Resource Overview - Cloud Object Storage | Store ... · This resource may be available in other Quantile ... a digit determines its value. ... how much a digit is “worth” as determined

This resource may be available in other Quantile utilities. For full access to these free utilities, visit www.quantiles.com/tools.aspx.

The Quantile® Framework for Mathematics, developed by educational measurement and research organization MetaMetrics®, comprises more than 500 skills and concepts (called QTaxons) taught from kindergarten through high school. The Quantile Framework depicts the

developmental nature of mathematics and the connections between mathematics content across the strands. By matching a student’s Quantile measure with the Quantile measure of a mathematical skill or concept, you can determine if the student is ready to learn that skill, needs to learn supporting concepts first, or has already learned it. For more information and to use free Quantile utilities, visit www.Quantiles.com.

1000 Park Forty Plaza Drive, Suite 120, Durham, North Carolina 27713

METAMETRICS®, the METAMETRICS® logo and tagline, QUANTILE®, QUANTILE FRAMEWORK® and the QUANTILE® logo are trademarks of MetaMetrics, Inc., and are registered in the United States and abroad. The names of other companies and products mentioned herein may be the trademarks of their respective owners.

Resource Overview

Quantile® Measure: 460Q

Skill or Concept:

Read and write word names for whole numbers from 101 to 999. (QT‐N‐68) Use place value with hundreds. (QT‐N‐71) Relate standard and expanded notation to 3‐ and 4‐digit numbers. (QT‐N‐110) Read, write, and compare whole numbers from 10,000 to less than one million using standard and expanded notation. (QT‐N‐152) Use place value with thousands. (QT‐N‐600)

Excerpted from:

Gourmet Learning 1937 IH 35 North Suite 105 New Braunfels, TX 78130 www.gourmetlearning.com © Gourmet Learning

Gourmet Curriculum Press, Inc.© 1

3rd Grade Number Concepts

Unit 1 – Lesson 1

The student uses place value to communicate about increasingly larger whole numbers in verbal and written form, including money. The student is expected to use place value to read, write (in symbols and words), and describe the value of whole numbers through 999,999.

Study the TEKS . . .

Prior Knowledge

In 2nd grade, the students used place value to 999. They also used symbols <, >, and =, so these symbols should be reinforced. The 2nd grade TEKS do not include writing numbers with written words. Therefore, the extended written form is a new skill in 3rd grade.

Next Steps

In 4th grade, the students will extend their knowledge of place value to the millions and add decimals involving tenths and hundredths. In 5th grade, they will use place value to the billions and decimals to the thousandths.

In third grade . . .

This is an important year for introducing the concept of a comma and relating the comma to a group of numbers. Students will add one comma using thousands, and each consecutive year, they will add another comma (into the millions and billions). Concrete models such as Base Ten Blocks become unmanageable as students investigate numbers reaching 9,999. This makes graphic organizers for place value important. Additionally, in 3rd grade, students must write numbers with words. Communication is the key!

3rd

Grade

Student Expectation: Students will use place value to read, write, and describe the value of whole numbers

Unit 1 – Lesson 1 Number Concepts

Gourmet Curriculum Press, Inc.©2

Focus Activity—Part I

Whole Numbers and Place Value

Teacher note: The object of this game is to guess a specific number, beginning with 3-digit numbers. For the first few rounds of this game, it is suggested that you lead the activity by recording the symbols, either on the overhead or on the board, while the students guess the number. After students display proficiency in the activity, some may enjoy taking a turn leading the game.

Group size: whole class

Materials: example, page 3; blank overhead transparency or board; marker

Before class: Gather necessary materials. You may want to copy the symbols and their meaning from the box below onto the board or overheard for student reference.

Directions:

• The leader will select a three-digit number and write the number on a piece of scratch paper (to verify authenticity at the end of the game).

• Students will try to guess the number by using place value clues and critical-thinking skills.

• The symbols below are the only clues the leader, who selected the number, may use to tell the other players whether the number is correct or incorrect.

• See the example provided on page 3.

Variations:

• This game may be played in pairs or small groups using paper and pencil.

• This game may be revisited throughout the year with larger mystery numbers as students extend their knowledge of place values to 999,999.

• To challenge students, try telling them how many numbers are correct, correct but in the wrong place, or totally wrong—but don’t tell them exactly which numbers.

Symbols:

Student Expectation: Students will deduce mystery numbers using place value clues

This symbol below a given number means the number is used in the mystery number, but it is not currently in the correct place.

This symbol below a given number means the number is not in the mystery number at all.

This symbol below a given number means the number is used in the mystery number and it is in the correct place.

An

C



Focus Activity—Part I—Example


Example:

The teacher chooses the number 431.

