Preschooler, experiencing the world through play as they explore and learn with great enthusiasm. Giving preschoolers a solid foundation in early math literacy is critical to their future academic success, not to mention how important it is to their day-to-day functioning.

How preschoolers learn the many aspects of math

Most preschoolers, even without guidance from adults, are naturally interested in math as it exists in the world around them. They learn math best by engaging in dynamic, hands-on games and projects. Preschoolers love to ask questions and play games that involve the many aspects of math. The table below lists the key aspects of preschool math, along with simple games and activities you can use to help your child learn them.

Math Games and Activities

• Count food items at snack time (e.g., 5 crackers, 20 raisins, 10 baby carrots)
• Use a calendar to count down the days to a birthday or special holiday. Help your child see the connection between a numeral like "5," the word "five," and five days on the calendar.
• Practice simple addition and subtraction using small toys and blocks.
• Play simple board games where your child moves a game piece from one position to the next.
• Have your child name the shapes of cookie cutters or blocks.
• Arrange cookie cutters in patterns on a cookie sheet or placemat. A simple pattern might be: star-circle-star-circle.
• Let your child help you measure ingredients for a simple recipe - preferably a favorite!
• Measure your child's height every month or so, showing how you use a yardstick or tape measure. Mark his or her height on a "growth chart" or a mark on a door frame. Do the same with any siblings. Help your child compare his or her own height to previous months and also to their siblings' heights.
• Talk through games and daily activities that involve math concepts.
• Have your child name numbers and shapes.
• Help them understand and express comparisons like more than/less than, bigger/smaller, and near/far.
• Play games where you direct your child to jump forward and back, to run far from you or stay nearby.
• Use songs with corresponding movements to teach concepts like in and out, up and down, and round and round.

Website Ideas

The Early Math Learning website (www. earlymathlearning.com) includes free downloads of PDF files of this Early Learning Math at Home booklet as well as individual chapters. Additional articles and resources for families will be added regularly.

The California Mathematics Council maintains a For Families section at its website (www.cmc-math.org/family/main.html). Here you will find articles on mathematics education issues of interest to parents, hands-on activities to do at home and information on how to host your own Family Math event at your preschool or education center.

The Math Forum (www.mathforum.org) is a web portal to everything “mathematics.” Here you can ask Dr. Math questions and get answers! You will also find weekly and monthly math challenges, Internet math hunts, and math resources organized by grade level.

Head Start–Early Childhood Learning and Knowledge Center (www.eclkc.ohs.acf.hhs.gov/hslc) is linked to the federal Head Start Program. Here you will find information about government programs for early learning, including resources that are available to families.

Thinkfinity (www.thinkfinity.org) is a project of the Verizon Foundation. This website has more than 55,000 resources—including many that focus on math—that have been screened by educators to ensure that content is accurate, up-to-date, unbiased, and appropriate for students. The resources on this website are grouped by grade level and subject area.

PBS Parents, the early education website of the Public Broadcasting Service (www.pbs.org/parents/education/math/activities), offers numerous resources, including the stages of mathematics learning listed for babies through second grade children. It is also a rich source of math activities to do at home

Math at Play (www.mathatplay.org) offers multimedia resources for anyone who works with children from birth to age five. Here you can explore early mathematical development and the important ways that caregivers nurture children’s understanding of math concepts through social-emotional relationships, language, everyday play experiences, materials, and teaching.

Let’s Read Math (www.letsreadmath.com/math-and-childrens-literature/ preschool/) wants to make parents and families aware of the growing body of children’s literature with themes related to mathematics. Here you will find a long annotated list of live links to preschool children’s books with math themes, listed by title, author, and mathematics topic.

• 90 percent of children with reading difficulties will achieve grade level in reading if they receive help by the first grade.
• 75 percent of children whose help is delayed to age nine or later continue to struggle throughout their school careers.
• If help is given in fourth grade, rather than in late kindergarten, it takes four times as long to improve the same skills by the same amount.

Key Six Pre-Reading Skills

(for children from birth through 5 years)

Print Motivation

• Being excited about and interested in books
• What can you do?
• Make sure book sharing time is fun.
• For children with short attention spans, keep it short, but read more often.
• Don’t get upset when they put books in their mouths.
• Read books you enjoy.
• Choose books about things that interest the child.
• Read with a natural, but cheerful voice.

