Enhanced Instructional Transition Guide / Unit 01: Suggested Duration: 5 days Unit 01: Place Value (12 days) Possible Lesson 01 (5 days) Possible Lesson 02 (7 days) POSSIBLE LESSON 01 (5 days) This lesson is one approach to teaching the State Standards associated with this unit. Districts are encouraged to customize this lesson by supplementing with district-approved resources, materials, and activities to best meet the needs of learners. The duration for this lesson is only a recommendation, and districts may modify the time frame to meet students needs. To better understand how your district is implementing CSCOPE lessons, please contact your child s teacher. (For your convenience, please find linked the TEA Commissioner s List of State Board of Education Approved Instructional Resources and Midcycle State Adopted Instructional Materials.) Lesson Synopsis: Students read, write, order, and compare whole numbers to 999,999,999 with concrete materials, such as base-ten blocks, place value charts, and digit cards. TEKS: The Texas Essential Knowledge and Skills (TEKS) listed below are the standards adopted by the State Board of Education, which are required by Texas law. Any standard that has a strike-through (e.g. sample phrase) indicates that portion of the standard is taught in a previous or subsequent unit. The TEKS are available on the Texas Education Agency website at http://www.tea.state.tx.us/index2.aspx?id=6148 4.1 Number, operation, and quantitative reasoning.. The student uses place value to represent whole numbers and decimals. The student is expected to: 4.1A Use place value to read, write, compare, and order whole numbers through 999,999,999. Supporting Standard Underlying Processes and Mathematical Tools TEKS: 4.14 Underlying processes and mathematical tools.. The student applies mathematics to solve problems connected to everyday experiences and activities in and outside of school. The student is expected to: 4.14A Identify the mathematics in everyday situations. page 1 of 45
Enhanced Instructional Transition Guide / Unit 01: Suggested Duration: 5 days 4.14C Select or develop an appropriate problem-solving plan or strategy, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem. 4.14D Use tools such as real objects, manipulatives, and technology to solve problems. 4.15 Underlying processes and mathematical tools.. The student communicates about mathematics using informal language. The student is expected to 4.15A Explain and record observations using objects, words, pictures, numbers, and technology. 4.15B Relate informal language to mathematical language and symbols. Performance Indicator(s): Grade4 Unit01 PI01 Identify a real-life situation that involves five numbers through the hundred millions place (e.g., the population of five states, the distance between the Sun and five other planets in the solar system in kilometers, etc.). Use technology to determine the five numbers that represent the situation, and record them in a table using standard form, expanded notation, and words. Explain in writing how to order the data, and then record two comparative statements using words and symbols to describe the real-life situations. Sample Performance Indicator: Use technology to determine, in kilometers, the distance between the Sun and five other planets in the solar system. The data identified should be represented using standard form, expanded notation, and words. Order the data in the table, and then write two comparative statements, using words and symbols, related to the real-life situation and a brief description of how the order was determined. Standard(s): 4.1A, 4.14A, 4.14C, 4.14D, 4.15A, 4.15B ELPS ELPS.c.1H, ELPS.c.4J, ELPS.c.5G Key Understanding(s): The place value system is based on multiples of 10 where, when moving left across the places, the values are multiplied by 10; or when moving right across the places, the values are divided by 10. The position of a digit, or place value, in a whole number determines the value of the number, which aids in the reading and writing of the number and in the expressing of verbal and written comparative statements using words and symbols. page 2 of 45
Enhanced Instructional Transition Guide / Unit 01: Suggested Duration: 5 days When observing and recording a variety of strategies and mathematical ideas to solve real-life problems involving place value and comparing and ordering whole numbers, thinking processes are revised, refined, and valued, all which sharpen mathematical understanding. Misconception(s)/Underdeveloped Concept(s): None identified Vocabulary of Instruction: digit expanded notation equal to greater than less than millions period place value standard form Materials List: base-ten blocks (10 1000-cubes, 10 100-flats, 10 10-longs, 10 units in each set) (1 set per student, 1 set per teacher) blank paper (1 sheet per student) brads (optional) (2 per student) cardstock (1 sheet per 2 students) cardstock (optional) (28 sheets per teacher) computer with Internet access (1 per student) decahedra die (1 per 2 students ) die (decahedra) (optional) (1 per 2 students) If You Made a Million, by David M. Schwartz (1 per teacher) index card (optional) (1 per 2 students) math journal (1 per student) plastic zip bag (gallon sized) (1 per 2 students, 1 per teacher) plastic zip bag (sandwich sized) (1 per 2 students) scissors (1 per student, 1 per teacher) sentence strips (1 per teacher, 1 per 2 students) tape (clear) (1 roll per 3 4 students) page 3 of 45
