Grade Four - Session 1 Number and Operations: Place Value
Participant Packet Mathematics – Grade Level Assessments and Content Expectations Developers
M-GLAnCE Project Directors
Debbie Ferry Carol Nowakowski Marie Copeland Macomb ISD Retired Warren Consolidated Mathematics Consultant Mathematics Consultant Macomb MSTC K-4 Project Coordinator 5-8 Project Coordinator 2004 Project Contributors
David Andrews William Ashton Lynn Bieszki Chippewa Valley Schools Fraser Public Schools Chippewa Valley Schools
Sharon Chriss Kimberly DeShon Barbara Diliegghio Romeo Schools Anchor Bay School District Retired, Math Consultant
Kimberly Dolan Jodi Giraud Julie Hessell Anchor Bay School District L’Anse Creuse Schools Romeo Schools
Amy Holloway Barbara Lipinski Linda Mayle Clintondale Schools Anchor Bay School District Romeo Schools
Therese Miekstyn James Navetta Gene Ogden Chippewa Valley Schools Chippewa Valley Schools Anchor Bay School District
Rebecca Phillion Charlene Pitrucelle Shirley Starman Richmond Comm. Schools Anchor Bay School District Van Dyke Public Schools
Ronald Studley Anchor Bay School District
2005 and 2006 Session/Module Developers Carol Nowakowski Deb Barnett Luann Murray Retired, Math Consultant Lake Shore Public Schools Genesee ISD Kathy Albrecht Jo-Anne Schimmelpfenneg Marie Copeland Retired, Math Consultant Retired, Math Consultant Warren Consolidated Terri Faitel Debbie Ferry Trenton Public Schools Macomb ISD Grade 4: Number Notation, Place Value, and Addition/Subtraction of Whole Numbers
N.ME.04.01 N.ME.04.02 N.ME.04.03 Read and write Compose and decompose Understand the magnitude of numbers to 1,000,000; numbers using place numbers up to 1,000,000; relate them to the value to 1,000,000, e.g., recognize the place values of quantities they 25,068 is 2 ten thousands, numbers, and the relationship represent; compare 5 thousands, 0 hundreds, of each place to the place to its and order. 6 tens, and 8 ones. right, e.g., 1,000 is 10 hundreds.
N.FL.04.08 N.FL.04.34 N.FL.04.35 N.FL.04.36 Add and Estimate the Know when approximation Make appropriate subtract answers to is appropriate and use it to estimations and whole calculations check the reasonableness of calculations fluently numbers involving answers; be familiar with with whole numbers fluently. addition and common place value errors using mental math subtraction. in calculations. strategies. Important Tips (Place Value):
In order to understand the base 10 number system, Look for common mistakes: students should explore whole numbers using a variety of 1. The student mistakes 306 for 36. models and contexts. 2. The student reads 81 as 18. Students need the opportunity to discuss new concepts and 3. The student is asked to record 408 and writes relate them to prior knowledge. 4008. By exploring the concept of place value on their own with 4. Using “and” when there is no decimal in the concrete materials, students formulate rules about how a number. digit changes value from one place to the next.
Hanging a place value chart in the classroom is important Understand that magnitude of number is concerned with to helping this information stick with the students. ability to sort things out into specific order. The compactness of a standard written method can hide Everyday life will provide you with a wealth of mathematical principals, e.g. children might use place opportunities to help your children develop their skills in
M-GLAnCE – 4th Grade – Session 1 – Number and Operations: Place Value – Participant Packet Page 3 value when working mentally, but be confused in written this area. work if they do not understand how place value links to A number tells quantity, place tells value. works like renaming (addition with composing) or subtraction with regrouping (subtraction with decomposing). Check frequently for understanding and misunderstanding both verbally and in writing. Use the language of place value when making groupings.
Important Tips (Addition and Subtraction):
Students who simply learn procedures will have only Research suggests that all too often students try to do procedural knowledge. exact computations when asked to estimate, and then Have students decompose numbers in many ways, esp. “round” their result to produce an estimate. composing or decomposing to a higher unit value (i.e. Many young children possess creative number sense 1,000 is 10 hundreds). strategies, but as they grow older and learn formal Left-to-right addition or subtraction may be a more viable algorithms, they lose their informal methods of operating alternative for some children who struggle with with numbers. understanding a traditional right-to-left algorithm. Example: 3 7 + 5 8 8 0 + 1 5 9 5
M-GLAnCE – 4th Grade – Session 1 – Number and Operations: Place Value – Participant Packet Page 4 Instructional Sequence
N.ME.04.03 Understand the magnitude of numbers Composing and Addition Subtraction up to 1,000,000; recognize place decomposing without without value and the relationship of each numbers to 10. carrying. regrouping. place value to the right.
