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Counting and Cardinality: Know

Goals for Preschoolers

  • P-MATH 1. Child knows number names and the count sequence.
  • P-MATH 2. Child recognizes the number of objects in a small set.
  • P-MATH 3. Child understands the relationship between numbers and quantities.
  • P-MATH 4. Child compares numbers.
  • P-MATH 5. Child associates a quantity with written numerals up to five and begins to write numbers.

Teaching Practices


Lead small group activities and discussions focused on counting and cardinality.
Yesterday, Ms. Lianna gave each 5-year-old in the small group 10 paint chips—a donation from a local store. She had the children write a numeral on each chip from one to 10, offering help to those who needed it. Then, the children put their paint chips in an envelope and labeled it with their name. Today, they continued the activity by punching holes in the cards—as many holes as needed to match the numeral on the chip. Emma says, “This is a three. I made one, two holes. Now I need one more. One, two, three. Done.” 

Ask questions that invite children to make predictions.
“How many steps do you think it is from the front door to the elevator?” asks Ms. Stone, a home visitor. Marcy, 3½, and Naomi, almost 5, state their guesses, “99,” and “one billion.” Their father, Mr. Vance, joins in, asking, “How can we find out?” “We could ask Momma,” says Naomi. “You could, but she is at work today. How else could we find out?” responds Mr. Vance. Ms. Stone and Mr. Vance both look toward the door. “Count them?” suggests Naomi. Mr. Vance says, “Okay. Let’s count.” He takes the children’s hands, heads out the door, and starts walking and counting. The children join in and Ms. Stone follows behind. When they get to the elevator, Mr. Vance asks, “How many steps did you count?” As the girls answer, Ms. Stone reminds them of their predictions and asks the girls if the number of steps they counted match the predictions.


Include materials in every learning center that encourage children to count and to write numbers.
The taco truck in the preschoolers’ dramatic play area is busy today. Maria, age 4½, is at the counter taking orders, while Bruno, also 4½, makes paper plate tacos. She asks a customer, “Orlando, how many tacos do you want?” “Cinco,” he says. Maria pretends to write down the number of tacos Orlando wants on a piece of paper. Then she relays the message to Bruno, who counts out five small plates, folding each one as he goes. He places them in a basket, adds some green tissue paper lettuce, and hands it to Maria. “Here you go. Cinco deliciosos tacos.”

Offer a wide range of materials that children can use to compare quantities.
Five-year-old Dion opens the jar of colored pompoms and dumps the contents on the table. “I’ll take the red ones and you can take the blue ones, he says to Boris, age 4. “Here’s a basket to put yours in.” The boys sort the pompoms until there are no blue or red ones left. Boris says, “I have the most. Look how full my basket is.” “No,” says Dion, “I have more.” Ms. Barnes, their teacher, asks, “How can you find out who has more pompoms?” “We’ll count them,” say both boys in unison. 


Ask open-ended questions to better understand a child’s mathematical thinking.
Family child care provider Ms. Adams watches as 3½-year-old Irma, who is deaf,uses sign language to count three cups as she gives them to her stuffed animals. Ms. Adams, also using sign language, asks, “I see you gave one cup to each of the stuffed animals, except for the pony. How will the pony drink his milk?” Irma thinks for a minute, then signs, “I need another cup.” As Ms. Adams hands her the additional cup, she signs, “Here is another cup, Irma. That makes four.” Irma places the cup in front of the pony then repeats her one-to-one counting, signing, “One, two, three, and this one for pony is four!”

Use teachable moments as opportunities to build counting skills and understanding of cardinality.
On their neighborhood walk, the preschoolers pass a small bed of red and yellow flowers. Ms. Nunez says, “Look at those beautiful tulips. I wonder how many there are.” Four-year-old Alejandro says, “Let’s count them. I’ll count the yellow ones.” “And we’ll count the red ones,” say 5-year-olds Kim and Hazel in unison. Alejandro lightly touches each yellow flower as he counts, “Uno, dos, tres, cuatro (one, two, three, four) yellow ones.” The girls say, “Four red ones,” without touching the flowers. “So,” says Ms. Nunez, “How many tulips altogether?” Alejandro and Hazel each hold up four fingers, looking puzzled. “I know,” says Kim. Without touching and counting each finger, Kim says, “Alejandro has four fingers. Hazel has four fingers.” Then, she touches and counts each finger, “One, two, three, four and five, six, seven, eight. Eight tulips.” Ms. Nunez takes a small pad out of her pocket and writes a few notes about what the three children know about counting, the number of objects in a small set, and cardinality.

Topic:School Readiness

Resource Type: Article

Last Updated: January 18, 2018