The first student to guess says “two hundred ninety-four.” (Have him/her write the digits for that number on the overhead transparency or board.)

The teacher marks it accordingly:

This means that the 4 is a correct number, but it is in the wrong place. The other two digits are not correct at all.

The second student says “four hundred sixteen” and writes the digits for that number under the first set. Discuss how he/she decided on these numbers.

The teacher marks it accordingly: 4 1 6

This means that the 4 is a correct number in the right place. The 1 is a correct number, but it is in the wrong place. The 6 is not correct at all.

The third student says “four hundred and thirty-one” and writes the digits for that number under the second set. Discuss how he/she decided on these numbers.

The teacher marks it accordingly: 4 3 1

This means that the number shown is completely correct.

To verify the number, the teacher reveals the paper on which the mystery number was originally written to the class.

Discuss the steps used to figure out the number before playing another round.

Student Expectation: Students will deduce mystery numbers using place value clues

2 9 4



Focus Activity—Part II


Teacher note: Some students do not realize why we need to use place value. This Focus Activity will help students see the importance of the order of digits and that the place of a digit determines its value.


Materials: 1 number cube (overhead number cube if available); chalk or overhead markers

Before class: Gather materials.

Directions: Use the following Instructional Strategy to guide students.

Ask: How many digits are there? (10. Many will reply 9, since that is the largest single digit number, but we must remember 0.)

Say: Let’s list all the digits. (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

Ask: Does it matter in what order we place them? Why or why not? (It is acceptable if students say “No” at this point. Simply poll the class to get an idea of students’ prior knowledge. This topic will be addressed in-depth later.)

Roll the number cube three times. With each roll, have a student write the number on the chalkboard. There must be three different numbers, so if you roll a repeat, continue to roll until you get a new number.

Say: Write a list of all the possible numbers you can make using all three of these digits. Each digit should only be used once. (Allow a few moments for students to complete this activity.)

Ask: Who was able to create two numbers using these digits? Who created three numbers? Who created the most? (There will be 6 different ways to write the digits to form new numbers without repeating a digit.)

Allow students to take turns listing the numbers on the board or overhead that they have created.

Ask: Does it matter in what order we place digits? Explain. (Students should now understand that it does matter and that 341, for example, is not the same as 413.)Pick two of the numbers listed on the board, and ask if they are the same. Ask the students to explain why or why not.

Say: It is place value that makes the difference. A four in the first position is different from a four in the last position. We are going to use place value to help us determine the value of a number.

Student Expectation: Students will investigate the importance of the order of digits in a number

Questioning Technique

Instructional Strategy

C


Gourmet Curriculum Press, Inc.© 5 ( T )

Initial Instruction—Part I


Other vocabulary words found in this unit:

Definitions:

digit: a symbol of the Arabic numerals 0 - 9 – A digit written in a combination with other digits forms a numeral which represents a number.

place value: how much a digit is “worth” as determined by its position in a number

Base Ten: the decimal numeral system; ten is a base

pictorial representation: visual used to show a number

written representation: words used to show a number

expanded form: the sum of the products of each digit and its place value of a number

standard form: numbers written without operations or exponents

Student Expectation: Students will learn vocabulary for whole numbers and place value

• sixteen• seventeen• eighteen• nineteen• twenty• thirty• forty• fifty• sixty• seventy• eighty• ninety• hundred• thousand

• one• two• three• four• five• six• seven• eight• nine• ten• eleven• twelve• thirteen• fourteen• fifteen

K



Initial Instruction—Part II


Teacher note: This lesson introduces students to vocabulary including place value and Base Ten Blocks. A classroom set of Base Ten Block manipulatives is highly recommended for use with this lesson. Otherwise, it will be necessary to copy pages 6-8 for each student, so they have manipulatives for these activities.


Materials: Direct Questioning, below; Base Ten Block sets; paper copies and transparencies of pages 7-9

Before class: Copy the Base Ten Blocks, pages 7-9, for each student. Copies should be on cardstock and cut out in sets for student’s use. Or, distribute a set of Base Ten Block manipulatives to each student. (Each set should include at least 10 ones, 8 tens, 3 hundreds, and 2 thousands.)

Directions: Follow the Direct Questioning below for each of the following examples.

Ask: What do we mean by “place value”? (List all responses. Continue discussion to solidify meaning.)Say: Looking at each word separately might help us understand this term.Ask: What comes to mind when I say “place”? (Answers will vary - a home, a spot to stand, a way to finish the race. Brainstorm and list ideas on the board or overhead.)Say: Identify characteristics these all have in common. (They are all locations.)Ask: What comes to mind when I say “value”? (Answers will vary - an amount, a total, worth, importance. Brainstorm and list ideas on the board or overhead.)Ask: What do these have in common? (They describe quantities.)Say: So, if we put these descriptions together, then “place value” is a location that determines a digit’s quantity.Place transparency page 7 on the overhead, and continue to question the class. For each of the pictures on pages 7-9, discuss the following two questions.Ask: What does each one of these represent using our Base Ten Blocks? Ask: Is there a reason they chose this picture to represent this number? Why?

