(3.1B) Number, operation, and quantitative reasoning. The student uses place value to communicate about increasingly large whole numbers in verbal and written form, including money. The student is expected to use place value to compare and order whole numbers through 9,999. Suggested Activities/Lessons: • Lesson: Compare and Order Numbers • Lesson: Compare and Order Using a Number Line • Number Top-‐It • Digit Discovery TAKS Objective:Objective 1 TEKS: 3.1 The student uses place value to communicate about increasingly large numbers in verbal and written form. Student Expectation: 3.1B Compare/order whole numbers through 9,999. Connection to EUS title: Constructing and Utilizing Essential Unit Patterns and Numbers of Study: Essential Questions: * Why is it important to know different ways to represent the value of a number? * What are some patterns you notice in our number system? * How does a digit's placement in a number change the value of the number? * How can numbers be expressed, ordered, and compared? Understandings: Overview: Materials: * Place value is based on groups of ten. * There are a variety of ways to break apart and put together whole numbers. This is a learning activity that practices the sequencing of numbers and place value decisions. See attached prerequisite lesson. Place Value Tools – Base Ten Materials and student copies of pictorial Base 10 Blocks of units, tens, hundreds and thousands. Student copy and a class set of expanded notation cards (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 00, 10, 20, 30, 40, 50, 60, 70, 80, 90, 000, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000) See attachments Place Value Mat to the 1000’s Place Value Path Game Boards Digit cards per student (2 sets of 0-9) Vocabulary: Procedure: compare digit greater than more than number numeral less than order place value valuecomparative symbols >, <, = equivalentexpanded notation (form) greatest standardized notation (form)word form ones hundreds thousands tens comma Each player has their own Place Value Path Board 100 1000. The teacher will model the game with students on overhead with digit cards. Game Directions: The digit cards are shuffled and placed face down. The teacher turns over 3 cards. When the cards are turned over, the players must decide what number to build,and which spot to place them in on the game board. The path must go from the smallest number to the largest number. Once a number is written in, it must stay in that spot. The first person to complete the path is the winner. The teacher draws and displays the three numerals. The teacher says, two, nine, four. Teacher asks,What numbers can you create with these digits? What is the largest number you can make? 942 = 900 + 40 + 2 9 groups of hundred, 4 groups of ten, 2 groups of one. What is the smallest number you can make? 249 = 200 + 40 + 9 2 groups of hundred, 4 groups of ten, nine groups of one. What are the other numbers you can make? Teacher lists the numbers the students share and continues to ask, Are there any other numbers that can be made? In our number, how many groups of one are there? In our number, how many groups of ten are there? In our number, how many groups of hundred are there? These are the “over and over” questions that students need to be asked in reference to the picture of the quantity, the expanded form of the quantity, and the standardized form of the quantity. 924 = 294 = 492 = 429 = 900 + 200 + 400 + 400 + 20 + 90 + 90 + 20 + 4 4 2 9 What makes these numbers different from one another? Listening for … that the digit’s placement changes the value of the number. Teachers says, Now, let’s chose one of the possible number choices and write it on one of spaces on the Place Value Path game board. Draw another three cards from the deck and read aloud. one, seven, five What numbers can you create with these digits? Look at your game board. Do you want to make a number larger than the number you just recorded or make a smaller number? How are you going to decide where to place your number on the game board? How do you know your number is larger than ______? How do you know that your number is smaller than ______? How do you know your number is between _____ and ______ ? Teacher should continue to facilitate the same questioning stated above for 3-4 rounds. The game continues until all spots on the board are filled. Once students seem to master the skill needed for the game you may have the students, pair up to play in small groups. This provides the teacher the opportunity to continue to work with the students who still need further guidance practicing the skill. There is a point where a player may not be able to use the cards and would have to skip a turn. There are two options for the cards after they are played. One option would be to play the game where the cards are reshuffled back into the deck. This would keep the probability of the deck constant. The other option would be to remove the cards once they have been played. Play would continue until the deck is used up and then the cards would be reshuffled and play continued until a path is completed. This option changes the probability of the deck