This week, we will briefly revisit the concept of one-to-one correspondence in math and discuss it a little further with you. At the beginning of math learning, one-to-one correspondence is a building block for developing number sense. It’s so incredibly important for young children's cognitive development to build those foundational math skills.
It’s very easy to do if you know what you’re doing: our free preschool homeschool curriculum lets you know which activities to focus on, and how to combine them effectively. I also wanted to offer you a few ideas for hands-on activities to keep it fresh and fun, and continue to work on one-to-one correspondence.
What is the learning objective of one-to-one correspondence?
One-to-one correspondence is the concept that numbers represent a specific quantity of things. When practicing one-to-one correspondence, children will count objects. As they count objects, they will touch each object once while assigning a number to it.
Often, when we teach counting, you’ll hear little songs designed to teach it, or we practice counting verbally. At this stage, preschoolers are reciting numbers and engaging in rote counting as the first step in learning. We often end up teaching it very much in the same way that you would teach a nursery rhyme or the alphabet.
The problem is that when you teach counting only in that way, either by counting a limited variety of objects or when you’re focused on counting verbally or written numbers, young children often confuse it in their minds with learning a nursery rhyme. It is a series of words that you say rather than grasping the foundational concept that these are amounts of a specific thing, and that each object should be counted only once.
The ability to connect counting words to objects is crucial for understanding one-to-one correspondence.
What is an example of one-to-one correspondence in preschool?
For example, the number symbol five, whether it’s the word we say or the written numeral five, stands for five things, and that’s a very abstract concept because it can apply to anything.
It can be:
- five ideas
- five shapes
- five students
- five cars
- five blocks
- Or five thoughts that you think
It can be five of anything, but five is always five, and it's always that quantity.
So that’s what you’re trying to do with one-to-one correspondence. Help your child understand that a specific number stands for a certain quantity of things, no matter what you apply it to. Five will always mean five. Six will always mean six. And as you go up in the pattern, each number stands for one more than the previous.
What to keep in mind when teaching one-to-one correspondence?
You don’t have to teach this explicitly. Children learn this implicitly by just focusing on counting a wide variety of objects.
I’ve seen a couple of moms struggle because they have a routine, and they teach counting with the same objects each time.
For instance, while they’re getting their child dressed, their child might have a poster on their bedroom wall with teddy bears lined up. So, every day, they will practice counting, and as they adjust their child. They will count the teddy bears. This is a wonderful thing to do.
But if you’re not careful to count a wide variety of things, then you’re only using one item like that. Then, children can easily develop the impression that, for instance, five stands for the blue teddy bear, which is the fifth in line. Instead, they need to understand that five is the fifth of anything that I’m counting. We could count the teddy bears in a different order, and the fifth bear would be a different one in line.
Hands-on one-to-one correspondence activities
There are many ways to incorporate one-to-one correspondence into your everyday routine, beyond counting, such as using a wide variety of different objects. We'll cover them below.
Dice
Dice is a fantastic tool for this. Children begin to quantify the dots, which will come in handy later in math when they’re working on worksheets and addition. You can also have children draw lines or dots to represent the numbers rolled on the dice, or use number lines as a visual aid to reinforce counting and one-to-one correspondence. Working with dots helps children visualize at least up to six, which is the maximum number on the standard dice. They will understand what one, two, three, or five looks like because they see that number of dots on the dice.
Dominoes
Similarly dominoes. If you play dominoes with dots, it's a matching game where you match up tiles with the same number of dots. It's a fantastic tool to use for one-to-one correspondence.
Match objects to the correct number
Anything that matches a quantity with a corresponding number is also a fantastic game, like our addition expedition game. Now that you've been working on number recognition for a while, your child may be quite comfortable recognizing numbers 1 through 10. You can now use this skill to your advantage for one-to-one correspondence.
One of my favorite games is to take the plastic eggs that you would find at Easter time (you can also use muffin tins or paper plates for this activity). You can write a different number with a marker on each egg from one to seven. You want to ensure that these are numbers your child is comfortable recognizing.
You can then do it in a couple of different ways. You can either pre-fill them with a certain amount of something, such as cereal pieces, or any other small item, and then have your child open them and count them.
Or, a little more advanced, have your child fill them with that number of items. So, you are going to dump a pile of cereal on the table or put it in a bowl and have your child put two pieces in the egg that has '2' written on it and five pieces in the egg that has '5' written on it.
So it's not only reinforcing counting and number recognition, but it's also reinforcing that one-to-one correspondence of that five. This symbol, written on the egg, represents five of a particular item. And again, you can switch up the items you're putting in the eggs if you want to help, which will further reinforce that concept.
Snack time fun
Snack time isn’t just for refueling. It’s also a highly effective way to practice one-to-one correspondence with young learners. Using small objects like goldfish crackers, grapes, or cereal pieces, you can turn a simple snack into a hands-on math lesson. For example, give your child five crackers and encourage them to count each one, assigning one number (use number cards or write numbers on post-it notes) to each object as they go.
And again, you can also turn this into a matching game: try using an egg carton or an ice cube tray. Have your child place matching number of objects in each space to match the corresponding number. This approach is also a fun way to develop fine motor skills.
Later on, snack time is also a great opportunity to introduce new concepts, such as writing numbers or number words, and to help your child build confidence with basic math concepts. By making snack time a regular part of your one-to-one correspondence activities, you’ll help your child develop a deeper understanding of numbers, matching, and counting: skills that are essential for future math success.
Practice counting in sequence
Young children benefit from counting objects using hands-on materials like blocks, popsicle sticks, toys, snacks, etc.
If you do count things in a sequence, for instance, line up toy cars and count the cars.
You might have 10 cars in a row, and then show your child how you can rearrange the cars in a totally different order and count them again. It will still be 10, and the order doesn't matter. It's the amount that matters.
Again, that will help to avoid confusion and some of the pitfalls that come with counting the same thing in the same order every time. It really helps to ingrain the concept of one-to-one correspondence in your child's mind without needing to explain this concept to them explicitly.
And once your child has a really strong grasp of this and they have an opportunity to practice, particularly with objects that come in sets of 10 and under, or when they're a little bit older, 20 and under, it's going to help them pick up on addition and subtraction just naturally and much faster. Many parents attempt to teach one-to-one correspondence in a very abstract way, when children are too focused on simply repeating numbers and counting them in sequence, without a solid foundation of what that means in the physical world.
What do those numbers stand for?
Once these children are in the classroom and get to addition and subtraction, it's a very abstract concept. They're dealing with symbols on a page without a profound understanding of what those symbols represent and that they're real things in real space.
By really working on one-to-one correspondence while they're still preschoolers, they will naturally see how two and three come together to make five. It's definitely well worth taking the time to really get that down, and yes, it will pay off big time in the future, for kindergarten, school, and beyond.