One - This one block represents one unit.

Ten - The ten blocks represent ten ones.

Hundred - Because there are ten squares across the rows and ten down each column, this represents 100 altogether.

T h o u s a n d -Because there are ten boxes across, ten down, and ten up each column, this represents 1,000 altogether.

Student Expectation: Students will be introduced to Base Ten Blocks and place value


Direct Questioning

CK

10

1010



Initial Instruction—Part II—Base Ten Blocks




Gourmet Curriculum Press, Inc.©8 ( T )











Initial Instruction—Part III


Teacher note: In this part of the Initial Instruction, students will recognize numbers in various forms and represent numbers using standard form, expanded form, with words, and with Base Ten Blocks.Group size: whole class Materials: Base Ten sets for each student; overhead transparency set of the Base Ten Blocks, pages 7-9; Instructional Strategy, pages 10-13; transparencies, pages 14-15; student chart, page 16; overhead (erasable) markers for studentsBefore class: Make an overhead transparency set of Base Ten Blocks by copying the manipulative pages 6-8 onto colored transparency paper and cutting out the figures. A blank copy of the chart on page 15 has been provided on page 16. Copy page 16 for each student, and laminate the charts.Directions: Use the Instructional Strategy, below and pages 11-13, to guide students.

Place transparency page 14 on the overhead.

Example 1: What numeral does this model represent? (1,367)

Recreate the figure with your overhead Base Ten Blocks.

Ask: Are there any thousands in this number? (Yes - there is one. Have a student come to the overhead and separate the thousand from the rest of the figures. Have the student explain how he/she determined there was one thousand included in the number.)

(Repeat this process for the hundreds, tens, and ones. Separate the blocks on the overhead so that students see a distinct split in the various types of blocks.)

Ask: What numeral is represented by one thousand? (1,000)

Say: Identify the numeral represented by three hundreds. (300)

Ask: What numeral is represented by 6 tens? (60)

Ask: What numeral is represented by 7 ones? (7)

Say: If we write this numeral in expanded form, then we will use all of these numbers you just formed. 1,000 + 300 + 60 + 7

Say: If we write this number in standard form, then we will just use the digits in the correct places. 1,367

Student Expectation: Students will translate numbers between various forms



CK Ap





Ask: Who can say this number aloud? (One thousand three hundred sixty-seven)

Say: Let’s write it in words on the board.

Ask: What words show us the place values? (thousand, hundred)

Place transparency page 15 on the overhead to help students see all four methods and to discuss the similarities and differences between them.

Ask: How are these four methods of naming a number the same? (Each method depends on place value.)

Ask: How are they different? (Base Ten Blocks use pictures. Written form uses words, and although both standard and expanded use numbers, the standard is a closed form and expanded is drawn out.)

Ask: Is there a time when one might be better to use than another? (Answers will vary; one example might be to look at a newspaper and help the students see that standard form is always used.)

Place transparency page 14 back on the overhead.

Example 2: How do you represent 1,231 with Base Ten Blocks?

Write the number 1,231 on the board. Under each number, have the students name the place, i.e., thousands, hundreds, etc.

Ask: What the largest place value shown? (thousands)

Ask: How many thousands are there? (There is a 1 in the thousands place.) (Take 1 thousand piece from your overhead transparency blocks, and place it on the overhead.)

Ask: How many hundreds, tens, and ones does this number have? Use your Base Ten Blocks to create the number. (Take 2 hundreds, 3 tens, and 1 one from your overhead transparency blocks, and place them one at a time on the overhead as students respond.)

Ask: Does anyone’s set look different than this one? (Some students may have placed their sets vertically or placed the ones first and the thousands last. This presents a discussion opportunity on how these sets all represent the same number, but traditionally and mathematically, we begin with the highest number and work to the lowest—all thousands together, hundreds together, then tens, and ones.)









Ask: What two ways have we already shown this number? (standard form and Base Ten Blocks) What is another way to show the number 1,231? (Have students show it in expanded form, 1,000 + 200 + 30 + 1, and written form, one thousand two hundred thirty-one.)

Discuss again how each of these representations shows the same number.

Extension: For an additional activity to ensure your students have learned the various forms of numbers, try this:

• Give each student a piece of paper. Students will fold the paper in half vertically and then horizontally, dividing the paper into four parts.

