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Title: Place Values
(Note: This is a 3-day mini-unit designed for Mrs. Carral’s 2nd Grade Bilingual
class at Grant Elementary School, Trenton, NJ.)
Overview:
This mini-unit is designed to teach students the concept of place
values. To accomplish this, a variety of techniques will be used, such as
lecture, worksheets, learning centers, and a game. Throughout this
mini-unit, the students will be asked to count and group various objects to
explore place values.
Prior Knowledge:
In the beginning of the month of October, the students were briefly introduced
to the topic of place values when they took part in an activity with Digi-Blocks.
(As part of the Math Literacy Tour, the Digi-Blocks company came to Grant School
to promote their products and learning system and to celebrate the first annual
Math Literacy Week.) Digi-Blocks are math manipulatives that help to teach
students to read and write numbers and understand basic operations.
Using the Digi-Blocks, the students were asked to solve questions, such as
“Maria packed some single blocks. She made 3 blocks-of-10. She has 6
single blocks left. How many single blocks did Maria have before packing?”
We will call upon and activate this prior knowledge when we execute these lesson
plans.
Rationale:
Children of this age need to develop a strong basis in mathematics in order to
achieve a greater understanding for the use and applications of numbers in
everyday experiences. With number sense comes an intuitive feel for
numbers and a common sense approach to using them. This mini-unit promotes
the importance of understanding mathematics (specifically place value) and
building the math skills that are necessary to succeed in today’s technological
world. Another goal of this mini-unit is to combine physical materials
with real-life experiences in order to create meanings for numbers.
Subject Area(s):
Mathematics / Arithmetic
Standards:
4.1A – Number Sense
4.1C – Estimation
Day One (Tuesday):
Purpose:
The purpose of today’s lesson is to introduce the topic of place values through
the use of math and music. This lesson will also provide the foundation
for future activities dealing with place values.
Objectives:
 | the students will identify the place value of the ones,
tens, and hundreds |
| the students will state how many ones are in one ten |
| the students will be able to write numbers using more than
one place value |
Materials:
| 18 copies of the two worksheets entitled “Tens and Ones”
and “Hundreds, Tens, and Ones” |
| a box of colored paper clips |
Time:
Approximately 1 hour
Hook:
We will tell the following story, which condenses the history of our numerical
system into a few moments. We will illustrate the numbers on the
blackboard as the story unfolds. (The following was taken from the book
Teaching Primary Math with Music.)
A long, long time ago when people did not have any pictures for numbers, they
used to count on their fingers. When they needed to count more than ten,
they used their toes. But when twenty was not enough, someone who was very
smart said, “Let’s make pictures to represent numbers.” Different groups
of people made different pictures to represent numbers. After a long time,
some people made a line that looked like the finger they had used for counting,
and it looked like our numeral 1. (Write “1” on the board.) Then
they made a picture to show two things. It looked like our numeral 2.
(Write “2” on the board.) Eventually, the picture for three things came to
look like our numeral 3. Then came 4, 5, 6, 7, 8, 9 (write the numbers on
the board), and the people said “Stop! If we keep making more of these pictures,
we will never be able to remember them all!”
But one person who was very smart said, “We have to have one more. We need
a picture to show when we have no things.” So they made one more picture,
called zero. They called the ten pictures “digits,” the word they had used
long ago for “fingers” – which they had used to count with.
“But how can we show big numbers with only these ten digits?” someone asked.
After thinking for quite a long time, they decided that all they needed were
these ten digits – if they had special places in which to put them. The
places would have special values. That is why we call the method they
invented place value.
To illustrate place value, the teacher can use links of a chain of colored paper
clips. The teacher will hold up one link (one colored paper clip) to
represent the digit 1 and write it on the blackboard. Ten links (ten
colored paper clips of the same color) joined together show that this is also 1
– one group of ten. But to show that it is not just one link, that digit
has to go in a different place, the tens’ place. The teacher can use a
group of one hundred links (one hundred colored paper clips where every 10 paper
clips are a different color) to show the hundreds’ place in the same way.
Activities:
| First, we will go through the “hook” activity, which will
involve telling a brief history of our numerical system. |
| Next, we will define and describe what place values are
using a two digit number. We will say the following: Numbers, such as
84, have two digits. Each digit is a different place value. The
left digit is the tens place. It tells you that there are 8 tens.
