9 weeks
In this unit students will:
- Understand the value placed on the digits within a three-digit number
- Recognize that a hundred is created from ten groups of ten
- Use skip counting strategies to skip count by 5s, 10s, and 100s within 1,000
- Represent numbers to 1,000 by using numbers, number names, and expanded form
- Compare two-digit number using >, =, <
- Cultivate an understanding of how addition and subtraction affect quantities and are related to each other
- Will reinforce the multiple meanings for addition (combine, join, and count on) and subtraction (take away, remove, count back, and compare)
- Further develop their understanding of the relationships between addition and subtraction
- Count with pennies, nickels, and dimes.
- Represent a money amount with words or digits and symbols (either cent or dollar signs).
- Represent and interpret data in picture and bar graphs.
- Use information from a bar graph to solve addition and subtraction equations.
Unit 1 Overview video Parent Letter (Spanish) Parent Standards Clarification Number Talks Vocabulary Cards Prerequisite Skills Assessment Sample Post Assessment Student Friendly Standards Concept Map
Topic 1: Place Value
Big Ideas/Enduring Understandings:
- Use models, diagrams, and number sentences to represent numbers within 1,000.
- Write numbers in expanded form and standard form using words and numerals.
- Identify a digit’s place and value when given a number within 1,000.
- Compare two 3-digit numbers with appropriate symbols (<, =, and >).
- Understand and explain the difference between place and value.
- The value of a digit depends upon its place in a number.
- Understand the digit zero and what it represents in a given number.
- Numbers can be represented in many ways, such as with base ten blocks, words, pictures, number lines, and expanded form.
- Place value determines which numbers are larger or smaller than other numbers.
- Explain how place value helps us solve problems.
- Why should we understand place value?
- What is the difference between place and value?
- How does place value help us solve problems?
- How does the value of a digit change when its position in a number changes?
- What does “0” represent in a number?
Content Standards
Content standards are interwoven and should be addressed throughout the year in as many different units and activities as possible in order to emphasize the natural connections that exist among mathematical topics.
MGSE2.NBT.1Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
a. 100 can be thought of as a bundle of ten tens — called a “hundred.”
b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
MGSE2.NBT.2Count within 1000; skip-count by 5’s, 10’s, and 100’s.
MGSE2.NBT.3Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
MGSE2.NBT.4Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.
Vertical Articulation
Kindergarten Place Value Standard
Work with numbers 11-19 to gain foundations for place value.
MGSEK.NBT.1 Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. / First Grade Place Value Standard
Understand place value
MGSE1.NBT.1 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:
- 10 can be thought of as a bundle on ten ones- called a “ten”.
- The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
- The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones)
Use place value understanding and properties of operations to perform multi-digit arithmetic.
MGSE3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 or 100.
Instructional Strategies
The understanding that 100 is equal to 10 groups of ten and 100 ones, is critical to understanding of place value. Using proportional models like base-ten blocks or bundles of tens along with place-value mats create connections between the physical and symbolic representations of a number and their magnitude. These models can build a stronger understanding when comparing two quantities and identifying the value of each place value position.
Van de Walle (p.127) notes that “the models that most clearly reflect the relationship of ones, tens, and hundreds are those for which the ten can actually be made or grouped from single pieces.” Groupable base ten models can be made from beans and cups, bundled straws or craft sticks, unifix cubes, etc. If children are struggling with base ten blocks, you may consider using number cubes or inexpensive homemade manipulatives to help develop their understanding.
Groupable Base Ten Models
/ /
Bean Counters and Cups:
Ten single cups are placed in a portion cup. To make a hundreds put ten cups in a larger tub. / Bundles of Sticks:
Use craft sticks or coffee stirers. To make a hundred, put ten bundles into a larger bunch held together with a rubber band. / Cubes:
Ten single cubes form a bar of ten.
To make a hundred put ten bars on cardboard backing
Model three-digit numbers using base-ten blocks in multiple ways. For example, 236 can be 236 ones, or 23 tens and 6 ones, or 2 hundreds, 3 tens and 6 ones, or 20 tens and 36 ones. Use activities and games that have students match different representations of the same quantity.
Provide games and other situations that allow students to practice skip-counting. Students can use nickels, dimes and dollar bills to skip count by 5, 10 and 100. Pictures of the coins and bills can be attached to models familiar to students: a nickel on a five-frame with 5 dots or pennies and a dime on a ten-frame with 10 dots or pennies.
On a number line, have students use a clothespin or marker to identify the number that is ten more than a given number or five more than a given number.