N.ME.04.01 N.ME.04.02 The composition of Read and write numbers to Compose and decompose numbers within 100. 1,000, 000; relate them to numbers using place value the quantities they to 1,000,000. represent. N.FL.04.35 Be familiar with common place value errors in Addition and calculations. subtraction as inverse Composing and operations. decomposing a higher unit value.
Additional and subtraction Addition and Addition and with regrouping of numbers Addition and subtraction with subtraction within 10. subtraction within 20. between 20 and 100. regrouping of large numbers.
N.FL.04.08 Add and subtract whole numbers fluently.
N.FL.04.34 Estimate answers to calculations.
N.FL.04.36 Make appropriate estimations and calculations fluently with whole numbers using mental math strategies.
M-GLAnCE – 4th Grade – Session 1 – Number and Operations: Place Value – Participant Packet Page 5 VOCABULARY/DEFINITIONS/EXAMPLES: Numeral – A symbol or group of symbols that represent a number The symbols "11", "eleven" and "XI" are different numerals, all representing the same number. Number – One of a series of symbols of unique meaning in a fixed order that can be derived by counting. 2, 3, 4, or -7, -6, -5 or 27, 28, 29 or -1, 0, 1 it represents something (you see 2 people walking down a street, you never see a number 2 walking down a street) Number Line – A line used to represent positive numbers, negative numbers, and zero
-----|------|------|------|------|------|------|------|------|------4 -3 -2 -1 0 1 2 3 4
Value – An assigned or calculated numerical quantity (how many). The value of 6 is one more than 5, and one less than 7 Place – A position in a numeral or series (magnitude or size). One, ten, hundred, one thousand, ten thousand, hundred thousand, one million, etc. Place Value – The numerical quantity and position of a number (how many of what size) Million Thousand Ones/Units One Hundred Ten One Hundred Ten One
Period – A group of digits separated by commas in a written number (standard form) The Ones/Units and Thousand and Million Period (one, ten, and hundred in each) Standard Form – A way of writing a number using only digits. 5 or 37 or 290 or 2,431 or 98,574 or 123,456 or 4,782,902 Expanded Form – A way of writing a number as the sum of the values of its digits. 37 = 30 + 7 or 290 = 200 + 90 or 2,431 = 2,000 + 400 + 30 + 1 or 98,574 = 90,000 + 8,000 + 500 + 70 + 4 Ascending Order – Going from the least (smallest) to the largest (greatest) 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 or 26, 34, 53, 71 or 127, 214, 398, 399, 526 Descending Order – Going form the largest (greatest) to the least (smallest) 526, 399, 398, 214, 127 or 71, 53, 34, 26, or 10, 9, 8, 7, 6, 5, 4, 3, 2, 1
M-GLAnCE – 4th Grade – Session 1 – Number and Operations: Place Value – Participant Packet Page 6 Resources
How Much Is a Million? By David M. Schwartz
Becker Bottle, One in a Million, Flinn Scientific, Inc.
Using Concrete Models to Teach Large Number Concepts, pgs. 6-9, Arithmetic Teacher, NCTM, Nov. 1990
The Giant Number, Connections: Grade 4, Creative Publications
Number Sense, Gr. 3-4 and Gr. 4-6, McIntosh, Reys, and Reys
M-GLAnCE – 4th Grade – Session 1 – Number and Operations: Place Value – Participant Packet Page 7 Recognizing 1,000
Build 1,000 in each row by completing the table and filling in a number for the question mark.
Thousands Hundreds Tens Ones
? 60
7 ?
?
8 ? 50
Make your own puzzles by building 1,000. Have other students tell what your question mark stands for.
Thousands Hundreds Tens Ones
Adapted from Connect to the Standards, Fourth Grade, Number and Operation
M-GLAnCE – 4th Grade – Session 1 – Number and Operations: Place Value – Participant Packet Page 8 The Chinese Numeration System The Chinese numeration system has characters that correspond to the numbers zero to nine. Unlike the number system we are used to, the Chinese system also has special characters to represent ten, a hundred, a thousand, ten thousand, as well as other multiples of ten.
0 zero 7 seven 1 one 8 eight 2 two 9 nine 3 three 10 ten
4 four one 100 hundred 5 five one 1000 6 six thousand ten 10000 thousand
The number 75 is written in Chinese using the characters 7, 10, and 5 or . In Chinese you need to say that you have 7 tens first. 7 tens is how 70 is represented. Once you have the tens place in Chinese, you can finish writing the number with the character for 5. Chinese has no character for ones, but a character is used for the other place values. The character for ten is needed. You cannot write 75 as .
