groups of ten in the number 54? Yes No 1

14. 2 Which is the correct grouping of the number 37? A 7 tens and 3 ones B 3 tens and 7 ones C 37 tens

15. 3 Which explanation is correct for the number 72? A 7 tens and 3 ones B 3 tens and 7 ones C 7 tens and 2 ones

16. 4 Which explanation is correct for the number 35? A 5 tens and 3 ones B 5 ones and 3 tens C 3 ones and 5 tens

17. tens ones 5 Enter the correct number for the illustration below.

18. tens ones 6 Is the number even or odd? A even B odd

19. 7 If you had 62 cupcakes, would have and even number to share with a friend. Yes No

20. 8 If you had 15 pencils, would have and even number to share with a friend. Yes No

21. Write 46 in words Step 1 Ask yourself questions about the number. How many groups of tens are in 46? four How many ones are in 46? six Step 2 Write the numbers as groups of tens and ones. 46 equals 4 groups of ten and 6 ones. ANSWER 46 = 4 tens + 6 ones

22. Write the following numbers to words in groups 98 ________________________ 9 tens and 8 ones Students Response 52 ________________________ 5 tens and 2 ones 64 ________________________ 6 tens and 4 ones 29 ________________________ 2 tens and 9 ones 125 ________________________ 1 hundred, 2 tens and 5 ones Erase to check

23. 9 The number 84 would have 8 tens and 5 ones. True False

24. 10 The number 749 would have 7 hundreds, 9 ones and 4 tens. True False

25. 11 The number 259 has 5 groups of ___ A ones B tens C hundreds

26. 12 Enter the correct number for 5 tens and 6 ones

27. 13 Enter the correct number for 4 hundreds and 3 tens

28. 14 Enter the correct number for 7 ones and 5 tens

29. 15 Enter the correct number for 3 ones and 4 hundreds

30. Place Value of Large Numbers,, 1741879 ones tens hundreds thousands ten-thousands hundred-thousands millions

31. ,, 1070450 ones tens hundreds thousands ten-thousands hundred-thousands millions Read the number. Be careful of the zeros!

32. Read the following numbers. 43,2011,000,281 673,50353,600 7,007 1,800,003 60,49284,905

33. 16 In the number 4632 six is in the hundreds place. True False

34. 17 In the number 5,002 the number five is in what place value? A tens B hundreds C thousands

35. 18 In the following number, which digit is in the millions place? 1,450,382

36. 19 In the following number, which digit is in the thousands place? 1,265,309

37. 20 In the following number, which digit is in the ten-thousands place? 841,032

38. 21 In the following number, which digit is in the hundreds place? 43,791

39. 22 In the following number, which digit is in the hundred-thousands place? 1,034,762

40. + + ++ + + Drag the place value digits to the right to make a 4 digit number.

41. Drag each digit to the left to see the expanded form. + + + + + +

42. Writing a Number in Expanded Form In order to represent a number in expanded form show the values as addition. 1236 = 1000 + 200 + 30 + 6

43. TRY THIS Write the value in expanded form. 3649 = 4216 = 9834 = 6203 = + + + + + + + + + + + +

44. Right the number for each Expanded Form 3000,000 + 40 + 1 300 + 40 + 1 30,000 + 4,000 + 1 300,000 + 4,000 + 10 30,000 + 400 + 1 3,000 + 400 + 1 3,000 + 40 + 1

45. 23 Which is the correct way to express 9,231 in expanded form? A 9 hundreds, 2 thousands, 3 tens, 1 one B 9 thousands, 2 hundreds, 3 tens, 1 one C 9 hundreds, 23 tens, 1 one

46. 24 Which is the correct way to express 73,040 in expanded form? A 700 + 30 + 4 B 70,000 + 3,000 + 400 C 70,000 + 3,000 + 40

47. 25Enter this number in standard form. 7000 + 300 + 20 + 7

48. 26Enter this number in standard form. 50,000 + 3,000 + 200 + 50 + 7

49. 27Enter this number in standard form. 60,000 + 500 + 20 + 1

50. 28Enter this number in standard form. 400,000 + 6,000 + 300 + 30 + 1

51. 29 Enter this number in standard form. 9,000 + 300 + 5

52. Place Value Number Line National Library of Virtual Manipulatives Click for web site Step 1 Step 2 Step 3 Note: The place value can be changed at the bottom of the web page.

