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13.31 B - Place Value Through the Millions

 


Author: David Riddick
Date Created: 7/20/2003 5:40:13 PM PST

 

Grade/Level:
4

Students:
27 Students. 14 boys and 13 girls. 4 EO's; 6 IFEP's; 3 RFEP's; 14 ELD3-4: GATE class - advanced learners

Subject Area(s):
Mathematics

Concept(s):
Students will learn to read and write California county populations through the millions in expanded form, standard form, and word form.

State Academic Content Standard(s):

CA- CCTC: Aligned CSTP's and TPE's

• Standard : CSTP: Standard for Assessing Student Learning
TPE: B. Assessing Student Learning
CSTP Description: Teachers establish and clearly communicate learning goals for all students. Teachers collect information about student performance from a variety of sources. Teachers involve all students in assessing their own learning. Teachers use information from a variety of ongoing assessments to plan and adjust learning opportunities that promote academic achievement and personal growth for all students. Teachers exchange information about student learning with students, families, and support personnel in ways that improve understanding and encourage further academic progress.

• CSTP Key Element : Collecting and using multiple sources of information to assess student learning.

 Question : use a variety of assessments to determine what students know and are able to do?

• Standard : CSTP: Standard for Planning Instruction and Designing Learning Experiences for all Students
TPE: D. Planning Instruction and Designing Learning Experiences for Students
CSTP Description: Teachers plan instruction that draws on and values students’ backgrounds, prior knowledge, and interests. Teachers establish challenging learning goals for all students based on student experience, language, development, and home and school expectations. Teachers sequence curriculum and design long-term and short-range plans that incorporate subject matter knowledge, reflect grade-level curriculum expectations, and include a repertoire of instructional strategies. Teachers use instructional activities that promote learning goals and connect with student experiences and interests. Teachers modify and adjust instructional plans according to student engagement and achievement.

• CSTP Key Element : Establishing and articulating goals for student learning.

 Question : design instructional activities so that all students participate in setting and achieving learning goals?


CA- California K-12 Academic Content Standards

• Subject : Mathematics

• Grade : Grade Four
By the end of grade four, students understand large numbers and addition, subtraction, multiplication, and division of whole numbers. They describe and compare simple fractions and decimals. They understand the properties of, and the relationships between, plane geometric figures. They collect, represent, and analyze data to answer questions.

• Area : Number Sense

• Sub-Strand 1.0: Students understand the place value of whole numbers and decimals to two decimal places and how whole numbers and decimals relate to simple fractions. Students use the concepts of negative numbers:

 Standard 1.1 (Key Standard): Read and write whole numbers in the millions.

• Subject : History & Social Science

• Grade : Grade Four

• Area : California: A Changing State
Students learn the story of their home state, unique in American history in terms of its vast and varied geography, its many waves of immigration beginning with pre-Columbian societies, its continuous diversity, economic energy, and rapid growth. In addition to the specific treatment of milestones in California history, students examine the state in the context of the rest of the nation, with an emphasis on the U.S. Constitu-tion and the relationship between state and federal government.

• Sub-Strand 4.1: Students demonstrate an understanding of the physical and human geographic features that define places and regions in California.

 Standard 5: Use maps, charts, and pictures to describe how communities in California vary in land use, vegetation, wildlife, climate, population density, architecture, services, and transportation.

Objective(s):
Cognitive: Students will know how the millions period and thousands period of a place value are alike and how they are different.

Observable: Students will read and write the California county populations in expanded form, standard form, and word form.

Criteria: Given a list of county populations, students will identify which numbers are in the millions period, thousands period, and ones period with 80% accuracy.

Prerequisite Background Skills/ Knowledge:
Students know California is broken up into many counties. These counties vary in population.

Students know how to read and write numbers through the hundred thousands.

Vocabulary/Language Skills:
Listening: Students listen to verbal instructions given during directed lesson. ELD students are given help by peer tutors as teacher speaks.

Speaking: Students participate in directed lesson by raising hands and answering questions.

Writing: Students will take notes and write in their Math notebooks.

