Counting Patterns
Providing developmentally appropriate activities for young children (ages 5-8) in the areas of word, quantity, symbol, relationships, and operations is a very important first step in the development of number sense. Each month DMG will focus on one of the important concepts and give ideas and activities that you can use with your child or students in number concepts and operations.
These important concepts create the early foundations of mathematical thinking. “Number sense is sometimes defined as having good intuition about numbers and their relationships. It develops gradually as a result of exploring numbers, visualizing them in a variety of contexts and relating them in ways that are not limited by traditional algorithms” (Howden 1989 p. 11). Number sense contributes directly to problem-solving abilities and flexible thinking in numerical situations. The self-confidence and positive attitudes displayed by children with good number concepts are in stark contrast to the insecurities of many upper-grade children and adults who still rely on finger counting (Van de Walle, 1990). Number sense can and should be promoted and developed through instruction, curriculum, and assessment.
WORD QUANTITY SYMBOL RELATIONSHIPS OPERATIONS
August 2007
This month our focus is
WORD
Oral Counting Patterns
Gelman and Gallistel (1978) refer to counting as a scheme in the Piagetian sense. That is, counting becomes a rote way of saying numbers not necessarily developing an understanding of quantity.
To count to 100, a child needs to know:
- the single digit sequence one to nine
- transitions are signaled by a nine (e.g. nineteen signals the end of the teens and the beginning of a new series)
- the transition terms for the new series (e.g. twenty follows nineteen)
- the rules for generating the new series (e.g. the twenties and all subsequent series are generated by combining the transition term with, in turn, each term in the single digit sequence)
- the exceptions to the rules (11-15)
Children beginning school typically can count to nine, if not nineteen (Fuson 1988). Many kindergartners, however, will not have the second component above and as a result, will overextend their counting rules (i.e. make rule-governed errors such as nineteen, tenteen, eleventeen or twenty-nine, twenty-ten, twenty-eleven"). Most will also not know the decade terms to begin the new series (e.g. they count to twenty-nine and stop because they do not know that thirty is next). Indeed, it is not until first grade that many children recognize that the decade series parallels the single-digit sequence (e.g. six+ty, seven+ty, eight+ty) and master the decades (e.g. twenty is followed by twenty+one, twenty+two). Finally, exceptions to counting patterns often cause difficulties, For example, fifteen is the most commonly missed teen (Fuson 1988).
WORD ACTIVITIES
Ages and Counting Range
2-3 yrs. 1 - 3
Pre-kindergarten 1 - 10
Kindergarten 1 - 20 Back from 5
Grade 1 Counting range 1-100 Back from 10
Grade 2 Counting range 1-1000 Back from 20
Oral Counting Forward
• Read counting books, sing songs, recite nursery rhymes
Examples of books:
Olivia Counts by Ian Falconer
Ten Black Dots by Donald Crews
Very Hungry Caterpillar by Eric Carle
Fish Eyes by Lois Ehlert
Counting Crocodiles by Judy Sierra
The M & Ms Brand Chocolate Candies Counting Book by Barbara McGrath
I Can Count 100 Bunnies and So Can You by Cindy Szekeres
Let's Count by Tana Hoban
Example of a Song:
"Ladybug Picnic" - Sesame Street
Examples of nursery rhymes:
"1-2 Buckle My Shoe"
"One Potato, Two Potato"
Oral Counting Back
• Read counting books, sing songs, recite nursery rhymes
Examples of books:
Five Little Monkeys Jumping on the Bed by Eileen Christelow
10 Rubber Duckies by William B. Winburn
Twenty is Too Many by Kate Duke
Example of a song:
"Five Little Speckled Frogs"
Examples of nursery rhymes:
"5 Little Monkeys Jumping on the Bed"
"Ten In the Bed"
More Activities:
• Reciting the number words in sequence
Repeat after me: "One, Two, Three"
Add number words as they learn the sequence
• Start from different numbers
Say: "I'm going to count and I want you to say it after me.
"Nine, ten. Let's do it again. Nine, ten."
Do for strings of counting words up to 5. Change the sequence
depending on the age of the child.
Change the sequence depending on the age of the child. As the child gets older, he or she should be able to count starting at different numbers. For example: a kindergarten child should be able to count starting at 10 and counting to 20. Watch for the transitions for older children. If you hear a child pause at the transition from 9 to 10 or 19 to 20 or 29 to 30 you know that they understand that there needs to be a change but he/she is not secure in the transition words yet. Help the child by having him/her learn the rote count of 10s to 100.
• Prepare a number cube with numbers 0 - 5
Have the child roll the cube. Adult says the number word. Then child counts up to that number. You can also have the child jump as he/she says the number or clap as he/she counts.
• Play an echo game with the child. Say three numbers in a row and have the child echo them back. When the child gets good at this then do "continue counting." Say three numbers and then the child continues with three more counts. You can also alternate counts.
