# Early math concepts

Before they start school, most children develop an understanding of addition and subtraction through everyday interactions. Learn what informal activities give children a head start on early math skills when they start school.

Children are using early math skills throughout their daily routines and activities. This is good news as these skills are important for being ready for school. But early math doesn’t mean taking out the calculator during playtime. Even before they start school, most children develop an understanding of addition and subtraction through everyday interactions. For example, Thomas has two cars; Joseph wants one. After Thomas shares one, he sees that he has one car left (Bowman, Donovan, & Burns, 2001, p. 201). Other math skills are introduced through daily routines you share with your child—counting steps as you go up or down, for example. Informal activities like this one give children a jumpstart on the formal math instruction that starts in school.

What math knowledge will your child need later on in elementary school? Early mathematical concepts and skills that first-grade mathematics curriculum builds on include: (Bowman et al., 2001, p. 76).

• Understanding size, shape, and patterns
• Ability to count verbally (first forward, then backward)
• Recognizing numerals
• Identifying more and less of a quantity
• Understanding one-to-one correspondence (i.e., matching sets, or knowing which group has four and which has five)

### Key Math Skills for School

More advanced mathematical skills are based on an early math “foundation”—just like a house is built on a strong foundation. In the toddler years, you can help your child begin to develop early math skills by introducing ideas like: (From Diezmann & Yelland, 2000, and Fromboluti & Rinck, 1999.)

#### Number Sense

This is the ability to count accurately—first forward. Then, later in school, children will learn to count backwards. A more complex skill related to number sense is the ability to see relationships between numbers—like adding and subtracting. Ben (age 2) saw the cupcakes on the plate. He counted with his dad: “One, two, three, four, five, six…”

#### Representation

Making mathematical ideas “real” by using words, pictures, symbols, and objects (like blocks). Casey (aged 3) was setting out a pretend picnic. He carefully laid out four plastic plates and four plastic cups: “So our whole family can come to the picnic!” There were four members in his family; he was able to apply this information to the number of plates and cups he chose.

#### Spatial sense

Later in school, children will call this “geometry.” But for toddlers it is introducing the ideas of shape, size, space, position, direction and movement. Aziz (28 months) was giggling at the bottom of the slide. “What’s so funny?” his Auntie wondered. “I comed up,” said Aziz, “Then I comed down!”

#### Measurement

Technically, this is finding the length, height, and weight of an object using units like inches, feet or pounds. Measurement of time (in minutes, for example) also falls under this skill area. Gabriella (36 months) asked her Abuela again and again: “Make cookies? Me do it!” Her Abuela showed her how to fill the measuring cup with sugar. “We need two cups, Gabi. Fill it up once and put it in the bowl, then fill it up again.”

#### Estimation

This is the ability to make a good guess about the amount or size of something. This is very difficult for young children to do. You can help them by showing them the meaning of words like more, less, bigger, smaller, more than, less than. Nolan (30 months) looked at the two bagels: one was a regular bagel, one was a mini-bagel. His dad asked: “Which one would you like?” Nolan pointed to the regular bagel. His dad said, “You must be hungry! That bagel is bigger. That bagel is smaller. Okay, I’ll give you the bigger one. Breakfast is coming up!”

#### Patterns

Patterns are things—numbers, shapes, images—that repeat in a logical way. Patterns help children learn to make predictions, to understand what comes next, to make logical connections, and to use reasoning skills. Ava (27 months) pointed to the moon: “Moon. Sun go night-night.” Her grandfather picked her up, “Yes, little Ava. In the morning, the sun comes out and the moon goes away. At night, the sun goes to sleep and the moon comes out to play. But it’s time for Ava to go to sleep now, just like the sun.”

#### Problem-solving

The ability to think through a problem, to recognize there is more than one path to the answer. It means using past knowledge and logical thinking skills to find an answer. Carl (15 months old) looked at the shape-sorter—a plastic drum with 3 holes in the top. The holes were in the shape of a triangle, a circle and a square. Carl looked at the chunky shapes on the floor. He picked up a triangle. He put it in his month, then banged it on the floor. He touched the edges with his fingers. Then he tried to stuff it in each of the holes of the new toy. Surprise! It fell inside the triangle hole! Carl reached for another block, a circular one this time…

### Math: One Part of the Whole

Math skills are just one part of a larger web of skills that children are developing in the early years—including language skills, physical skills, and social skills. Each of these skill areas is dependent on and influences the others.

Trina (18 months old) was stacking blocks. She had put two square blocks on top of one another, then a triangle block on top of that. She discovered that no more blocks would balance on top of the triangle-shaped block. She looked up at her dad and showed him the block she couldn’t get to stay on top, essentially telling him with her gesture, “Dad, I need help figuring this out.” Her father showed her that if she took the triangle block off and used a square one instead, she could stack more on top. She then added two more blocks to her tower before proudly showing her creation to her dad: “Dada, Ook! Ook!”