as the cards are removed. Listen for … Does the student accurately read the numbers using the proper number naming patterns? Does the student clearly describe a reasonablestrategy for placing the numbers on the game board? Does the student's strategy and explanations involve place value? Look for … Can the student place numbers on the game board accurately? Does the student demonstrate a good grasp of the number system and place value? Does the student apply useful benchmark numbers when placing the numbers on the Place Value Path game board? Does the student successfully compare and order numbers on the Place Value Path game board? Does the student use place value and patterns in number relationships to compare, order, and place numbers on game board? Struggling students may need to use the pictorial Base 10 blocks or expanded notation cards. Debriefing Questions: Chose two numbers from your game board. What are your numbers? (For example, two hundred ninety-four and seven hundred fifteen.) Can you show the value of your numbers using the pictorial Base 10 blocks? What number is the greater? How do you know? What number is the least? How did you decide this? Write two numbers in your mathematics journal and use a number symbol (>, <, = ) to compare the two numbers. Why did you write this symbol? (For example, 294 < 715.) Is there another number sentence that you can write comparing 294 and 715? (For example, 715 > 294.) If you add/subtract 10 to each of your numbers, how would the new numbers compare? How do you know? What are the new numbers? If you add/subtract 100 to each of your numbers, how would the new numbers compare? How do you know? What are the new numbers? If you add/subtract 1000 to each of your numbers, how would the new numbers compare? How do you know? What are the new numbers? Listen for…How does the student determine the new numbers? Does s/he use concrete models, count on, use mental arithmetic, pencil and paper to find the new numbers, or another method? Guided Practice: Evidence of Learning: Students can replay the game using the Place Value Path 100 – 1,000 or the Place Value Path 1,000 – 10,000 Game board Using the digits eight, one, four and five, rearrange the numbers to create a four-digit number. 1,548 Write 5 things about your number: 1. the digit in the hundreds place is the same number of sides on a pentagon 2. the number is even 3. if you add up all the digits it is equal to eighteen 4. the digit in the tens place is the number of angles and sides on a square 5. the number in the tens place 4, is half the number in the ones place 8 Rearrange the numbers to make: the smallest number: ____________________ the largest number: _____________________ an even number: ________________________ an odd number: ________________________ a number less than 2000: _________________ a number more than 5000: ________________ Assessment Objective 1 TEKS 3.1B Name _____________ Date _______ The lengths of the longest four rivers in Texas are the Rio Grande River with 1,896 miles, the Red River with 1,360 miles, Brazos River 1,280 miles and the Pecos River 926 miles. Using words, write the lengths of the rivers in order from the shortest river to the longest river. Explain your process. The numbers below are arranged from least to greatest. 4, 174 4,628 4,873 5,047 Which of the following numbers belong in the empty pentagon? Mark your answer. a. b. c. d. 4,874 4,761 4,627 5,050 Prior to this lesson students should have experience in building numbers with concrete and pictorial Base 10 materials. For example, Students have their Base 10 Tool Kit and are using the expanded notation cards and digit cards. The expanded notation cards (large set) are handed out to students. The teacher calls out a number 264. The teacher then models building the number on the overhead or document camera using the Base 10 materials. If a student is holding a card that is part of the value of the number, he/she comes to the front of the room. The student with the 200 card would come up, followed by the student who has the 60 card and the student with the 4 card would come up. The students would be lined up to show 200 + 60 + 4. The teacher calls out “expanded notation” or “expanded form.” The seated students would also build their number w/ paper base ten materials as well as with the expanded form cards. The teachers calls out “standardized notation” or “standardized form” and students in front of the class slide their cards together to show 264. Students manipulate their own expanded notation cards. Can be made on sentence strips This strategy connects the picture of the quantity with the abstract meaning of 200 + 60 + 4 to the use of digit cards 264 Place Value Pocket Thousands Hundreds Tens Ones 2 0 0 6 0 4 “Expanded Notation” 264 “Standardized Notation” Continue practice with this activity using larger numbers up to 9,999 for the 3.1B lesson. Place Value Mats and digit cards are important tools in building number sense tools that students construct. Place Value Questions. The teacher can ask these questions: In our number, how many groups of one are there? 5 groups of one = 5 In our number, how many groups of ten are there? 