Enhanced Instructional Transition Guide / Unit 01: Suggested Duration: 5 days Attachments: All attachments associated with this lesson are referenced in the body of the lesson. Due to considerations for grading or student assessment, attachments that are connected with Performance Indicators or serve as answer keys are available in the district site and are not accessible on the public website. If You Made a Million Concept Map Place Value Prompt Activity Teacher Notes Base-Ten Block Model Cards Paper Hundred Centimeter Grids Paper Thousand Block Directions Digit Cards Understanding Place Value KEY Understanding Place Value Blank Place Value Chart Blank Understanding Place Value Chart Comparing and Ordering Whole Numbers Notes Connecting the Dots for Comparison Graphic Creating Movable Comparison Symbols Using the Place Value Chart Stay on Target page 4 of 45
Enhanced Instructional Transition Guide / Unit 01: Suggested Duration: 5 days Population Place Value KEY Population Place Value PI GETTING READY FOR INSTRUCTION Teachers are encouraged to supplement and substitute resources, materials, and activities to meet the needs of learners. These lessons are one approach to teaching the TEKS/Specificity as well as addressing the Performance Indicators associated with each unit. District personnel may create original lessons using the Content Creator in the Tools Tab. All originally authored lessons can be saved in the My CSCOPE Tab within the My Content area. Suggested Day Suggested Instructional Procedures Notes for Teacher 1 Topics: Introduce whole number place value through the hundred millions period Engage 1 Students use the book If You Made a Million to become familiar with the concept of whole numbers through the hundred millions. Instructional Procedures: 1. Distribute handout: If You Made a Million Concept Map to each student. 2. Read the book If You Made a Million to students. Instruct students to make notes on their handout: If You Made a Million Concept Map to guide their understanding of different dollar amounts as they listen to the book. Allow time for students to complete the concept map. Monitor and assess students to check for understanding. Facilitate a class discussion about the completed concept maps. Spiraling Review ATTACHMENTS Handout: If You Made a Million Concept Map (1 per student) Teacher Resource (optional): Place Value Prompt Activity Teacher Notes (1 per teacher) MATERIALS If You Made a Million, by David M. Schwartz (1 per teacher page 5 of 45
Enhanced Instructional Transition Guide / Unit 01: Suggested Duration: 5 days Suggested Day Suggested Instructional Procedures Notes for Teacher Ask: What is an example of how to pay $10,000 in the story? Answers may vary. Pennies, 10 one-thousand dollar bills; etc. What are some examples of $1,000,000 in the story? Answers may vary. Stack of pennies ninety-five miles high; etc. How many sets of a 100,000 would equal one million? (10) Can you describe or draw a picture to show how you know? Answers may vary. You could draw 999 thousand, then 1 more thousand would be one million; etc. TEACHER NOTE Other books to consider are: A Million Fish More or Less by Patricia McKissack; or Millions of Cats by Wanda Gag. If literature is not available, use teacher resource (optional): Place Value Prompt Activity Teacher Notes to facilitate the concept of magnitude of numbers through the hundred millions place. 2 Topics: Model place value through the hundred thousand place using base-ten blocks Explore 1 Students use base-ten blocks to model whole numbers through the hundred thousands place. These models are used to show that the base-ten block patterns of 1-unit, 10-long, and 100-flat repeat in each period. Instructional Procedures: 1. Prior to instruction, create a set of base-ten blocks for each student and a set for each teacher by placing 10 1000-cubes, 10 100-flats, 10 10-longs, and 10 units in a plastic zip bag. If base-ten blocks are not available, use teacher resource (optional): Base-Ten Block Model Cards to create sets of base-ten blocks by copying on cardstock, cutting apart, and laminating. Spiraling Review ATTACHMENTS Teacher Resource (optional): Base-Ten Block Model Cards (1 set per student, 1 set per teacher) Handout: Paper Hundred Centimeter Grids (4 per student) Teacher Resource: Paper Thousand Block Directions (1 per teacher) MATERIALS page 6 of 45
Enhanced Instructional Transition Guide / Unit 01: Suggested Duration: 5 days Suggested Day Suggested Instructional Procedures 2. Place students in groups of 3 4 and distribute a set of base ten blocks to each group. Display the number 134,572 for the class to see. Ask: Is it possible to model this number using base-ten blocks? Answers may vary. Yes, if I am given more blocks; No, because I do not have enough blocks; etc. What number can you make using the base-ten blocks in your group? Answers may vary. If you were able to combine all of the 1000-cubes in the groups, would you have enough blocks to make 134, 572? How do you know? (No, I would need 134 thousand 1000-cubes.) 3. Display teacher resource: Paper Thousand Block Directions. Distribute a pair of scissors and 4 copies of handout: Paper Hundred Centimeter Grids to each student. Additionally, distribute a roll of tape to each group. Instruct students to follow the directions from the displayed teacher resource: Paper Thousand Block Directions to make 4 or 5 1000-cubes, enough to have 100 1000-cubes for the entire class. Ask: How can you represent the ones using base-ten blocks? Tens? Hundreds? Thousands? Ten thousands? Hundred thousands? (units; 10-long; 100-flat; 1000-cube; a 10-long where each cube represents a 1000-cube to look like a giant 10-long; a 100-flat composed of a 10 giant 10-longs connected to look like a giant 100- flat) How is the relationship between the units, 10-longs, and 100-flats similar to the relationship between the 1000-cube, the giant 10-long, and the giant 100- flat? Answers may vary. The units figure resembles the 1000-cube for one thousand; the 10-long resembles Notes for Teacher base-ten blocks (10 1000-cubes, 10 100- flats, 10 10-longs, 10 units in each set) (1 set per student, 1 set per teacher) plastic zip bag (gallon sized) (1 per 2 students, 1 per teacher) cardstock (optional) (28 sheets per teacher) scissors (1 per student, 1 per teacher) tape (clear) (1 roll per 3 4 students) blank paper (1 sheet per student) math journal (1 per student) TEACHER NOTE To ensure consistent vocabulary, base-ten blocks will be identified as a 100-flat, 10-long, and unit throughout the lessons in CSCOPE. TEACHER NOTE Handout: Paper Hundred Centimeter Grids may be taped together to make more 1000-cubes if the regular base-ten 1000-cubes needed are not page 7 of 45