You can see in this ordinary interaction how all areas of Trina’s development are working together. Her physical ability allows her to manipulate the blocks and use her thinking skills to execute her plan to make a tower. She uses her language and social skills as she asks her father for help. Her effective communication allows Dad to respond and provide the helps she needs (further enhancing her social skills as she sees herself as important and a good communicator). This then further builds her thinking skills as she learns how to solve the problem of making the tower taller.

### What You Can Do

The tips below highlight ways that you can help your child learn early math skills by building on their natural curiosity and having fun together. (Note: Most of these tips are designed for older children—ages 2–3. Younger children can be exposed to stories and songs using repetition, rhymes and numbers.)

##### Shape up.

Play with shape-sorters. Talk with your child about each shape—count the sides, describe the colors. Make your own shapes by cutting large shapes out of colored construction paper. Ask your child to “hop on the circle” or “jump on the red shape.”

##### Count and sort.

Gather together a basket of small toys, shells, pebbles or buttons. Count them with your child. Sort them based on size, color, or what they do (i.e., all the cars in one pile, all the animals in another).

##### Place the call.

With your 3-year-old, begin teaching her the address and phone number of your home. Talk with your child about how each house has a number, and how their house or apartment is one of a series, each with its own number.

##### What size is it?

Notice the sizes of objects in the world around you: That pink pocketbook is the biggest. The blue pocketbook is the smallest. Ask your child to think about his own size relative to other objects (“Do you fit under the table? Under the chair?”).

##### You’re cookin’ now!

Even young children can help fill, stir, and pour. Through these activities, children learn, quite naturally, to count, measure, add, and estimate.

##### Walk it off.

Taking a walk gives children many opportunities to compare (which stone is bigger?), assess (how many acorns did we find?), note similarities and differences (does the duck have fur like the bunny does?) and categorize (see if you can find some red leaves). You can also talk about size (by taking big and little steps), estimate distance (is the park close to our house or far away?), and practice counting (let’s count how many steps until we get to the corner).

##### Picture time.

Use an hourglass, stopwatch, or timer to time short (1–3 minute) activities. This helps children develop a sense of time and to understand that some things take longer than others.

##### Shape up.

Point out the different shapes and colors you see during the day. On a walk, you may see a triangle-shaped sign that’s yellow. Inside a store you may see a rectangle-shaped sign that’s red.

Sing songs that rhyme, repeat, or have numbers in them. Songs reinforce patterns (which is a math skill as well). They also are fun ways to practice language and foster social skills like cooperation.

##### Start today.

Use a calendar to talk about the date, the day of the week, and the weather. Calendars reinforce counting, sequences, and patterns. Build logical thinking skills by talking about cold weather and asking your child: What do we wear when it’s cold? This encourages your child to make the link between cold weather and warm clothing.

##### Pass it around.

Ask for your child’s help in distributing items like snacks or in laying napkins out on the dinner table. Help him give one cracker to each child. This helps children understand one-to-one correspondence. When you are distributing items, emphasize the number concept: “One for you, one for me, one for Daddy.” Or, “We are putting on our shoes: One, two.”

##### Big on blocks.

Give your child the chance to play with wooden blocks, plastic interlocking blocks, empty boxes, milk cartons, etc. Stacking and manipulating these toys help children learn about shapes and the relationships between shapes (e.g., two triangles make a square). Nesting boxes and cups for younger children help them understand the relationship between different sized objects.

##### Tunnel time.

Open a large cardboard box at each end to turn it into a tunnel. This helps children understand where their body is in space and in relation to other objects.

##### The long and the short of it.

Cut a few (3–5) pieces of ribbon, yarn or paper in different lengths. Talk about ideas like long and short. With your child, put in order of longest to shortest.

##### Learn through touch.

Cut shapes—circle, square, triangle—out of sturdy cardboard. Let your child touch the shape with her eyes open and then closed.

##### Pattern play.

Have fun with patterns by letting children arrange dry macaroni, chunky beads, different types of dry cereal, or pieces of paper in different patterns or designs. Supervise your child carefully during this activity to prevent choking, and put away all items when you are done.

##### Laundry learning.

Make household jobs fun. As you sort the laundry, ask your child to make a pile of shirts and a pile of socks. Ask him which pile is the bigger (estimation). Together, count how many shirts. See if he can make pairs of socks: Can you take two socks out and put them in their own pile? (Don’t worry if they don’t match! This activity is more about counting than matching.)

##### Playground math.

As your child plays, make comparisons based on height (high/low), position (over/under), or size (big/little).

##### Dress for math success.

Ask your child to pick out a shirt for the day. Ask: What color is your shirt? Yes, yellow. Can you find something in your room that is also yellow? As your child nears three and beyond, notice patterns in his clothing—like stripes, colors, shapes, or pictures: I see a pattern on your shirt. There are stripes that go red, blue, red, blue. Or, Your shirt is covered with ponies—a big pony next to a little pony, all over your shirt!