53. A B C D 0 1,000 500 30Where does 600 go on the number line?

54. 200 400 A B C D 31 Where does 310 go on the number line?

55. 500 700 A B C D 32 Where does 625 go on the number line?

56. 0 10,000 5,000 AB C D 33 Where does 7,300 go on the number line?

57. 0 10,000 5,000 A B C D 34Where does 2,100 go on the number line?

58. 0 10,000 5,000 A B C D 35 Where does 7,800 go on the number line?

59. ? 0 10,000 36What number does the "?" on the number line represent?

60. 500 250 ? 0 37What number does the "?" on the number line represent?

61. 500 250 ? 0 38What number does the "?" on the number line represent?

62. More Practice

63. 39Even numbers can be divided into equal groups with nothing left over? True False

64. 40If you have 30 balloons you can.... A put them in 3 groups of ten B put them in 4 groups of 5 C put them in 2 groups 25

65. 41The number is 11 is even? True False

66. 42If you have 5 hundreds, 4 tens, and zero ones you have what number?

67. 43 Cindi has 7 dimes and 8 pennies. How much does Cindi have? A 87 cents B 7.80 cents C 78 cents

68. ______hundreds + _____tens + ____ ones 44When writing 978 in expanded form, the number ____ would be in the ones position.

69. 454 thousands + 8 hundreds + 5 ones = ___________

70. 46In the number 6,014 the number zero is in what place value? A thousands B hundreds C tens

71. + 4000300 10 9 ++ 47What number is represented below?

72. 46Which numbers are represented in standard form? (You can pick more than one.) A 4,031 B 4,000 + 30 + 1 C 60,009 D 60,000 + 9

73. Compare Numbers Click to return to the table of contents

74. There are two symbols we use to compare numbers. > (greater than) < (less than) One number goes on the left of the symbol and another number goes on the right of the symbol. The number on the left of the ">" shows the larger number. For example: 2 > 1 The number on the left of the "<" shows the smaller number. For example: 1 < 2

75. Remember, one number goes on the left of the symbol and another number goes on the right of the symbol. The number on the left of the ">" shows the larger number. For example: 2 > 1 This means that "2 is greater than 1" The number on the left of the "<" shows the smaller number. For example: 1 < 2 This means that "2 is less than 1"

76. Symbols and Words to remember when comparing numbers SYMBOL WORDS > < = greater than/largest less than/ smallest equal

77. SYMBOLMEANING EXAMPLES IN SYMBOLS EXAMPLES IN WORDS > Greater than More than Bigger than Larger than 8 > 3 8 is greater than 3 8 is more than 3 8 is bigger than 3 8 is larger than 3 < Less than Fewer than Smaller than 3 < 8 3 is less than 8 3 has fewer than 8 3 is smaller than 8 = Equal to Same as 8 = 8 8 is equal to 8 8 is the same as 8

78. Way 1 to compare numbers is by a number line. The number farthest to the right is the greatest. The number farthest to the left is the least. Move numbers to their place on the number line 8 23 Fill in the blanks using the symbols _____ > _____ > ______ 1 0 23 45 67 8 9 10

79. greatest number least number ____ > _____ 0 500 1,000 625 350

80. greatest number least number ____ < _____ 0 500 1,000 213 401

81. greatest number least number ____ < _____ 0 5000 10,000 6,421 3,509

82. greatest number least number ____ > _____ 0 5000 10,000 1,059 7,995

83. 0 10,000 5,000 4,031 2,500 49Use the number line to help determine which symbol to use. A > B < C =

84. 0 10,000 5,000 50Use the number line to help determine which symbol to use. A > B < C = 8,300 830

85. 0 10,000 5,000 51Use the number line to help determine which symbol to use. A > B < C = 7,250 7,900

86. 0 10,000 5,000 52Use the number line to help determine which symbol to use. A > B < C = 3,040 6,030

