Place Value to Hundred Thousands Lesson Plan
Name:
Grade level:
Content area:
Subject matter within the Content area:
State adopted textbook:
Van de Walle chapter/page reference:
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Standards-based Learning Objective:
The students will demonstrate an understanding of place value through 999,999 by reading and writing numbers in standard and word form,
as demonstrated by completing pp. 8-11 (Lesson 2) of Houghton Mifflin Mathematics with at least 80% accuracy.
California Mathematics Content Standard:
a.
NS 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.
b.
This lesson is the second lesson in the first chapter of the textbook. The lesson sequence in the chapter is the following: (1) How big
is 1 million? (2) Place value through hundred thousands; (3) Place value through hundred millions; (4) Expanded notation; and (5)
Problem solving. The first lesson in the chapter is a hands on lesson about the value of a million. In the subsequent lesson, students
read and write numbers through 999,999,999 in standard and word form. The Preview-Review activity and the game “Digit” will be
utilized to set up the lesson as well as the chapter.
c.
This lesson is one of the first one taught in the school year. Due to the summer break, it is anticipated that there could possibly be
difficulties in student retention of the place value concepts that they learned in the third grade. Even though a Unit pre-assessment
was administered before teaching this lesson to determine student abilities, it is anticipated that student progress will need to be
closely monitored during this lesson. It is anticipated that there may be some additional difficulties in understanding the word
problems. Due to district scheduling mandates that have resulted in teaching mathematics immediately after lunch, it is anticipated
that there may also be difficulties maintaining focus on the lesson unless I include active engagement activities. Additionally, it is
anticipated that students will enjoy listening to the story (Preview-Review) and the game Digit. These activities should help in
gaining focus on mathematics instruction.
Materials
Book The Rajah’s Rice: A Mathematical Folktale from India, adapted by David Berry
Number line with mathematical periods and transparency
A large number line chart in the classroom with the number words denoted by the periods
Classroom chart with vocabulary and visual representations
“Watch Out for the Googols” exponent sheet and transparency
Place value chart (Workmat 2)
One strip per student of yellow construction paper, 3” x 12” for a digit mat
One strip per student of red construction paper, 3” x 12” for a digit mat
11 rectangles per student of index cards, 2 1/2” x 3” for each student
Portfolios or envelopes for storage of the “Digit” game
Houghton Mifflin Mathematics Chapter 1 Lesson 2
1 pencil per student
1 piece per student of lined notebook paper
Overhead projector
Overhead pen
Lesson quiz
Student mathematics journals
Reward tickets
Vocabulary
The following mathematical vocabulary will be reviewed during this lesson: digit, period, standard form, and word form. The students
should already have been familiar with these words from the first lesson, and from the third grade. However, the teacher will explicitly
review these words by defining and then showing how each term is used within the context of the lesson. The teacher will also ask students
to listen, say, and write these words during the lesson. Furthermore the teacher will verbally recognize students who use this language during
their responses and conversations.
Procedures
a.
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Preview and/or Review (Anticipatory Set)
Instructional Strategies
And Progress Monitoring
Preview: The teacher will explicitly state and write on the board the
objective of today’s lesson, which is to write numbers through 999,999
in standard and word form.
The teacher will explicitly state, explain, and model each vocabulary
word. The teacher will refer to the classroom vocabulary chart that will
provide a visual during the lesson.
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Student Activities:
Students actively listen and chorally restate the lesson
objective.
The students will listen, say, and then write the definitions
in their mathematics journals.
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In order for students to begin thinking about very large numbers and the
relative magnitudes of numbers, the teacher will read the story The
Rajah’s Rice: A Mathematical Folktale from India, adapted by David
Berry. This folktale demonstrates the power of doubling numbers, by
taking two grains of rice and doubling it 64 times (the number of squares
on a chessboard). This results in the number
18,446,744,073,709,551,616 - enough grains of rice to fill a great
volcano, such as Mt. Kilimanjaro.
The teacher will place a transparency of the number
18, 446,744,073,709,551,616 on the overhead. The teacher then
distributes the “Watch Out for Googles” number sheet, and asks students
to work in their cooperative groups to read the number.
Progress monitoring (check for understanding): The teacher will call
on individual students to read the number, and immediately correct any
difficulties. Students may have problems with inappropriately using the
word “and” while reading the number.
The teacher will ask the groups to report to the whole group how to read
the number. The entire class then reads the number together.
The teacher will then restate the lesson objective and mentions that, even
though the class will not be working with such a large number as in the
story, they will be reading and writing numbers through 999,999,999
during this chapter.
b.
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The students will actively listen to the teacher as the story
is read.
Students will work in their cooperative groups of 4 to try
to read the number.
Students will raise their hands if they wish to respond,
and those selected try reading the number.
