# Fourth Grade Number Sense and Algebraic Concepts

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1 Slide 1 / 308

2 Slide 2 / 308 Fourth Grade Number Sense and Algebraic Concepts

3 Compare numbers Round Numbers Patterns Slide 3 / 308 Table of Contents Algebraic Equations/Number Sentences Problem Solving Order Numbers Click on a topic to go to that section Place Value/Number Sense Through the Millions Read and Represent Multi-Digit Numbers Analyze Number Lines Using Number Sense Glossary

4 Slide 4 / 308 Vocabulary words are identified with a dotted underline. Sometimes when you subtract the fractions, find that you can't because the first numerator is smaller than the second! When this happens, you need to regroup from the whole number. How many thirds are in 1 whole? How many fifths are in 1 whole? How many ninths are in 1 whole? you (Click on the dotted underline.) The underline is linked to the page in the presentation's glossary containing the vocab chart.

5 Slide 5 / Vocabulary Word The charts have 4 parts. Factor 2 Its meaning (as used in the lesson) A whole number that can divide into another number with no remainder = 5 3 is a factor of 15 3 Examples/ Counterexamples 3 x 5 = 15 3 and 5 are factors of 15 A whole number that multiplies with another number to make a third number. 3 5 R is not a factor of 16 4 Link to return to the instructional page. Back to Instruction

7 Slide 7 / 308 What is an Equation/Number Sentence? Brainstorm the important parts of an equation and record results below: An equation is another name for a number sentence that contains an EQUALS symbol, an operation(s), number(s), and/or variable(s). An equation says that two things are equal. What is on the left Click is equal for Definition to what is on the right. LEFT = RIGHT Therefore, an equation is like a statement "this equals that".

8 Slide 8 / y = 10 equals sign (relation symbol) To understand equations, we also need to know what operations are. Use the green box on the left to list the ideas you brainstormed. Four Click basic for symbols/signs: answers + addition subtraction x multiplication division Definition of OPERATION:

9 Slide 9 / 308 Let's Review Some Vocabulary Use this equation to help you define the important terms: 6 + Y = 10 First, without using the word 'equal', what does the equal sign mean? Use the red box below to list the ideas you brainstormed. is are was were will be The same value as total comes to sold Click for for equivalent answers to The same as Definition of the EQUAL sign:

10 Slide 10 / 308 operation 6 + y = 10 equals sign (relation symbol) Finally, let's brainstorm what we know about a variable. Use the gray box on the left to list the ideas you brainstormed. Click for answers A symbol (LETTER) used in the place of a number ( examples: y, a,n, w) The solution is the number that fits in the place of the variable. Definition of VARIABLE:

11 Slide 11 / 308 Review What operation is this symbol? 6 + y = 10 equals What sign is the (relation name symbol) of this symbol? Identify variable this symbol This type of equation is called an algebraic equation. Algebraic Equation: An equation that includes one or more variables

12 Slide 12 / 308 Why are equations/number sentences important? Let me introduce you to QUIGLEE the equation! Please click inside the oval. QUIGLEE will tell us why equations (number sentences) are so important and review some important vocabulary. Please click the microphone on Quiglee's mouth. Knowing how to create sentences by correctly organizing words helps you understand and learn a language. Equations are a way to organize numbers to help you understand math and learn how to problem solve.

13 Slide 13 / An EXPRESSION in math is like a phrase/sentence fragment. It can contain numbers, operators, and variables. It is a part of an equation. An EQUATION in math is like a sentence. It is a mathematical sentenc in which two things are the same and are joined by an equal sign. It can only be true or false. Expressio n Expressio n Equatio n = Is QUIGLEE's equation true or false? True Click for Answer How do you know? Both sides of Click the for equation Answer are equal.

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15 Slide 15 / Which choice best explains what a variable is? A A symbol that tells you to add. B It is a sign that tells you two items are the same. C It replaces a number in an equation. D It can be also called a relation symbol.

16 Slide 16 / Choose the algebraic equation below. A = 10 B 6 - h = 4 C 18 = 9 x 2 D 78 + y

17 Slide 17 / Which of the following are expressions? A 8 - b B m + 4 = 9 C 4 + y = D 2y + 7 E 2 x 3

18 Slide 18 / What would be needed to make the expression below a complete equation. A a variable B an equals sign 7 - p C an operation symbol D a solution

19 Slide 19 / Is the equation below true or false? 8-6 = 2 x 2 True False

20 Slide 20 / 308 Determining the Solutions to Algebraic Equations A solution/answer to an algebraic equation is a number that makes the equation true. In order to determine if a number is a solution, replace the variable with the number and evaluate/solve the equation. If the number makes the equation true, it is a solution. If the number makes the equation false, it is not a solution.

21 Slide 21 / 308 Determining the Solutions to Algebraic Equations The algebraic equation is TRUE if the two expressions (left side and right side) are balanced with an equal sign. Algebraic Equation or Open Number Sentence = v + 6 What number would replace the variable and make this algebraic equation TRUE (Balanced)?

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23 Slide 23 / 308 Evaluate the following expression and balance the algebraic equation. Use QUIGLEE'S Magic Mirror to check your answer. 1. Evaluate the expression: (14 - n) for n = 8 Solution: Balance the algebric equation: 17 + y = 2 x 10 The variable y is: y = 2 x 10 Click Simplify for strategy equation 17 for + y #2 = 20 To be balanced the left = right. 20 = 20 So, y = 3.