Print Awareness

• Understanding that print on a page represents words that are spoken, knowing how to follow words on a page, and knowing how to hold a book.
• What can you do?
• Allow children to handle the book and turn pages.
• Use your finger to point out words as you move across the page.
• Pointing out signs in your environment.
• Read books with large bold print.
• Introduce the cover and talk about the author and illustrator.

Phonological Awareness

• Understanding that words are made up of smaller sounds. Hearing and playing with smaller sounds in words. Phonological Awareness comes before phonics.
• What can you do?
• Encourage your baby to babble, changing the beginning sounds.
• Sing songs. Clap along with the song. Use rhythm sticks and shakers.
• Do action rhymes.
• Learn nursery rhymes. For older children, substitute a non-rhyming word in place of the rhyming word and see if they notice the difference.
• Read books with rhyming texts.
• Play “Say it fast; say it slow.” Butterfly Butt er fly Turtle Tur tle

Vocabulary

• Knowing the names of things, feelings, concepts, and ideas. Knowing the meaning of words and connecting words to objects, events, or concepts in the world.
• What can you do?
• Any book will help with this, but choosing ones with words not used in daily conversation and nonfiction books are especially helpful.
• Label things.

Narrative Skills

• Being able to describe things and events. Being able to tell and understand stories.
• What can you do?
• Talk with children about what you are doing. Ask them “What?” or other open-ended questions that cannot be answered with a simple “Yes” or “No.”
• Ask, “What happens next?”
• Allow young children time to respond. Be patient.
• Tell stories.
• Encourage pretend play.
• Let them help you tell flannel board stories.
• Read stories with a beginning, middle, and end.

Letter Knowledge

• Understanding that letters are different from each other. Recognizing letters and knowing that they have different names and sounds.
• What can you do?
• Let babies play with shapes.
• Allow children to handle letter shapes.
• Learn the alphabet song.
• Read alphabet books and books about shapes.
• Books where you have to find things.
• Help your child identify the first letter in his/her name. Then find that letter in books, on signs, and other things in the environment.

It’s a busy life filled with lots of things to do and even more distractions. All that’s needed is a comfy place, an adult, one child or more, and a good book to share.

The question becomes-How do you choose what to read aloud to a child? The first thing to ask yourself is simply: Do I like it? Then consider if you’re comfortable with the content. Is there something that you may want to omit or that you’d rather not tackle with your child? Children seem to know instinctively when an adult really likes something or if they’re just faking it.

Sometimes children respond differently to a book than the adults who try to share it. A book that the adult thinks is fantastic may get a ho-hum or downright negative response from the listener or sometimes the reverse is true, too. That’s OK; children have tastes, though sometimes they’re just not ready for a particular book. It’s perfectly okay not finish the book. Just try another one.

What are you looking for? 

Is there something for listeners to grab hold of? For young children, is there a phrase or perhaps something hidden in the illustration to keep them actively engaged? For older children, is there something to think about or talk about or even follow up about? Does it build on a child’s existing interest or maybe introduce a new one?

There are lots of educational reasons to read aloud to children. Reading aloud with children of all ages not only builds language — a key ingredient to success in school — but most importantly, it’s a time for adults to share with the children in their lives and to build a common, positive experience that lasts long after a book is closed.

Babies and Toddlers Picture Book Recommendations 

It’s never too early to start reading to young children. Young children are building vocabularies long before they can say them or use them in conversation. Try one of my favorite books with your baby or toddler. It doesn’t matter if you don’t read every word, but it is important that you share your enthusiasm. You can even do some of the actions suggested by the words or pictures, or you can make up your own. Maybe you just want to talk about the pictures and point to them as you do. It’s the sharing that’s important!

All Fall Down
By: Helen Oxenbury
Young children will appreciate the game played by children (also in Tickle Tickle) in this sturdy book. Rhyming text and uncluttered illustrations are just right to share with the youngest child.

All of Baby, Nose to Toes
By: Victoria Adler
All of a newborn, from head to toe, is appreciated and loved by various members of an adoring family. Lively language and joyful illustrations are used in this ebullient celebratory book.

Diggers Go
By: Steve Light
What sound does an excavator or a forklift make? Each makes its own noise, presented here in bold, dramatic typefaces dynamically shown on sturdy horizontal pages. Children can be encouraged to repeat sounds made by the variety of equipment — likely to delight construction aficionados.

I Kissed the Baby!
By: Mary Murphy
A new baby creates lots of excitement and all the animals want to kiss the baby duckling! Black pages with bold white lines depict the animals with splashes of color to highlight the joy and a repeating text makes this just right to encourage young children.

