Hands-On Math Lab

Skip Counting & Multiples
Counting People and Hands & Fingers
Arithmetic Calculator


SKIP COUNTING & MULTIPLES
Fran Endicott Armstrong, Ph.D.

WHISPER-SHOUT (a simple counting game devised by Rick Armstrong for our daughter, Suzanne)

Two individuals or the teacher and the class alternate counting, but the one individual (or the teacher) whispers the numbers and the other individual (or the class) shouts the numbers (but not too loudly). For example, the teacher might start by whispering "1" and the class says in a louder voice "2" and the teacher whispers "3" and the class calls out "4" and so forth. An individual can eventually do whisper-shout by him/herself. 1, 2, 3, 4, 5, 6 and so forth. This is a bridge to skip counting.

Variations:
1. ) The first person shouts and the second person whispers: 1, 2, 3, 4, 5, 6, 7, 8, 9 and so forth.

2.) Whisper two numbers, then say loudly the next one, whisper the next two and then say loudly the next one and so on whisper two numbers and saying loudly every third number. 1, 2, 3, 4, 5, 6, 7, 8, 9 and so forth.

3.) Whisper three numbers and then shout every fourth number. 1, 2, 3, 4, 5, 6, 7, 8 and so forth.

4.) Start with a natural number higher than one.

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COUNTING PEOPLE & HANDS AND FINGERS

Have one person come up to the front of the room. Have that person put his/her hands up in front of his/her shoulders at a comfortable distance. "How many fingers?" "10." Have another person join the first person in front of the room with hands in front. "How many fingers showing in front of the room now?" "20." Some students may know that there are 20 fingers and others may need to count. So the teacher can point to each finger while the class counts. Continue adding people and counting fingers. You can make a table to show the data.

Number of People 1 2 3 4 5

Number of Fingers 10 20 30 40 50

You can also discuss the names of the decade numbers as follows. "What letter does the word 'ten' start with?" "T." "We'll let 'T' stand for 'ten.' " The word "twenty" means "two tens" or "2 T." "Twenty" is a corruption of "2 T." "Thirty" is a corruption of "3 T." "Forty" comes from "4 T." (You can have a spelling lesson here-"fourty" gets corrupted to "forty".) "Fifty" is a corruption of "5 T." (Change the "v" to "f " and drop the "e" before adding "ty.") Sixty, seventy, eighty, and ninety are exactly what they say they are--6 T for 6 tens, 7 T for 7 tens, 8 T for 8 tens and 9 T for 9 tens.
(Note: 'Forty" means "four tens" or "four times ten" but "fourteen" means "four plus ten." "Eleven" would be better called "oneteen" and "twelve" would make more sense if it were "twoteen." For young children it is nice to put numbers on the steps of a stairway on the right counting up from the bottom and put numbers counting down on the right as you walk down the steps. Then the children can count their way up and down the stairs and can also learn to count backwards when they are ready. You may also want to put odd numbers in one color and evens in a different color.)

A variation on people and fingers to develop counting by 5s is to have successive people join the line at the front of the room and just put up one hand of fingers.

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ARITHMETIC CALCULATOR
for skip counting and patterns adding and subtracting

Some arithmetic calculators have the following property:
If you press 1  +  =  =  =  =  =  =  = . . .
the display will show 1  1  1  2  3  4  5  6  7  8 . . . .
This is a way children can practice counting with a calculator starting from the first = pressed.
(Some arithmetic calculators don't iterate or repeat the previous operation with the specified number when = is pressed consecutively.)
And, of course, a student can also practice skip counting by 2s by pressing 2  +  =  =   =  = . . .
to get on the display 2  2  2  4  6  8 . . .

or by 3s by pressing 3  +   =   =   =   = . . .
to get on the display 3   3  3   6   9   12 . . . .

Students can also watch for patterns by recording on paper the results of pressing a sequence such as the following
8 + 5 =   =   =   =   =  =  =   =  =  =   =   =   =  . . .
to get on the display
8   8  5   13   18   23   28   33  38  43   48   53  58  63   68   73 . . .
(What's the pattern?)

or the sequence
5 + 8 =   =   =   =   =   =  =   =  =   =  =   = . . .
to get on the display
5  5  8  13  21   29   37   45  53   61   69  77  85   93   101 . . .
(What's the pattern? It's more complicated.).

An arithmetic calculator that iterates the previous operation with the previous number can also be used to explore multiplication patterns (e.g., 3 x 8 =   =   =   =   which will, on some calculators, repeatedly multiply by 3 not 8) and exponentiation (e.g., 3 x =   =   = which will give the successive powers of 3).

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St. Louis Community College at Meramec
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Updated 12/1/99