The last or right digit is the ones place, which is 4 in this example.
Therefore, there are 8 sets of 10 plus 4 ones in the number 84.
|
| We will illustrate the following on the board:
8 4
|
|__ones place
|_________tens place |
| Next, we will use a three digit number to continue our
discussion on place values. We will say the following: Numbers, such as
784, have three digits. Each digit is a different place value. The
first digit is called the hundreds place. It tells you how many sets of
one hundred are in the number. The number 784 has seven hundreds.
The middle digit is the tens place. It tells you that there are 8 tens
in addition to the seven hundreds. The last or right digit is the ones
place, which is 4 in this example. Therefore, there are 7 sets of 100
plus 8 sets of 10 plus 4 ones in the number 784. |
| We will illustrate the following on the board:
7 8 4
| |
|__ones place
|
|_________tens place
|________________hundreds place |
| Next, we will make the distinction that words that end in
“ty” mean “tens.” It is important that students learn to decode words
like sixty as six tens. We will go over a few examples, such as: 30
means 3 tens and no ones. |
| After reviewing the material stated above and answering any
questions the students may have, we will hand out two worksheets entitled
“Tens and Ones” and “Hundreds, Tens and Ones.” These worksheets will
test the students’ understanding of the information they were just taught. |
Day Two (Wednesday):
Purpose:
The purpose of this lesson is to build the students’ knowledge of place values
utilizing a more hands-on “thinking approach.”
Objectives:
| using prediction strategies, the students will show their
ability to order digits to create the highest or lowest possible number |
| the students will compute numbers using the concept of
hundreds, tens, and units place values |
| the students will fine tune their interpersonal skills by
working in groups |
| the students will display cooperative work techniques and
will show their ability to work together in small groups to achieve a common
goal |
Materials:
| a big dice, approximately 4”x4” |
| a clear container filled with buttons |
| 6 baggies |
| 4-6 egg cartons |
| 3 plastic containers |
| masking tape |
| a set of nine buttons (preferably of the same color, size,
and type) |
| 18 copies of scoring sheets for the students
|
Time:
Approximately 1 hour and 20 minutes
Hook:
We will inform the students that they will be partaking in learning centers
today. We will explain that a learning center is a designated area within
the classroom where students will participate in a learning activity that will
enhance their knowledge on a certain topic, in this case place values.
(These students have taken part in various learning centers within their
classroom prior to today’s lesson so this will not be a new concept for them.)
Activities:
| After explaining to the students that today’s activity will
involve learning centers, we will divide the class into three groups of six.
Each group will be assigned to one learning center for 20 minutes. After
20 minutes, the groups will switch and proceed to a learning center they have
not been to yet for another 20 minutes. After that 20 minute interval,
the groups will switch one final time. This will ensure that every
student has a chance to participate at each station. We are using the
approach of learning centers because children, as well as adults, learn
difficult concepts more thoroughly when the ideas are presented many different
times and in different ways. |
| Each teacher will be assigned to one of the learning
centers to assist the students with the activities. |
| The first learning center is called “A Whole Lot of
Buttons.” The teacher will hold up a clear container filled with buttons
and ask the students to estimate the number of pieces in the container.
The teacher will write down each student’s guess on a sheet of paper.
When all the students in the group have had a chance to make an estimate, the
buttons in the container will be split into little baggies. The students
will be given an egg carton and a bag of buttons. They will be
instructed to make groups of ten using the pouches in the egg carton as
partitions. When the students have finished they can see how many tens
they have and how many ones are left over. Next, they will be instructed
to add up the tens and ones to determine how many buttons were in the clear
container originally. The students can then go back and see who had the
closest estimation. |
| The second learning center is called “Three Pots.”
First, the teacher will place three plastic containers on the floor.
Each container has the words “ones,” “tens,” or “hundreds” written on it.
Once the teacher places these containers on the floor in ranking order, she
will place a strip of masking tape on the floor, two or three feet away from
the first container. Sitting or standing behind the line, the students
will throw buttons at the containers. Each student will be given nine
buttons that they will pitch one at a time. The teacher will act as the
catcher. When a student fails to land a button, she will hand it back to
him/her. That student’s turn does not end until all nine buttons are
settled in one or another container. When all the buttons are in place,
the student will tally up how many hundreds, tens, and ones he/she
accumulated. The student will then write this number on a score sheet.