##### Graphing games.

As your child nears three and beyond, make a chart where your child can put a sticker each time it rains or each time it is sunny. At the end of a week, you can estimate together which column has more or less stickers, and count how many to be sure.

### References

Bowman, B.T., Donovan, M.S., & Burns, M.S., (Eds.). (2001). Eager to learn: Educating our preschoolers. Washington, DC: National Academy of Sciences.

Diezmann, C., & Yelland, N. J. (2000). Developing mathematical literacy in the early childhood years. In Yelland, N.J. (Ed.), Promoting meaningful learning: Innovations in educating early childhood professionals. (pp.47–58). Washington, DC: National Association for the Education of Young Children.

Fromboluti, C. S., & Rinck, N. (1999 June). Early childhood: Where learning begins. U.S. Department of Education, Office of Educational Research and Improvement, National Institute on Early Childhood Development and Education. Retrieved on May 11, 2018 from https://www2.ed.gov/pubs/EarlyMath/title.html

## The Most Important Math Concepts Kids Learn in Pre-K

Although there’s a lot of emphasis placed on emergent reading, experts show that pre-k math skills are just as important for your child’s learning development.

Understanding what skills your child will be exposed to as a math beginner will give you an idea of what concepts you can emphasize in fun, easy ways at home!

Fortunately, kids are exposed to many math concepts from a very young age — putting puzzles together, sorting objects, and even playing with building blocks. These activities all help build a good foundation for math.

In this article, we’ll take you through the most important pre-k math concepts so you can encourage and motivate your budding mathematician!

• What Are The Components Of Pre-K Math?
• Basic Pre-K Math Checklist
• Pre-K Math Development
• 9 Fun Pre-K Math Activities

### What Are The Components Of Pre-K Math?

There are five basic components of pre-k math. They act like umbrella terms, each with many different elements hidden inside their broad concepts.

Your child will become acquainted with all of these essential concepts when they begin learning pre-k math.

#### 1) Numbers And Counting

Children typically start with the bedrock of math — numbers! They’ll learn number names and how to write numbers, typically beginning with 1-10.

Counting is not easy business! While your child learns how to count — first with physical objects, then conceptually — they are bound to make mistakes here and there. This is perfectly all right. Counting will take time to master.

Most of kids’ initial exposure will be through representational counting. This could mean counting the number of strawberries in their lunch box, how many blocks are on the floor, and so on. These counting activities will set the stage for a strong foundation in counting.

By understanding that numbers represent objects, your child will begin to understand one-to-one correspondence (each object counted gets its own number and only that number) as well as the counting principle that when counting the number of objects, the last number counted equals the amount present.

Over time, a child’s reliance on physical objects for counting will decrease. They’ll depend more on conceptual counting as their skills develop.

This conceptual counting is called “number sense.” They’ll understand that quantities, whether tangible or theoretical, are countable. They’ll also learn that numbers can be compared: two or more numbers can have a more-than, less-than, or same-as number relationship.

There are many fun ways to get your child comfortable with numbers and counting at home without making it feel burdensome.

Here are a few simple yet effective strategies you can try:

• Encourage your child to touch and count objects they see in everyday life — for example, a bunch of bananas or a stack of books.
• After they count a set of objects, help them write down the corresponding number on a piece of paper.
• Have your child compare different items using the appropriate language. For example, “Let’s count the number of blueberries and strawberries on the plate. Are there more strawberries than blueberries?”
• Hang a simple number line on the wall or tape one to your refrigerator. Throughout the day, point to each number with your child and count from 1-10 together.
• Ask your child to help set the table by counting out the right number of forks and spoons. Once they have collected them, they can count them again as they put one at each place setting.

These simple activities allow children to make sense of numbers. And the more they practice counting principles outside of the classroom, the more they’ll realize how relevant they are to everyday life.

Once your child has a firm grasp on counting and is developing number sense, they’ll explore the relationships between numbers more often. Describing how numbers are the same or different will lead into learning how to combine two numbers to make a new number!

Similar to the last concept, children will typically learn how to add and subtract by relying on counting activities with tangible objects. For example, you could set up two separate groups of apples and ask how many you will have if you join them together.

The first group may have three apples, while the second group has two apples. At first, many children will count one group and then start over to count the second group. It is a good idea to count both groups individually and then bring them together and count the total amount.

This is their first introduction to addition! The same idea works for subtracting. What happens when you begin with five apples and then take away two of them?

“Taking away” objects may be a little harder for your child to master at first. This is why many children will remove apples first and then count the remaining apples rather than counting backward.

To help, practice counting backward together. Pretend to be a rocket ship, and start counting down from five to one, gradually increasing the beginning number each time. After you get to one, shout, “Blastoff!” and jump into the air as high as you can. This fun game can help your child become more comfortable with counting down.