Lots of Lambs
By: Laura Numeroff
Feel the lamb's wool, then lift the umbrella to find lambs. There are lambs of all types and in many moods doing lots of things. Staccato, rhyming, catchy text is accompanied by expressive images of lively lambs that encourage active engagement with each page.

Lullaby and Kisses Sweet: Poems to Love with Your Baby
By: Lee Bennett Hopkins
Every day, young children and their families can celebrate familiar things and activities in this sturdy, handsome, and appealing collection of 30 poems. Each short piece by a range of poets is about food, family, firsts, play and bedtime, creating a memorable collection just right for the youngest listener.

Maisy's Animals/Los animales de Maisy
By: Lucy Cousins
Maisy’s favorite animals are introduced in both English and Spanish accompanied by Cousin’s signature illustrations on sturdy pages. Maisy is a familiar character with a simplicity of illustration and text that captivates young children.

Max's First Word
By: Rosemary Wells
No matter how hard Ruby tries to get her baby brother to say the names of the objects around him, Max will only say “Bang!” One day, however, Ruby gets a big surprise from Max’s first real word. Understated humor and bright, bold illustrations appeal to children and their adults.

One, Two, Buckle My Shoe
By: Jane Cabrera
The familiar rhyme continues all the way to 20 as a rabbit helps the farm animals get ready for a party. A small chick on each page encourages young readers to look closely as chicks are hidden on each spread. Bright, boldly lined illustrations are appealing and child-like.

Peek-a Who?
By: Nina Laden
What can you “peek-a” through the die-cut window? Does it “moo”, say “boo” or could it be YOU? Turn the page and find out! A predictable format and bold illustrations are sure to engage and delight.

Peekaboo Kisses
By: Barney Saltzberg
Peekaboo! What do you see? Lift the flap and see the kissable, touchable baby animal & dash; until the final spread. The mirror on the final pages lets young children see themselves in this boldly illustrated, participatory book.

Say Goodnight
By: Helen Oxenbury
Even the most active baby or toddler must sleep sometime, and in this story the children "say goodnight." Similar to Tickle Tickle and All Fall Down, this is a sure hit to share with babies and toddlers.

Say Hello Like This!
By: Mary Murphy
How do animals greet everyone? With woofs and meows for a big hello! Beginning with a dog's "licky and loud … bow-wow-wow-wow!" the split pages hide the sounds until the turn — sure to delight young readers. Bold, colorful illustrations exude joy and spirit.

Tickle Tickle
By: Helen Oxenbury
Chubby cheeked babies of many hues are shown in crisp illustrations doing things that babies do. The simple words are playful and energetic, just like the children in this and others by Oxenbury such as Clap Hands and All Fall Down.

My favorite preschool read aloud to come. Even in my current position in Intermediate Elementary students my student's love when I do story hour. Have a great weekend.

Preschool is a beginning of learning to weaver letters into words. They build their language skills and start to make sense of the sound/letter system to begin to read. These days preschool is structured to prepare preschoolers for reading and math. Below are some ideas to what parents can to foster beginning reading skills.

At this stage, students uses their ever-increasing language skills to become a “big talker” and develops an awareness of the power of the written word. Parents and caregivers of preschoolers can help them develop into readers and writers by playing with letters and their sounds, promoting dramatic play using characters from books, and reading lots of books together.

Through daily experiences, preschoolers learns more and more about the way things work in the world. At the same time, they are able to use his ever-increasing vocabulary and language skills to share their observations, ideas, and imaginary worlds with other children and adults. Young children can be entertaining storytellers, engaging conversational partners, and frustrating negotiators. During the preschool years, students become aware that the world is filled with letters and may begin to recognize familiar words.

Parents can help your preschooler become an eager reader and writer through simple conversations and reading together. It helps to plan regular times to read with your young child and talk together daily about things that interest him. You can turn everyday experiences such as waiting in lines, doing errands, and riding the bus into conversation starters. By talking about your child’s ideas, observations, and feelings, you prepare your young child for reading and writing about the world.