Enhanced Instructional Transition Guide / Unit 01: Suggested Duration: 5 days Suggested Day Suggested Instructional Procedures the giant 10-long for ten thousand; the 100-flat resembles the giant 100-flat for one hundred thousand. The relationship between the units, tens, and hundreds increases by multiples of ten through the period as does the relationship between thousands, ten thousands, and hundred thousands; etc. 4. Distribute a sheet of blank paper to each student. Instruct students to sketch a picture of the base-ten blocks needed to model 134,572 and describe what they have discovered about modeling a hundred-thousand and how this can be used to model a million. Facilitate a class discussion about the model for one million. Ask: How can you represent one million using base-ten blocks? (10 giant 100-flats connected to look like a giant cube) 5. Facilitate a class discussion about base-ten blocks. Instruct students to summarize responses in their math journal. Ask: Notes for Teacher available. It is highly recommended that the teacher allow time for students to build the 1000- cubes themselves. However, as an alternative the 1000-cubes teacher resource: Base-Ten Block Model Cards may be used in place of the manipulatives. RESEARCH John Van De Walle (2006) tells teachers that although students will not see concepts simply by seeing or by handling mathematical models, these various tools can help them learn important mathematical ideas (p. 8). How can you use base-ten blocks to read and write whole numbers? Answers may vary. Base-ten blocks can help represent and organize numbers in terms of units, tens, and hundreds; etc. How can you use base-ten blocks to compare and order whole numbers? Answers may vary. Base-ten blocks can help represent and organize numbers in terms of units, tens, and hundreds; it makes it easier to determine each number s value, which makes it easier to compare and/or order; etc. page 8 of 45
Enhanced Instructional Transition Guide / Unit 01: Suggested Duration: 5 days Suggested Day Suggested Instructional Procedures Notes for Teacher 3 Topics: Name, compare, and order whole numbers through the hundred millions using expanded notation and place value charts Explain 1 Students use expanded notation and place value charts to name, compare, and order whole numbers through the hundred millions. Instructional Procedures: 1. Prior to instruction create a class resource: Digit Cards for every 2 students by copying on cardstock, cutting apart, laminating, and placing in a plastic zip bag. In addition, record the number 2,643,578 in expanded notation on a sentence strip and then fold the strip so that when it is folded (accordion style) only the first digit of each number can be seen. When each end of the strip is pulled-out, the students can see the number in expanded notation. Conversely, when the strip is folded, the students see the standard form of the number. 2. Display the folded sentence strip for the number 2,643,578. Instruct students to chorally read the number. Read the number 2,643,578 aloud, and as each number is said, unfold the sentence strip Spiraling Review ATTACHMENTS Class Resource: Digit Cards (1 set per 2 students) Teacher Resource: Understanding Place Value KEY (1 per teacher) Handout: Understanding Place Value (1 per student) Handout (optional): Blank Place Value Chart (1 per student) Handout (optional): Blank Understanding Place Value Chart (1 per student) Teacher Resource: Comparing and Ordering Whole Numbers Notes (1 per teacher) Handout (optional): Comparing and Ordering Whole Numbers Notes (1 per student) Handout (optional): Connecting the Dots for Comparison Graphic (1 per student) Handout (optional): Creating Movable Comparison Symbols (1 per student) page 9 of 45
Enhanced Instructional Transition Guide / Unit 01: Suggested Duration: 5 days Suggested Day Suggested Instructional Procedures to reveal the expanded notation of the number. Remind students that writing numbers using a number sentence (2,000,000 + 600,000 + 40,000 + 3,000 + 500 + 70 + 8) is called expanded notation and writing numbers in standard form is the way a whole number is usually written (2,643,578). 