Pictures can also help your child master addition and subtraction concepts. For addition practice, present one sheet of paper with three apples and another with two. Then say, “Count the apples on both pieces of paper. How many apples do you have total?”

For subtraction problems, present this scenario: “On our paper, we have five apples total. How many apples will you see if I cover up two of them?” Then, count the remaining apples together.

Pictures are an effective way for your child to visualize mathematical problems. But, if you prefer not to draw, you can also use real objects instead. You could get out several apples (stuffed animals, cups, or whatever) and count them. Then, use those items for math practice.

Remember that adding and subtracting are basically making comparisons between numbers or establishing relationships between them. There are many strategies a child might use to solve a problem, which is a good thing since our main goal is to help children think mathematically.

#### 3) Geometry And Spatial Reasoning

Shapes are everywhere in our world, which will be one of your greatest assets when it comes to teaching your child about shapes and spatial reasoning.

They’ll start out by learning about the basic 2-D shapes that are used in math: squares, triangles, circles, rectangles, rhombuses, and ovals. Learning how to draw these basic shape illustrations can be helpful for their learning process.

Some of these shapes you’ll be able to reference easily in your day-to-day life. This will help reinforce your child’s understanding of the shapes after their initial introduction.

For example, when making breakfast with your child, you could hold up a plate and ask them, “What shape is this? Do you think it’s a square or a circle?”

Other shapes, like triangles or rhombuses, may be a little harder to find hanging around. Challenge your child to find these shapes in nature. Are there any flower petals in your garden that are shaped like triangles (or an aloe vera plant hanging in their windowsill)?

Encourage your child to be creative with identifying shapes! It will help them with learning geometry in the long run.

Next, learning 3-D shapes will come after learning 2-D shapes. Like their flatter cousins, 3-D shapes are all around the world, too! Your child’s soccer ball is a sphere; the paper towel roll in the kitchen is a cylinder.

We recommend learning the basic form of these shapes and how they appear first. Then, you can use the natural 3-D shapes in your child’s environment to reinforce their learning!

Point out shapes when you see them and play a shape version of “I Spy” to practice. If your child has a set of blocks, talk about the different shapes of the blocks. Challenge them to use only one shape to build something. Then, see what they can make by using all of the shapes.

Kids also learn about spatial reasoning by discovering how to describe the shapes they see and play with. They can compare them with dimensional adjectives like “big” and “small,” or characteristics of their shape like “straight” and “curvy.”

This includes the spatial relationship between different objects, too. Look out for observations using location adverbs like “under,” “beside,” or “around.” These are all different ways for your child to “measure” or observe how shapes take up space.

#### 4) Sorting And Patterns

We categorize things in our daily lives without even realizing it. Your child probably already does this, too — they may arrange their stuffed animals or toys in a certain way. For example, they may keep farm animals separated from dinosaurs.

Sorting and patterns are related to categorical reasoning. In the same way grocery stores sort out items by their parallel uses, your child will learn how to sort things based on their characteristics and how they are the same or different from other objects.

They’ll sort objects by weight, shape, quantity, texture, color, and other traits, often without even realizing it!

It’s important to note here that sorting and counting aren’t sequential. Your child might begin sorting before they begin counting, in fact.

For instance, if you want your child to sort a bowl of fruit, you can ask them to count all of the strawberries. They’ll sort the strawberries from the rest of the fruit. If you ask them to count the red fruit, they’ll sort out strawberries, cherries, and watermelon and count them together.

Once a child has learned to isolate characteristics, they can begin to identify, extend, and even create patterns. Your child will learn how to:

• Copy a pattern
• Identify the parts that repeat and continue a pattern
• Correct a mistake in a pattern
• Explain a pattern
• Create their own patterns

To encourage your child to explore patterns, take a few moments to build a pattern for them when you play together. Use whatever materials you have available and create a simple AB pattern, such as truck, car, truck, car.

Next, point to each object. Say its name aloud. Then, when you get to the end of the row, ask them what comes next. If they aren’t sure, grab the next object and put it down. Once you’ve completed one round, start at the beginning and repeat each item to reinforce the pattern.

#### 5) The Language Of Math

Part of learning how to do math means learning how to “speak” math. We don’t mean your child will turn into C-3PO — just that they will learn how to use mathematically correct language, or how to tell a story with math terms.

This can happen in daily life. While picking at an afternoon snack, your younger child may say, “Hey! My brother has more crackers than me!” Then you might agree to “add” to the cookies on the younger child’s plate so that both plates are “equal.”

These skills may be naturally exciting for your child — they’ll feel like they’re learning how to speak “grown up!” Show them how fun it is to incorporate mathematically appropriate language into their daily speech and use it to tell stories about what’s going on around them.