The class will respond in unison to reading the number.
Students will actively listen to the teacher’s explanation.
Explicit (Direct) Instruction (“I Do”)
Instructional Strategies
And Progress Monitoring
The teacher will use the transparency of the Place Value Chart (Workmat
2) to explain mathematical periods, and how “commas” are utilized to
denote periods.
Progress monitoring (check for understanding): The teacher will ask
students in their cooperative groups to share what was just demonstrated.
The teacher closely checks for student understanding through their
correct utilization of the academic vocabulary, and answers any
questions that they still may have.
The teacher explains that students will now play the game “Digit” in
order to develop further understanding how large numbers are made with
mathematical periods.
Please note: The “Digit” activity includes Direct instruction and Guided
Practice segments as students play the game “Digit” with the teacher
closely monitoring.
Student Activities:
Students will actively listen to the teacher’s explanation.
Students will think about and then share within their
groups the teacher’s explanation. They write down any
questions that they may still have.
With teacher direction, the students will make their digit
cards by writing one digit on each index card (0, 1, 2, 3, 4,
5, 6, 7, 8, 9, 0) and writing a comma on the last card.
Once they have made their cards, they will shuffle the
number cards and place them face down on their desks.
The students will make the yellow digit mat. They fold
their paper in half lengthwise, and then fold their paper in
thirds. In the far right section, they write “ones.” In the
middle section, they write “tens,” and in the far left
section, they write “hundreds:”
Hundreds
The teacher will tell the students that they will be trying to build the
highest number. The teacher will model how to play the game by
turning over the first card and verbalizing the decision making that goes
into its placement. Once the card is placed, it cannot be moved. Play
continues until all three cards have been played.
Progress monitoring (check for understanding): The teacher will
circulate among cooperative groups and closely monitors student
abilities to verbally read the numbers that they have made.
After students have demonstrated proficiency with numbers through 987,
the teacher will demonstrate how to play “Digit” by adding the red digit
mat, and placing the “comma” card between the two digit mats:
Hundreds
Thousands Period
Tens
Ones
2
Ones
The students will place the strip in front of them.
The students will practice building numbers. They try to
build the highest number, the lowest number, and the
number closest to 500. The students will take turns
reading their numbers to the members of their cooperative
groups.
The students will practice building numbers through the
hundred thousands.
Hundreds
Progress monitoring (check for understanding): If students have
difficulty reading numbers in the hundred thousands, the teacher may
first want students to practice building numbers in the thousands, ten
Tens
Ones Period
Tens
Ones
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thousands, and then hundred thousands.
The teacher will review how digits are used to form numbers. The
teacher then directs students to place their “Digit” materials in the
Manila folder.
The teacher will direct students to turn to page 8 in Houghton Mifflin
Mathematics. The teacher reads and discusses the “Learn by Example”
section on p. 8. This will be familiar to the students because of the game
of “Digit” that they just played. The teacher directs the students to write
the number 271,035 on their Place-Value Chart (Workmat 2), and then to
hold up their answers.
Note: This number should be motivating and relevant to students
because it is the population of their hometown.
Progress monitoring (check for understanding): The teacher will
check students’ written responses.
Using the overhead, and while students look in their books, the teacher
will tell students they will be using two ways to express numbers:
standard form and word form. The teacher then writes the number
271,035 using both ways. The teacher directs students to choral read
and then write the number.
Progress monitoring (check for understanding): The teacher checks
students’ written responses.
The teacher will pass out lined notebook paper, explain, explain, and
model the correct heading for the paper.
Progress monitoring (check for understanding): The teacher will
circulate the room to check student work.
c.
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Using the Place-Value Chart (Workmat 2), students will
write the number 271,035 under the direction of the
teacher and then hold up their answers.
Students will choral read and then write the number
271,035 in word form on their Place-Value Chart
(Workmat 2). The Place-Value Chart will assist students
in writing the number in word form.
Students write the heading using correct form.
Guided Practice (“We Do”)
Instructional Strategies
And Progress Monitoring
The teacher will model the think aloud strategy to work problem 1. The
teacher will direct students to write the answer on their paper. For
problems 2 and 3, the teacher will give the students working in their
cooperative groups two minutes to write the problems by themselves.
The teacher will then call on different cooperative groups for their
answers, and then write the answers on the overhead.
Similarly, teacher will complete problems 4, 6 on the overhead and
direct students to complete 5, 7 – 9, and Math Talk in their groups.
Progress monitoring (check for understanding): While students are
working, the teacher will monitor their responses by checking student
responses. When the answer is correct, the teacher writes a “C” (for
correct) by the problem. If the response is incorrect, the teacher asks the
student to erase the response, the teacher explains to the student the
correct solution, and the student tries again. If student groups are having
trouble with a problem, then the teacher returns to the overhead for
direct instruction.