• In the top left square, students will write “standard form.”

• In the top right square, they will write “expanded form.”

• In the bottom left square, they will write “written form.”

• In the bottom right square, they will write “Base Ten Blocks.”

• Write the standard form of a number up to 10,000 on a note card. Make one card for each student, and place all note cards in a bowl. Each student will draw a number and record the four representations on his/her paper. Allow each student to then present his/her number to the class and explain the different representations. This process may be repeated by having students use the back of the paper.

Example 3: What number does this model represent?

What needs to be added to this number to have the number 275?

Ask: Where should we begin in answering this second question? (Allow students to brainstorm approaches.)

Say: We need to understand what we have now and what we need to have. We have to find the difference between the two numbers.



These are hundreds. There are two. 200

200 + 50 + 3 = 253

Two hundred fifty-three

These are tens.There are five of them.

50

These are ones.There are three of them.

3





Ask: How many hundreds are in the original number? (2)

Ask: How many hundreds are needed in the new number? (2)

Ask: So, do we need to add any hundreds to have the number 275? (No) Why? (We already have enough hundreds.)

Ask: How many tens are in the original number? (5)

Ask: How many tens are needed in the new number? (7)

Ask: Do we need to add tens to make the number 275? (Yes, add 2 tens.) Why? (to raise 50 to 70 for the new number)

Ask: How many ones are in the original number? (3)

Ask: How many ones are needed in the new number? (5)

Ask: Do we need to add any ones? (Yes, add 2 ones.) Why? (to raise 3 to 5)

Say: So, we need to add 2 tens and 2 ones. (Write 20 + 2 = 22 on the board.)

Say: We add 22 to 253 to get 275.

Ask: What does this look like in Base Ten Blocks?

Teacher note: Using overhead (erasable) markers and their Base Ten Block sets, students will practice creating their answers to additional problems in all four forms. Place some Base Ten overhead blocks on the overhead. Allow students to separate the numbers into the place values on their charts. Then they will complete the other three forms with their markers. This activity may also be used in learning centers.






Initial Instruction—Part III—Examples


Example 2: How do you represent 1,231 with Base Ten Blocks?

Example 3: What number does this model represent?

What needs to be added to this number to show 275?

Example 1: What numeral does this model represent?




Initial Instruction—Part III—Examples


Student Expectation: Students will translate numbers between various formsB

AS

E T

EN

BL

OC

KS

THOUSANDS HUNDREDS TENS ONES

ONETHOUSAND

THREEHUNDRED

SIXTY SEVEN

1,000 300 60 7

1 3 6 7

ST

AN

DA

RD

F

OR

ME

XP

AN

DE

D

FOR

MW

RIT

TE

N

FO

RM



Initial Instruction—Part III—Student Chart




ST

AN

DA

RD

F

OR

ME

XP

AN

DE

D

FOR

MW

RIT

TE

N

FO

RM

BA

SE

TE

N B

LO

CK

S



Teacher note: In this part of the Initial Instruction, students will learn that other pictorial representations, other than Base Ten Blocks, can represent numbers.


Materials: Instructional Strategy, below and page 18; examples, transparency page 19

Before class: Gather necessary materials.

Directions: Use the following Instructional Strategy to guide your students through this portion of the Initial Instruction.

Ask: What have we used in all of our examples so far to visually show numbers? (Base Ten Blocks)

Say: Explain how Base Ten Blocks display or represent numbers. (Encourage students’ discussion reviewing how the Base Ten Blocks represent numbers.)

Say: Sometimes we use other pictures to identify numbers.

Place transparency page 19 on the overhead.

Example 1: Look at the following picture. What number does this show?

Ask: What important information is given in this picture? (The key states that there are ten marbles in each bag.)

Say: Numbers represented through pictures are called pictorial representations. Base Ten Blocks are one pictorial representation. These marbles are another pictorial representation.

Ask: Which Base Ten Block is equivalent to one bag? (the 10 strip)

Ask: Which Base Ten Block is equivalent to one marble? (the one square)

Ask: How did you determine this information? (Answers will vary.)

Ask: How many bags do we have? (4) What number does this represent? (4 tens, which is 40)

Ask: How many extra marbles do we have? (6) What number does this represent? (6 ones, which is 6).

Ask: So, what does this picture represent? (40 + 6 = 46)

Ask: How could we represent a hundred or thousand with pictures like these? (Answers may vary—a larger container with 10 bags in it could represent a hundred, and a thousand could be a bigger crate with 10 hundreds in it.)

Initial Instruction—Part IV


Student Expectation: Students will represent numbers using pictures



SK



Ask: Are numbers always represented with bags and marbles? (No. Students should understand that anything could be used as a pictorial representation; e.g., baseballs, ballet shoes, musical notes.)