Using words to describe things in their lives will help them give ownership over ideas and observations. Motivate them to think about the order of the world around them and use different words to describe them, such as:

• More than
• Less than
• Shape names
• Light or heavy
• Small or big

Mastering math language will help them in their quest to become robust mathematicians! It’ll also help them develop a strong vocabulary so they’re better prepared for kindergarten.

### Basic Pre-K Math Checklist

Now that you know some of the concepts your child will be learning in pre-k math, let’s look at some of the skills they’ll build during this time.

• Rote count to 10
• Use one-to-one correspondence to count up to 10 objects and tell how many there are altogether
• Recognize basic shapes (circle, triangle, square)
• Understand the concept of quantity (more/less)
• Sort objects by one characteristic
• Understand and use directional terms, such as up, down, in, out
• Pick what object goes next in a simple pattern

While these aren’t all of the math skills your child might learn in pre-k, they will give your child a solid mathematical foundation to build on in kindergarten. And they’re all skills you can practice in fun ways!

### Pre-K Math Development

As your child grows and learns, they’ll work through three phases of mathematical development: concrete, representational, and abstract. They’ll likely be in the concrete stage at the beginning of pre-k.

During this phase, students need hands-on activities and real-world examples to help them understand mathematical concepts. This is why math manipulatives are so crucial in the early years. It’s also essential to present math concepts in a very concrete way during this stage.

For example, if you’re teaching your child about numbers, don’t just tell them that five is more than three. Instead, show them five objects and three objects, and let them count for themselves. This will help them understand the concept of more and less.

As your child continues to learn and practice a mathematical concept, they can move into the representational phase. Here, students can count pictures or images instead of actual objects. For example, they realize that numbers can be represented by lines or drawings.

Then, they’ll be ready to try the abstract stage. At this point, children understand that numbers can be represented by symbols. They don’t need manipulatives or visual aids to do math problems. They can start using numbers and symbols such as + or – to solve math problems.

The activities above will help your child to build their understanding of mathematical concepts so they can move through the different stages.

But, in pre-k, it’s important to focus on the process, not the answer. So don’t worry if your child doesn’t get the solution right away. Let them work through the problem and try to figure it out for themselves.

A strong foundation in pre-k math sets children up for success when they start kindergarten. By providing opportunities for them to explore and experiment with math, you can help them develop the skills they need to be successful in school and beyond.

### 9 Fun Pre-K Math Activities

Now that you’re clear on all of the exciting new math concepts your pre-kindergartener will be exposed to and what skills they’ll practice, let’s talk about some games and activities you can play at home to help your child hone them.

We’ve already discussed some math activities you can incorporate into everyday life. Now, we’re sharing our list of fun games to encourage your young learner to love math even more.

#### 1) What Did I Do?

This game helps reinforce counting, adding, and subtracting. It’s quick to play, so it’s perfect for when you have a few extra minutes.

##### What You’ll Need
• Small objects (e.g., paper clips)
##### What To Do

Place some paper clips (or any other small objects) in your hand, and let your child count how many you have. After they’ve done this, put your hands behind your back and either add or remove some.

Next, show your child the new quantity and ask them to count how many there are now. You can ask your child questions, such as, “Did I add or take away some paper clips?” or “How many did I add or take away?”

For even more fun and learning opportunities, take turns playing the game. And when it’s your turn to guess, it’s OK to guess wrong — “I think you took away 10!… No! I added two!” This back and forth offers lots of laughs and critical thinking for your little mathematician.

Remember that because your child is in pre-k, the concepts of addition and subtraction are still new. Therefore, it’s best to keep the number of objects used in this game low (e.g., 1-10 clips) so they aren’t confused or overwhelmed.

#### 2) Math Tic-Tac-Toe

Add a mathematical twist to the classic game of Tic-Tac-Toe!

##### What You’ll Need
• Paper
• Pencil
• Ruler
• Markers (or colored pencils)
##### What To Do

Start by dividing your sheet of paper into squares by drawing lines (three horizontal by three vertical). In traditional tic-tac-toe, you’d leave these squares blank until the game starts. Not this time.

For this version of the game, you’ll need to fill each box with dots and have your child tell you how many dots are in a box before placing their X or O in it. The first player to get three Xs or Os wins!

The Xs or Os don’t have to be in order at this point, but you can add that requirement as a challenge once your child gets the hang of playing the game.

This activity helps kids work on their counting skills while also incorporating lots of fun.

#### 3) NumberBow

Your child will add numbers to create a beautiful rainbow in this game.

##### What You’ll Need
• Two dice
• Two sheets of paper
• Colored pencils (or crayons)
• Pencil
##### What To Do

Draw two identical rainbow-shaped boards (one on each sheet of paper) with numbered boxes on the rainbows. (You can check out this link for reference.). The aim of the game is to color the numbered boxes in.

To play, each player throws two dice, then adds the numbers from the throw together and colors in the corresponding box on their rainbow.

For example, if your child throws a three and a one, they’d need to add 3+1 and color in the “4” box. If they’ve already colored that box in, they’d have to wait for their next turn. Each player gets 10 turns to have the most colorful rainbow at the end!