24 Slide 24 / Choose the equation below that is balanced. A = 5 x 2 B 5 x 2 = C 8-5 = D = 10

25 Slide 25 / Evaluate the expression below when t = 5. 3 x t

26 Slide 26 / In order for the algebraic equation below to be true, what whole number must replace the variable w? 9 + w =

27 Slide 27 / Choose the answers that would make the algebraic equation false. A p = 3 B p = 18 3 x p = C p = 6 D p = 9

28 Slide 28 / Choose the algebraic equations that are true when g = 3. A 6 x g = 9 B 4 + g = C g + g = 9 D 8 - g = 5 E 20 - g = 18

29 Slide 29 / What value of k would make the algebraic equation below true? 5 + k = 3 x 3

31 Slide 31 / 308 K.E.Y.S to Problem Solving Throughout this unit and beyond you will apply the skills you are learning (plus the skills you already know) to solve problems. These application problems are known as word problems. There are important (key) things that great problem solvers always do when they see an application/word problem. KAYLEE the Key will help guide you through the important parts of problem solving. Are you ready to learn the K.E.Y.S. to problem solving? K E Y S

32 Slide 32 / 308 The K.E.Y.S. to Problem Solving K E Y S K: Know the important information in the problem. Read the problem (more than once and first find the main idea. (MAIN IDEA = What is the problem asking you to find out?) Find all the important information that supports the main idea. E: Equation (or equations) is created to plan your strategy and organize the important information. Use equations to develop a strategy (i.e. algorithm, diagram). The strategy must be organized and easy to follow. Y: Yes, I have checked over my strategy and my answer is readonable (makes sense). Use an estimate to check if your answer is reasonable. Use an estimate to check if your answer is reasonable. S: Solution is written in a complete sentence with the correct label.

33 Slide 33 / 308 K: Know the important information in the problem. Let's practice the first part of the problem solving acronym. This is the first thing you do when looking at an application/word problem like the one below. KAYLEE wants to figure out how many word problems she solved this week. Last week, she solved 16 problems. This week, she solved 7 problems on Monday, 5 problems on Wednesday, and 9 problems on Friday. How many problems did she solve this week? Teacher Notes / Answers What do you need to do to complete the first step (K) of K.E.Y.S.?

34 Slide 34 / 308 E: Equation (or equations) is created to plan your strategy and organize the important information Next, let's organize the important information to create an equation IMPORTANT INFORMATION Main Idea of problem: How many problems did KAYLEE solve THIS week? 7 problems 5 problems 9 problems When solving a problem we are usually asked to answer a question. The part of the problem we are trying to find is not known at first. This unknown part of the problem is a mystery we have to solve. When writing an algebraic equation, the unknown part is called the... Click for Answer VARIABLE Teacher Notes / Answers

35 Slide 35 / 308 E: Equation For this problem, let's use the variable p since we are trying to find out how many PROBLEMS KAYLEE solved this week. The parts of the algebraic equation we have so far are shown in the box below p What pieces of the algebraic equation are missing? Click for Answer EQUALS SIGN = Click for Answer OPERATION (OPERATOR) What operation (or operations) do we use for this problem?

36 Slide 36 / 308 E: Equation When figuring out what operation to use, you can look for key words in the problem to help you. On the next slide, look at the bank of words and phrases below. Each word or phrase is a clue as to what operation you should perform. Sort the words/phrases by the four operations. Teacher Notes / Answers

37 Slide 37 / 308 addition (+) subtraction (-) multiplication (x) division ( ) WORD BANK total half divided by sum altogether in all remaining quotient decrease fewer than difference combined product split evenly how many per...in all more increased by each...in all per plus each less than left over doubled minus times

38 Slide 38 / 308 E: Equation Underline the word that means "equals". Then, drag and drop the algebraic equation below that represents the words. 1 Words 10 is the same value as a number plus 6. Equation 2 8 is 5 less than a number. 3 three times a number is A number divided by 2 gives you 6. 3 x n = 15 n/2 = 6 8 = n = n 3 x 15 = n 10 = n = n 6/2 = n

39 Slide 39 / 308 E: Equation It's time to get back to the problem we started with (shown below): KAYLEE wants to figure out how many word problems she solved this week. Last week, she solved 16 problems. This week, she solved 7 problems on Monday, 5 problems on Wednesday, and 9 problems on Friday. How many problems did she solve this week? The parts of the algebraic equation we have so far are shown in the box below p = Teacher Notes / Answers

40 Slide 40 / 308 E: Equation The only thing we are missing to create an algebraic equation is an operation or operations (operators). What key words (clues) do you see? KAYLEE wants to figure out how many word problems she solved this week. Last week, she solved 16 problems. This week, she solved 7 problems on Monday, 5 problems on Wednesday, and 9 problems on Friday. How many problems did she solve this week? The words HOW MANY appear twice in the problem. Click for key words and explanation We are trying to find HOW MANY problems total, in all, altogether, or combined. All of these words are clues that we need to ADD.