Discuss other pictorial representations; then move onto example 2.

Example 2: Show a pictorial representation of the number 627. (Answers will vary, but students should use reasonable pictures to represent hundreds, tens, and ones and show that there are 6 hundreds, 2 tens, and 7 ones in their pictures.)

Discuss: Allow students to share their pictures. Compare and contrast the different answers. How are they alike? What makes them different? Is there a best answer in the group? Why?

Rewrite: Have students show their answers in Base Ten Blocks, standard form, expanded form, and written form.

Compare and Contrast: Use a Venn diagram to solidify the idea that using pictures is similar to using Base Ten Blocks by comparing and contrasting the methods. (Answers will vary, but one example might look like the following.)

Base Ten Blocks Pictorial Representation

• Same representation

• Hard to show numbers over 1,000

• Easy to draw

• Items represent ones, tens, hundreds, thousands, etc.

• Different representations

• Can make a picture represent large numbers

• Hard to draw sometimes

Initial Instruction—Part IV







Example 1:

Look at the following picture. What number does this picture show?

Example 2:

Show a pictorial representation of the number 627.

Use a Venn diagram to compare and contrast using pictures to represent numbers and using the Base Ten Blocks.

Venn Diagram

Key

= 10 marbles

Initial Instruction—Part IV—Examples



Base Ten Blocks Pictorial Representation

Similarities



Initial Instruction—Part V


Optional Reading Activity

Teacher note: The following activity uses the book A Place for Zero by Angeline Sparagna LoPresti to discuss moving horizontally from right to left on the place value chart, i.e., what comes after 9, etc. This relates to pages 24-32 in the book. The book can also be used before Initial Instruction - Part VI to discuss using zeros as place holders to create larger numbers. The first part of the book discusses the additive and multiplicative nature of zero, which are not in this unit, but are valid mathematical concepts.


Materials: Instructional Strategy, below; a copy of the book A Place for Zero; 3 pocket folders without brads; tag board or poster board strips (9” by 3”); markers; tape

Before class:

1. To make a place value chart, tape the three opened folders together, side-by-side, and label each pocket with a place value:

2. Cut out 90 tagboard strips. At the top of each strip, when turned vertically, write a number. There should be 9 of each digit, 0 - 9. Laminate the strips if possible.

Directions: Read the book A Place for Zero aloud to the class, or allow students to take turns reading. The activity below refers specifically to pages 24-32 from the book.

Place a small digit (a 2 or 3) in the far right side of the ones pocket. Have the students discuss what this means (2 or 3 ones).

Ask: What happens if we add one to this number? (It increases by one. Make the change on the chart. Continue to do this until you get to the digit 9.)

Ask: What happens if we add one to the number 9? (It increases by one, but now a 0 must be placed in the ones place, and a 1 goes in the tens place.)

Repeat this process to discuss what happens after numbers like 19, 99, 109, 199, 1999, etc.

Student Expectation: Students will use a literature connection to place value

HUNDRED THOUSANDS

TEN THOUSANDS


CK





Initial Instruction—Part VI


Teacher note: In this lesson, students will use a place value chart to determine the value of a number.


Materials: Instructional Strategy, pages 21-22; place value chart, transparency page 23; digits, transparency page 24

Before class: Cut out the digits from page 24 for use on the overhead with the place value chart, transparency page 23.

Directions: Use the following Instructional Strategy, below and page 22, to guide your students through this portion of the Initial Instruction.

Place transparency page 23 on the overhead, and put a 9 in the ones column on the place value chart.

Say: Numbers get too large and can no longer be represented with concrete models or pictures. However, there is something that can help us determine the value for a number. We call it a “place value chart.”

Say: Let’s read the headings on this chart. Have we seen any of these recently? (The headings “thousands,” “hundreds,” “tens,” and “ones” were all Base Ten Blocks and used in pictures as well.)

Ask: What does this digit represent? (the number 9 or nine ones)

Ask: What number comes after 9? (10)

Say: Explain what happens on the place value chart. (Attempt to put the 10 in the ones column; then move the 1 to the tens column. If necessary, explain that only one digit is allowed to be placed in each column on the chart.)

Using the overhead digits from page 24, show the students number 2.

Ask: What number is this? (2) (Place the 2 in the ones column.)

Ask: When placed here, what does this number represent? (2 ones or 2)

Move the 2 to the tens column.

Ask: When placed here, what does this number represent? (2 tens or 20)

Place the 2 in each of the other columns one at a time asking similar questions. 2 hundreds or 200; 2 thousands or 2,000; 2 ten thousands or 20,000; 2 hundred thousands or 200,000.