While this is an effective game to help your child work on their addition skills, some children might experience difficulty adding larger numbers together (e. g., 5 and 6). If you need to help them, that’s OK!

Remember that exposure and repetition are very beneficial for young learners.

#### 4) Fill The Cup

This game can be challenging for younger children, so if it causes frustration, play other math games until your child is more comfortable with adding and counting.

##### What You’ll Need
• Dice
• Plastic cup
• Small objects that are easy to count (e.g., paper clips, dried beans, pebbles, etc.)
##### What To Do

To begin the game, players roll the dice at the same time. The number rolled indicates the number of items you can add to your cup. For example, if you roll a five, you add five dried beans. The goal for your child is to be the first one to fill their cup.

At the pre-kindergarten stage, some children might not be comfortable with the steps needed to play this game (rolling the dice, reading the number aloud, adding the items to the cup). So, before starting, take a few minutes to get them used to the process.

If you notice that it’s still too challenging, you can make it easier by choosing to roll the dice for each other. In this option, you can roll the dice and then help your child read the number and add the right amount of items to their cup.

Whichever variation you choose, this is a fun and engaging way to help children learn numbers and practice counting.

#### 5) Stand Up, Sit Down

Kids enjoy playing this active game where they get to use their bodies and their brains! (Note: This game requires more than one child player, so it’s a great activity for siblings or to do when your child has a friend over.)

• Index cards
• Marker
##### What To Do

Write the numbers 1-10 on the index cards (one number per card) and hand three to each participant. Then, say a math equation (or word problem) out loud.

If the answer matches a number they’re holding, the child will stand. If they don’t have the answer, they remain seated.

For example, if the question is, “If I have three dried beans and I throw away one, how many do I have left?”, the child with “2” would then need to stand up and show their card.

The player who has the least number of cards left at the end of five rounds wins. Note: To make it easier, you can give children small items (e.g., blocks, dried beans, paper clips, etc.) to help them count.

Stand Up, Sit Down is also helpful for children learning shapes. Instead of writing numbers on the cards and handing them out, you can draw different 2-D and 3-D shapes that children learn in pre-k (as discussed above) and hand those out.

To play, someone describes a shape and the player who has that shape stands up and says what it is. For example, “If you are holding a shape that has three sides, stand up right now!”

When the child stands up, they’ll need to say that their shape is a triangle, and they get the point. In this version of the game, the player with the most points at the end wins.

Using this game allows children to learn the names and attributes of the different 2-D and 3-D shapes they get exposed to in pre-kindergarten.

#### 6) Who Has More?

This game is perfect for helping kids understand the concepts of more and less, which are critical in early math development.

##### What You’ll Need
• A small bowl or container
• A teaspoon
• A handful of objects (e.g., buttons, pennies, cereal pieces, etc.)
##### What To Do

Place the objects in one bowl. Have your child scoop a teaspoon of them out and count them. Then, you do the same and see who got the most. That person’s the winner!

Note: Counting past 10 is difficult at this age, so you’ll want to use big enough items (such as large kidney beans) and stick to a teaspoon for scooping so your child doesn’t end up with more than 10 per spoonful.

##### What You’ll Need
• A mathematical-themed book to read together (see some recommendations below)
##### What To Do

Grab one of the following books and snuggle up with your little one for a math-themed storytime. As you read, point out any mathematical concepts in the book.

• From the Garden by Michael Dahl
• The Shape of Me and Other Stuff by Dr. Seuss
• The Button Box by Margarette S. Reid
• A Pair of Socks by Stuart J. Murphy
• The Berenstain Bears and the Spooky Old Tree by Stan and Jan Berenstain
• Pattern Fish by Trudy Harris

When you finish reading, discuss any new math concepts your child learned. You could even do a related activity or two to reinforce what they’ve learned.

#### 8) In The Box

This game helps your child practice prepositions or direction words, like “under,” “behind,” and “in front of.” These concepts are essential for mathematical development as well as reading comprehension.

##### What You’ll Need
• A stuffed animal
• An empty box large enough for the animal to fit inside
##### What To Do

Ask your child to put the animal inside the box. If they have difficulty understanding what you mean, give them some clues. For example, you could say, “Put the animal in the box so that its head is sticking out,” or “Put the animal in the box so that only its tail is showing.”

Once the animal is in the box, ask them to describe where it is using prepositions. So, they might say, “The animal is in the box.”

Then, take the animal out and place it behind the box. Ask your child to describe its location again. For example, they might say, “The animal is behind the box.”

Next, let them take a turn placing the animal in, on, under, next to, etc. the box. When they’re done, you describe where it is. Continue taking turns as you practice different prepositions.

#### 9) Number Line Race

This game helps kids with number recognition as well as one-to-one correspondence.