3 groups of ten = 30 In our number, how many groups of a hundred are there? 7 groups of hundred = 700 In our number, how many groups of a thousand are there? 2 groups of thousand = 2000 Place Value Path100 - 1000 TAKS Objective 1: The student will demonstrate an understanding of numbers, operations, and quantitative reasoning. TEKS 3.1:The student uses place value to communicate about increasingly large whole numbers in verbal and written form, including money. Student Expectation 3.1B:The student is expected to use place value to compare and order whole numbers through 999,999. Connection to ESU title: Place Value and Money Essential Unit Essential Questions: What are some of Study: patterns you notice in our number system? Understandings: Students will understand that symbols are used to represent formal math language. Students will explore strategies for comparing and Overview: Materials: Vocabulary: Procedure: ordering whole numbers utilizing place value and the number line. Decks of cards Game sheet for Who Has More? Dry erase boards for student responses Compare, order, place value, hundred thousands, ten thousands, one thousands, hundreds, tens, ones, greater than, less than, larger than, smaller than, symbol, <, > Today we are going to explore and use strategies to compare and order large whole numbers. Which number is less 503 or 350? [350] How do you know? [3 hundreds is less than 5 hundreds; 350 comes before 503] You used what you knew about place value to help you compare the numbers. What words would you say to compare the numbers? [503 is greater than 350 or 350 is less than 503] What math symbols could we use to show that comparison? [< or >] Write a sentence showing that comparison. [350 < 503 or 503 > 350] Read that sentence. [350 is less than 503 or 503 is greater than 350] How did you know which symbol to use? Talk with your partner. [The open part of the symbol always points to the larger number.] How would you compare 108,464 and 97,996 using the math symbols for greater than and less than? [108,464 > 97,996 or 97,996 < 108,464] What strategy did you use to compare the numbers? Talk with a partner. [108,464 has more digits than 97,996 so it is greater; 97,996 has less digits than 108,464 so it is less; 108,464 has a digit in the hundred thousands place while 97,996 has only a digit in the ten thousands place so it is greater; 97,996 has a digit in the ten thousands place while 108,464 has a digit in the hundred thousands place so it is less] What symbol, < or >, would make this sentence true? (record on board) 673,024 ___ 692,102 [<] How do you know? Share with a partner. [Both numbers have 6 in the hundred thousands place. But, the digits in the ten thousands place are different. 70,000 is less than 90,000 so 673,024 is less than 692,102.] If we wanted to put the following numbers in order from least to greatest, how would using a number line help? 476 267 742 [267 would come before 476 on the number line and 476 would come before 742 on the number line. So the order of the numbers from least to greatest would be: 267 476 742] Debriefing Questions: Guided Practice: Evidence of Learning: How could you use place value to order these numbers least to greatest? [200 is less than 400 and 400 is less than 700] Order these numbers from greatest to least: 25,716 25,961 25,381 [25,961 25,716 25,381] How did you figure that out? Share with a partner your strategy. [All 3 numbers started the same with 25 thousand, but the hundreds were different. 900 is more than 700 and 700 is more than 300.] 1. What math symbols or words can we use to compare whole numbers? [< or >; greater than, more than, less than, smaller than] 2. Explain what the symbols mean. [> means greater than; < means less than; the mouth or open part always opens to the greater number] 3. If you want to compare or order whole numbers, what are some strategies you could use? [position on the number line: if the number is to the left of the other number or numbers then it is smaller or the smallest; use place value to determine the value of the digits: the more digits the larger the number, the higher the place the greater the number; starting from the left find where the digits in the same place are different and then compare their value] Play game: Who Has More? Materials: deck of cards (0-9), game sheet for each student pair Players will use the cards to make 5 digit numbers and compare them using the symbols. Teacher checks with each group to check for accuracy or misunderstandings. 