Student Expectation: Students will practice using place value charts to read numbers



SC



Place the number 99 on the place value chart.

Ask: What does this number represent? (the number 99; 9 tens and 9 ones)

Ask: What number comes after 99? (100)

Ask: What happens on the place value chart? (Attempt to put the 10 in the tens column; then move the 1 to the hundreds column.)

Place the number 999 on the place value chart.

Ask: What does this represent? (the number 999; 9 hundreds, 9 tens, and 9 ones)

Ask: What number comes after 999? (1,000)

Ask: How should this appear on the place value chart? (Attempt to put the 10 in the hundreds column; then move the “1” to the thousands.)

Say: Write a rule for the pattern that we have just witnessed. (Answers will vary. Possible responses include: Once you get up to the number nine, the next number will be 0 and a 1 will carry over to the next place; the numbers must be regrouped after digit 9.)

Say: Test your rule by showing what the next number is above 9,999. What do we call that number? Repeat for 99,999.

Ask: What number comes after 9,999? (10,000) What figure would represent this using Base Ten Blocks? What other pictures could we create to represent this number?

Place various combinations of numbers on the chart, and practice having the students read them using the place values seen in the headers. Have them show the numbers in standard form, written form, and expanded form. Start with smaller numbers and expand. When you think the students have the concept of how a place value chart works, then you are ready to move on to the next Initial Instruction part.




Initial Instruction—Part VI




Hu

nd

red

T

ho

usa

nd

sT

en

T

ho

usa

nd

sT

ho

usa

nd

sH

un

dre

ds

Ten

sO

nes

Place

Va

lue C

ha

rt


Initial Instruction—Part VI—Place Value Chart




0 0

32

211

9887

76655

443

9


Initial Instruction—Part VI—Digits




Initial Instruction—Part VII


Teacher note: In this activity, students will learn to insert commas into the place value charts and read numbers using commas.


Materials: Instructional Strategy, below and page 26; “The Secrets of Commas” and steps, transparency page 27; examples, transparency page 28

Before class: Cut out a large comma from any kind of paper (not transparency film). Gather other necessary materials.

Directions: Use “The Secrets of Commas” and example with steps on transparency page 27 to instruct students on inserting commas and reading numbers with commas. Then, using the Instructional Strategy and examples, have students come to the board and place a comma where it belongs in the example numbers and then read the number aloud.

Place transparency page 28 on the board.

Example 1: How would this number be read?

Group in threes starting on the right. Discuss with the students that it does not matter if the last circle to the left has three numbers, but the rest must. Place the comma in between the groups of three.

Ask: How many commas are there? (One. Its name is “thousands.”)

Ask: What is the number to the left of the comma? (fifty-two)

Ask: What is the number to the right of the comma? (eight hundred fifty-three)

Say: So, altogether we have fifty-two thousand, eight hundred fifty-three.

Hundred Thousands

Ten Thousands

Thousands Hundreds Tens Ones

,

Student Expectation: Students will insert commas into the place value charts and read numbers using commas

CK



5 2 8 5 3



Initial Instruction—Part VII


Example 2: How would this numeral be read?

Two hundred seventeen thousand, seven hundred and thirty-two.

Example 3: Write the following in expanded form, standard form, and written form.

200,000 + 40,000 + 7,000 + 700 + 30 + 6

247,736

Two hundred forty-seven thousand, seven hundred thirty-six


Hundred Thousands

Ten Thousands


2 4 7 7 3 6,

Hundred Thousands

Ten Thousands


2 1 7 7 3 2,





Example:

Step 1: Group the number in sets of 3 starting from the right.

Step 2: Place a comma in between each set of numbers.

Step 3: Name the comma. Since there is only one in this number, it is called “thousand.”

Step 4: Read from left to right. Say the word “thousand” when you get to the comma.

“fifty-three THOUSAND, one hundred forty-eight”

Hundred Thousands

Ten Thousands


5 3 1 4 8

5 3 1 4 8

5 3 1 4 8,

Shhhh...The Secrets of Commas

• Commas separate digits arranged in groups of three. (Arrange them starting at the right side.)

• Commas have different names depending on the number of groups of three.

• If there is only one comma, it is called “thousand.”

• If there are two commas, the first one on the left is “million,” and the second one is called “thousand.” (Read the number from left to right.)

Initial Instruction—Part VII—Secrets and Steps






Hundred Thousands

Ten Thousands


5 2 8 5 3

Example 3: Write the following in expanded form, standard form, and written form.

2 4 7 7 3 6


2 1 7 7 3 2

Initial Instruction—Part VII—Examples



Hundred Thousands

Ten Thousands


Hundred Thousands

Ten Thousands




Initial Instruction—Part VIII


Teacher note: This portion of the lesson will focus on zero as a whole number and how it shows the number of items in a set. This can be an abstract concept for third graders, and this is justification for including this concept with whole numbers and place value.