How to Help Your Preschooler Get Ready for Reading

• Point to the words as you read aloud. When you point to the words as you read or talk about the title and author, you help your child learn about the different parts of the book. You also show him that reading involves connecting spoken words to printed ones.
• Repeat your child’s words the right way. Most young children make grammatical errors while they are learning to talk. Instead of correcting, try repeating your child’s words the correct way. This way, you teach her proper grammar and demonstrate that making mistakes is how we learn.
• Join your child in pretend play. Pretending actually helps children develop language and literacy skills. They use new words and ways of speaking when they play different roles. They also practice making up stories, a skill that helps them understand books read aloud to them.
• Make up rhymes as you go about your day. Rhyming and other kinds of word play help your child to hear differences between sounds to understand that words are made up of sounds. Being able to rhyme will actually help your child learn to read and write.
• Draw and write alongside your child. One way to encourage your child to write is to show him how you write. When you write, talk to him about what you are doing. That way, you teach your child how we use writing in everything from grocery lists to phone messages.

One of the most important math skills students need to learn is number sense. It is the bases for more completed math skills we learn through elementary. I have included some games you can play this summer to build number sense while having fun!

Preschool number activities often involve counting, but merely reciting the number words isn't enough. Kids 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 concepts, including:

• Relative magnitudes
• The one-to-one principle of counting and cardinality (two sets are equal if the items in each set can be matched, one-to-one, with no items left over)
• The one-to-one principle of counting (each item to be counted is counted once and only once)
• The stable order principle (number words must be recited in the same order)
• The principle of increasing magnitudes (the later number words refer to greater cardinality)
• The cardinal principle   

Common Core Standards These Games Target:

Know number names and the count sequence.
CCSS.MATH.CONTENT.K.CC.A.1: Count to 100 by ones and by tens.
CCSS.MATH.CONTENT.K.CC.A.2: Count forward beginning from a given number within the known sequence (instead of having to begin at 1).
CCSS.MATH.CONTENT.K.CC.A.3: Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). K.CC.B:
Count to tell the number of objects.
CCSS.MATH.CONTENT.K.CC.B.4: Understand the relationship between numbers and quantities; connect counting to cardinality.
CCSS.MATH.CONTENT.K.CC.B.4.A: When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.
CCSS.MATH.CONTENT.K.CC.B.4.B: Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.
CCSS.MATH.CONTENT.K.CC.B.4.C: Understand that each successive number name refers to a quantity that is one larger.
CCSS.MATH.CONTENT.K.CC.B.5: Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects.
Compare numbers.
CCSS.MATH.CONTENT.K.CC.C.6: Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.
CCSS.MATH.CONTENT.K.CC.C.7: Compare two numbers between 1 and 10 presented as written numerals.

Most activities use a set of cards and counting tokens. Here’s what you need to get started. Preparing for preschool number activities:

Cards

Cards will be used in two ways, (1) as displays of dots for kids to count, and (2) as templates for kids to cover with tokens. Make your cards from heavy-stock writing paper, marking each with an Arabic numeral (1-10) and the corresponding number of dots.

Make your dots conspicuous, and space them far enough apart that your child can easily place one and only one token on top of each dot. The larger your tokens, the larger your cards will need to be.

In addition, you might make multiple cards for the same number--each card bearing dots arranged in different configurations. For example, one “three” card might show three dots arranged in a triangular configuration. Another might show the dots arranged in a line. Still another might show the dots that appear to have been placed randomly. But whatever your configuration, leave enough space between dots for your child to place a token over each dot.

Tokens

Kids can use a variety of objects for tokens, but keep in mind two points.

1. Children under the age of three years are at special risk of choking, so choose big tokens. According to the U.S. Consumer Product Safety Commission, a ball-shaped object is unsafe if it 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.

2. Kids can get distracted if your tokens are too interesting, so it's best to avoid the fancy plastic frogs or spiders

Games to play

One you have your cards and tokens, you can play any of the preschool number activities below. As you play, keep in mind the points raised in 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.

The basic game: One-to-one matching

Place a card, face up, before your child. Then ask your child to place the correct number of tokens on the card—one token over each dot.

After the child has finished the task, replace the card and tokens and start again with a new card. Once your child has got the hang of this, you can modify the game by helping your child count each token as he puts it in place.

The Tea Party: Relative magnitudes

Choose two cards, each displaying a different number of dots, taking care that the cards 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.

Next, set one card in front of your child and the other in front of you. Have your child cover all the dots with tokens (pretending they are cookies) and ask her

“Which of us has more cookies?”

After she answers you, you can count to check the answer. But I’d skip this step if you are working with larger numbers (like 6 vs. 12) that are beyond your child’s current grasp. You don’t want to make this game feel like a tedious exercise.

As your child becomes better at this game, you can try somewhat smaller ratios (like 5 vs. 9).

And for another variant, ask your child to compare the total amount of cookies shared between you with the cookies represented on another, third card. In recent experiments, adults who practiced making these sorts of “guesstimates” experienced a boost in their basic arithmetic skills.

