Counting and Place Value

Carole Gills                   Edward Coles School
535 West 87th Street           8440 S. Phillips
Chicago IL 60620               Chicago IL 60617
(312)994-1592                  (312)535-6550

Objective:

     The objective of this lesson is to give first grade students a concrete
understanding of place value by providing concrete opportunities to use place
value to practice counting, adding and subtracting using a phenomenological
approach.

Materials Needed:

     interlocking cubes            containers of various objects:
     bell                            pencils
     place value boards              Pokeno chips
     number flips                    beans
     small and medium                straws
        sized containers            strips of adding machine paper

Strategy:

Review numbers 0-9 and have the students practice counting various objects in  
the classroom from 1 to 9.  Leave the numbers on the board where the students  
can see them.

Give each student a place value board.  The board may be constructed of poster 
board or construction paper.  The left side of the place value board (referred 
to as the PVB in the remainder of this paper) is blue.  The right side is white.
                                                                             
Explain how to read the PVB.  Ask the students what is on the board.  When 
they respond that there is nothing on the board, ask them the number word for
nothing.  After they say "zero" tell them to read the board zero and zero, 
which means that there is nothing on the left (blue) side of the PVB and       
nothing on the right (white) side.  Remind the students that we will read the 
PVB the same way we read a book, that is, from left to right.

Next show the students the bell.  The ringing of the bell one time means add one
cube to the PVB.  We always place a single cube on the right side of the PVB.  
This side of the board is called the ones' column.  Have students practice 
adding a cube each time the bell rings.  Have them read their boards each time 
a cube is placed on the board.  When they have nine cubes on the white side of 
their boards, explain that ONLY 9 cubes can go in that column.  Ring the bell
and ask students what they will do now.  Help them come to the conclusion that 
they will put the cubes on the blue side of the PVB after they interlock them. 
These 10 cubes make up one ten.  Tens are placed on the blue side of the
board which is called the tens' column.

Continue the procedure of ringing the bell, allowing students to add cubes and 
read their boards until they appear comfortable with the routine.  Next, 
introduce the connecting step.  Students will use number flips to show the 
number symbol that corresponds with the number of objects shown on the board. 

It goes like this:  Teacher:  (rings bell one time)
                    Student:  (adds one cube)
                    Teacher:  "Flip" (indicating to flip to correct number)
                    Student:   (flips to correct number symbol)
                    Teacher:  "Read"
                    Student:  "Zero tens and one"

After the students add to 9 tens and 9 ones, they can practice subtracting the
cubes in the same manner described above.  When no single cubes are available
the students will use a ten from the blue side of the PVB, take it apart to 
subtract a single cube and leave the nine remaining cubes on the white side of  
their PVB.

The final step involves recording what has been practiced.  Give each student
a strip of adding machine paper that has been folded in half vertically.  Clear 
the boards and start the adding procedure again.  After the students add, flip, 
and read, have one student at a time put a PVB on the floor showing the number 
that was constructed.  The boards should line up from top to bottom.  After 
every student has had the opportunity to put a PVB on the floor, show them how 
to write the numbers that show on their boards.  Copy the numbers showing on the 
boards on the strips of paper, putting the ones on the right side of the fold 
and the tens on the left, and underline each number as follows: 00, 01, 02 and 
so on. 

To extend the concept of place value, give the students many different concrete 
objects to count on the PVB.  For example, beans can be used instead of inter-
locking cubes.  Each time ten beans are counted, they can be placed in a small 
container before placing them in the tens' column.  Eventually the 10 small cups 
filled with 10 beans will be placed in a medium sized container and put in a 
third column called the hundreds' column.  Two overlapping PVBs will provide 
this third column.  Instead of cubes and beans, students may practice with 
Pokeno chips, straws, pencils, coins and many other objects. 

Performance Assessment:

Students will be able to demonstrate, on a PVB, numbers up to 9 tens and 9 ones 
successfully.  They will be able to read and/or write the numbers from 00 to 
99, indicating that 1 ten and 1 is the same as eleven, 1 ten and 2 is the same 
as twelve, etc.

Conclusions:

The procedure described can be extended to the hundreds, thousands, etc. for
higher grade levels.  It can also be helpful in working with money concepts.

References:

Mathematics Their Way by Mary Baratta-Lorton