Reading: Students read from math textbook and Handout, "Populations of California Counties"

Vocabulary: counties, population, period, standard form, word form, short word form, expanded form

Materials:
1) Pencil & Paper
2) Transparencies
3) Transparency pen
4) Math Textbook
5) Social Studies folder
6) Handout "Populations of California Counties"
7) Handout "Population Map of California"
8) Handout "California Place Value - Practice"
9) Handout "California Place Value - Quiz"

Classroom Management:
During directed lesson, students are seated in assigned seats, which are 2-person desks.

I will give out extra credit points for students who participate and cooperate with lesson.

Extra credit points for actively engaged students

Models of Instruction:
Cooperative Learning

 

 

Procedure

 

 

 

 

Open:
As an attention getter, display the color coded California county map from the previous lesson. Ask students to locate the most populated counties. Write one of the least populated counties on the board.

For Example:
San Benito County

Input:
1st: Point out the standards we are working on (posted).

2nd: Ask students to read the population number for San Benito and give the value of each digit:

San Benito County
53,234

Ask students to read the number and give the value of each digit:
(50,00; 3,000; 200; 30; 4)

3rd: Ask students to read the population number for a large county.

Los Angeles County
9,519,338

Ask students to read the number and give the value of each digit:
(9,000,000; 500,000; 10,000; 9,000; 300; 30; 8)

4th: Each group of three numbers is called a period or comma. These commas separate one period from the next and help students read the number.

5th: Explain four ways to write the population for Los Angeles County.
9,519,338

1) Standard Form
9,519,338

2) Word Form
Nine Million, five hundred nineteen thousand, three hundred thirty three.

3) Short Word Form
9 million, 519 thousand, 338

4) Expanded Word Form
9,000,000 + 500,000 + 10,000 + 9,000 + 300 + 30 + 8

6th: Students will work in cooperative groups to write 5 county populations in the above four different ways. High achieving students will work with lower achieving students.

Guided Practice:
Model for students how to read and write a county population in four different ways.

1) Standard Form
2) Word Form
3) Short Word Form
4) Expanded Word Form

Ask students how the millions period and the thousands period of a place value are alike and how they are different. Discuss how both millions and thousands places have places for hundreds, tens, and ones. Both have greater values as you move from right to left. Each place value has a different value.

Independent Practice:
Students will work in cooperative groups to question one another on the value of each digit of a county population number.

Students will work in cooperative groups to write 5 county populations in the above four different ways. High achieving students will work with lower achieving students.

High achieving students may write 3 different six-digit numbers using the digits 1,2,3,4,5, and 6. Students will identify the value of 6 in each number.

Close:
To close the lesson students will share ways they understand how to read and write place value through the millions.

High achieving students may share their 3 different six-digit numbers with the class.

Students will understand numbers can be written in different ways. Place value can help students read and write numbers.

 

 

Assessment/ Reflection

 

 

 

 

Assessment:
Students will identify which California county population numbers are in the millions period, thousands period, and ones period with 80% accuracy.

Attachments:

 1. 

California County Population.xls

 2. 

California Place Value - Quiz.xls

 3. 

California Place Value - Practice.xls

 4. 

California Place Value -More Practice.xls

 

Links:

 1. 

United States Population by State

Reflection:
The objective of the lesson was achieved. Students were able to identify which California county population numbers are in the millions period, thousands period, and ones period with 80% accuracy. The lesson allowed students to make a connection with a number in the millions place to a tangible population of a county. Several students made an extension to the lesson by memorizing a few of the California county populations. Students did this on their own to understand how to read and write population numbers.

I did not anticipate the great disparity of understanding. Some of the students finished the assignment in minutes while others struggled with a basic understanding of place value. I allowed the high achieving students to work with one another in finding other California counties to write out the population numbers in various ways. I also allowed high achieving students to work with low achieving students.

I’ve tried to create a culture where students feel comfortable asking one another for help. Students also made posters to explain how to read and write their answers. This lesson was appropriate and on grade level because I collected and used multiple sources of information to assess student learning.