41 Slide 41 / 308 IMPORTANT REMINDER The exact key words are not always found in a word/application problem. Sometimes you have to figure out what the problem is asking and fill in the key words yourself. In this problem, the key words TOTAL, IN ALL, ALTOGETHER, or COMBINED were not in the problem. By understanding the main idea of the problem we know that we are trying to find "How many problems did she solve this week?". Therefore, we have to COMBINE the problems from Monday, Wednesday, and Friday to find the TOTAL problems (how many problems IN ALL or ALTOGETHER.)

42 Slide 42 / 308 E: Equation Let's put it all together p = + Drag the digits, relation symbol, and operation(s) in the box above to create an algebraic equation that we can use to plan our strategy. algebraic equation click to reveal Plus Is = p Teacher Notes / Answers Number of problems solved on Monday Number of problems solved on Wednesday Number of problems solved on Friday Total Number of problems (in all) for this week

43 Slide 43 / The algebraic equation below could be used to solve the following problem: QUIGLEE solved 9 equations and KAYLEE solved 4. How many more equations did QUIGLEE solve? True = E False

44 Slide 44 / Which algebraic equation would correctly organize the information in the application problem below. QUIGLEE did homework for 5 hours last weekend. He worked on his homework for 3 hours on Saturday. How many hours of homework did he do on Sunday? A = h B 3 + h = 5 C 5 x 3 = h D = h

45 Slide 45 / Choose the algebraic equations that would correctly solve the problem below. QUIGLEE bought 5 packs of pencils for school. Each pack contains 12 pencils. How many pencils did QUIGLEE buy? A = p B = p C 5 + p = 12 D 12-5 = p E 5 x 12 = p

46 Slide 46 / Which algebraic expression would you use to show half of 24? A 24 2 B C 24 x 2 D 2 + 4

47 Slide 47 / Solve (balance) the algebraic equation below. p =? = p

48 Slide 48 / = p Possible Strategies 1. Add up all digits at the same time Add up two of the digits first and then add the third = Make a friendly group of 10 first using the take one from the 7 and add it to 9 to make take 4 from the 5 and add it to 6 to make = 21

51 Slide 51 / 308 S: Solution Solution is written in a complete sentence with the correct label. The last step when problem solving is to make sure your solution/ answer is labeled and can be easily understood = p = 21 Remember that our variable (p) was chosen to help us remember our label (problems solved). Therefore, a complete answer with a label would be: KAYLEE solved a total of 21 problems this week.

52 Slide 52 / 308 Let's use our problem solving acronym (K.E.Y.S.) to solve the word problem below: z K E Y S z zz KALEE sleeps 8 hours a night. She works 9 hours a day. How many hours does she sleep in one week? We want to find out how many hours KALEE sleeps in one week. 8 hours a night is important! What else is important? How many nights are in 1 week? 7 days Click space above for answer. What type of equation do we create to plan our problem?

53 Slide 53 / Choose all the important pieces of this problem that you need to use to solve it. KALEE sleeps 8 hours a night. She works 9 hours a day. How many hours does she sleep in one week? A 7 nights B 9 hours C 8 hours D How many hours will she sleep in one week?

54 Slide 54 / What algebraic equation would be best to solve this problem? KALEE sleeps 8 hours a night. She works 9 hours a day. How many hours does she sleep in one week? A = h B 7 x 8 = h C = h D = h E 7 x 9 = h

55 Slide 55 / Evaluate the algebraic expression you used for the last question and find the solution for this problem. KALEE sleeps 8 hours a night. She works 9 hours a day. How many hours does she sleep in one week?

56 Slide 56 / What is the best label that you could use so your solution is clearly understood? KALEE sleeps 8 hours a night. She works 9 hours a day. How many hours does she sleep in one week? A weeks B hours worked in one week C hours D hours of sleep in one week E total hours for work and sleep

57 Slide 57 / What are the important things all problem solvers should do when solving a word/application problem? A Check over work to see if it makes sense. B Create algebraic equation(s) with important information. C Know all important information in the problem. D Use a clear label for the solution. E Understand the main idea of the problem.

59 Slide 59 / 308 PLACE VALUE / NUMBER SENSE REVIEW Number Sense : A person's ability to use and understand numbers. First, we will focus on whole numbers. Once we have mastered number sense and place value with whole numbers, we can move on to fractions and decimals. Whole numbers : The numbers 0, 1, 2, 3, 4, 5, 6, These are known as counting numbers and do not include decimals or fractions (the numbers between whole numbers).

60 Slide 60 / 308 Even and Odd Numbers One of the first things we learned about whole numbers is whether a given whole number is even or odd. We have a choice to memorize the numbers that are even and odd or we can make sense of numbers and figure out what makes a number even or odd. Even: Odd: Even numbers make pairs. Odd numbers have one left over. Single-digit even and odd numbers can be remembered as follows: Even Numbers: 1, 2, 4, 6, and 8 Odd Numbers: 1, 3, 5, 7, and 9

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66 Slide 66 / 308 Money can also be used to represent place values. Two-digit numbers can be represented with one dollar bills and ten dollar bills 3 tens + 5 ones = 35 dollars = \$35 or \$35.00

67 Slide 67 / tens represents 40 6 ones represents = 46 dollars (\$46 or \$46.00)

68 Slide 68 / There are only 4 groups of 10 in the number 54. A B Yes No

69 Slide 69 / Which explanation is correct for the number 72? A 6 tens and 12 ones B 2 ones and 7 tens C 7 ones and 2 tens