87. 0 10,000 5,000 53Use the number line to help determine which symbol to use. A > B < C = 9,500

88. Way 2 Place Value ones tens hundreds thousands ten thousands Take the number Place each digit in the proper place value box 4, 37 2 Start with the greatest place value and move right to where the numbers are different. The bigger of the two numbers is 4,398 ones tens hundreds thousands ten thousands 4,39 8

89. 8, 29 7 2 89 ______ > ______ ones tens hundreds thousands ten thousands ones tens hundreds thousands ten thousands

90. ones tens hundreds thousands ten thousands tens thousands ones hundreds ten thousands 1 1 2 5,3 6 2 3 7 ______ > ______

91. ones tens hundreds thousands ten thousands ones tens hundreds thousands ten thousands 6 1 7 1, 8 2 7 9 0 ______ < ______

92. 54The number 765 is smaller than 769? True False

93. 55Which number is the largest? A 325 B 335 C 343

94. 56 Of these four numbers, which is the smallest? 888, 898, 878, 899

95. 57Compare the numbers using the correct symbol. A > B < C = 5,429 5,409

96. 58 Compare the numbers using the correct symbol. A > B < C = 32,461 32,086

97. 59Compare the numbers using the correct symbol. A > B < C = 8,730 87,300

98. 60Compare the numbers using the correct symbol. A > B < C = 540,389 540,389

99. 61Compare the numbers using the correct symbol. A > B < C = 9,049 9,051

100. 62 Kyle has $15.25, Harry has $13.50, and Leon has $17. Which of the following correctly compares the amount of money each person has? A 17 > 15.25 > 13.50 B 15.25 > 13.5 < 17 C 17 < 13.50 < 15.25

101. 63Sam is 54 inches tall, Tatiana is 52 inches tall and Ariana is 49 inches tall. Which of the following correctly compares their heights? A 54 49 B 49 < 52 < 54 C 49 54

102. Order Numbers Click to return to the table of contents

103. To order a group of numbers, you need to compare the digits. If the numbers all have the same number of digits, look left to right to see the which one is greatest or smallest.

104. Order these numbers least to greatest. 1,791 2,871 1,732 1,489 1,491

105. Order these numbers least to greatest. 1,791 2,871 1,732 1,489 1,491 Step 1 look at the farthest left digit. 2 is greater than 1, so this is the greatest number.

106. Order these numbers least to greatest. 1,791 1,732 1,489 1,491 Step 2 - Look at the next digit (hundreds place) 4 is less than 7, so 1,489 and 1,491 are less. 2,871 greatest least

107. Order these numbers least to greatest. 1,791 1,732 1,489 1,491 Step 3 - 8 is less than 9, so this is the smallest number 2,871 greatest least

108. Order these numbers least to greatest. 1,791 1,732 Step 4 - 3 is less than 9, so 1,732 is less than 1,791 greatest least 1,489 1,491 2871

109. Order these numbers least to greatest. greatest least 1,489 1,491 1,732 1,791 2,871

110. Put these numbers in order from least to greatest. 6,503 6,531 4,921 7,000 7,008 4,871 4,874 4,329

111. Put these numbers in order from greatest to least. 13,671 13,607 11,461 11,462 13,208 15,298 13,099 15,321

112. 64 Which of the following shows the numbers in least to greatest order? A 2516, 2561, 2615, 2651 B 2651, 2615, 2561, 2516 C 2561, 2516, 2651, 2615

113. 65Which of the following shows the numbers in greatest to least order? A 4508, 4502, 3281, 3287 B 3281, 3287, 4502, 4508 C 4508, 4502, 3287, 3281

114. A 6,591 B 6,509 C 6,541 6,474 6,539 ______ 6,597 ? 66Which number can go in the blank to make the numbers be ordered least to greatest?

115. 3,289 ______ 3,300 3,481 ? A 3,309 B 3,294 C 3,280 67Which number can go in the blank to make the numbers be ordered least to greatest?

116. 15,86115,809 ______ 15,721 ? A 15,811 B 15,711 C 15,750 68Which number can go in the blank to make the numbers be ordered greatest to least?