3. Place students in pairs and distribute a sentence strip to each pair. Instruct student pairs to create a number in the millions, thousands, and units periods and record this number in expanded notation on their sentence strip. Facilitate a class discussion about the numbers created allowing student pairs to read and listen to the various numbers created. Ask: How is it possible to write so many different numbers with just 10 digits: 0 9? Answers may vary. Digits can be arranged in many ways using different place values; etc. What is the difference between a digit and the value of a digit? Answers may vary. A digit is a numeral 0 9, but the value of a digit depends on where it is placed in a number; etc. What does expand mean? Answers may vary. To stretch out; to spread out; etc. What are some things that can be expanded? Answers may vary. Rubber bands, balloons; etc. What does expanded notation mean in our number system? Answers may vary. A way to write numbers that shows the place value of each digit; writing out the numbers so you can see what each place is worth; etc. Explain to students that sometimes expanded notation is also referred to as expanded form and that the key word is expanded. Notes for Teacher Handout: Using the Place Value Chart (1 per student) MATERIALS cardstock (1 sheet per 2 students) scissors (1 per teacher) plastic zip bag (sandwich sized) (1 per 2 students) sentence strips (1 per teacher, 1 per 2 students) index card (optional) (1 per 2 students) brads (optional) (2 per student) die (decahedra) (optional) (1 per 2 students) TEACHER NOTE Some discussion may be needed regarding the meaning of the words standard form and expanded notation. Have students suggest synonyms for standard (normal, regular, usual) and for expanded (stretch out, spread out). What pattern do you see with the zeroes in each addend as you recorded your TEACHER NOTE page 10 of 45
Enhanced Instructional Transition Guide / Unit 01: Suggested Duration: 5 days Suggested Day Suggested Instructional Procedures number in expanded notation? Answers may vary. The number of zeroes decreased or increased by 1 for each place value depending on which way the numbers are read; the number of zeroes changed with each place; etc. What is the purpose of the zeroes in each addend? Answers may vary. The zeroes show the multiples of ten by which the digit in that place is being multiplied; the zeroes are placeholders for that particular place value; etc. What would happen if you did not write the zeroes in the expanded notation of your number? (The value of the number would change.) Did anyone create a number with a zero in one of the places? Answers may vary. 4. Display the number 2,603,578 for the class to see. Ask: How is this number written in words? (two million, six hundred three thousand, five hundred seventy-eight) How is this number written in expanded notation? (2,000,000 + 600,000 + 3,000 + 500 + 70 + 8) 5. Record the expanded notation next to the standard from of the number 2,603,578. Remind students that it is not necessary to write 0 ten thousands in expanded notation even though the zero holds the place on the place value chart and will be used when the value of each digit is written. If the place is not written, it is understood, that the value of that place is 0. Explain to students that when writing the number in standard form, the zero must be written to hold the place. Facilitate a class discussion about the purpose of a zero in a number written in standard form. Notes for Teacher A vocabulary word wall with examples will help students understand the definitions. Allow students to use their own definitions first and then agree on a class definition making connections between the two. TEACHER NOTE Discuss relationships between pairs of words. Numbers are made up of digits ; a digit gets its value from its place ; numbers in expanded notation show the place value of each digit while a number in standard form shows a single digit for each place value. TEACHER NOTE Remind students that numbers are hyphenated beginning with twenty-one through ninety-nine. A good way for students to get a mental picture of these numbers is to emphasize the T sound allowing students to associate the sound with tens (e.g., Thirty-one would be 3 tens (30) and 1 more unit.). page 11 of 45
Enhanced Instructional Transition Guide / Unit 01: Suggested Duration: 5 days Suggested Day Suggested Instructional Procedures Notes for Teacher Ask: What would the number 2,603,578 look like if you left the zero out when writing it in standard form? (2,63,578) Record the number 2,63,578 below the displayed number 2,603,578. What happened to the number when you did not write the zero in the ten thousands place? Answers may vary. The number became 63,000 instead of 603,000; There are not 3 places in the thousands period; etc. Remind students that this is why the zero is referred to as a place holder. The zero in 2,603,578 is holding the ten thousands place. 6. Distribute handout: Understanding Place Value to each student. Instruct students to write each number in standard form, expanded notation, and written form. Allow time for students to complete the handout. Monitor and assess students to check for understanding. Facilitate a class discussion about the activity. Ask: What role does the comma play in naming a large number? Answers may vary. It is used to separate groups of 3 digits; it separates the periods; etc. How can you determine which number is the greatest? Answers may vary. Starting at the millions period and determining the digit with the value; etc. Which number is the greatest? (777,777,777) How is this number written in expanded notation? (700,000,000 + 70,000,000 + 7,000,000 + 700,000 + 70,000 + 7,000 + 700 + 70 +7) State Resources TEXTEAMS: Rethinking Elementary Part I Expanding Numbers may be used to reinforce these concepts or used as an alternative activity. TEACHER NOTE Discuss when reading a number on a place value chart, the number is read from left-to-right. Each time a comma is encountered, the name of the period is used. TEACHER NOTE Some discussion may need to take place regarding the meaning of the word period. Students can brainstorm what they already know about the word which should lead to the mathematical use of the word. TEACHER NOTE Struggling students may need to name each number by period first and read or write the number attaching the period name. page 12 of 45