How would you write 893? 893 is written in Chinese as 8 hundreds, 9 tens, and 3. This is how 893 is written: .
There is one more rule to writing numbers in Chinese. If a number ends in zeros, you do not need to include the zero character. However, if a zero digit does not end a number you need to include the zero character. The number 890 is written as: (8 hundreds, 9 tens). The number 809 is written as: (8 hundreds, zero, nine). The zero character is included in the number, but you do not need to say 0 tens. Just the 0 character is fine!
The number 1004 is written as: (1 thousands, zero, four). Since 1004 has a zero followed by a non-zero digit, the zero character is used. If a zero digit is followed by one or more zero digits, only one zero character is used.
M-GLAnCE – 4th Grade – Session 1 – Number and Operations: Place Value – Participant Packet Page 9 The Chinese Numeration System - More Samples
1. Number Expanded Form Chinese
1003 1000 + 3 2. 51 50 + 1 3. 33 30 + 3 4. 43035 40000 + 3000 + 30 + 5 5. 5242 5000 + 200 + 40 + 2 6. 41 40 + 1 7. 11727 10000 + 1000 + 700 + 20 + 7 8. 771 700 + 70 + 1 9. 38 30 + 8 10. 1825 1000 + 800 + 20 + 5 11. 1544 1000 + 500 + 40 + 4 12. 30341 30000 + 300 + 40 + 1
M-GLAnCE – 4th Grade – Session 1 – Number and Operations: Place Value – Participant Packet Page 10 Name ______Date ______
Complete the table.
Sample This is only a sample pre-made worksheet. Sign up now!
1. Number Expanded Form Chinese
41 2. 11 10 + 1 3. 54 50 + 4 4. 75 5. 1640 1000 + 600 + 40 6. 9113 7. 19 10 + 9 8. 9. 1401 10. 100 + 40 + 3 11. 70 + 8 12. 3335
M-GLAnCE – 4th Grade – Session 1 – Number and Operations: Place Value – Participant Packet Page 11 Name ______Date ______
Complete the table.
Sample This is only a sample pre-made worksheet. Sign up now!
1. Number Expanded Form Chinese
90 90 2. 14 10 + 4 3. 20 + 3 4. 80 + 6 5. 79098 70000 + 9000 + 90 + 8 6. 8870 7. 85 8. 65458 9. 132 10. 8000 + 70 + 6 11. 20000 + 3000 + 900 + 10 + 6 12.
M-GLAnCE – 4th Grade – Session 1 – Number and Operations: Place Value – Participant Packet Page 12 How Much Is a Billion?
Consider…
The next time you hear a politician use the word “billion” casually, think about whether you want the politician spending your tax money.
A billion is a difficult number to comprehend, but one advertising agency did a good job of putting that figure into perspective in one of its releases.
A billion seconds ago it was 1959.
A billion minutes ago Jesus was alive.
A billion hours ago our ancestors were living in the Stone Age.
A billion days ago no one walked on two feet on earth.
A billion dollars ago was only 8 hours and 20 minutes, at the rate our government spends it.
M-GLAnCE – 4th Grade – Session 1 – Number and Operations: Place Value – Participant Packet Page 13 How Close to 0? Record Sheet Player 1 Player 2 Round 1 10,000 10,000 ─ ─ ______
Round 2 ─ ─ ______
Round 3 ─ ─ ______
Round 4 ─ ─ ______
Round 5 ─ ─ ______
Round 6 ─ ─ ______
Round 7 ─ ─ ______
M-GLAnCE – 4th Grade – Session 1 – Number and Operations: Place Value – Participant Packet Page 14 Mental Math or Paper-Pencil ????
Which of these computations are easy to do in your head? Why?
1. 450 + 50 8. 456 + 789
2. 650 + 150 9. 338 + 467
3. 670 + 99 10. 785 - 500
4. 8,000 + 6,000 11. 9,000 – 4,000
5. 954 – 60 12. 357 – 269
6. 100 – 27 13. 660 + 330
7. 1,000 – 399 14. 870 – 600
Which is the better estimate. Explain your answer.
1. 438 + 327 3. 5,383 + 7,143
over 800 over 10,000 under 800 under 10,000
2. 65,734 + 6,387 4. 71,645 + 5,899 + 6,375
over 70,000 over 90,000 under 70,000 under 90,000
Adapted from Number Sense/Grades 4-6
M-GLAnCE – 4th Grade – Session 1 – Number and Operations: Place Value – Participant Packet Page 15