70 Slide 70 / 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

71 Slide 71 / The number 749 would have 7 hundreds, 9 ones, and 4 tens. True False

72 Slide 72 / The number 259 has 5 groups of. A ones B tens C hundreds

73 Slide 73 / Enter the correct number (in standard form) for 5 tens and 6 ones.

74 Slide 74 / Write 4 hundreds and 3 tens in standard form.

75 Slide 75 / Enter the number in standard form for 7 ones and 5 tens.

76 Slide 76 / Enter the correct number in standard form for 3 ones and 4 hundreds.

77 Slide 77 / If you had 15 pencils, would you have an even number to share with a friend? Yes No Teacher Notes / Answers

78 Slide 78 / Is the number represented below even or odd? A Even B Odd tens ones

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80 Slide 80 / 308 Thousands

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82 Slide 82 / 308 Let's use equations to represent this pattern. 10 ones make 1 ten 10 times 1 is 1 ten or 10 ones 10 x 1 = 10 We say 1 ten is 10 times as many as one 10 tens make 1 hundred 10 times 10 is 1 hundred or 10 tens 10 x 10 = 100 We say 1 hundred is 10 times as many as ten

83 Slide 83 / 308 Therefore, each place value is related as follows: Every time we get 10, we bundle and make it a bigger unit. We copy a unit 10 times to make the next larger unit. If we take any of the place value units, the next unit on the left is ten times as many. 1 ten = 10 x 1 one (1 ten is 10 times as much as 1 one) 1 hundred = 10 x 1 ten 1 thousand = 10 x 1 hundred

84 Slide 84 / 308 Look at the place value chart to the millions below. What other patterns do you notice? Millions, Hundred Thousands Ten Thousands Thousands,Hundreds Tens Ones Teacher Notes What place values would come after (to the left) of the Millions place?

85 Slide 85 / 308 Millions Instead of base ten blocks, let's use tally marks to represent how many of each place value we have., Hundred Thousands Ten Thousands Thousands, Hundreds Tens Ones click 1. What is this number in standard or numeric form? 3,541 click 2. If you have 9 more ones, the new number will be? 3,550 Use a place value chart to show your work.

86 Slide 86 / 308,, Millions Hundred Thousands Ten Thousands Thousands Hundreds Tens Ones Show the 9 additional ones 9 ones plus 1 one = 10 ones 10 ones makes 1 ten Millions Hundred,Thousands Ten Thousands Thousands, Hundreds Tens Ones New number has 5 tens and 0 ones.

87 Slide 87 / 308 Additional Questions Explain this number sentence to your partner using your model. 10 x 3 ones = 30 ones = 3 tens Repeat this process with 10 times as many as 5 tens. 10 x 5 tens = 50 tens = 5 hundreds (Problems derived from )

88 Teacher Notes Slide 88 / 308 Place Value of Large Numbers 1, 7 4 1, millions hundred-thousands ten-thousands thousands hundreds tens ones

89 Slide 89 / 308 Read the number. Be careful of the zeros!, millions hundred-thousands ten-thousands thousands, hundreds tens ones

90 Slide 90 / In the number 4632, six is in the hundreds place. True False

91 Slide 91 / The five is in what place value in the number 5,002? A ones B tens C hundreds D thousands

92 Slide 92 / The place value chart and tally marks below represents what number in standard form? Million s, Hundred Thousands Ten Thousands Thousand s, Hundred s Tens One s

93 Slide 93 / The place value chart and tally marks below represents what number in standard form? Millions, Hundred Thousands Ten Thousands Thousands, Hundreds Tens Ones

94 Slide 94 / The number 10,010 is written in standard form. Which choice below shows this number correctly written in word form? A one thousand ten B one thousand one C ten thousand one D ten thousand ten

96 Slide 96 / 308 Write 46 in Words Step 1 Ask yourself questions about the number. How many groups of tens are in 46? click four How many ones are in 46? click six Step 2 Write the numbers as groups of tens and ones. 46 equals 4 groups of ten and 6 ones. click ANSWER 46 = 4 tens + 6 ones

97 Slide 97 / 308 Word Form Response Erase to Check 98 9 tens and8 ones w 52 5 tens and2 ones 64 6 tens and4 ones 29 2 tens and9 ones hundred, 2 tens and 5 ones

98 Slide 98 / 308 Read the Following Numbers 43,201 1,000, ,503 53,600 7,007 1,800,003 60,492 84,905

99 Slide 99 / In the following number, which digit is in the millions place? 1,450,382 Answer

100 Slide 100 / In the following number, which digit is in the thousands place? 1,265,309 Answer

101 Slide 101 / In the following number, which digit is in the tenthousands place? 841,032 Answer

102 Slide 102 / In the following number, which digit is in the hundreds place? 43,791 Answer

103 Slide 103 / In the following number, which digit is in the hundredthousands place? 1,034,762 Answer

104 Slide 104 / 308 Drag the place value digits to the right to make a 4 digit number

105 Slide 105 / 308 Drag each digit to the left to see the expanded form

106 Slide 106 / 308 Writing a Number in Expanded Form In order to represent a number in expanded form show the values as addition =

