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 math beginners 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 by color, 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?
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 orange crayons are in a pack, 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?”
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.
2) Addition And Subtraction
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.
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?”
Pictures are an effective way for your child to visualize mathematical problems.
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!
Kids also learn about spatial reasoning by discovering how to describe these shapes. 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 will likely learn how to sort things before they learn to count them, 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.
Sorting leads to patterns. Just like in our last example, your child will learn how to pinpoint a pattern rule (such as a strawberry-blueberry-strawberry-blueberry chain) and apply it. 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
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 CP30 — 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!
5 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, let’s talk about some games and activities you can play at home to help your child hone these skills.
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?
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
What You’ll Need
- 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.
What You’ll Need
- Two dice
- Two sheets of paper
- Colored pencils (or crayons)
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
What You’ll Need
- 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
What You’ll Need
- Index cards
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.
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!