##### What You’ll Need
• Number cards (we recommend the ones from the HOMER Explore Numbers Kit)
• A die
##### What To Do:

Spread the cards out in numerical order, with a bit of space between each one. They should form a line on the floor, though it doesn’t need to be perfectly straight.

Have your child stand on the card with the number one on it. Hand them the die and let them roll it. Call out the number they rolled. Next, ask them to move that many numbers forward, moving from one index card to the next as they count aloud.

If they land on a number that would take them off the end of the line, they start from the beginning for their next throw (each player gets five throws). Then, it’s your turn! Start on one and see how far you can get, too.

The person to end on the card with the highest number is the winner!

### Encouraging A Love Of Pre-K Math At Home

Pre-k math isn’t just reserved for pre-k classes. You can help your child explore the exciting world of pre-k math right from your home!

HOMER is always here to help and happy to be your at-home learning partner. Our Learn & Grow app offers tons of opportunities for your child to develop their pre-k math skills from conception to execution.

Our games are personalized to accommodate your child’s specific interests. They include pattern-identification games like Ribbons or shape-building games like the Castle Creator.

Your child can also explore the Shapery Bakery, where they help the cute, cuddly Tisa the Cat by sorting treats based on their shape. All that and so much more can help your child develop their pre-k math skills!

## The first mathematical theories in Ancient Greece

Article

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Plan:
Thales. School of Pythagoras.
Arithmetic of integers, fractions. The first theory of relations.
The first irrationalities.
Geometric Algebra. The algebra of the ancients and the geometry of compasses and rulers.
The first unsolvable problems.
Euclid. Axiomatics

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Jerusalem, 2008, 222 p. The book is devoted to the history of the methodology of mathematics, not the history of mathematics. Therefore, the main attention is paid to the historical change in attitudes towards basic mathematical concepts, as well as the ways in which mathematical reasoning is carried out, both on the part of mathematicians and other circles of society. Much less attention is paid to mathematical theories and mathematical results. Likewise, we give more preference to...

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Saransk: Mordovian book publishing house, 1977. -370 p. [Ed. 2nd, rev. and additional ] The book contains essays on the history of mathematics in Ancient Egypt, Babylonia, Greece, China and Ancient India. It is written taking into account recent research, many of which belong to the author himself. The book is intended for students of the history of mathematics, and students of the physics and mathematics departments of universities and pedagogical institutes, teachers of mathematics in secondary schools . ...

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Subject of the history of mathematics. The emergence of the first mathematical concepts and methods. Mathematics of ancient Egypt and Babylon The first mathematical theories in ancient Greece Axiomatic construction of mathematics in the era of Hellenism. "Beginnings" of Euclid Infinitesimal methods in ancient Greece. Mathematical creativity of Archimedes Theory of conic sections and other mathematical; theories and methods of late antiquity Features of the development of mathematics in China ...

HELP FOR YOUR CHILD TO DEVELOP EARLY MATH SKILLS

Before going to school, most children develop an understanding of addition and subtraction through everyday interactions. Find out which informal activities give kids a head start when they start learning math at school.

Children use their first math skills in daily activities and activities. This is good news as these skills are important. to prepare for school. But early math doesn't mean taking out a calculator during the game. Even before they start school, most children develop understanding addition and subtraction through everyday interaction. For example, Thomas has two cars; Joseph wants one. After Thomas shared one, he sees that he has one car left (Bowman, Donovan, & Burns, 2001, p. 201). Other mathematical skills are acquired during daily activities that you share with your child, such as counting steps as you go up or down. informal classes, like this give kids a boost in formal math education that starts at school.

What math skills will your child need? later in elementary school? Early mathematical concepts and skills that the curriculum for mathematics in the first grade is being built, include:

· Understanding size, shape and patterns

· Ability to count verbally (first forward, then back)

· Digit recognition

Over and under detection

· Understanding one-to-one compliance

Key math skills for school

More advanced math skills are based on initial mathematical "foundation" - just like a house is built on solid foundation. In the early years of education, you can help your child start developing math skills at an early age by introducing ideas like:

This ability to accurately count - first striker. Then, later in school, children will learn to count backwards. okay. A more complex skill related to number sense is the ability to see relationships between numbers, such as addition and subtraction.

Make mathematical ideas “ real” using words, images, symbols, and objects (such as blocks).

Spatial sense. Later in school kids will call it "geometry". But for kids, he introduces ideas of form, size, space, position, direction, and movement.

Dimension . Technically this defining the length, height, and weight of an object in units such as inches, feet, or pounds. The measurement of time (e.g. in minutes) also belongs to this area skills.

Estimated . It's ability guess the quantity or size of something. To small children it is very difficult. You can help them by showing them the meaning of words like more, less, more, less, more than, less than.

Patterns are things, numbers, forms, images that logically repeat. Templates help kids learn to make predictions, understand what will happen next, establish logical communication and use reasoning skills.