107 Slide 107 / 308 Try This Write the value in expanded form = = = = + + +

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109 Slide 109 / Which is the correct way to express 9,231 in expanded form? A B C 9 hundreds, 2 thousands, 3 tens, 1 one 9 thousands, 2 hundreds, 3 tens, 1 one 9 hundreds, 23 tens, 1 one Answer

110 Slide 110 / Which is the correct way to express 73,040 in expanded form? A B 70, , C 70, , Answer

111 Slide 111 / Enter this number in standard form Answer

112 Slide 112 / Enter this number in standard form. 50, , Answer

113 Slide 113 / Enter this number in standard form. 60, Answer

114 Slide 114 / Enter this number in standard form. 400, , Answer

115 Slide 115 / Enter this number in standard form. 9, Answer

117 Slide 117 / 308 Before using number lines, Mr. Number Line will review the important components (parts). vertical 1. A line goes on forever in both directions. 2. Each tick mark on a number line represents a number. 3. The space between each tick mark is called an interval or jump. 4. All intervals (jumps) on a number line must be equal. This is called the scale. Number Lines are COOL! Each interval (jump) must be equal. What interval works best? # # tick mark intervals (jumps) horizontal

118 Slide 118 / 308 To best understand number lines it helps to practice creating one. Mr. Number Line will guide you! Use a number line to find the number exactly halfway between 90 and 120. Create a neat number line with a scale that makes sense. 1. First draw a line without any numbers. 2. Then put in the minimum and maximum numbers from the problem on opposite ends of the line Middle is about here Number lines are a great tool to use to find the number in the middle. # #

119 Slide 119 / Next figure out a scale that would help you create easy-to-use (friendly) jumps (intervals) between tick marks. You could jump by 1s, 2s, 5s, 10s, 20s... If you jumped by 1s or 2s, you'd have to make a lot of tick marks. Let's try an interval (jump) of 10. Use a friendly number for your interval. # # Middle is about here 4. Once you choose a scale and create tick marks, you may decide to change your scale to make it easier.

120 Slide 120 / An interval (jump) of 5 will make finding the middle easier Middle is about here The number 105 is halfway between 90 and 120.

121 Slide 121 / 308 Try creating a number line to solve the problem below. Use a number line to find the number exactly halfway between 200 and 340. Create a neat number line with a scale that makes sense. Number lines are COOL! # # Use a Each interval (jump) must be equal. What interval works best? friendly number for your interval.

122 Slide 122 / 308 Place Value Number Line National Library of Virtual Manipulatives Click for web site Step 1 Step 2 Note: The place value can be changed at the bottom of the web page. Step 3

123 Slide 123 / Where does 600 go on the number line? A B C D 1,000 Answer

124 Slide 124 / Where does 310 go on the number line? 200 A BC D 400 Answer

125 Slide 125 / Where does 625 go on the number line? 500 A B C D 700 Answer

126 Slide 126 / Where does 7,300 go on the number line? 0 A BC D 5,000 10,000 Answer

127 Slide 127 / Where does 2,100 go on the number line? 0 A B C D 5,000 10,000 Answer

128 Slide 128 / Where does 7,800 go on the number line? 0 5,000 A BC D 10,000 Answer

129 Slide 129 / What number does the "?" on the number line represent? The "?" is halfway between the tick marks. 0? Answer

130 Slide 130 / What number does the "?" on the number line represent? 0? Answer

131 Slide 131 / What number does the "?" on the number line represent? The "?" is halfway between the tick marks. 0? Answer

132 Slide 132 / 308 More Practice

133 Slide 133 / Even numbers can be divided into equal groups with nothing left over. True False Answer

134 Slide 134 / If 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 Answer

135 Slide 135 / The number 11 is even? True False Answer

136 Slide 136 / If you have 5 hundreds, 4 tens, and zero ones you have what number? Answer

137 Slide 137 / Cindi has 7 dimes and 8 pennies. How much does Cindi have? A B C 87 cents 7.80 cents 78 cents Answer

138 Slide 138 / When writing 978 in expanded form, the number would be in the ones position. hundreds + tens + ones Answer

139 Slide 139 / thousands + 8 hundreds + 5 ones = Answer

140 Slide 140 / In the number 6,014 the number zero is in what place value? A B C thousands hundreds tens Answer

141 Slide 141 / What number is represented below? Answer

142 Slide 142 / Which numbers are represented in standard form? (You can pick more than one.) A 4,031 B 4, C 60,009 D 60, Answer

144 Slide 144 / 308 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

145 Slide 145 / 308 Symbols 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"

146 Slide 146 / 308 Symbols and Words to remember when comparing numbers SYMBOL > < = WORDS greater than/largest less than/ smallest equal

147 Slide 147 / 308 SYMBOL MEANING 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

148 Slide 148 / 308 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 Fill in the blanks using the symbols > >

149 Slide 149 / 308 least number greatest number , > Teacher Notes / Answers

150 Slide 150 / 308 least number greatest number , > Teacher Notes / Answers

151 Slide 151 / 308 least number greatest number 0 5,000 10,000 6,421 3,509 > Teacher Notes / Answers

152 Slide 152 / 308 least number 1,059 7,995 greatest number 0 5,000 10,000 Teacher Notes / Answers >

153 Slide 153 / Use the number line to help determine which symbol to use. A > B < C = 4,031 2, ,000 10,000

154 Slide 154 / Use the number line to help determine which symbol to use. A > B < C = 8, ,000 10,000

155 Slide 155 / Use the number line to help determine which symbol to use. A > B < C = 7,250 7, ,000 10,000

156 Slide 156 / Use the number line to help determine which symbol to use. A > B < C = 3,040 6, ,000 10,000

157 Slide 157 / Use the number line to help determine which symbol to use. A > B < C = 9,500 9, ,000 10,000

158 Slide 158 / 308 ones tens hundreds thousands ten thousands ones tens hundreds thousands ten thousands Way 2 Place Value 4, Take the number Place each digit in the proper place value box 4,398 Start with the greatest place value and move right to where the numbers are different. The bigger of the two numbers is 4,398.