Have students create and compare all the three-digit numbers that can be made using digits from 0 to 9. For instance, using the numbers 1, 3, and 9, students will write the numbers 139, 193, 319, 391, 913 and 931. When students compare the digits in the hundreds place, they should conclude that the two numbers with 9 hundreds would be greater than the numbers showing 1 hundred or 3 hundreds. When two numbers have the same digit in the hundreds place, students need to compare their digits in the tens place to determine which number is larger.
NBT.1
This standard calls for students to work on decomposing numbers by place value. Students should have ample experiences with concrete materials and pictorial representations examining that numbers all numbers between 100 and 999 can be decomposed into hundreds, tens, and ones and then into several different combinations.
Example:
285 can be shown as 2 hundreds, 8 tens, and 5 ones but it is also correct to show as 28 tens and 5 ones OR 1 hundred, 18 tens, and 5 ones and so on.
Interpret the value of a digit (1-9 and 0) in a multi-digit numeral by its position within the number with models, words, and numerals.
Use 10 as a benchmark number to compose and decompose when adding and subtracting whole numbers.
NBT.1a calls for students to extend their work from 1st Grade by exploring a hundred as a unit (or bundle) of ten tens.
NBT.1bbuilds on the work of 2.NBT.2a. Students should explore the idea that numbers such as 100, 200, 300, etc., are groups of hundreds that have no tens or ones. Students can represent this with place value (base 10) blocks.
Understanding that 10 ones make one ten and that 10 tens make one hundred is fundamental to students’ mathematical development.
Students need multiple opportunities counting and “bundling” groups of tens in first grade. In second grade, students build on their understanding by making bundles of 100s with or without leftovers using base ten blocks, cubes in towers of 10, ten frames, etc. This emphasis on bundling hundreds will support students’ discovery of place value patterns.
As students are representing the various amounts, it is important that emphasis is placed on the language associated with the quantity.
For example, 243 can be expressed in multiple wayssuch as 2 groups of hundred, 4 groups of ten and 3 ones, as well as 24 tens and 3 ones.
When students read numbers, they should read in standard form as well as using place value concepts. For example, 243 should be read as “two hundred forty-three” as well as two hundreds, 4 tens, 3 ones.
A document camera or interactive whiteboard can also be used to demonstrate “bundling” of objects. This gives students the opportunity to communicate their thinking.
NBT.2
The standard calls for students to count within 1,000. This means that students are expected to “count on” from any number and say the next few numbers that come afterwards.
Understand that counting by 2s, 5s and 10s is counting groups of items by that amount.
Example:
What are the next 3 numbers after 498? 499, 500, 501.
When you count back from 201, what are the first 3 numbers that you say? 200, 199, 198.
This standard also introduces skip counting by 5s and 100s. Students are introduced to skip counting by 10s in First Grade.
Students should explore the patterns of numbers when they skip count. When students skip count by 5s, the ones digit alternates between 5 and 0. When students skip count by 100s, the hundreds digit is the only digit that changes, and it increases by one number.
Students need many opportunities counting, up to 1000, from different starting points (Example: Skip count by 3s starting at 10). They should also have many experiences skip counting by 5s, 10s, and 100s to develop the concept of place value.
Examples:
The use of the 100s chart may be helpful for students to identify the counting patterns.
The use of money (nickels, dimes, dollars) or base ten blocks may be helpful visual cues.
The use of an interactive whiteboard may also be used to develop counting skills.
The ultimate goal for second graders is to be able to count in multiple ways with no visual support.
NBT.3
This standard calls for students to read, write and represent a number of objects with a written numeral (number form or standard form). These representations can include place value (base 10) blocks, pictorial representations or other concrete materials. Remember that when reading and writing whole numbers, the word “and” should notbe used between any of the whole-number words – “and” represents the decimal point.
Example:
235 is written and spoken as two hundred thirty-five.
Students need many opportunities reading and writing numerals in multiple ways.
Examples:
Base-ten numerals 637 (standard form)
Number names six hundred thirty seven (written form)
Expanded form 600 + 30 + 7 (expanded notation)
Short word form can also be used - 6 hundreds + 3 tens + 7 ones
When students say the expanded form, it may sound like this: “6 hundreds plus 3 tens plus 7 ones” OR 600 plus 30 plus 7.”
NBT.4
This standard builds on the work of 2.NBT.1 and 2.NBT.3by having students compare two numbers by examining the amount of hundreds, tens and ones in each number.
Students are introduced to the symbols greater than (>), less than (<) and equal to (=) in First Grade, and use them in Second Grade with numbers within 1,000.
