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Supporting Young Children’s Mathematical Thinking at Home

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The following ideas are adapted from chapter 5 of Young Children’s Mathematics, by Thomas P. Carpenter, Megan L. Franke, Nicholas C. Johnson, Angela Chan Turrou, and Anita Wager.


There are many opportunities for children to learn to count and begin to solve problems at home. During this time of remote teaching and learning, teachers can help parents and caregivers notice, support, and extend children’s math thinking in various situations. In fact, mathematical understanding can emerge from many of the everyday activities children already do.

Children in preschool and primary grades frequently engage in counting and problem solving when they play with materials that we don’t think of as inherently mathematical or when they are making up stories. By asking simple questions that support students’ thinking, families and caregivers can help young learners build mathematical understandings as they play and discover.

Download a Sample Chapter of Young Children’s Mathematics


Below are some ideas that teachers can share with families to use with their students at home.

Outdoor Play and Collecting

If families have access to safe outdoor spaces where children can play, they can explore important ideas about counting through the objects children collect or see. Asking, “How many leaves do you have?” or “How many birds are on the tree?” gives children a chance to share their counting with you. Briefly mathematizing children’s play like this helps you learn about a child’s thinking without taking away from their ability to explore on their own.


Counting collections of objects provides children with opportunities to engage in a variety of practices that support oral counting, grouping, recording, and representing their thinking. Provide children with a variety of collections of different numbers of objects – keys, coins, shells, buttons, sticks, or whatever you have handy. Listen to children as they count. Are they able to:

  • Keep track of the sequence of numbers (1, 2, 3…)? How far can they keep the sequence? Are there places where they stumble or skip numbers (this often occurs in the teen numbers and crossing decades, such as going from 19 to 20 or 21 to 30)? Even if they skip numbers, is the sequence they use consistent?
  • Maintain one-to-one correspondence (matching each object to one and only one number)? How do they organize the objects to keep track?
  • Identify the last number they say as the total number of objects? If you ask, “How many are there?” after they count, do they tell you the number, or do they recount?

These three aspects of the understanding of counting develop at different rates for different children. Lots of practice counting collections of objects helps build all three.


Dramatic and Pretend Play

Many children love playing make-believe games, and these games provide more opportunities for the same kind of brief mathematical interactions. Playing store, pretend baking or cooking, and other kinds of pretend play involve lots of math. Playing store lets children think about money amounts, making change, and how much money they have left. If children are making pretend cookies, you can ask questions like, “How many round cookies are there?” “Are there more blue cookies or red cookies?” or “You have 4 cookies. How many more would you need to have 10 cookies?” This can lead to new numerical discoveries for students, like Kazadi, who gave pretend cookies to other children and then told his teacher that he had fewer cookies because he gave some away. The teacher asked him some questions about how many he started with, how many he gave away, and how many he had left. These “how many” questions supported him to reflect on the quantities involved in the situation – without unduly interrupting his play.
In all these examples, adults need to be ready to jump into the play and to walk a fine line between taking over and sitting back, asking just enough questions. It is important to ask children “How many?” when they are playing with countable materials, but there are other mathematically productive questions that help adults learn about children’s thinking and help children think about the everyday mathematics they were engaging in. For instance:

  • “Are there more blue cookies or red cookies?” requires children to compare quantities.
  • “You have 4 cookies. How many more would you need to have 10 cookies?” helps children think about joining and separating numbers, the foundation of addition and subtraction.
  • “How many cookies did you start with? How many did you give away? How many do you have left?” also encourages children to think about joining and separating.

Math Games

Games, particularly linear board games, provide opportunities to support children’s counting. Asking children to count spaces as they move a game piece supports one-to-one correspondence and the counting sequence. Other games using simple materials include:

The Shake and Build Game: This game requires one 6-sided die or number cube, and connecting cubes or other stackable objects. You can also create a sheet or mat with the numbers 1-6 on it. Children roll the die and make a stack of cubes to match the number rolled, aiming to fill each spot on the mat. On their own, children often begin to pose their own problems and make discoveries, like Joaquin, who noticed that his tower of 5 cubes was 1 shorter than his tower of 6 cubes. His teacher asked, “So does that mean that 5 is one less than 6?” to which, after some thinking, he said “Yes!”

The Objects in a Pail Game: This game uses five cups (the “pails”) numbered 1-5 and craft sticks or other items that will be visible when put into the cups. The original version of the game just asks children to put the number of sticks on the cup into that cup, but some children invented a new version of their own. In this version, one child chooses one of the cups, turns it so the label is not visible to other players, then puts the matching number of sticks into the cup. The other children have to say what the hidden number is.

As with Objects in a Pail, encourage children to explore materials and invent their own games. They will surprise you with their creativity – and their mathematical curiosity and understanding.

Additional Resources: 

Linda Levi, one of the authors of Children’s Mathematics and Extending Children’s Mathematics, shared more ideas for parents in this blog post. Finder her on Twitter at @LLeviCGIMath

Heinemann Fellow Kent Haines maintains a collection of math games with tips for playing them at Gamesforyoungminds.com. Find him on Twitter at @KentHaines

Learn more about Cognitively Guided Instruction and CGI Professional Books:

Learn More About Cognitively Guided Instruction

Posted by: Jennifer MoorePublished:

Topics: Thomas Carpenter, Young Children's Mathematics, Linda Levi, Kent Haines, Distance Learning, Covid_19

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