Preschool number activities
© 2008 - 2017 Gwen Dewar, Ph.D., all rights reserved
Preschool number activities often involve counting, but
merely reciting the number words isn't enough.
Children also need to develop "number sense," an
intuitive feeling for the actual quantity associated with a given number.
That's where these activities can help. Inspired by
research, the following games encourage kids to think about several key
- The one-to-one principle of numerosity (two sets are equal
if and only if their items can be placed in perfect, one-to-one correspondence)
- The principle of increasing magnitudes (the later number
words refer to greater numerosities)
- The one-to-one principle of counting (each item is to be
counted is counted once and only once)
- The stable order principle (number words must be recited in
the same order)
- The cardinal principle (the last word counted represents the
numerosity of the set)
As your child engages in these preschool number activities, keep in mind this advice (from my evidence-based guide to preschool math lessons):
Start small. It's important to adjust the game to your child's attention span and developmental level. For beginners, this means counting tasks that focus on very small numbers (up to 3 or 4).
Keep it fun. If it's not playful and fun, it's time to stop.
Be patient. It takes young children about a year to learn how the counting system works.
Six evidence-based preschool number activities
1. Matching sets: Teaching the one-to-one principle of numerosity
Matching items one-to-one is a surprisingly important mathematical concept. It's how we prove that two quantities are equal. Two sets contain the same number of items if the items in each set can be matched, one-to-one, with no items left over.
Researchers call this the "one-to-one principle of numerosity," and you can help kids master the concept with these simple, preschool number activities.
First, present kids with a small set of tokens arranged on a table or floor. Then ask them to create an identical copy of this set using additional tokens. When finished, make a count of the items in each set -- the original and the copy.
Second, you can present kids with two sets at once. In this case, make sure each set contains the same number of tokens, but arrange the tokens in different spatial patterns. Then have your child reproduce both of these sets, and do an end count to confirm that all sets are equal.
It can take almost a year for a two- or three-year-old to really understand how the counting system works, so don't be surprised if younger children have trouble counting beyond "1-2-3." Help kids with counting if needed, and challenge them to a greater number of tokens as their skills grow.
For another approach to these games, use printed cards, each
with a picture depicting a set of dots or other small items. The child views
the card and creates a matching set of items using tokens. You can make the
cards yourself, or buy some ready-made.
What should you use for tokens? For children under the age
of three years, it's important to choose something that won't pose a choking
hazard. According to the U.S. Consumer Product Safety Commission, a ball-shaped
object is unsafe for children under 3 years if the item is smaller than a 1.75"
diameter golf ball. Other objects are unsafe if they can fit inside a tube with
a diameter of 1.25" inches. Pieces from your toddler's building block set
might do the job.
Also, try to stick with plain-looking tokens and card
symbols. You might think that little toy frogs or spiders would make counting
more fun. But researchers have found that young children tend to get distracted
by these details. They learn more from preschool number activities when they
manipulate simpler, more abstract items (Petersen and McNeil 2012). Plastic
chips -- like those used for poker or bingo -- are a good choice for kids aged
3 and up.
at the tea party: Dividing up tokens into equal portions
Here is another activity to help kids practice one-to-one
matching, inspired by the research of Brian Butterworth and his colleagues (2008).
Choose three toy creatures to play the part of party
attendees, and have your child set the table for them. Then give your child a
set of "goodies" (tokens or real edibles) to share with the party
guests. The total number of goodies should be a multiple of 3, so your child
can distribute all the items equally and have no leftovers.
If your child makes a mistake and gives one creature too
many tokens, you can play the part of another creature and complain.
You can also play the part of tea party host and
deliberately make a mistake. Ask for your child's help? Did someone get too
many tokens? Or not enough? Have your child fix it.
Once your child gets the hang of things, try providing him
with one token too many and discuss what to do about this leftover.
One solution is to divide the remainder into three equal
bits. But your child may come up with other, non-mathematical solutions, like
eating the extra bit himself.
3. Sorting by quantity: Teaching the principle of increasing magnitudes
For these preschool number activities, use cards like those
described in #1. You can use them in three ways.
First, shuffle the cards, and then ask your child to place
them, side by side, in a sequence of increasing magnitude.
For children who haven't yet learned to count, use cards
that vary by a substantial amount, e.g., 3, 6, 10, and 15. Experiments show
that even babies can spot differences this large, and practicing these tasks
may help children hone their estimation abilities -- abilities which are
essential for future mathematics achievement. For children with emerging
counting skills, use cards that differ by a single dot, and have kids guess first, then check their answers by counting.
Second, select two cards, each displaying a different number
of dots, and show them to your child. Which card has more dots?
To play this game, make sure you start with cards that
differ by a ratio of at least 2:1. For
instance, try 1 vs. 2, 2 vs. 4, and 2 vs. 5. You can also try larger numbers,
like 6 vs. 12.
As your child gets practice with these easy-to-discriminate differences, you can present her with increasingly difficult choices (like 6 versus 8; or even 9 versus 10).
For a more playful variant of the game, you can use
tokens instead of cards, and pretend they are something fun, like cakes. Dole
out different amounts between you and ask, "Who has more?"
Be sure to give your child feedback about the correct
In a recent study, researchers tested five-year-olds with computer-based versions of these preschool number activities. The children weren't given enough time to count; they simply took a quick look and answered based on their intuitive, visual impression. Kids who practiced making progressively more difficult discriminations -- getting accurate feedback after each attempt -- experienced subsequent improvements in their ability to solve problems using symbolic numbers (Wang et al 2016).
