Return to Mathematics IndexCounting and Place Value

Carole Gills Edward Coles School

8440 S. Phillips

Chicago IL 60617

(312)535-6550Objective:

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 paperStrategy:

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:00,01,02and

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 Wayby Mary Baratta-Lorton