Group size: whole class, then small groups

Materials: Instructional Strategy, below; guided instruction, transparency page 30; Instructional Strategy, page 31; examples, transparency page 32; lined paper; pencils

Before class: Gather materials.

Directions:

• On a sheet of lined paper, each student should list as many characteristics of zero as possible.

• After a few minutes, place students in small groups.

• Students will share their identified characteristics and combine them into one group list.

• When all groups have finished, allow each group to share one characteristic, and record it on the board. Continue until all characteristics have been identified.

• Then use the Instructional Strategy below and transparency page 30 to discuss the purpose of zeros.

• Finally, use the Instructional Strategy, page 31, to guide students in using zeros in numbers with the examples on transparency page 32.

Place page 30 on the overhead.Ask: Are there things that are the same in these 2 numerals? (Yes - four digits are the same (1, 5, 6, 7), three of which are in the same places. So, they have the same value—567.)Ask: So, are these numbers the same or different? (different) What makes them different? (The place value of the 1 has changed from one thousand to ten thousand, and the zero holds the thousand place.)Say: Write each number in expanded form. (1,000 + 500 + 60 + 7; 10,000 + 500 + 60 + 7)Ask: What do we put when we come to the zero? (nothing or 0)Say: Zeros are a place holder to use when there is nothing else to put in that space.Say: Let’s look back at the list of characteristics for zero on the board. (Undoubtedly, the students listed things like “nothing” when they made their lists.) Does zero mean “nothing” in place value? (In a way it does - it represents no items in that place, but it represents more.)Ask: What does this zero represent? (The fact that there are no thousands - we have 1 ten thousand and 5 hundreds, so we need to separate those. However, we have no thousands in between them. We need a place holder.)Now discuss the example for reading numbers with zeros, steps 1-4. Then place transparency page 32 on the overhead for students to practice placing zeros in numbers.

Student Expectation: Students will formalize the use of zeros in place value



CK



Compare the following two numbers:

1,567 10,567

Zeros have a very special purpose in our place value charts. They are place holders to use when there is nothing else to put in a space.

For example: 50108

Step 1: Group the numbers in 3 starting on the right.

Step 2: Place a comma between each set of numbers.

Step 3: Name the comma(s): thousand.

Step 4: Read from left to right, and say the word “thousand” when you reach the comma.

Fifty thousand, one hundred eight.

5 0 1 0 8

5 0 1 0 8,

Initial Instruction—Part VIII—Guided Instruction





Example 1: Write the number shown in the place value chart below in expanded form, written form, and standard form.

Example 2: Show this numeral in a place value chart: 7,501.

7 5 0 1

Hundred Thousands

Ten Thousands


9 0 2 3 0 8

902,308 (standard) 900,000 + 2,000 + 300 + 8 (expanded)Nine hundred two thousand, three hundred eight (written)

5 0 2 6 8

50,268 (standard)50,000 + 200 + 60 + 8 (expanded)Fifty thousand, two hundred sixty-eight (written)

1 0 0 3 9 0

100,390 (standard)100,000 + 300 + 90 (expanded)One hundred thousand, three hundred ninety (written)

Teacher note: Remind students to put the numbers in the place value chart starting on the far right and working left. This will prevent errors in alignment.

Ask: What if we started on the far left? (The 7 would be in the hundred thousands place, representing 700,000. This would change the value of each digit.)

Initial Instruction—Part VIII—Examples



Hundred Thousands

Ten Thousands


Hundred Thousands

Ten Thousands


Hundred Thousands

Ten Thousands






Example 2: Show this numeral in a place value chart: 7,501.

Which number did you place in your chart first? Why?

1 0 0 3 9 0

5 0 2 6 8

9 0 2 3 0 8

Initial Instruction—Part VIII—Examples


Example 1: Write the number shown in the place value chart below in expanded form, written form, and standard form.


Hundred Thousands

Ten Thousands


Hundred Thousands

Ten Thousands


Hundred Thousands

Ten Thousands


Hundred Thousands

Ten Thousands




Initial Instruction—Guided Practice


Teacher note: The guided practice section is included as an individual activity followed by whole-group discussion to assess what the students gained during the Initial Instruction.


Materials: problems, transparency pages 33-34; answer key, page 67 (Optional: Use copies of pages 23 and 24 and overhead Base Ten Blocks as manipulatives during the discussion.)

Before class: Gather necessary materials.

Directions:

• Place the first transparency on the overhead.

• Allow students time to complete the first question on their own paper.