Enhanced Instructional Transition Guide / Unit 01: Suggested Duration: 5 days Suggested Day Suggested Instructional Procedures How is this number written in words? (seven hundred seventy-seven million, seven hundred seventy-seven thousand, seven hundred seventy-seven) 7. Instruct students to record number 777,777,777 on the back of their handout: Understanding Place Value and then order the remaining numbers from greatest to least. Allow time for students to complete the activity. Monitor and assess students to check for understanding. Facilitate a class discussion about the different methods used to order the numbers. Ask: How many digits does the largest number have? (9) the smallest number? (8) How many 9-digit numbers are there? (3) How did you determine which number to write first? Answers may vary. I looked at the value of the digits in the largest place value, selected the largest digit, and ordered accordingly; etc. 8. Display teacher resource: Comparing and Ordering Whole Numbers Notes. Explain to students that when determining how to compare and order numbers, place value can be used. Model the process of how to use place value to compare and order whole numbers. Explain to students that if a set of numbers is lined up in a vertical list or in a place value chart, they can be easily compared by examining the value of the farthest left digit in each number. Demonstrate how to place 2 dots next to the larger number and 1 dot next to the smaller number to create the appropriate comparison symbol. Notes for Teacher TEACHER NOTE Handout (optional): Blank Place Value Chart may be used to help students compare values within numbers. Additionally, handout (optional): Blank Understanding Place Value Chart may be provided as additional practice and can be used with class resource: Digit Cards or a decahedra die to create their own numbers. TEACHER NOTE Individual copies of handout (optional): Comparing and Ordering Whole Numbers Notes may be provided for students as needed. TEACHER NOTE For struggling students, handout (optional): Connect the Dots for Comparison Graphic may be used to assist in the understanding of how to use, read, and write each of the comparison symbols. 9. Instruct students to select 2 numbers from their handout: Understanding Place Value, use TEACHER NOTE For students who are still struggling with how to page 13 of 45
Enhanced Instructional Transition Guide / Unit 01: Suggested Duration: 5 days Suggested Day Suggested Instructional Procedures place value to compare the 2 numbers, and write a comparison statement using symbols and words for the 2 numbers. 10. Place students in pairs. Distribute handout: Using the Place Value Chart to each student and a class resource: Digit Cards to each student pair. 11. Instruct student pairs to shuffle their cards from class resource: Digit Cards, place in a stack, turn over each card at a time, and record the digit in any place within the millions period in the first row of the blank place value chart on their handout: Using the Place Value Chart. In other words, students can place the digit in the one millions, ten millions, or hundred millions place for the first 3 cards drawn. Explain to students that they are to repeat the process for the thousands period, and then the units period until all the cards have been used to create a 9-digit number in the first row of the blank place value chart. Allow time for students to record their number and repeat the process to create 4 additional 9-digit numbers. Facilitate a class discussion about the numbers created. Ask: Notes for Teacher use and/or read the comparison symbols appropriately, handout (optional): Creating Movable Comparison Symbols may be used as a way to make the use of the symbols more hands on. What digit did you place in the hundred millions place? ten millions place? one millions place? Answers may vary. How can using the place value chart be used to compare and order numbers? Answers may vary. The place value chart allows you to organize the digits according to their value, determine the value of the number, and compare that value to the value of another number; etc. 12. Instruct students to use the 5 9-digit numbers created on their handout: Using the Place Value Chart to complete the remainder of the handout as independent practice or homework. page 14 of 45
Enhanced Instructional Transition Guide / Unit 01: Suggested Duration: 5 days Suggested Day Suggested Instructional Procedures Notes for Teacher 4 Topics: Read, write, compare, and order whole numbers through 999,999,999 Elaborate 1 Students read, write, compare, and order whole numbers through the hundred millions in a game format. Instructional Procedures: 1. Facilitate a class discussion to debrief handout: Using the Place Value Chart as a class. Spiraling Review ATTACHMENTS Handout: Stay on Target (1 per student) MATERIALS decahedra die (1 per 2 students ) 2. Place students in pairs. Distribute handout: Stay on Target to each student and a decahedra die to each student pair. 3. Instruct student pairs to take turns rolling the decahedra die, and record the numeral rolled in section A of the target on their handout: Staying on Target. Explain to students that they are to take turns rolling the die until all of section "A" of the target has been completed. Allow time for students to complete the target. 4. Instruct students to complete the questions in section "A" at the bottom of handout: Staying on Target. Allow time for students to complete their responses. Monitor and assess students to check for understanding. Facilitate a class discussion about the activity. Ask: How is the target chart like the place value chart? Answers may vary. It has places 1 s, 10 s; etc. How is the target chart different from the place value chart? Answers may vary. It doesn t have the periods separated; it is round instead of horizontal; etc. page 15 of 45
