# Preschool number activities: How do you introduce numbers to preschoolers?

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 amount associated with a given number.

Where does number sense come from?

Experiments suggest that even 6-month-old infants can tell the difference between 4 cookies and 8. And 14-month-old babies seem to grasp that counting tells us something about quantity (Wang and Feigenson 2019).

So that's a start. What's needed -- as kids get older -- are hands-on experiences. Inspired by research, the following games encourage kids to think about several key concepts, including

• 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.

### 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.

Kids 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.

### 2. Sharing 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.

Game one: Guess the right order.

To play this game, 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.

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.

What's the point of all this guesswork?

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 example, 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).

Game two: Guess which card has more dots?

To play this game, select two cards, each displaying a different number of dots, and show them to your child. Which card has more dots?

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?"

Game three: Big guys eat more.

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 similar 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).

### 4. Spot the goof: Teaching the one-to-one principle of counting and the principle of cardinality

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 value.

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 Parenting Science 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.

For educational purposes only. If you suspect you have a medical problem, please see a physician.

### 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 and Feigenson 2019.  Infants recognize counting as numerically relevant. Developmental Science 22(6): e12805.

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.

Image credits for "Preschool number activities"

title image of young children with number board by Ivan Radic / flickr

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