The teacher will ask students in cooperative groups to share their
responses to the Math Talk. Using popsicle sticks, the teacher will call
on students to share their Math Talk responses whole class.
Progress monitoring (check for understanding): The teacher will
closely monitor student responses as a check for understanding of place
value, and for the use of academic vocabulary in the explanations. This
is an important segment to check for mathematical understanding. If
students demonstrate understanding, they will be directed to complete
the rest of the problems by themselves. If not, the guided practice will
continue.
d.
Students will place their Digit game in their desks for
expanded use during the next day’s lesson.
Student Activities:
Students working in cooperative groups will write
answers to problems, as directed. They will use their
Place Value Chart to assist in writing the problems in
word form, and to determine the value of the underlined
digits (problems 7 and 8).
Students share their Math Talk responses in cooperative
groups and whole class.
Independent Practice (“I Do”)
Instructional Strategies
And Progress Monitoring
The teacher will direct students to complete problems 10 – 29, the Key
Standards Review, and the Mystery Number by themselves.
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Student Activities:
Students will complete the rest of the problems
independently. If they have difficulty with a problem,
they ask for assistance from cooperative group members.
If the group is having difficulty with a problem, the
Group Leader for the Day raises his/her hand for
assistance from the teacher.
Progress monitoring (check for understanding): While students are
working independently, the teacher will monitor their responses. When
the answer is correct, the teacher will write a “C” (for correct) by the
problem. If the response is incorrect, the teacher will ask the student to
erase the response, the teacher will explain to the student, and the
student will try again. If students are still having difficulty with
understanding the concept, the teacher will provide small group
instruction at the back table.
e. Closure
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Instructional Strategies
And Progress Monitoring
The teacher will review the lesson’s key vocabulary and mathematical
concepts. The teacher will then direct students to discuss what they
learned in the lesson. The teacher will circulate and give reward tickets
to those students and groups who correctly use academic vocabulary in
their discussion.
Progress monitoring (check for understanding): The teacher will
place a transparency of the Lesson Quiz on the overhead.
For homework, the teacher will direct students to complete the
textbook’s Chapter 1 Lesson 2 Homework and Problem Solving page.
Also, the teacher will ask students to bring to class tomorrow an example
of a very large number, such as the distance of the earth from the sun, or
the number of people in the world. The students may find large numbers
mentioned in the newspaper, in a magazine, or by looking for
information on the Internet. The teacher will tell students that the next
lesson will be on how to read and write numbers through 999,999,999.
Student Activities:
In cooperative groups, students will use the academic
vocabulary in their discussion of today’s lesson.
Students will individually write their answers to the
Lesson Quiz.
Students will complete the assigned homework – the
textbook page and finding examples of large numbers.
f. Back-up strategies:
For students who may have difficulties understanding numbers through 999,999, the teacher will begin the lesson with a review of
numbers <1000 and <100,000; have charts posted that show the spelling of numbers for word forms. Also, if students are having
problems in understanding, the teacher will continue the guided practice throughout the lesson, conduct small group lessons with
struggling students (either with an aide or a classroom volunteer), or use peer tutoring.
As part of the anticipatory set, the teacher may also discuss real world applications of large numbers. Students find how large numbers
are used in newspaper stories (this may also be used as a homework lesson as a follow-up). An alternative book would be How Much Is a
Million by David Schwartz. Working in groups, students may provide examples of how much is a hundred, a thousand (10 x 100); one
ten-thousand (10 x 1000); a hundred-thousand (100 x 1000); and then a million (1000 x 1000).
g. Rationale:
This lesson meets the fourth grade Academic Content Standard because it is taken directly from the district adopted and state approved
textbook. Specifically, it addresses Number Sense Standard 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. This lesson also addresses fourth
grade Academic Content Standards in Mathematical Reasoning. The subsequent lesson in the textbook is directly related to NS 1.1:
Students read and write whole numbers in the millions.
7.
This lesson is developmentally appropriate for fourth grade students for several reasons. First, it is a continuation of the third grade
Academic Content Standards in Mathematics where students master reading and writing numbers to 10,000. The lesson provides
numerous active engagement responses throughout – including the read-aloud of an age appropriate mathematical tale from India, the
game Digit, the Place Value Chart, the cooperative group responses. The lesson has also been carefully planned to take into consideration
that it will be conducted immediately after lunch when students will need some calming right after they come in (the mathematical story),
followed by active engagement activities. Additionally, students work in cooperative groups for most of the lesson, and the lesson has
been carefully scaffolded to ensure student mastery - explicit direct instruction, guided practice, independent practice, and closure. The
progress monitoring that occurs throughout the lesson will allow the teacher to monitor and adjust instruction to meet the needs of
students
Assessment
Entry level assessment:
a. Three and two days prior to this lesson, students will have taken the textbook’s Beginning of the Year Inventory and Unit 1 preassessments. These assessments will provide background knowledge about what students have learned and retained from their third
grade year. A review of assessment data from the students’ California Standards Test will also provide a picture of content mastery of
the third grade standards – both individually and collectively. Additionally, informal assessment will provide information regarding
individual strengths and weaknesses in completing the academic tasks necessary for successful completion of the mathematical tasks –
such as student learning styles, ability to work individually and in groups, and the motivation to complete assignments.