Enhanced Instructional Transition Guide / Unit 01: Suggested Duration: 5 days Suggested Day Suggested Instructional Procedures Notes for Teacher 5. Instruct students to complete the remainder of handout: Staying on Target by repeating the process of rolling the decahedra die, recording the numeral to complete sections B and C of the target, and answering the questions for each section. Allow time for students to complete the handout. Monitor and assess students to check for understanding. Facilitate a class discussion about student responses from the handout. 5 Evaluate 1 Instructional Procedures: 1. Assess student understanding of related concepts and processes by using the Performance Indicator(s) aligned to this lesson. Performance Indicator(s): ATTACHMENTS Teacher Resource (optional): Population Place Value KEY (1 per teacher) Handout (optional): Population Place Value PI (1 per student) MATERIALS page 16 of 45
Enhanced Instructional Transition Guide / Unit 01: Suggested Duration: 5 days Suggested Day Suggested Instructional Procedures Notes for Teacher Grade4 Unit01 PI01 Identify a real-life situation that involves five numbers through the hundred millions place (e.g., the population of five states, the distance between the Sun and five other planets in the solar system in kilometers, etc.). Use technology to determine the five numbers that represent the situation, and record them in a table using standard form, expanded notation, and words. Explain in writing how to order the data, and then record two comparative statements using words and symbols to describe the real-life situations. Sample Performance Indicator: computer with Internet access (1 per student) TEACHER NOTE If time permits, in addition to the Performance Indicator assessment, handout (optional): Population Place Value PI may be used as an additional assessment tool. Consider including populations of countries (for hundred millions). Use technology to determine, in kilometers, the distance between the Sun and five other planets in the solar system. The data identified should be represented using standard form, expanded notation, and words. Order the data in the table, and then write two comparative statements, using words and symbols, related to the real-life situation and a brief description of how the order was determined. Standard(s): 4.1A, 4.14A, 4.14C, 4.14D, 4.15A, 4.15B ELPS ELPS.c.1H, ELPS.c.4J, ELPS.c.5G 03/26/13 page 17 of 45
If You Made A Million Concept Map Use the empty boxes to write a description or draw a picture of the main ideas or important details in If You Made a Million. If You Made a Million Examples of $1,000,000 Examples of $100,000 Examples of $10,000 2012, TESCCC 05/17/12 page 1 of 1
Place Value Prompt Activity Teacher Notes Write the number 500,000 on the board or overhead and have the students make a list of things that could describe 500,000. Sample example: 500,000 could be the number of hairs on a gorilla. Students can do this in math journals individually, or scribe a group response. Discuss/list results as a class. Use a student example that might not be correct or ask students if a gorilla could weigh 500,000 lbs. Sample Answer: No, but 500,000 lbs could be the weight of..). Leave this sentence unfinished and allow students to come up with their own completion. Write on the board or overhead: could not be the number of, but it could be the number of. Have students suggest some large numbers (hundred thousands to millions) and list these on the board. Have students pick a number from the list and use it to begin the sentence written on the board/overhead. Students are to then complete the sentence and illustrate what they wrote. Example: Discuss results/drawings in groups and as a class. Some of what the students write may be called into question by others in the class. This is an opportunity for students to learn from one another about numbers. As the class discussion evolves, prompt students to explain their reasoning. Possible prompts should include: Is it possible? How do you know? What if.? Talk with the people at your table and see what you come up with. 2012, TESCCC 03/21/13 page 1 of 1
Base-Ten Block Model Cards 2012, TESCCC 05/17/12 page 1 of 4
Base-Ten Block Model Cards 2012, TESCCC 05/17/12 page 2 of 4
Base-Ten Block Model Cards 2012, TESCCC 05/17/12 page 3 of 4
Base-Ten Block Model Cards 2012, TESCCC 05/17/12 page 4 of 4
Paper Hundred Centimeter Grids 2012, TESCCC 05/17/12 page 1 of 1
Paper Thousand Block Directions Follow these directions and the pictures to make a thousands-block out of paper. (1) Take six centimeter hundreds grids and place them on your desk. Tape them together as shown. (2) Fold up the grids to make a box shape. Be sure the grid lines are on the outside of the cube. Tape the entire box together. 2012, TESCCC 05/17/12 page 1 of 1
Digit Cards 0 1 2 3 4 5 6 7 8 9 2012, TESCCC 03/02/12 page 1 of 1