117. Take these numbers and order them greatest to least (numbers will move into boxes) 10,315 823 5643 819 4329 When looking at multi-digit numbers it is easiest to group the numbers by the number of digits. Then move right to where the numbers are different. Since 10,315 is the only number that has five digits, it makes sense that it is the largest number. Both 823 and 819 have three digits but when moving right the digit 2 is bigger than 1, therefore 819 is smaller than 823. click 5 digits 4 digits 3 digits

118. 625 674 1,390 1,399 32,961 32,768 Order the numbers least to greatest 216,712 3 digits 4 digits 5 digits 6 digits 499

119. 450 405 8,761 16,300 16,099 679,043 741 8,768 Order the numbers greatest to least 6 digits 5 digits 4 digits 3 digits 879,043

120. Put these numbers in order from least to greatest. 31,729 15,851 7,436 5,871 15,825 29,410 15,829 5,902

121. Put these numbers in order from greatest to least. 64,329 5,999 7,329 64,842 67,328 7,261 67,305 26

122. 69Which of the following shows the numbers in least to greatest order? A 1653, 16539, 15789, 15809 B 16539, 1653, 15809, 15789 C 15789, 15809, 16539, 1653

123. 70Which of the following shows the numbers in greatest to least order? A 671, 659, 5783, 5780 B 5783, 5780, 671, 659 C 659, 671, 5780, 5783

124. 71Which of the following shows the numbers in least to greatest order? A 33, 3003, 303, 30003 B 30003, 3003, 303, 33 C 33, 303, 3003, 30003

125. 134 140 ______ 1,142 1,204 10,503 ? A 1,201 B 129 C 72Which number can go in the blank to make the numbers be ordered least to greatest? 1099

126. 45,381 40,619 9,321 ______ 7,905 ? A 8,893B 9,500 C 73Which number can go in the blank to make the numbers be ordered greatest to least? 794

127. Round Numbers Click to return to the table of contents

128. Rounding makes numbers that are easier to work with in your head. Rounded numbers are only approximate. An exact answer generally can not be obtained using rounded numbers. Use rounding to get an answer that is close but that does not have to be exact.

129. Step 1: Find 132 on the number line and label it. Step 2: Is 132 closer to 130 or 140? _____ Step 3: What is 132 rounded to the nearest ten? _____ 130 140 135 The number line is useful to help when rounding numbers.

130. Step 1: Find 132 on the number line and label it. Step 2: Is 132 closer to 130 or 140? _____ Step 3: What is 132 rounded to the nearest ten? _____ 130140135 132

131. Step 1: Find 132 on the number line and label it. Step 2: Is 132 closer to 130 or 140? _____ Step 3: What is 132 rounded to the nearest ten? _____ 130140135 132

132. Step 1: Find 3365 on the number line and label it. Step 2: Is 3365 closer to 3200 or 3300? _____ Step 3: What is 3365 rounded to the nearest hundred? _____ 33003400 3350

133. Step 1: Find 3365 on the number line and label it. Step 2: Is 3365 closer to 3200 or 3300? _____ Step 3: What is 3365 rounded to the nearest hundred? _____ 33003400 3350 3365

134. Step 1: Find 3365 on the number line and label it. Step 2: Is 3365 closer to 3200 or 3300? _____ Step 3: What is 3365 rounded to the nearest hundred? _____ 33003400 3350 3365

135. 74 What is 38 rounded to the nearest ten? 3040 35

136. 75 What is 874 rounded to the nearest ten? 870880 875

137. 76 What is 527 rounded to the nearest hundred? 500600 550

138. 77 What is 3,721 rounded to the nearest hundred? 37003800 3750

139. 78 What is 5,835 rounded to the nearest hundred? 5800 5900 5850

140. Rounding numbers means identifying a designated place value and the number (digit) in that place. Rule One. Determine what your rounding digit is and look to the right side of it. If the digit is 0, 1, 2, 3, or 4 do not change the rounding digit. All digits that are to the right hand side of the requested rounding digit become 0. Rule Two. Determine what your rounding digit is and look to the right side of it. If the digit is 5, 6, 7, 8, or 9 your rounding digit rounds up by one number. All digits that are to the right side of the requested rounding digit become 0. Round Numbers

141. 1. Put your pencil point under the digit in the tens place. Look to the right. 2. Is the digit 5 or more? Yes OR No 3. What happens to the digit? Increases by 1 OR remains the same 4. What happens to everything to the left of the tens place? Those digits always remain the same. 5. Write the answer ____________ Round 641 to the nearest ten.

