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Operations and Algebraic Thinking: Know

Goals for Preschoolers

  • P-MATH 6. Child understands addition as adding to and subtraction as taking away from.
  • P-MATH 7. Child understands simple patterns.

Teaching Practices


Play games that involve adding to and taking away from.
A group of 3½- and 4-year-old preschoolers are getting ready to play musical hula hoops. They place five hula hoops on the floor, and four children stand in each hoop. Ms. Barco, their teacher, turns on the music and the children jump out of their hoops and run around. When the music stops, Ms. Barco removes a hoop, then turns on the music again. The children now squeeze into four hoops, not five. She asks, “How many hoops did we start with? How many do we have now?” The game continues until there are two hoops left. She asks, “Will you all fit in two hoops? Let’s see.” This time, the children stand with one foot in and one foot out of the hoops so everyone will fit. Ms. Barco has the children count as they step out of the hoops. When they get to 20 she says, “That’s everyone.” 

Lead activities that allow children to make patterns.
Several children are making a snack with Ms. Starr, their family child care provider. It’s a familiar recipe, ants on a log, but with a twist. In addition to raisins, children can make ants using dried cranberries. Four-year-old Sara slathers cream cheese in her celery stick then tops it with cranberries and raisins. She makes an ABABAB pattern—one cranberry, one raisin, one cranberry, one raisin, and so on. Lamar, almost 5, makes a more complex BBABBA—two raisins, one cranberry, two raisins, one cranberry, and so on. Ms. Starr points out these two patterns and others around the table.


Include materials throughout the setting that encourage children to add and take away.
Three-year-olds Wendell and Patricia are building a tall tower with large foam blocks. Wendell says, “Let’s make it as high as us.” “Okay,” says Patricia, then adds three blocks to the tower. Wendell stands next to the tower and says, “Uh, oh. Now it’s bigger than us.” Mr. Unger says to the children, “Yes, I see six foam blocks in your tower, and the tower is taller than you. What can you do to fix the tower?” Wendell removes one block and stands next to the tower again. “Good,” he says. “Now it’s the same size as us.” Mr. Unger agrees and adds, “You had six blocks. You took one block away. Now how many blocks do you have?”

Offer a wide range of materials that children can use to make patterns.
The music area in the preschool room is stocked with a variety of drums—homemade and purchased. Today, Ms. Lansky models a musical pattern on a large gathering drum. A group of 4-year-old children listen to the pattern, then repeat it on their own hand drums. Ms. Lansky makes the pattern more and more complex to challenge the children’s listening, drumming, and patterning skills.


Point out patterns in the indoor and outdoor environments.
When Ms. Dodds arrives for a home visit, Jaimie, 3½, opens the door. She says, “Hello, Jaimie. What a colorful shirt you are wearing. Let’s see if it has a pattern—red, blue, red, blue, red, blue.” “That’s a pattern,” says Jaimie, “and you have one, too. Your scarf goes blue, green, black, blue, green, black.” Jaimie’s mom, Ms. Chaco, invites Ms. Dodds to sit down and says, “Since your last visit, Jaimie has been pointing out patterns all day, every day.” “That’s great,” says Ms. Dodds. “I brought some bottle caps so he can make patterns. They are different sizes and colors and shapes. You might want to start your own collection of bottle caps. They are a fun and easy way to make patterns.” Ms. Chaco responds, “We can do that! There are several bottle caps in our recycling bin and I can ask my friends to save some for us.”

Use teachable moments as opportunities to discuss adding, subtracting, and patterns.
“You are hungry today, Margot. You ate four crackers with cheese,” says Ms. Moore. “I’m still hungry,” says 4-year-old Margot. “I need one more. Then I will be full.” “Okay,” says Ms. Moore. “Then you will have had four crackers and cheese plus one more.” “I know,” says Margot while counting on her fingers. “One, two, three, four, and this pinky finger too, five. Five crackers with cheese!”

Topic:School Readiness

Resource Type: Article

Last Updated: January 18, 2018