Understanding Place Value KEY Complete the chart to find the value of each number. 1. Millions Thousands Units,,,,,,,, Hundreds Tens Ones Hundreds Tens Ones Hundreds Tens Ones Digit 7 7 7 7 7 7 7 7 7 Standard Form 777,777,777 Expanded Notation 700,000,000 + 70,000,000 + 7,000,000 + 700,000 + 70,000 + 7,000 + 700 + 70 +7 Word Form Seven hundred seventy-seven million, seven hundred seventy-seven thousand, seven hundred seventy-seven 2. Millions Thousands Units Hundreds Tens Ones Hundreds Tens Ones Hundreds Tens Ones Digit 6 0 4 5 1 1 0 1 3 Standard Form 604,511,013 Expanded Notation 600,000,000 + 4,000,000 + 500,000 + 10,000 + 1,000 + 10 +3 Word Form Six hundred four million, five hundred eleven thousand, thirteen 3. Millions Thousands Units Hundreds Tens Ones Hundreds Tens Ones Hundreds Tens Ones Digit 8 9 3 6 5 0 0 2 Standard Form 89,365,002 Expanded Notation 80,000,000 + 9,000,000 + 300,000 + 60,000 + 5,000 + 2 Word Form Eighty-nine million, three hundred sixty-five thousand, two 4. Millions Thousands Units Hundreds Tens Ones Hundreds Tens Ones Hundreds Tens Ones Digit 5 8 1 0 2 3 6 0 7 Standard Form 581,023,607 Expanded Notation 500,000,000 + 80,000,000 + 1,000,000 + 20,000 + 3,000 + 600 + 7 Word Form Five hundred eighty-one million, twenty-three thousand, six hundred seven 2012, TESCCC 05/17/12 page 1 of 1
Understanding Place Value Complete the chart to find the value of each number. 1. Millions Thousands Units,,,,,,,, Hundreds Tens Ones Hundreds Tens Ones Hundreds Tens Ones Digit 7 7 7 7 7 7 7 7 7 Standard Form Expanded Notation Word Form 2. Millions Thousands Units Hundreds Tens Ones Hundreds Tens Ones Hundreds Tens Ones Digit 6 0 4 5 1 1 0 1 3 Standard Form Expanded Notation Word Form 3. Millions Thousands Units Hundreds Tens Ones Hundreds Tens Ones Hundreds Tens Ones Digit 8 9 3 6 5 0 0 2 Standard Form Expanded Notation Word Form 4. Millions Thousands Units Hundreds Tens Ones Hundreds Tens Ones Hundreds Tens Ones Digit 5 8 1 0 2 3 6 0 7 Standard Form Expanded Notation Word Form 2012, TESCCC 05/17/12 page 1 of 1
Blank Place Value Chart,, Millions Thousands Units Hundreds Tens Ones Hundreds Tens Ones Hundreds Tens Ones 2012, TESCCC 05/17/12 page 1 of 1
Blank Understanding Place Value Complete the chart to find the value of each number. Millions Thousands Units Hundreds Tens Ones Hundreds Tens Ones Hundreds Tens Ones 1. Digit Standard Form Expanded Notation Word Form 2. Digit Standard Form Expanded Notation Word Form 3. Digit Standard Form Expanded Notation Word Form 4. Digit Standard Form Expanded Notation Word Form Millions Thousands Units Hundreds Tens Ones Hundreds Tens Ones Hundreds Tens Ones Millions Thousands Units Hundreds Tens Ones Hundreds Tens Ones Hundreds Tens Ones Millions Thousands Units Hundreds Tens Ones Hundreds Tens Ones Hundreds Tens Ones 2012, TESCCC 05/17/12 page 1 of 1
Comparing and Ordering Whole Numbers - Notes Comparing Two Numbers Compare 250,812 and 251,420 1. Draw a Place Value Chart 2. Line up the numbers in the chart 3. Start comparing from left to right Compare the numbers using comparison symbols: Ordering Many Numbers OR Put these numbers in order from greatest to least: 250,812 251,420 250,120 1. Draw a Place Value Chart 2. Line up the numbers in the chart 3. Start comparing from left to right. Place the order number out to the side of each row as a guide. H Th 2 2 2 T Th Th H T O 5 0 8 1 2 5 1 4 2 0 5 0 1 2 0 2 1 3 4. Pay attention to ordering: Least Greatest OR Greatest Least All of the numbers have 2 hundred thousands. All of the numbers have 5 ten thousands. 1 thousand is greater than 0 thousands, so the middle number is the greatest. Then, continue comparing the other 2 numbers. 8 hundred is greater than 1 hundred, so the top number is the second greatest number. Answer: 251,420 250,812 250,120 2012, TESCCC 05/17/12 page 1 of 1
Connecting the Dots for Comparison Graphic Place two dots next to the larger number and 1 dot next to the smaller number. OR Connect the dots as shown. OR Read the comparison statement. 324 is greater than 271 OR 271 is less than 324 Remember 2012, TESCCC 05/17/12 page 1 of 1
Creating Movable Comparison Symbols 1. Cut 2 small half-inch strips from the short side of a 3 x 5 index card. CUT CUT 2. Draw a thick black line down the center of each small strip, and then cut the ends of the strips to form points as shown below. CUT CUT CUT CUT 3. Fold each strip in half and then reopen to find the middle points. Push a brad through the midpoint of each strip as shown below. brad brad 4. Push the brads in the strips through the dots on the Movable Comparison Symbol Template, and fasten each brad down as shown below. brad brad 5. Move the strips to form whichever comparison symbol is needed based on the numbers placed on each side of the template. See an example below. brad brad Adapted from Region12 Education Service Center, Jazz Up math with Journaling, Greater-Less Than Greedy Gator (2009). 2012, TESCCC 03/25/13 page 1 of 2
Movable Comparison Symbol Template Greater Than ~ Less Than ~ Equal To Place your two numbers on each side of the movable equal sign. Read the numbers from left to right and decide if you should keep the sign showing equal to or change it to show greater than or less than. Record each number sentence you make below. Number Sentence Comparison in Words Adapted from Region12 Education Service Center, Jazz Up math with Journaling, Greater-Less Than Greedy Gator (2009). 2012, TESCCC 03/25/13 page 2 of 2
Using the Place Value Chart MILLIONS THOUSANDS UNITS hundred millions ten millions millions hundred thousands ten thousands thousands,, hundreds tens ones 1. 2. 3. 4. 5. Write each number you created above in words. 1. 2. 3. 4. 5. Write each number you created above in expanded notation. 1. 2. 3. 4. 5. 2012, TESCCC 05/17/12 page 1 of 2
Using the Place Value Chart For the first number you created which digit is in the - 1. ones place? 2. hundreds place? 3. ten thousands place? 4. hundred thousands place? 5. millions place? For the second number you created which digit is in the - 1. ones place? 2. hundreds place? 3. ten thousands place? 4. hundred thousands place? 5. millions place? Order each number you created from least to greatest and explain your reasoning. 2012, TESCCC 05/17/12 page 2 of 2