142. Round each number to the nearest ten. 42 1,284 754 3,527 45 5,521 1,289 758

143. Practice - Round to Tens 273 = 544 = 912 = 1232 = 4542 = 7334 =

144. 1. Put your pencil point under the digit in the hundreds place. Look to the right. 2. Is the digit 5 or more? Yes OR No 3. What happens to the digit? Increases by 1 OR remains the same 4. What happens to everything to the left of the hundreds place? Those digits always remain the same. 5. Write the answer ____________ Round 8,702 to the nearest hundred.

145. Round each number to the nearest hundred. 5,750 749 115,709 15,799 780 115,760 5,738 15,729

146. Practice - Round to Hundreds 939 = 509 = 627 = 3921 = 4644 = 6233 =

147. 79In the number 5,439 the number 4 is in the______ place value. A tens B hundreds C thousands

148. 80What digit is in the tens place? 9632

149. 81 Sam has 491 sea shells. He wants to round his collection to the nearest hundred. He says he would then have 400 sea shells. Is he correct? True False

150. 82 If you round 863 to the nearest hundred you would get? A 800 B 963 C 900

151. 83 Round 739 to the nearest ten.

152. 84Round 5,685 to the nearest ten.

153. 85Round 5,685 to the nearest hundred.

154. 86Round 65,380 to the nearest hundred.

155. 87 Round 839 to the nearest ten.

156. 88Round 541 to the nearest ten.

157. 89Round 585 to the nearest hundred.

158. 90Round 3,471 to the nearest hundred.

159. 91Round 227 to the nearest ten.

160. 92Round 227 to the nearest hundred.

161. 1. Put your pencil point under the digit in the thousands place. Look to the right. 2. Is the digit 5 or more? Yes OR No 3. What happens to the digit? Increases by 1 OR remains the same 4. What happens to everything to the left of the thousands place? Those digits always remain the same. 5. Write the answer ____________ Round 15,821 to the nearest thousand.

162. Round each number to the nearest thousand. 7,4595,189 5,5554,524 7,0585,803 4,8017,239 5,9245,458 6,4685,067 6,9106,078 6,7036,589

163. 1. Put your pencil point under the digit in the ten-thousands place. Look to the right. 2. Is the digit 5 or more? Yes OR No 3. What happens to the digit? Increases by 1 OR remains the same 4. What happens to everything to the left of the ten thousands place? Those digits always remain the same. 5. Write the answer ____________ Round 74,891 to the nearest ten-thousand.

164. Round each number to the nearest ten thousand. 41,58759,303 55,43051,768 44,32145,341 57,87638,568 58,41040,571 35,72148,201 49,00053,008 60,89961,487

165. 93In the number 54,718 the number 5 is in the______ place value. A hundreds B thousands C ten thousands

166. 83,517 94Which digit is in the thousands place?

167. 95Round 3,471 to the nearest thousand.

168. 96Round 25,512 to the nearest thousand.

169. 97Round 7,831 to the nearest thousand.

170. 98Round 27,813 to the nearest ten-thousand.

171. 99Round 643,712 to the nearest ten-thousand.

172. 100Round 94,785 to the nearest thousand.

173. 101Round 743,876 to the nearest ten-thousand.

174. 102Round 543,802 to the nearest thousand.