b. The teacher will utilize this information obtained from entry level assessments in lesson planning. I will specifically address areas
where students are struggling. This will also include reteaching concepts by alternative methods (see backup strategies), and future
review lessons.
Progress monitoring (informal assessment, check for understanding):
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8.
9.
10.
By checking student responses and by circulating the room, the teacher will monitor progress throughout the lesson including both their
verbal and written responses. During guided and independent practice the teacher will carefully monitor individual student progress
toward lesson mastery. When the answer is correct, the teacher will write a “C” (for correct) by the problem. If the response is incorrect,
the teacher asks the student to erase the response, the teacher explains to the student the correct solution, and the student tries again. If
several students are having trouble with a problem, then the teacher will either return to the overhead for direct instruction or invite
students to go to the back table for additional direct instruction.
Formal assessment:
The teacher will determine student mastery for this lesson by students completing the problems of this lesson with at least 80% accuracy.
Additionally, at the end of the lesson, students will complete the Lesson Quiz (see Closure).
Student and Parent Notification
Through close and careful progress monitoring, students will be aware of difficulties as soon as the teacher detects them.
A Parent newsletter will be sent home to parents at the beginning of each unit that explains what and how students will be learning the
mathematics. The letter also includes the definitions of the vocabulary words that students will be expected to know and understand.
Furthermore, the corrected work will be sent home the following day with a grade. If students have difficulty with this assignment, a note
will be attached informing the parent(s) of a problem with student mastery. If further difficulties occur in student understanding, the teacher
will request a parent conference.
Periodic review, reinforcement, and practice
Students will complete the “Daily Routines” section at the beginning of each lesson. This Spiral Review includes a Problem of the Day, a
Number Sense Review, a Number of the Day, and Facts Practice. Students will also complete the Leveled Practice and Writing depending
upon their individual needs – Reteach (Extra Support), On Level, and Enrichment (Challenge). Extra practice and reinforcement will occur
when they complete the homework page. Additionally, extra practice and reinforcement will occur in the subsequent lessons of this chapter,
as content has been carefully scaffolded.
Adaptations for Special Needs Students (English learners and students with learning problems)
Adaptations
Rationale (how and why)
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All students will be placed in
This will ensure careful monitoring by the teacher
heterogeneous cooperative groups in
such a manner that all students will be
able to see the overhead without
turning around. Students with special
needs will be part of cooperative
groups near the front of the room.
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Place Value Chart and classroom chart
These visuals will assist students with references to the concepts and the spelling
of number words
of number words. This will accommodate student difficulties with requiring and
remembering academic information.
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The game Digit
This game will explain how large numbers are put together, as well as the
importance of the comma to show number periods. The game also will increase
student motivation to participate.
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Progress monitoring throughout the
By the teacher closely monitoring the guided and independent practices, the
lesson
teacher will be able to immediately detect problems. If students are having
difficulties with the page, then the teacher may have to use guided practice
procedures for the entire lesson, especially where there is reading involved.
Additionally careful monitoring will help the teacher decide whether to return to
the overhead for additional practice and/or to provide small group instruction.
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Individual tutoring
An instructional aide or parent volunteer may assist the special needs student(s)
individually. Additionally, the special needs student(s) may also receive teacher
assistance in an after school tutoring sessions. In the classroom, peer or cross-age
tutoring may be options.
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Students repeat, summarize, and
This will occur throughout the lesson, with the teacher closely monitoring student
paraphrase
responses. Additional measures that may be incorporated are the use of white
boards, or thumbs up-thumbs down strategies.
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Choral responses by students
This will accommodate low rates of voluntary student participation.
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Advance organizers and post
This will accommodate students in acquiring and remembering academic
organizers (Preview-review, stating
information.
objective at the beginning, middle, and
ending of the lesson, reinforcing key
vocabulary words in meaningful
ways).
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Periodic review, reinforcement, and
This will allow for student retention, maintenance, and possible generalization.
practice
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Use of popsicle sticks to randomly call This will accommodate low rates of student participation, and show all students
on students and cooperative groups
that their input is essential.
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Giving extra time for student response, This will accommodate student difficulties with verbal expression.
and provide cues or hints
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