Stay on Target! Roll the decahedra die. Write the number in a space in section A. Pass the die to your partner. Take turns rolling the die until all of section A has been completed. Then, answer the questions below for section A. Follow the same procedure the sections B and C. B A C 1 10 100 1000 10,000 100,000 1,000,000 10,000,000 100,000,000 Section A: (1) Write your number in standard form: (2) Write your number in expanded notation: (3) Write your number in words: (4) Compare your number with your partner s. Whose is greatest? How do you know? (5) Use a comparison symbol and words to show how the two numbers from (4) compare. Number Sentence Comparison in Words 2012, TESCCC 05/17/12 page 1 of 3
Section B: Stay on Target! (1) Write your number in standard form: (2) Write your number in expanded notation: (3) Write your number in words: (4) Compare your number with your partner s. Whose is greatest? How do you know? (5) Use a comparison symbol and words to show how the two numbers from (4) compare. Number Sentence Comparison in Words Section C: (1) Write your number in standard form: (2) Write your number in expanded notation: (3) Write your number in words: (4) Compare your number with your partner s. Whose is greatest? How do you know? (5) Use a comparison symbol and words to show how the two numbers from (4) compare. Number Sentence Comparison in Words 2012, TESCCC 05/17/12 page 2 of 3
Stay on Target! Conclusion: List and order all the numbers created by you, and all of your partners, in order from greatest to least. Explain your reasoning. 2012, TESCCC 05/17/12 page 3 of 3
Population Place Value KEY This table shows the population of some of the largest states in the U.S. according to the estimated 2005 census. State Population Texas 22,859,968 Michigan 10,120,860 California 36,132,147 Florida 17,789,864 Alabama 4,557,808 Ohio 11,464,042 New York 19,254,630 Illinois 12,763,371 Use the table below to write each state s population in expanded notation and then in word form. State Expanded Notation Word Form Texas 20,000,000 + 2,000,000 + 800,000 + 50,000 + 9,000 + 900 + 60 + 8 Twenty-two million, eight hundred fifty-nine thousand, nine hundred sixty-eight Michigan 10,000,000 + 100,000 + 20,000 + 800 + 60 Ten million, one hundred twenty thousand, eight hundred sixty California 30,000,000 + 6,000,000 + 100,000 + 30,000 + 2,000 + 100 + 40 + 7 Thirty-six million, one hundred thirty-two thousand,one hundred forty-seven Florida 17,000,000 + 700,000 + 80,000 + 9,000 + 800 + 60 + 4 Alabama 4,000,000 + 500,000 + 50,000 + 7,000 + 800 + 8 Seventeen million, seven hundred eighty-nine thousand, eight hundred sixty-four Four million, five hundred fifty-seven thousand, eight hundred eight 2012, TESCCC 05/17/12 page 1 of 3
Population Place Value KEY State Expanded Notation Word Form Ohio 11,000,000 + 400,000 + 60,000 + 4,000 + 40 + 2 Eleven million, four hundred sixty-four thousand, fortytwo New York 19,000,000 + 200,000 + 50,000 + 4,000 + 600 + 30 Nineteen million, two hundred fifty-four thousand, six hundred thirty Illinois 12,000,000 + 700,000 + 60,000 + 3,000 + 300 + 70 + 1 Twelve million, seven hundred sixty-three thousand, three hundred, seventy-one List these state s populations in order from greatest to least. State Population 1. California 36,132,147 2. Texas 22,859,968 3. New York 19,254,630 4. Florida 17,789,864 5. Illinois 12,763,371 6. Ohio 11,464,042 7. Michigan 10,120,860 8. Alabama 4,557,808 Explain the process of how you determined the population order from greatest to least. Answers may vary but should include using a place value chart or place value to determine the correct order. 2012, TESCCC 05/17/12 page 2 of 3
Population Place Value KEY Use a comparison symbol and words to describe Florida s population and New York s population. Number Sentence Comparison in Words 17,789,864 19,254,630 19,254,630 17,789,864 OR Seventeen million, seven hundred eighty-nine thousand, eight hundred sixty-four is less than nineteen million, two hundred fifty-four thousand, six hundred thirty Nineteen million, two hundred fifty-four thousand, six hundred thirty is greater than seventeen million, seven hundred eighty-nine thousand, eight hundred sixty-four Use a comparison symbol and words to describe Ohio s population and Michigan s population. Number Sentence Comparison in Words 10,120,860 11,464,042 11,464,042 10,120,860 OR Ten million, one hundred twenty thousand, eight hundred sixty is less than eleven million, four hundred sixty-four thousand, forty-two Eleven million, four hundred sixty-four thousand, fortytwo is greater than ten million, one hundred twenty thousand, eight hundred sixty 2012, TESCCC 05/17/12 page 3 of 3
Population Place Value PI This table shows the population of some of the largest states in the U.S. according to the estimated 2005 census. State Population Texas 22,859,968 Michigan 10,120,860 California 36,132,147 Florida 17,789,864 Alabama 4,557,808 Ohio 11,464,042 New York 19,254,630 Illinois 12,763,371 Use the table below to write each state s population in expanded notation and then in word form. State Expanded Notation Word Form Texas Michigan California Florida Alabama 2012, TESCCC 05/17/12 page 1 of 3
Population Place Value PI State Expanded Notation Word Form Ohio New York Illinois List these state s populations in order from greatest to least. 1. 2. 3. 4. 5. 6. 7. 8. State Population Explain your process for determining the population order from greatest to least. 2012, TESCCC 05/17/12 page 2 of 3
Population Place Value PI Use a comparison symbol and words to describe Florida s population and New York s population. Number Sentence Comparison in Words Use a comparison symbol and words to describe Ohio s population and Michigan s population. Number Sentence Comparison in Words 2012, TESCCC 05/17/12 page 3 of 3