175. Rounding Special Cases

176. Step 1: Find 1955 on the number line and label it. Step 2: Is 1955 closer to 1900 or 2000? _____ Step 3: What is 1955 rounded to the nearest hundred? _____ Round 1955 to the nearest hundred. 19002000 1950

177. Step 1: Find 1955 on the number line and label it. Step 2: Is 1955 closer to 1900 or 2000? _____ Step 3: What is 1955 rounded to the nearest hundred? _____ Round 1955 to the nearest hundred. 19002000 1950 1955

178. Step 1: Find 1955 on the number line and label it. Step 2: Is 1955 closer to 1900 or 2000? _____ Step 3: What is 1955 rounded to the nearest hundred? _____ Round 1955 to the nearest hundred. 19002000 1950 1955

179. What happens when the 9 needs to increase by 1? 1. Put your pencil point under the digit in the hundreds place. Look to the right. 2. Is the digit 5 or more? Yes OR No 3. What happens to the digit? Increases by 1 OR remains the same 4. What happens to everything to the left of the hundreds place? Those digits always remain the same. 5. Write the answer ____________ Round 1955 to the nearest hundred.

180. Step 1: Find 5995 on the number line and label it. Step 2: Is 5995 closer to 5900 or 6000? _____ Step 3: What is 5995 rounded to the nearest ten? _____ Round 5,995 to the nearest ten. 59006000 5950

181. 5995 Step 1: Find 5995 on the number line and label it. Step 2: Is 5995 closer to 5900 or 6000? _____ Step 3: What is 5995 rounded to the nearest ten? _____ Round 5,995 to the nearest ten. 59006000 5950

182. 5995 Step 1: Find 5995 on the number line and label it. Step 2: Is 5995 closer to 5900 or 6000? _____ Step 3: What is 5995 rounded to the nearest ten? _____ Round 5,995 to the nearest ten. 59006000 5950

183. What happens when the 9 needs to increase by 1? 1. Put your pencil point under the digit in the hundreds place. Look to the right. 2. Is the digit 5 or more? Yes OR No 3. What happens to the digit? Increases by 1 OR remains the same 4. What happens to everything to the left of the tens place? Those digits always remain the same. 5. Write the answer ____________ Round 5995 to the nearest ten.

184. Round each. 1961 rounded to the nearest 100 ________ 197 rounded to the nearest ten ________ 194 rounded to the nearest ten ________ 963 rounded to the nearest hundred ________ 95 rounded to the nearest ten ________ 145 rounded to the nearest ten ________

185. 103Round 79,621 to the nearest thousand.

186. 104Round 3,992 to the nearest hundred.

187. 105Round 97 to the nearest ten.

188. 106Round 1,499,000 to the nearest ten-thousand.

189. 107Round 19,997 to the nearest hundred.

190. 108Round 469,971 to the nearest hundred.

191. 109The middle school has 1,498 students this year. The principal wants to buy student planners for next year. The principal will order by rounding to the nearest ten. How many will be ordered?

192. 110A large jar has 1,539 marbles in it. What is this number rounded to the nearest thousand?

193. 111New Jersey is 166 miles in length from the northern most point to the southern most point. What is this number rounded to the nearest hundred?

194. Patterns Click to return to the table of contents

195. Patterns A pattern or sequence is either shapes or umbers that continue to repeat in a specific order (pattern). You can describe a pattern by using a rule to get to the next shape or number. What would be the rule for the pattern in the quilt?

196. Patterns are almost everywhere you look. Look around the classroom and name some of the patterns.

197. What is the pattern in this example? Move the shapes to complete pattern What is the rule?

198. Create your own geometric pattern using these two shapes. Describe your geometric pattern (write the rule).

199. Patterns can also be represented by rotating a shape. Draw the next shape

200. 112 What would be the tenth shape if this pattern were continued? A B C

201. 113 Which would be the next shape in this pattern? A B C

202. 114 What would be the eleventh shape in this pattern? A B C

203. Now we will look at number patterns. Move the numbers to complete pattern

204. Finding a Missing Number in a Pattern or Sequence Step 1: Determine if the order of numbers is getting larger or smaller. Step 2: Find the difference between numbers that are next to each other. Step 3: Use the difference between numbers to find the missing number.