Students should have ample experiences communicating their comparisons in wordsbefore using only symbols in this standard.
Example:452 _____ 455
Students may use models, number lines, base ten blocks, interactive whiteboards, document cameras, written words, and/or spoken words that represent two three-digit numbers.
To compare, students apply their understanding of place value. They first attend to the numeral in the hundreds place, then the numeral in tens place, then, if necessary, to the numeral in the ones place.
Comparative language includes but is not limited to: more than, less than, greater than, most, greatest, least, same as, equal to and not equal to. Students use the appropriate symbols to record the comparisons.
Engage NY Lessons are included in the activity file. Coming Soon…
Common Misconceptions
Some students may not move beyond thinking of the number 358 as 300 ones plus 50 ones plus 8 ones to the concept of 8 singles, 5 bundles of 10 singles or tens, and 3 bundles of 10 tens or hundreds. Use base-ten blocks to model the collecting of 10 ones (singles) to make a ten (a rod) or 10 tens to make a hundred (a flat). It is important that students connect a group of 10 ones with the word ten and a group of 10 tens with the word hundred.
- When counting tens and ones (or hundreds, tens, and ones), the student misapplies the procedure for counting on and treats tens and ones (or hundreds, tens, and ones) as separate numbers. When asked to count collections of bundled tens and ones such as 32, student counts 10, 20, 30, 1, 2, instead of 10, 20, 30, 31, 32.
- The student has alternative conception of multi-digit numbers and sees them as numbers independent of place value. Student reads the number 32 as “thirty-two” and can count out 32 objects to demonstrate the value of the number, but when asked to write the number in expanded form, he/she writes “3 + 2.” Student reads the number 32 as “thirty-two” and can count out 32 objects to demonstrate the value of the number, but when asked the value of the digits in the number, he/she responds that the values are “3” and “2.”
- The student recognizes simple multi-digit numbers, such as thirty (30) or 400 (four hundred),but she does not understand that the position of a digit determines its value. Student mistakes the numeral 306 for thirty-six. Student writes 4008 when asked to record four hundred eight.
- The student misapplies the rule for reading numbers from left to right. Student reads 81 as eighteen. The teen numbers often cause this difficulty.
- The student orders numbers based on the value of the digits, instead of place value. 69 > 102, because 6 and 9 are bigger than 1 and 2.
Differentiation
Increase the Rigor
NBT.1
- Represent the number 592 two different ways using base ten blocks (or another base ten manipulative).
- Does this model represent the number 321? Why or why not? Can you show 321 a different way?
- How many bundles of tens are equivalent to 500? How do you know? Show me.
- Are 7 tens and 5 ones the same as 5 tens and 7 ones? Why or why not? Explain your thinking.
- A number is less than 200, the ones digit is 2 more than the hundreds digit, the tens digit is less than the ones digit and two of the digits are the same. What is the number? (113)
- Sam created a number using 9 base ten blocks. What different numbers could Sam have made?
- How many different numbers can you make between 700 and 750 with a 6 in the tens place? With a 6 in the ones place?
- How are 867 and 464 alike and how are they different?
- If you count by 5’s, and start at 27, what other numbers will be in the pattern?
- If you start at 438 and count by 5s and then start at 438 and count by 10s, what are three numbers that will come up in each pattern? (10s: 438, 448, 458, 468, 478) (5s: 438, 443, 448, 453, 458, 463, 468, 473, 478)
- Starting at 100, what are all the numbers you can skip count by to get to 150? Give examples to support your answer.
- If you start at 17 and count by 10s, will you land on 100? Why or why not?
- What patterns do you see in the ones, tens, and hundreds place when skip counting by 5s? 10s? 100s?
- Summer started on 205. She counted by 100s. Is 808 in her pattern? Explain how you know.
- Write 3 numbers where the digit in the tens place is 2 more than the ones place.
- Write the expanded form for a number that is 100 more than 546.
- List all the different numbers you can make between 400 and 450 that have a 2 in the tens place? With a 2 in the ones place?
- Using the digits 8, 3, and 7, make the largest possible number. Make the smallest possible number.
- A two-digit number has more ones than tens. What could the number be? Name five possibilities.
- Summer and Tara are comparing numbers. Summer wrote 59 and Tara wrote 112. Summer says you start at left when comparing numbers, so she says her number is largest because 5>1. Tara says her number is largest because it has more digits. Who is correct and why? Use what you know about place value to explain your answer.
- Using the digits 4, 6, and 2, create three different three-digit numbers and then order them greatest to least.
- Write three numbers that are even and greater than 300. Write three numbers that are odd and less than 300.