Finally, try this game of sorting magnitudes.
To play, use your cards, as well as three soft animal toys or dolls of varying size -- small, medium, and large. Pretend the toys are party guests, and the items on the cards treats. Then
- line up the three toys in order of size,
- present your child with three cards, each card depicting a different number of dots, and
- ask your child to give the greatest number of treats to the largest toy, the second-greatest number to the second-largest toy, and the smallest number to the smallest toy.
Tell your child when he responds correctly ("That's right!"), and, if he makes a mistake, guide him to make another attempt ("That's not right -- try again!").
If you prefer, you can play the game with tokens instead of cards. And once you child learns to read and understand number symbols, you can use cards that display only Arabic numerals.
When researchers tested these preschool number activities, they found that both dot-based and numeral-based games helped children develop better intuitions about quantity. But kids who played the Arabic numeral version of the game experienced greater growth in basic arithmetic skills (Honoré and Noël 2016).
Image of preschool number activities from study by Honoré and Noël (2016).
the goof: Teaching the one-to-one principle of counting and the principle of
Here's another "one-to-one" principle -- this time
the one-to-one principle of counting. Kids need to learn that each item in a
series is counted once and only once. And they also need to learn the principle
of cardinality, the idea that the last word in our count represents the
numerosity of a set.
Children learn these ideas through practice. But they might
also learn by correcting others who make mistakes. In one study, researchers
asked preschoolers to watch--and help--a rather incompetent puppet count a set
of objects (Gelman et al 1986). The puppet would occasionally violate the
one-to-one principle by double-counting (e.g., “one, two, three, three,
four...). He also sometimes skipped an object or repeated the wrong cardinal
Kids ranging in age from 3 to 5 were pretty good at detecting these violations. So your child might have fun correcting your own goofball at home.
What if your child doesn't notice an error? Correct the goofball yourself. And either way, ask your child to explain what went wrong. In another, similar study, researchers found that preschoolers didn't make conceptual progress unless they were asked to explain the puppet's mistakes (Muldoon et al 2007).
For a discussion of how self-explanation can make preschool number activities and other educational experiences more valuable, see this review of the evidence.
5. One less / one more: Helping preschoolers develop intuitions about addition and subtraction
Young children have a long way to go before they are ready to perform basic arithmetic calculations like "2 +3 = 5," or "7 - 3 = 4." But research suggests we can help pave the way with preschool number activities like these.
Have a puppet or other toy character "bake cakes"
(a set of tokens) and ask your child to count the treats. (You can count
together if your child needs help.) Next, have the puppet bake one more cake
and add it to the set.
Are there more cakes or fewer cakes now? Ask your
child, and provide him with correct feedback afterwards.
Try the same thing with subtraction by having the puppet
"eat" a cake. And vary the game by adding or subtracting other small
amounts, like two or three.
Should we expect children to come up with accurate answers? Not necessary -- especially not if they are under the age of three years (Izard et al 2014).
But the experience of predicting and
checking is valuable, and even when kids get the precise number wrong, they do
a good job coming up with reasonable guesses. When researchers asked 3-, 4- and
5-year-olds to perform these tasks, they found that 90% of the guesses were in
the right direction (Zur and Gelman 2004).
6. The Big Race: Increasing magnitudes and the number line
As your child begins to master the first few number words, you can also try these research-tested preschool number activities for teaching kids about the number line.
References: Preschool number activities
Butterworth B, Reeve R, and Lloyd D. 2008. Numerical thought with and
without words: Evidence from indigenous Australian children.
Proceedings of the National Academy of Sciences 105(35): 13179-13184.
Gelman R, Meck E, and Merkin S. 1986. Young children's numerical competence. Cognitive Development 1(1): 1-29.
Honoré N and Noël MP. 2016. Improving Preschoolers'
Arithmetic through Number Magnitude Training: The Impact of Non-Symbolic and
Symbolic Training. PLoS One. 11(11):e0166685.
Izard V, Streri A, Spelke ES. 2014. Toward exact number:
young children use one-to-one correspondence to measure set identity but not
numerical equality. Cogn Psychol. 72:27-53.
Muldoon KP, Lewis C, Francis B. 2007. Using cardinality to
compare quantities: the role of social-cognitive conflict in early
numeracy. Developmental Psychology 10(5):694-711.
Park J and Brannon EM. 2013. Training the Approximate Number
System Improves Math Proficiency. Psychol Sci. 2013 Oct;24(10):2013-9.
Petersen LA and McNeil NM. 2013. Effects of Perceptually Rich
Manipulatives on Preschoolers' Counting Performance: Established
Knowledge Counts. Child Dev. 84(3):1020-33.
Wang JJ, Odic D, Halberda J, Feigenson L. 2016. Changing the
precision of preschoolers' approximate number system representations changes
their symbolic math performance. J Exp Child Psychol. 147:82-99.
Zur O and Gelman R. 2004. Young children can add and subtract by
predicting and checking. Early childhood Research Quarterly 19: 121-137.
Content of "Preschool number activities" last modified 9/17
Image credits for "Preschool number activities"
title image by istock
images of supplies for preschool number activities copyright Parenting Science
image of teddy bear tea party by Virginia State Parks
photograph of child looking at bears by Tom Page / flickr
image of bears and bags courtesy N. Honoré and MP Noël / PLos One 2016
image of puppet copyright Parenting Science