205. 1. The order is going down (getting smaller). 2. The difference between numbers 15 - 13 = 2 3. Since the order is going down subtract 2 from 13. The missing number is 11. 4. Now that you know the pattern is subtract 2, take the last digit and subtract 2 and you will get 7. Find the missing number: 15, 13, ___, 9, ___ 15, 13, 11, 9, 7 click

206. Finding a Missing Number in a Pattern or Sequence 1. Determine if the order of numbers is getting larger or smaller in value, which mathematical function is being used (+, -, x, ÷) and how many numbers are involved in the repeating pattern. 2. Find the difference between the numbers that are next to each other.

207. Find the missing number 5, 10, 8, 16, 14, 28, ___, ___, ___ x 2 - 2

208. 115In the pattern 25, 50, 100, 200, the rule would be to keep adding 25. True False

209. 116What is the missing number in this pattern? 16, 20, 24, ___, 32, 36

210. 117Charles was riding his bicycle down the sidewalk. He was looking at the addresses on each house as he went by. The first four addresses he saw were 2455, 2485, 2515, 2545. What address will Charles see next?

211. 118Mrs. Hall wrote the following number pattern on the board. 4; 16; 64; 376 What was the pattern? A Add 12 B Multiply by 4 C Multiply by 3

212. 119The water in Sam's full bathtub is 50 gallons deep. He is draining the bathtub and measuring the water depth each minute. The first four measurements were 50 gal., 44 gals., 38 gals., 32 gals. What depth will Sam see next?

213. 120What are the next two numbers in the pattern? 3, 12, 10, 19, 17, 26,.... A 33, 24 B 24, 33 C 35, 33

214. 6 4 2 36 24 12 Mr. Block made a function machine that uses a rule to change a number into a different number. He put three numbers through the machine. What rule did Mr. Block use to make his machine? Look at each machine. What happens to the input number inside the machine to turn it into the output number? 6 x 6 = 36 4 x 6 = 24 2 x 6 = 12 The rule for Mr. Block's function machine is multiply by 6. click

215. Use Mr. Block's function machine from the example to answer Numbers 1 through 3 1. Maria chose 12 as her input number. What was output number? 72 2. Jose chose 8 as his input number. What was output number? 48 3. Caleb put a number through the machine, and his output number was 120. What number did Caleb put through the machine? 20 click

216. 4. What is the rule for Ms. Collins machine when it is in reverse? divide by 9 5. Kareem chose 108 as his input number. What was his output number? 12 6. Carmen chose her output number as 15. What was her input number? 135 Use the following information to answer Numbers 4 through 6 Ms. Collins made a machine like Mr. Blocks', but she wanted it to work in reverse. When she put in the number 27, the output number was 3. She put in 81, and the output number was 9. She put in 54 and the output number was 6. click

217. 3 121What is the rule for this function machine? A multiply by 3 B multiply by 8 C divide by 3 24

218. 9 122The rule for this function machine is multiply by 5, what is the output? ?

219. ? 123The rule for this function machine is multiply by 7, what is the input? 42

220. Patterns in Tables Sometimes you can find number patterns in tables. A function table is a table of ordered pairs that follow a rule. The rule can be found by going from one column to the other column. Numbers from a function machine can also be put into a table.

221. Example What is the rule for the function table going from column x to column y? x y 3 9 4 12 515 6 18 7 21 Each number in column y is 3 times the number in column x. The rule going from column x to column y is multiply by 3. Multiply 5 by 3 to find the missing value in the function table.

222. You can also use number patterns in tables to solve real-world math problems. Example Sidney ran the same number of laps around the track every day for 6 days. He made the table below to show the total number of laps he had run after each of the six days. What is the total number of laps Sidney had run after six days? DAY 1 2 3 4 5 6 Number of Laps 6 12 18 24 3036 The rule for going from the first row (Day) to the second row (Number of Laps) is multiply by 6. This means that Sidney ran 6 laps every day. To find out how many total laps he had run after 6 days, multiply 6 by 6.

223. Attempted 21 35 42 9 Completed Passes 3 5 6 7 124The rule for the table below of attempted passes and completed passes is multiply by 7. True False

224. xy 332 736 1039 1746 125What is the correct rule for this function table going from column x to y? A add 27 B multiply by 3 C add 29

225. xy 225175 255205 125? 9747 126 What is the missing value in the function table?