Return to Mathematics IndexPrimary Understanding and Use of Place Value

Eleanor Brzozowski Hanson Park School

5411 W. Fullerton Avenue

Chicago IL 60639

312-534-3100Objectives:

1. To give students an awareness of some of the peoples that have

contributed to the development of modern arithmetic. (Number systems)

2. To help students gain a better understanding of our base 10 number system

and its application to real life problems.

3. To increase a student's ability to add and subtract two numbers having as

many as three digits and involving renaming in the ones place and in the tens

place.Materials Needed:

Place Value board Dice

Base ten blocks Activity sheets

Chip-trading boards Number Wheel Response Cards (Optional)

Chips (4 colors) Multicultural materialsStrategy:

1. Discuss with the children some of the number systems used by other

peoples such as the Romans, Egyptians and Mayas. Roman Numerals contain a

symbol for one (I), five (V), ten (X), fifty (L), one hundred (C), five hundred

(D) and one thousand (M). It lacks a symbol for zero and place value. Explain

that Egyptian numerals are base ten as are our Hindu-Arabic numerals and are

additive. The Egyptian numerials are usually written from right to left, do not

use place value and the symbols used to write their numbers are called

hieroglyphics. Mayan numerals are base 20, with place value and a zero place-

holder. The increasing powers of 20 go up vertically instead of horizontally.

2. Put two Roman numerals on the board such as CX (110) and XLV (45). Ask

children, "How did the Romans add?" As they see the problems encountered in

doing this, lead the discussion to an explanation of our base 10 system and its

advantages, the 10 symbols used are called digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

and how the groupings by tens form a place value system. It is, therefore,

possible to represent any number using only the ten basic symbols (digits). The

position of each digit in the numeral determines the value of that digit. This

makes the task of doing arithmetic operations much easier than in systems like

the Romans or Egyptians.

3. Using a place-value chart showing ones, tens, hundreds and thousands,

model with base ten blocks four problems -- the addition of two 3 digit numbers

with and without regrouping and two subtraction problems up to 3 digits with and

without regrouping. At the same time of modeling and solving the problems, have

a student at the board showing abstractly what is being done as it is being

modeled. This will enable the student to transfer what he sees concretely to

the abstract. Be sure to stress that the largest digit each place value can

have is a nine and that exchanges must be made for numbers larger than nine.

4. Give students experience in renaming or making exchanges by playing "Chip

Trading". Give each student a playing board made from 8 x 11 inch manila paper

marked in four vertical columns. At the top of the left-hand column, paste a

small rectangular piece of black construction paper, red at the top of the next

column, then blue and white. Cut out circles of these same colors and use for

chips -- white representing ones, blue representing tens, red representing

hundreds, and black thousands.

Children play in groups of two to four. Each player throws the dice in

turn and always takes the number of white chips corresponding to the sum of the

numbers shown on the dice. Using 10 as the number (or base) for making

exchanges, whenever a player has 10 or more chips of one color, a trade must be

made. (10 whites are traded for 1 blue; 10 blue for 1 red; 10 red for 1 black).

The first player to obtain a red chip (when playing to 100) or a black chip

(when playing to 1000) is the winner.

Variation: Use other numbers as rates of exchanges such as 2, 3, 5, 8,

etc..

5. Provide students with appropriate activity sheets for reinforcing

addition and subtraction skills presented in lesson.Performance Assessment:

Children will be given three problems, one orally and two written, to assess

how well the objectives of the lesson were met.

A. Oral:

Students will write two 3-digit numbers from clues given orally by the

teacher and then find the sum. Example: In the first number, the ones' digit

is 5. The tens' digit is l more than the ones' digit. The hundreds' digit is 2

more than the tens' digit. The second number has 4 ones. The tens' digit

equals the number of boys in the class. The hundreds' digit is the number of

feet a chicken has.

B. Written:

(1) Write a question that can be answered using the information in the

story. Then find the answer.

Mary swam 567 meters at the indoor pool today. Yesterday she swam 498

meters.

(2) Write a story problem that you can solve using this number

sentence: 459 + 64 = ?Additional Activities:

1. Cooperative Problem Solving -- In groups of four, give each group an

envelope with four papers in it. Each paper states the problem with a different

clue on it. The group discusses the problem and the four clues. The first

group that solves the problem and can explain how the solution was obtained

wins. Example: Problem: How many seeds are in the sunflower? Clue 1: The

number uses the digits 2, 7, and 8, not in that order. Clue 2: The 2 is not in

the ones' place. Each digit is used once. Clue 3: The 7 is not in the

hundreds' place. Clue 4: The 2 is not in the hundreds' place.

2. Rolling-the-Cube -- On a piece of paper, students make three short

lines and directly below that three more short lines in preparation for adding

two 3 digit numbers. A cube or die is rolled. The number appearing on the cube

is put on one of the six blanks. The cube or die is rolled again and the second

number is placed in one of the remaining blanks. The process is repeated until

all six blanks are filled in. The two numbers are then added, and the student

with the largest sum is the winner.

3. Find-Hide-Show -- Give students a "Number Wheel Response Card" (Open

Court Publishing Co.). State a number to make on their cards. After they find

the number, they "hide" the card by their chest and when the teacher says

"show", they hold up their card. Teachers can easily identify students having

an understanding of place value and those needing additional help.Extension:

To provide students with experiences in regrouping larger numbers, make a

three dimensional mat called the "Daily Depositor" with places up to one

million. Have the class predict whether they can accumulate one million dollars

by the year's end if each day the class receives the number of $100 bills for

the date of the month. For example, on the third of the month $300 is put into

the Depositor and on the 27th of the month $2700 is added to the Depositor. The

accumulation occurs throughout the years so there is experience with large

numbers and regrouping (hundreds in the early months and thousands in the later

months). Use play money from a game such as Life.