The score sheet is a piece of paper with three dashes on it. The dash on
the left is the hundreds place. This is where he/she will write the
number of buttons that he/she manages to get in the hundreds container.
The dash in the middle is the tens place. That is where he/she will
write the number of buttons landed in the tens container. The dash on
the right is the ones place, and there he/she will write the number of buttons
that landed in the ones container. The students should eventually become
aware that a button is worth more in the hundreds container than in the ones
container. Even if all of the buttons look the same, the place (its
container) where it lands changes its value. When all the students in
that group have had a chance to throw their buttons and tally up a score, the
group members can compare their scores. Whoever has the highest number
is the winner. The teacher will then ask the students what the highest
and lowest possible score could have been. |
| The third learning center is called “Rolling Dice.”
Each student will have a piece of paper that is divided into columns and rows.
The number of columns dictates how far you want the place value lesson to go.
In this case, the number of columns is three, which goes into the hundreds.
The number of rows dictates the number of games to be played. The
teacher has one of the students roll the dice to see what the first digit is
that needs to be placed. Once the digit is revealed, the student needs
to decide where that digit should be placed. The goal is to create the
highest number. This being said, if the first digit rolled is 1,
hopefully the student will not place it into the hundreds column but into the
ones column instead. Once that student has written down where that first
digit is located, he/she will roll the dice again. The student will
decide where to place the number that results. And finally, the same
student will roll the dice a third time and place the number in the column
that is not yet occupied. Ultimately, each student will roll the dice
three times. When everyone has completed their turn, the students will
compare their scores. Whoever has the highest number is the winner.
The teacher will then ask the students what the highest and lowest possible
numbers could have been. |
Day Three (Thursday):
Purpose:
The purpose of today’s lesson is to further enhance the students’ knowledge and
understanding on the topic of place values.
Objectives:
| the students will display cooperative work techniques and
will show their ability to work together in small groups to achieve a common
goal |
| the students will be able to tell the difference between a
number in the hundreds, tens, and ones place |
| the students will identify numbers in the hundreds, tens,
and ones place |
Materials:
None
Time:
Approximately 25-30 minutes
Hook:
We will inform the students that we will be practicing math in the form of a
game called the “Place Value Clap.”
Activities:
| The teacher will model an example to show the students how
the game is played. |
| The teacher will write a three digit number on the board
and choose three children to come to the front of the room. |
| The students will decide between themselves who is to clap
hundreds, who will clap tens, and who will clap units. |
| Lining up in the correct place, they clap their digit or
fold their arms for a zero. For example, if the number was 205, the
student in the hundreds place would clap twice. The student standing in
the tens place would fold his/her arms while the student in the units place
would clap five times. |
| The “hundreds” person then has to say the whole number
correctly. |
| The teacher will ask the class if they have any questions
as to how the game is played. |
| The teacher will then pick three different students and
assign them a different number without letting the class see or hear what the
number is. |
| Next, the students will decide between themselves who is to
clap hundreds, who will clap tens, and who will clap units. |
| After they clap out their number, the class will try to say
the number correctly. |
| The activity is again repeated until everyone in the class
has had a chance to clap out a number. |
| After all the students are given a chance to partake in the
activity, the teachers will offer the students a challenge number that uses
four place values: thousands, hundreds, tens, and ones. |
Assessment for All Three Days:
We will assess the children’s understanding of the topic and their interest
level throughout the mini-unit. Their answers to our questions, along with
their facial expressions and behavior, will indicate to us whether the subject
and presentation is capturing their interest. In addition, the group work
and the way in which the children answer problems on their worksheets will tell
us whether they understand the concepts presented.
WORKS CITED
Cottle, Morgan. “Reinforcement Lesson in Place Value.” Netscape
Navigator. Online. AskEric. 7 November 2002.
Kaye, Peggy. Games for Math. New York: Pantheon Books, 1987.
Mendlesohn, Esther. Teaching Primary Math with Music Grades K-3.
Palo Alto: Dale Seymour
Publications, 1990.
Welchman-Tischler, Rosamond. How to Use Children’s Literature to Teach
Mathematics.
Reston: The National Council of Teachers of Mathematics, Inc., 1992.
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