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Operations and Algebraic Thinking: Do


Try the following practices with preschool-aged children. Find out how home visitors can put these practices to work with families.


  • Use books, songs, and games to introduce and reinforce the concepts of addition (adding to) and subtraction (taking away from).
    • For example: Create a flannel board activity using the “Bagel Shop” song to illustrate subtraction. “Five little bagels in the bagel shop. Sprinkled poppy seeds on the very top. Along came Arial with two pennies to pay. He bought two bagels and walked away.”
  • Bring real-life settings into the learning environment to provide a meaningful context for counting and simple adding and subtracting (e.g., a grocery store, shoe store, a train with a conductor collecting tickets from passengers).
  • Watch for opportunities to pose simple number problems during daily routines, interactions, and activities; for example:
    • If you give me one crayon, how many will you have left?
    • You have three apple slices. If I give you one more apple slice, how many apple slices will you have all together?
  • Point out patterns in indoor and outdoor environments. Invite children to identify patterns they see.
  • Scaffold pattern-making activities by initially limiting the choices of objects available to keep the patterns simple (e.g., two different colors, two different shapes, two different sizes). Gradually increase the range of choices.
  • Invite children to create patterns physically through marching, sitting, jumping, or clapping (e.g., jump-jump-clap-clap, jump-jump-clap-clap or stand-clap-sit, stand-clap-sit). Sing songs which involve the use of physical patterns, like “If You’re Happy and You Know It, Clap Your Hands” or “Hokey Pokey.”
  • Create patterns with sounds by using rhythm instruments such as shakers or sticks.
  • Share books, stories, and nursery rhyme songs that have repetitive structures, phrases, or rhymes (e.g., “The Wheels on the Bus” or “Old MacDonald Had a Farm”).

Home Visitors

Home visitors can support parents in identifying, adapting, and trying the practices listed above during home visits and group socializations. Here are more ideas.

  • Talk with parents about their experiences and comfort level with using counting, comparing numbers and quantities, and solving addition and subtraction problems in their own lives as well as with their child.
  • Encourage parents to use the language(s) they know best when talking with their child about counting, comparing numbers and quantities, and solving simple addition and subtraction problems. Identify number-related songs, rhymes, and chants that reinforce these concepts that parents can sing with their child.
  • Share children’s books that involve numbers, quantities, simple adding and subtracting, and patterns with parents, particularly those that can be found in the local library or your program’s lending library. Share strategies for using number concept books with their child; model these strategies as appropriate.
  • Work with parents to identify materials and household objects they can use to help their child learn to solve simple addition and subtraction problems and identify and create patterns. Brainstorm opportunities to reinforce these concepts with their child during daily routines and family activities.

1California Department of Education, California Preschool Curriculum Framework Volume 1 (Sacramento, CA: California Department of Education, 2010), 255–257, Understanding Number Relationships and Operations, http://www.cde.ca.gov/sp/cd/re/documents/psframeworkkvol1.pdf [PDF, 8.8MB].

2National Head Start Family Literacy Center (NHSFLC), High Five Mathematize: An Early Head Start and Head Start Math Resource Guide (Washington, DC: HHS, ACF, OHS, NHSFLC, 2010), 39, 54, https://eclkc.ohs.acf.hhs.gov/publication/high-five-mathematize.

3California Department of Education, California Preschool Curriculum Framework Volume 1 (Sacramento, CA: California Department of Education, 2010), 265–268, Algebra and Functions, Patterning, http://www.cde.ca.gov/sp/cd/re/documents/psframeworkkvol1.pdf [PDF, 8.8MB].

Topic:School Readiness

Resource Type: Article

Last Updated: January 30, 2018