Troubleshooting . The ability to think through the problem, to recognize that there are several ways to answer. This means using past knowledge and logical thinking skills to find answer

Math : one part whole. Math skills are just one part of a wider network skills that children develop at an early age, including language, physical and social skills. Each of these skill areas depends on the others and influences on them.

In this normal interaction, you can see how all areas of development work together. Physical abilities allow manipulate blocks and use your mental abilities to fulfillment of his plan for the construction of the tower. The child uses his tongue and social skills when asking for help from his father. His effective communication allows the father to respond and provide the necessary assistance (further development her social skills as she considers herself important and good communicator). This will then further strengthen her thinking skills as she learns how to solve the problem of increasing the height of the tower.

WHAT YOU CAN DO

The tips below show how you can help your child learn math skills at an early age by relying on on his natural curiosity and having fun together. (Note: most of these tips are for older children - aged from 2 to 3 years. Young children can be introduced to stories and songs using repetition, rhymes and numbers.)

Pull up . Play with shape sorters. Talk to your child about each shape - count the sides, describe the colors. Create your own shapes by cutting large forms of colored thick paper. Ask the child to "jump on the circle" or "jump on the red piece".

Count and sort. Assemble a basket of small toys, shells, pebbles or buttons. Count them together with baby. Sort them by size, color, or purpose (i.e. all machines in one pile, all the animals in another).

Make a call. Together with a three-year-old child, start learning her address and the phone number of your house. Talk to your child about how every house has a number and how his house or The apartment is part of a series, each of which has its own number.

What size is this? Pay pay attention to the size of objects in the world around you: this pink wallet is the most big. The blue wallet is the smallest. Ask your child to think about their size compared to other items (“Do you fit under the table? Under chair?").

Now you're cooking!

Even small bottles can fill, stir and pour children. Through these exercises, children naturally learn to count, measure, add and evaluate.

Go away. Walk gives children plenty of opportunities to compare (which stone is bigger?). Estimate (how many acorns did we find?), note the similarities and differences (does the duck have fur, like a rabbit?) and classify (see if you can find red leaves). You can also talk about size (by doing big and small steps), estimate the distance (whether the park is near our house or far?) And practice counting (let's count how many steps until we we won't reach the corner).

Picture time. Use hourglass, stopwatch or timer for short (1-3 minutes) activities. This helps children develop a sense of time and understand that one thing takes more time than others.

Pull up. Please contact attention to the different shapes and colors you see throughout the day. During walking you can see a sign in the form of a yellow triangle. Inside store, you can see a red rectangle.

Read and sing your numbers. Sing songs that rhyme, repeat, or contain numbers. Songs fix patterns (which is also a math skill). They are also an interesting way to practice the language and develop such social skills like cooperation.

Start today. Use calendar to talk about the date, day of the week and weather. Calendars amplify counting, sequences and patterns. Develop logical skills thinking, talking about cold weather and asking the child: what do we wear when Cold? This encourages your child to make connections between cold weather and warm clothes.

Send it. Ask your child to help distribute snacks or lay out napkins at the dining area. table. Help him give each child a cracker. It helps children understand individual communications. When you distribute items, emphasize number concept: "One for you, one for me, one for dad." Or: "We put on shoes: one, two.

Large for blocks. Give the child the opportunity to play with wooden blocks, plastic blocks, empty boxes, milk cartons, etc. Putting these toys into stacking and manipulating them helps kids learn about shapes and relationships between shapes (for example, two triangles form a square). Birdhouses and cups for young children help them understand the relationship between objects of different size.

Tunnel time. Open large cardboard boxes at each end to turn them into a tunnel. This helps children understand where their body is in space and in relation to other objects.

Long and short. Cut off several (3-5) pieces of tape, yarn or paper of different lengths. talk about such ideas, both long and short. Arrange the child in order from longest to the shortest.

Learn by touch. Cut out figures - a circle, a square, a triangle - from a strong cardboard. Let your child touches the figure with open and then closed eyes.

Pattern game. Have fun with patterns, allowing children to lay out dry pasta, large beads, different types of dry flakes or pieces of paper in different patterns or designs. In During this activity, keep a close eye on your child to avoid choking, and put away all the items when you're done.

Laundry training. Make homework interesting. When sorting laundry, ask your child to make a pile shirts and a stack of socks. Ask him which stack is bigger (estimate). Together count how many shirts. See if he can make a pair of socks: you can you take out two socks and put them in a pile? (Don't worry if they don't match up! This exercise is more about counting than matching.)

Math playground. Bye your child is playing, compare him by height (tall/short), position (larger / smaller) or size (large / small).

Dress for success in math. Ask child to choose a shirt for the day. Ask: What color is your shirt? Yes, yellow. Can you find anything yellow in your room? When your the child will approach three years and older, pay attention to the patterns on his clothes - for example, stripes, colors, shapes or images: I see a pattern on your shirt.