• Immerse the class in a group discussion of their answers before moving on to #2.

• Repeat this process for problems #2 and #3 on transparency page 34.

1. What number does this model represent? Divide a piece of paper into four sections. In one section show the number in expanded form. In the second section, show the number in standard form. In the third section give a written representation of the number. In the last section, show the number in a place value chart.

Student Expectation: Students will practice using various representations of numbers

CK



8 0 5 3 2 1

3. Write this numeral in expanded form, standard form, and written form.

Initial Instruction—Guided Practice


2. Given the following model, what needs to be added or subtracted so that the picture will represent the number four hundred seventy-five?

Student Expectation: Students will practice using various representations of numbers

Hundred Thousands

Ten Thousands



Unit 1 – Practice #1 Number ConceptsDirections: Read each problem carefully. Decide which answer best completes the question. Show your work.

Problem #4

Which numeral shows six hundreds, four tens, and three ones?

F 346

G 634

H 436

J 643

Problem #5

George bought a pool that is thirty-three thousand, five hundred cubic feet. How is this number written as a numeral?

A 3,350

B 330,500

C 33,500

D 33,050

Problem #6

How is this numeral written in words?

F Forty-three thousand, two hundred fifty-three

G Four hundred thirty-two thousand, five hundred three

H Four hundred thirty-two million, five hundred three

J Four hundred thirty-two thousand, fifty-three

Use the following Base Ten Blocks to answer questions #1 and #2.

Problem #1

What number does the model represent?

A 143

B 134

C 431

D 341

Problem #2

How is this numeral written in words?

Problem #3

What is the place value of the 4 in the number 42,590?

A Thousands

B Hundreds

C Ten Thousands

D Hundred Thousands

4 3 2 5 0 3


Unit 1 – Practice #1 Number ConceptsDirections: Read each problem carefully. Decide which answer best completes the question. Show your work.

Problem #7

How is fifty-three thousand, six hundred forty represented?

A

B

C

D

Problem #8

Which numeral has a 3 in the ten thousands place?

F 62,317

G 39,417

H 43,619

J 74,913

Problem #9

Which of the following is NOT another way to represent the number of pizza slices shown above?

F G 302

H Thirty-two J 30 + 2

5 3 6 4 0

5 3 6 0 4

5 3 6 4 0 0

5 3 0 6 4 0

Hu

nd

red

T

ho

usa

nd

s

Ten

Th

ou

san

ds

Th

ou

san

ds

Hu

nd

red

sT

en

sO

nes

Problem #10

Write the following number in the place value chart. You will have to turn this page sideways to write in the place value chart.

Four hundred twenty-three thousand, eleven


Unit 1 – Application #1 Number ConceptsDirections: Read each problem carefully. Decide which answer best completes the question. Show your work.

Problem #4

What numeral does this model represent? 247

724

274

742

Problem #5

Shelly has 7 bags of marbles. Each bag contains ten marbles. She also has six marbles not in a bag. How many marbles does she have?

67

17

16

76

Problem #1

The number 45,236 has —

2 tens

4 thousands

5 hundreds

6 ones

Problem #2

Which number has a 4 in the hundred thousands place?

472,892

743,251

374,321

658,453

Problem #3

Which number means the same as 80,000 + 6,000 + 30 + 1?

80,631

86,301

86,031

86,310


Unit 1 – Application #1 Number ConceptsDirections: Read each problem carefully. Decide which answer best completes the question. Show your work.

Problem #6

Write 60,235 in expanded form.

60,000 + 200 + 30 + 5

6,000 + 200 + 30 + 5

60,000 + 2,000 + 300 + 5

60,000 + 2,000 + 30 + 5

Problem #7

Aaron owns a ranch that is 15,205 acres. How would you read this numeral?

Fifteen thousand, two hundred fifty

Fifteen thousand, twenty-five

Fifteen thousand, two hundred five

One thousand, five hundred twenty-five

Problem #8

Which 5-digit number has a 6 in the thousands place and a 7 in the hundreds place?

6,720

56,870

76,795

86,578

Problem #9

Write a 6-digit number that has a 7 in the thousands place, a 2 in the hundred thousands place, a 4 in the tens place, and a 1 in the hundreds place.

Also express this numeral in expanded form and written form.

Problem #10

Write the following number in the place value chart. You will have to turn this page sideways to write in the place value chart.

Nine hundred eight thousand, seven hundred twenty

Hu

nd

red

T

ho

usa

nd

sT

en

Th

ou

san

ds

Th

ou

san

ds

Hu

nd

red

sT

ens

On

es

Documents

Resource Overview - Cloud Object Storage | Store ... · This resource may be available in other Quantile ... a digit determines its value. ... how much a digit is “worth” as determined