- Sue and Julie each have a 3-digit number that contains the digits 2, 8, and 6. Sue’s number is larger. What could Sue and Julie’s numbers be? What are two other numbers they could be?
- 432 > 423 even though each number has the same digits. Using place value vocabulary, explain why this is true.
Evidence of Learning
By completion of this lesson, students will be able to:
- Use models, diagrams, and number sentences to represent numbers within 1,000.
- Write numbers in expanded form and standard form using words and numerals.
- Identify a digit’s place and value when given a number within 1,000.
- Compare two 3-digit numbers with appropriate symbols (<, =, and >).
- Understand the difference between place and value.
Elementary Formative Assessment Lesson: MGSE2.NBT.1What's The Value of the Place? pg.38
Shared Assessments: See the formative assessment folder for Topic 1.
Adopted Resources
My Math:
Chapter 5: Place Value to 1,000
5.1 Hundreds
5.2 Hundreds
5.3 Place Value to 1,000
5.4 Problem Solving
5.5 Read and Write Numbers to 1,000
5.6 Count by 5’s, 10s, and 100s
5.7 Compare Numbers to 1,000
*These lessons are not to be completed in consecutive days as it is way too much material. They are designed to help support you as you teach your standards. / Adopted Online Resources
Teacher User ID: ccsde0(enumber)
Password: cobbmath1
Student User ID: ccsd(student ID)
Password: cobbmath1
User: Cobb Email
Password: cobbmath
Suggested Exemplars:
- Flowers for the Hallway (NBT.2)
- Pets (NBT.2)
- Collecting Shells (NBT.4)
- Counting Corners (NBT.4)
- Dinosaur Models (NBT.4)
- Eating Apples (NBT.4)
- Picking Up Shapes (NBT.4)
Chapter 3: Place Value
3.1 Estimating and Counting Larger Numbers
3.2 Grouping by Tens and Hundreds
3.3 Representing Two-Digit Numbers
3.4 Representing Three-Digit Numbers
3.6 Using Place Value to Compare
3.7 Connecting Numbers and Words
3.8 Working with Hundreds, Tens and Ones
3.9 Problem Solving Strategy
Additional Web Resources
K-5 Math Teaching Resources
NBT.1
Make Ten Bundles
Base Ten Concentration (ver. 2)
NBT.2
Counting Collections
Count by Fives (ver.4)
NBT.3
Make Six Numbers
Roll 3 Digits
Numeral Writing Barrier Game
NBT.4
Comparing 3-Digit Numbers
Place Value Challenge (ver.1)
Illustrative Mathematics
NBT.1
Boxes and Cartons of Pencils
Bundling and Unbundling
Counting Stamps
Largest Number Game
Looking at Numbers Every Which Way (also incorporates standard NBT.3)
Making 124
One, Ten, and One Hundred More and Less
Regrouping
Ten $10s make $100
Three Composing/Decomposing Problems
Party Favors (NBT.1a)
NBT.2
Saving Money (also incorporates standards OA.1 and NBT.5)
NBT.4
Ordering 3-Digit Numbers
Comparisons 1
Number Line Comparisons
Digits 2-5-7
Comparisons 2
Using Pictures to Explain Number Comparisons
Mathematics TEKS Toolkit
Estimation 180
Greg Tang
For additional assistance with this unit, please watch the unit webinar
Suggested Manipulatives
base ten blocks
place value mat
number line
hundred chart
thousand chart
Expanda-numbers / Vocabulary
base tens
hundred
thousand
place value
expanded form
greater than >
less than < / Suggested Literature
A Fair Bear Share
17 Kings and 42 Elephants
The Kings Commissioners
One Hundred Hungry Ants
How Many Snails?
A Counting Book
My Little Sister Ate One Hare
Five Little Monkeys
Frog in the Bog
Count on Pablo
Videos
SEDL NBT.4
Task Descriptions
Scaffolding Task / Task that build up to the learning task.
Constructing Task / Task in which students are constructing understanding through deep/rich contextualized problem solving
Practice Task / Task that provide students opportunities to practice skills and concepts.
Culminating Task / Task designed to require students to use several concepts learned during the unit to answer a new or unique situation.
Formative Assessment Lesson (FAL) / Lessons that support teachers in formative assessment which both reveal and develop students’ understanding of key mathematical ideas and applications.
3-Act Task / Whole-group mathematical task consisting of 3 distinct parts: an engaging and perplexing Act One, an information and solution seeking Act Two, and a solution discussion and solution revealing Act Three.
State Tasks