159 Slide 159 / 308 ones tens hundreds thousands ten thousands 8, ones tens hundreds thousands ten thousands 8,289 >

160 Slide 160 / 308 ones tens hundreds thousands ten thousands ones tens hundreds thousands ten thousands 25,361 25,371 >

161 Slide 161 / 308 ones tens hundreds thousands ten thousands ones tens hundreds thousands ten thousands 71,826 71,901 >

162 Slide 162 / The number 765 is smaller than 769? True False

163 Slide 163 / Which number is the largest? A 325 B 335 C 343

164 Slide 164 / Of these four numbers, which is the smallest? 888, 898, 878, 899

165 Slide 165 / Compare the numbers using the correct symbol. A > B < C = 5,429 5,409

166 Slide 166 / Compare the numbers using the correct symbol. A > B < C = 32,461 32,086

167 Slide 167 / Compare the numbers using the correct symbol. A > B < C = 8,730 87,300

168 Slide 168 / Compare the numbers using the correct symbol. A > B < C = 540, ,389

169 Slide 169 / Compare the numbers using the correct symbol. A > B < C = 9,049 9,051

170 Slide 170 / 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 > > B > 13.5 < 17 C 17 < < Teacher Notes / Answers

171 Slide 171 / Sam 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 < 52 > 49 B 49 < 52 < 54 C 49 < 52 > 54 Answer

173 Slide 173 / 308 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.

174 Slide 174 / 308 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. 2,871 least greatest

175 Slide 175 / 308 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 least greatest

176 Slide 176 / 308 Order these numbers least to greatest. 1,491 1,489 Step 3-8 is less than 9, so this is the smallest number 1,489 least 1,491 2,871 greatest

177 Slide 177 / 308 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 1,489 1,491 1,791 1,732 least 2,871 greatest

178 Slide 178 / 308 Ordering From Least to Greatest

179 Slide 179 / 308 Ordering From Greatest to Least

180 Slide 180 / 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

181 Slide 181 / Which 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

182 Slide 182 / Which number can go in the blank to make the numbers be ordered least to greatest? A 6,491 B 6,509 C 6,541 6,474 6,539? 6,597

183 Slide 183 / Which number can go in the blank to make the numbers be ordered least to greatest? A 3,309 B 3,294 C 3,280? 3,289 3,300 3,481

184 Slide 184 / Which number can go in the blank to make the numbers be ordered greatest to least? A 15,811 B 15,711 C 15,750? 15,861 15,809 15,721

185 Slide 185 / 308 Take these numbers and order them greatest to least. 10, digits 4 digits 3 digits 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 click is the only number that has five digits, it makes sense that it is the largest number. Both 823 and click 819 have three digits but when moving right the digit 2 is bigger than 1, therefore 819 is smaller than 823.

186 Slide 186 / 308 Order the numbers least to greatest ,390 1,399 32, ,712 32,768 3 digits 4 digits 5 digits 6 digits

187 879,043 8,768 Slide 187 / 308 Order the numbers greatest to least , , ,043 16, digits 5 digits 4 digits 3 digits

188 Slide 188 / 308 Order the Numbers From Least to Greatest

189 Slide 189 / 308 Order the Numbers from Greatest to Least

190 Slide 190 / Which of the following shows the numbers in least to greatest order? A 1653, 16539, 15789, B 16539, 1653, 15809, C 1653, 15789, 15809, 16539

191 Slide 191 / Which 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

192 Slide 192 / Which of the following shows the numbers in least to greatest order? A 33, 3003, 303, B 30003, 3003, 303, 33 C 33, 303, 3003, 30003

193 Slide 193 / Which number can go in the blank to make the numbers be ordered least to greatest? A 1,201 B 129 C 1, ? 1,142 1,204 10,503

194 Slide 194 / Which number can go in the blank to make the numbers be ordered greatest to least? A 8,893 B 9,500 C ,381 40,619 9,321? 7,905

196 Slide 196 / 308 Rounding 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.

197 Slide 197 / 308 The number line is useful to help when rounding numbers 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?

198 Slide 198 / 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?

199 Slide 199 / 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?

200 Slide 200 / Step 1: Find 3365 on the number line and label it. Step 2: Is 3365 closer to 3300 or 3400? Step 3: What is 3365 rounded to the nearest hundred?

201 Slide 201 / Step 1: Find 3365 on the number line and label it. Step 2: Is 3365 closer to 3300 or 3400? Step 3: What is 3365 rounded to the nearest hundred?