1.Which of these numbers is less than 10,580? a. 10,791 b. 10,601 c. 10,589 d. 10,578 2. The numbers are arranged from greatest to least. Write a number that could belong on the empty line. 6,521 ___ 5,942 5,601 5,578 3. Use < or > to make the sentences true. 45,181 ___ 46,758 346,521 ___ 344,099 200,425 ___ 39,939 4. Academy has 8,674 tennis balls in the store. Sports Authority has 8,903 tennis balls. Which store has more tennis balls? Circle the store name. Academy Sports Authority Assessment for Learning Objective 1 – TEKS 3.1B Name ________________________ Date _____________ 1. Which of these numbers is less than 10,580? a. 10,791 b. 10,601 c. 10,589 d. 10,578 2. The numbers are arranged from greatest to least. Write a number that could belong on the empty line. 6,521 ____________ 5,942 5,601 5,587 3. Use < or > to make the sentences true. 45,181 ____ 46,758 346,521 ____ 344,099 200,425 ____ 39,939 4. Academy has 8,674 tennis balls for sale in their store and Sports Authority has 8,903 tennis balls for sale. Which store has more tennis balls? Circle the store name. Academy Sports Authority TEKS 3.1B Game Sheet Who Has More? Object of game: To find which created 5 digit number is greater than the other. Number of Players: 2 Materials: deck of cards (0-9), game sheet per pair Directions: 1. Shuffle the deck of cards. 2. Each player draws 5 cards. 3. Player 1 turns over the cards and records the numbers in the order turned over to create a 5 digit number for Round 1. 4. Player 2 does the same thing. 5. The player with the largest number records the symbol in the box to make the sentence true. 6. Play for 5 rounds. 7. At the end of the game, each player orders their numbers from greatest to least. Who Has More? Use < or >. Player 1 Player 2 Round 1 Round 2 Round 3 Round 4 Round 5 Order your numbers from greatest to least. Player 1 Player 2 S t r a n d s Numeration; IVIeasurement and Reference Frames S k i l l Practice finding tine total value of coins G a m e s K i t M a t e r i a l s Cper group] Game Master 114 (record sheet) 16 nickels, 40 pennies Players 2 Object of the game To have the greater amount of money. Nickel/Penny Grab Record Sheet SiA 144 1 grabbact I have ® and a, Myparlnerhas 1. Players m i x the coins together. 2. One player grabs a handful of coins; the other player takes the coins that are left. 3. Players help each other count the coin collections and determine which player has more money. 4. The player w i t h more money wins the game. ©. c. Who has ma™? . f 1 grabbed Direct ® ai My partner grabbed _ S t r a n d Numeration S k i l l Practice comparing numbers G a m e s K i t M a t e r i a l s (per group) Nunnber Top-Zf Gameboard (or Game Masters 115 and 116,1 copy for every 2 players) Everything Math Deck Grade 3 , Grade 4 (number cards 0-9, 4 of each) Players 2-5 228 \ Z Grade I 204 \ J 287^ Object of the game To make the greatest 7-digit number. Direct 128 Game Directions 1. The dealer shuffles the cards and places the deck number-sidedown on the playing surface. 2. The Place-Value M a t has rows of boxes. Each player uses one row of boxes on the game mat or uses the space on the playing surface below the gameboard. c I n each round, players take turns turning over the top card from the deck and placing i t on any one of their empty boxes. Each player takes 7 turns and places 7 cards on his or her row of the game mat. 7-Drgit Place-Value M a t aSI, 1 1 S W ' A t the end of each round, players read their numbers aloud and compare them to the other players' numbers. The player w i t h the greatest number for the round scores 1 point. The player w i t h the next-larger number scores 2 points, and so on. Players play 5 rounds for a game. One player shuffles the deck between each round. The player w i t h the least number of points at the end of 5 rounds wins the game. =;tXAMPItTwo players finished''One;Tound of 7-6\^ Number Top-It Here are the results. Millions c/.:; • HundredTenThousands Thousands Thousands Hundreds 4 '2 7 \ 5 Tens Ones 0 Player 1 ] 0 ^ 2 1 Player 2 s Player t's number is larger than Player 2's number. So Player 1 scores 1 point for this round. Player 2 scores 2 points. V a r i a t i o n (recommended for Grade 3) Students can play an easier version of the game by l i m i t i n g the numbers to 5 digits. Players do not use the Millions box or the Hundred-Thousands box on the Place-Value Mat. 3 7-Digit P l a c e - V a l u e M a t (...tl gS'., 116<< 5 Game Directions 129 Name Date Time g- 7-Di'git Place-Value Mat Saster 115 t f f. 1 f ® f /Si, ^: 11 2 9 8 Game Masters 0 I 1 I iVwOT^'er Top-/* Name Date 7-Digit Place-Value Mat (cont.) Time Game Master w 0) c O tn c 0 I- V5 (A T3 O •a c (0 C CO Number Top-It Game Masters 2 9 9 strand Numeration Skill Practice place-value skills and comparing numbers Wlaterials Cper group) cdlored chalk (optional) 3 sets of the number cards 0 - 9 (each set of numbers written in a different color such as red, blue, and green) P l a y e r s whole class Object of the game To use clues to form 3-digit numbers. lirections 1. 2. 3. Use colored chalk, if available, to write the place-value names along the top ofthe board. For example, write "hundreds" i n red, "tens" in blue, and "ones" in green. Mix and distribute the colored number cards so that each student has at least one. Give clues to summon students to the board. Say / am the largest 3-digit number. Students with red 9, blue 9, and green 9 come to the board and stand under their colors, holding up their number cards. Say I am 10 less than the number up there now. Blue 9 sits down and is replaced by blue 8. Say / am 500 less than the number up there now. Red 9 sits down and is replaced by red 4. Variation Ask students to make up the clues. 64 Game Directions

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