Bigger and bigger: Increasing magnitudes

Instead of playing with the tokens, have your child place the cards side-by-side in correct numeric sequence. For beginners, try this with very small numbers (1, 2, 3) and with numbers that vary by a large degree (e.g., 1, 3, 6, 12).

Sharing at the tea party: The one-to-one principle

Choose three toy creatures as party attendees and have your child set the table—providing one and only plate, cup, and spoon to each toy. Then give your child a set of “cookies” (tokens or real edibles) and ask her to share these among the party guests so they each receive the same amount. Make it simple by giving your child 6 or 9 tokens so that none will be left over.

As always, go at your child’s pace and quit if it isn’t fun. 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.

Matching patterns: Counting

Play the basic game as described above, but instead of having your child place the tokens directly over the dots, have your child place the tokens alongside the card. Ask your child to arrange his tokens in the same pattern that is illustrated on the card. And count!

Matching patterns: Conservation of number

For this game, use cards bearing dots only--no numerals. To play, place two cards--each bearing the same number of dots, but arranged in different patterns--side by side. Ask your child to recreate each pattern using his tokens. When she’s done, help her count the number of tokens in each pattern. The patterns look different, but they use the same number of dots/tokens.

The cookie maker: Making predictions about changes to a set

Even before kids master counting, they can learn about the concepts of addition and subtraction. Have a puppet “bake cookies” (a set of tokens) and ask your child to count the cookies (helping if necessary). Then then have the puppet bake one more cookie and add it to the set. Are there more cookies or fewer cookies now? Ask your child to predict how many cookies are left. Then count again to check the answer. Try the same thing with subtraction by having the puppet eat a cookie.

Don’t expect answers that are precise and correct. But you may find that your child is good at getting the gist. When researchers asked 3-, 4- and 5-year olds to perform similar tasks, they found that 90% of the predictions went in the right direction.

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. Games can be very useful for reinforcing and developing ideas and procedures previously introduced to children. Although a suggested age group is given for each of the following games, it is the children's level of experience that should determine the suitability of the game. Several demonstration games should be played, until the children become comfortable with the rules and procedures of the games.

Deal and Copy (4-5 years) 3-4 players
Materials: 15 dot cards with a variety of dot patterns representing the numbers from one to five and a plentiful supply of counters or buttons.

Rules: One child deals out one card face up to each other player. Each child then uses the counters to replicate the arrangement of dots on his/her card and says the number aloud. The dealer checks each result, then deals out a new card to each player, placing it on top of the previous card. The children then rearrange their counters to match the new card. This continues until all the cards have been used.

Variations/Extensions:

Each child can predict aloud whether the new card has more, less or the same number of dots as the previous card. The prediction is checked by the dealer, by observing whether counters need to be taken away or added.

Increase the number of dots on the cards.

Memory Match (5-7 years) 2 players
Materials: 12 dot cards, consisting of six pairs of cards showing two different arrangements of a particular number of dots, from 1 to 6 dots. (For example, a pair for 5 might be Card A and Card B from the set above).
Rules: Spread all the cards out face down. The first player turns over any two cards. If they are a pair (i.e. have the same number of dots), the player removes the cards and scores a point. If they are not a pair, both cards are turned back down in their places. The second player then turns over two cards and so on. When all the cards have been matched, the player with more pairs wins.

Variations/Extensions

• Increase the number of pairs of cards used.
• Use a greater number of dots on the cards.
• Pair a dot card with a numeral card.

What's the Difference? (7-8 years) 2-4 players

Materials: A pack of 20 to 30 dot cards (1 to 10 dots in dice and regular patterns), counters.
Rules: Spread out 10 cards face down and place the rest of the cards in a pile face down. The first player turns over the top pile card and places beside the pile. They then turns over one of the spread cards. The player works out the difference between the number of dots on each card, and takes that number of counters. (example: If one card showed 3 dots and the other 8, the player would take 5 counters.) The spread card is turned face down again in its place and the next player turns the top pile card and so on. Play continues until all the pile cards have been used. The winner is the player with the most counters; therefore the strategy is to remember the value of the spread cards so the one that gives the maximum difference can be chosen.

Variations/Extensions:
Try to turn the spread cards that give the minimum difference, so the winner is the player with the fewest counters. Roll a die instead of using pile cards. Start with a set number of counters (say 20), so that when all the counters have been claimed the game ends. Use dot cards with random arrangements of dots.