202 Slide 202 / 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?

203 Slide 203 / What is 38 rounded to the nearest ten? Teacher Notes / Answers

204 Slide 204 / What is 874 rounded to the nearest ten?

205 Slide 205 / What is 527 rounded to the nearest hundred?

206 Slide 206 / What is 3,721 rounded to the nearest hundred?

207 Slide 207 / What is 5,835 rounded to the nearest hundred?

208 Slide 208 / 308 Round Numbers Rounding numbers means identifying a given 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.

209 Slide 209 / 308 Round 641 to the Nearest Ten. 1. Put your pencil point under the digit in the tens place and look to the right. 2. Is the digit 5 or more? Yes or No 3. What happens to the digit in the tens place? Increases by 1 or stays the same 4. What happens to everything to the left of the tens place? Those digits always remain the same. 5. Write the answer

210 Slide 210 / 308

211 Slide 211 / 308 Practice - Round to Tens 273 = 544 = 912 = 1232 = 4542 = 7334 =

212 Slide 212 / 308 Round 8,702 to the nearest hundred. 1. Put your pencil point under the digit in the hundreds place and look to the right. 2. Is the digit 5 or more? Yes OR No 3. What happens to the digit in the hundreds place? 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

213 Slide 213 / 308

214 Slide 214 / 308 Practice - Round to Hundreds 939 = 509 = 627 = 3921 = 4644 = 6233 =

215 Slide 215 / In the number 5,439 the number 4 is in the place value. A B C tens hundreds thousands

216 Slide 216 / What digit is in the tens place? 9632

217 Slide 217 / 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

218 Slide 218 / If you round 863 to the nearest hundred you would get? A 800 B 963 C 900

219 Slide 219 / Round 739 to the nearest ten.

220 Slide 220 / Round 5,685 to the nearest ten.

221 Slide 221 / Round 5,685 to the nearest hundred.

222 Slide 222 / Round 65,380 to the nearest hundred.

223 Slide 223 / Round 839 to the nearest ten.

224 Slide 224 / Round 541 to the nearest ten.

225 Slide 225 / Round 585 to the nearest hundred.

226 Slide 226 / Round 3,471 to the nearest hundred.

227 Slide 227 / Round 227 to the nearest ten.

228 Slide 228 / Round 227 to the nearest hundred.

229 Slide 229 / 308 Round 15,821 to the Nearest Thousand 1. Put your pencil point under the digit in the thousands place and look to the right. 2. Is the digit 5 or more? Yes OR No 3. What happens to the digit in the thousands place? 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

230 Slide 230 / 308 Round to the Nearest Thousand

231 Slide 231 / 308 Round 74,891 to the Nearest Ten-Thousand 1. Put your pencil point under the digit in the ten-thousands place and look to the right. 2. Is the digit 5 or more? Yes OR No 3. What happens to the digit in the ten-thousands place? 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

232 Slide 232 / 308 Round to the Nearest Ten-Thousand

233 Slide 233 / In the number 54,718 the number 5 is in the place value. A B C hundreds thousands ten-thousands

234 Slide 234 / Which digit is in the thousands place? 83,517

235 Slide 235 / Round 3,471 to the nearest thousand.

236 Slide 236 / Round 25,512 to the nearest thousand.

237 Slide 237 / Round 7,831 to the nearest thousand.

238 Slide 238 / Round 27,813 to the nearest ten-thousand.

239 Slide 239 / Round 643,712 to the nearest ten-thousand.

240 Slide 240 / Round 94,785 to the nearest thousand.

241 Slide 241 / Round 743,876 to the nearest ten-thousand.

242 Slide 242 / Round 543,802 to the nearest thousand.

243 Slide 243 / 308 Rounding Special Cases

244 Slide 244 / 308 Round 1955 to the Nearest Hundred 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?

245 Slide 245 / 308 Round 1955 to the Nearest Hundred 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?

246 Slide 246 / 308 Round 1955 to the Nearest Hundred 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?

247 Slide 247 / 308 Round 1955 to the Nearest Hundred 1. Put your pencil point under the digit in the hundreds place and look to the right. 2. Is the digit 5 or more? Yes OR No 3. What happens to the digit in the hundreds place? Increases by 1 OR remains the same What happens when the 9 needs to increase by 1? 4. What happens to everything to the left of the hundreds place? Those digits always remain the same. 5. Write the answer

248 Slide 248 / 308 Round 5,995 to the Nearest Ten 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?

249 Slide 249 / 308 Round 5,995 to the Nearest Ten 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?

250 Slide 250 / 308 Round 5,995 to the Nearest Ten 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?

251 Slide 251 / 308 Round 5,995 to the Nearest Ten 1. Put your pencil point under the digit in the hundreds place and 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 What happens when the 9 needs to increase by 1? 4. What happens to everything to the left of the tens place? Those digits always remain the same. 5. Write the answer

252 Slide 252 / 308

253 Slide 253 / Round 79,621 to the nearest thousand.

254 Slide 254 / Round 3,992 to the nearest hundred.

255 Slide 255 / Round 97 to the nearest ten.

256 Slide 256 / Round 1,499,000 to the nearest ten-thousand.

257 Slide 257 / Round 19,997 to the nearest hundred.

258 Slide 258 / Round 469,971 to the nearest hundred.

259 Slide 259 / 308

260 Slide 260 / A large jar has 1,539 marbles in it. What is this number rounded to the nearest thousand?

261 Slide 261 / New 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?

263 Slide 263 / 308 Patterns A pattern or sequence is either shapes or numbers 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?

