Place Value

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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:

bulletthe students will identify the place value of the ones, tens, and hundreds
bulletthe students will state how many ones are in one ten
bulletthe students will be able to write numbers using more than one place value

Materials:

bullet18 copies of the two worksheets entitled “Tens and Ones” and “Hundreds, Tens, and Ones”
bulleta 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:

bulletFirst, we will go through the “hook” activity, which will involve telling a brief history of our numerical system.
bulletNext, 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.
bulletWe will illustrate the following on the board:
            8 4
            |  |__ones place
            |_________tens place
bulletNext, 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.
bulletWe will illustrate the following on the board:
            7 8 4
            |  |  |__ones place
            |  |_________tens place
            |________________hundreds place
bulletNext, 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.
bulletAfter 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:

bulletusing prediction strategies, the students will show their ability to order digits to create the highest or lowest possible number
bulletthe students will compute numbers using the concept of hundreds, tens, and units place values
bulletthe students will fine tune their interpersonal skills by working in groups
bulletthe students will display cooperative work techniques and will show their ability to work together in small groups to achieve a common goal

Materials:

bulleta big dice, approximately 4”x4”
bulleta clear container filled with buttons
bullet6 baggies
bullet4-6 egg cartons
bullet3 plastic containers
bulletmasking tape
bulleta set of nine buttons (preferably of the same color, size, and type)
bullet18 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:

bulletAfter 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.
bulletEach teacher will be assigned to one of the learning centers to assist the students with the activities.
bulletThe 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.
bulletThe 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.
bulletThe 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:

bulletthe students will display cooperative work techniques and will show their ability to work together in small groups to achieve a common goal
bulletthe students will be able to tell the difference between a number in the hundreds, tens, and ones place
bulletthe 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:

bulletThe teacher will model an example to show the students how the game is played.
bulletThe teacher will write a three digit number on the board and choose three children to come to the front of the room.
bulletThe students will decide between themselves who is to clap hundreds, who will clap tens, and who will clap units.
bulletLining 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.
bulletThe “hundreds” person then has to say the whole number correctly.
bulletThe teacher will ask the class if they have any questions as to how the game is played.
bulletThe teacher will then pick three different students and assign them a different number without letting the class see or hear what the number is.
bulletNext, the students will decide between themselves who is to clap hundreds, who will clap tens, and who will clap units.
bulletAfter they clap out their number, the class will try to say the number correctly.
bulletThe activity is again repeated until everyone in the class has had a chance to clap out a number.
bulletAfter 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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