264 Slide 264 / 308 Patterns Patterns are almost everywhere you look. Can you identify patterns around the classroom?

265 Slide 265 / 308 What is the pattern in this example? Move the shapes to complete pattern What is the rule?

266 Slide 266 / 308 Create your own geometric pattern using these two shapes. Describe your geometric pattern (write the rule).

267 Slide 267 / 308 Patterns can also be represented by rotating a shape. Draw the next shape

268 Slide 268 / What would be the tenth shape if this pattern were continued? A B C

269 Slide 269 / Which would be the next shape in this pattern? A B C

270 Slide 270 / What would be the eleventh shape in this pattern? A B C

271 Slide 271 / 308

272 Slide 272 / 308 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.

273 Slide 273 / 308 Find the missing number: 15, 13,, 9, 1. The order is going down (getting smaller). 2. The difference between numbers = 2 3. Since the order is going down subtract 2 from 13. The missing number is Now that you know the pattern is subtract 2, take the last digit and subtract 2 and you will get 7. 15, 13, 11, 9, 7 click

274 Slide 274 / 308 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.

275 Slide 275 / 308 Find the Missing Number 5, 10, 8, 16, 14, 28,,, x 2-2 x 2-2

276 Slide 276 / In the pattern 25, 50, 100, 200, the rule would be to keep adding 25. True False

277 Slide 277 / What is the missing number in this pattern? 16, 20, 24,, 32, 36

278 Slide 278 / Charles 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, What address will Charles see next?

279 Slide 279 / Mrs. Hall wrote the following number pattern on the board. 4; 16; 64; 256 What was the rule for this pattern? A Add 12 B Multiply by 4 C Multiply by 3

280 Slide 280 / The 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?

281 Slide 281 / What are the next two numbers in the pattern? 3, 12, 10, 19, 17, 26,.... A 33, 24 B 24, 33 C 35, 33

282 Slide 282 / 308 Function Machine 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?

283 Slide 283 / 308 Function 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 is multiply by 6. click

284 Slide 284 / 308

285 Slide 285 / 308 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 click 2. Jose chose 8 as his input number. What was output number? 48 click 3. Caleb put a number through the machine, and his output number was 120. What number did Caleb put through the machine? 20 click

286 Slide 286 / 308 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 What is the rule for Ms. Collins machine when it is in reverse? divide by 9 click 5. Kareem chose 108 as his input number. What was his output number? 12 click 6. Carmen chose her output number as 15. What was her input number? 135 click

287 Slide 287 / What is the rule for this function machine? A multiply by 3 B multiply by 8 C divide by Teacher Notes / Answers

288 Slide 288 / The rule for this function machine is multiply by 5, what is the output? 9 Teacher Notes / Answers?

289 Slide 289 / The rule for this function machine is multiply by 7, what is the input?? 42

290 Slide 290 / 308 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.

291 Slide 291 / 308 Example What is the rule for the function table going from column x to column y? x y 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.

292 Slide 292 / 308 Example You can also use number patterns in tables to solve real-world math problems. 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? Answer DAY Number of Laps

293 Slide 293 / The rule for the table below of attempted passes and completed passes is multply by 7. Attempted Completed Passes True False

294 Slide 294 / What is the correct rule for this function table going from column x to y? x y A add 27 B multply by 3 C add 29

295 Slide 295 / What is the missing value in the function table? x y ? 97 47

297 Slide 297 / 308 Algebraic Equation States that two things are the same using mathematical symbols and an equal sign. Has a least one variable = y equals sign: (relation symbol) number: operation: variable: Can be either true or false depending on what values are used for the variable. 4x number: operation: variable: equals sign? Back to Instruction

298 Slide 298 / 308 Equation Two expressions that are equivalent to each other. Equivalence is shown with an equal sign. 4x2 = 8 equivalent expressions 5+3 = 9-1 equivalent expressions 3 3 no equivalence Back to Instruction

299 Slide 299 / 308 Equivalent Equal; the same amount or value. = 3+3=3x1 Back to Instruction

300 Slide 300 / 308 Expression Numbers, symbols and operations grouped together that show the value of something An expression is one side of an equation. 2 x 3 = 6 Expressions DO NOT have equals signs. Back to Instruction

301 Slide 301 / 308 Open Number Sentence Numbers and operation(s) with a relation symbol (usually an equation) that contains at least one variable = y equals sign: (relation symbol) number: operation: variable: Can be either true or false depending on what values are used for the variable. 4x number: variable: Operation and equals sign? Back to Instruction

302 Slide 302 / 308 Operation A calculation by a mathematical process. y 3 = = y y y exponents are operations too calculators perform o perations + - x < > Back to Instruction

303 Slide 303 / 308 Solution A value you can put in place of a variable that would make the statement true. The answer to a math problem. x + 4 = 9 Solution: x = 5 3y 6 Solution: y 2 x + 4 = 9 x = 6 Back to Instruction

304 Slide 304 / 308 Variable A letter or symbol that represents a changeable or unknown value. 4x + 2 variable x x x =? Back to Instruction

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