Pre-Kindergarten Overview: Introduction to the Math World

This is the very beginning of an amazing trip into the world of mathematics! It will turn out to be a life-long journey, as math is so much more than part of the educational process. For the Pre-Kindergarten curriculum, Happy Numbers collected all the best exercises on logic and structural thinking, which are so important for students to grasp at this stage. They learn the basics of counting, sorting, and comparing, become familiar with simple geometric shapes, study numbers up to 10, and even lightly touch on using abstract visual models.

Emerging readers will have no problem working with it on their own, as the app features text read aloud in English or Spanish. In addition, everything can be repeated as many times as your students need.

The design of the Pre-Kindergarten exercises is very friendly and includes a lot of game-like tasks because the youngest students need to engage in the learning process and connect their previous game-based cognition to real science. In addition, students learn to describe the relative position of objects by such terms as top, bottom, etc., which widens their skills of orientation in space. They encounter concepts of length, weight, and capacity and learn to compare them. At the end of this grade, they will smoothly transition from the comparative concept of counting and comparing to the concept of basic math operations such as addition and subtraction with numbers from 1 to 5. It is an important year of great leaps in math understanding!

Happy Numbers empowers your Math Stations with software, developed using latest educational technologies and best practices, that provides students with a strong foundation and a real math mindset. Take a short tour through the Pre-Kindergarten curriculum with this overview.

All exercises mentioned below are part of the Happy Numbers course for Pre-Kindergarten. Visit to explore our full curriculum and sign up for a free trial.

Objects and Their Properties

First of all, Happy Numbers introduces basic features, which help to differentiate objects one from another. New terms such as the same and different are shown through interactive tasks with familiar characters like frogs or bugs, which students will pick, drag, and even paint over.

As a first step, the software explains the term by actions with cartoon characters, as well as by text and audio comments.


Then students prove their understanding by solving a simple task. Here’s one way they do so with such properties as the same / different:


… and larger / smaller:


Before introducing new tasks, Happy Numbers shows a short tutorial to prepare students. Here they explore sorting by color:

Counting Begins!

Gradually, students come to counting. Initially, Happy Numbers suggests they count together with tapping, as touching makes the process tangible and easier to understand. They learn numbers up to 5 using real objects. Happy Numbers adds energetic calls to action to involve the whole class!


In this task, students combine skills of sorting objects into uniform groups and then counting them:


Happy Numbers smoothly transitions them from word form of quantity notation to standard form. A keyboard with numbers they will use to type answers appears at the bottom of the screen:


Insofar as quick mental arithmetic is a very important skill, Happy Numbers urges students not to count each object, but to visually recognize their quantity. At first, the software provides them with vivid, moving hints.


By offering an application problem, Happy Numbers leads students to practice their knowledge. Here they repeat number sequencing while helping a cat to reach its station.


In Happy Numbers’ curriculum for primary school, there are many tasks with tangible elements called manipulatives. They’re an amazing instrument for building conceptual understanding of basic math, especially for the youngest students! For them, movement is so essential that it seems impossible to convince them to sit quietly at their desk. That is why manipulatives will be the greatest addition for math practice, as they fulfill their need for movement and deliver concrete, sensory experiences that help develop an understanding of complex, abstract concepts. You will find many exercises with manipulatives in the Pre-Kindergarten curriculum and in higher grades.

In Happy Numbers pedagogy, there are targeted approaches that actually boost students’ progress. Look at this exercise. Students get 5 strawberries, presented as manipulatives, which they split differently by dragging. It builds the foundation for addition and subtraction they will learn in depth in Kindergarten and Grade 1, and surprisingly develops a skill for grouping, which they will need for division.


Another effective type of exercise is ‘one more’ and ‘one less’. In fact, it’s the same as if students add or subtract one, but for now they just need to grasp the pattern. The concept of ‘one more’ is shown on a lifestyle scenario, where such an abstract visual element as a cube is presented as a toy and can be dragged through the screen.

Happy Numbers introduces the concept of ‘one less’ with real objects. Birds, which are flying away, are a clear associative model that students have already encountered in life.


Intro into Geometry

Already in Pre-K, students become familiar with basic geometric shapes such as circles, squares, triangles, and rectangles. Happy Numbers leads them to the understanding of shapes through associations with real objects. That’s how a piece of tasty pizza turns into a two-dimensional triangle.

Then they learn some terms about an object’s position. Friendly animals show what it means to be above or below, next to, and in front or behind.


Numbers up to 10

Students continue learning numbers to 10. They work only with real objects, like fruits or animals. Each new number they explore is added to the keypad at the bottom of the screen.


(see Pre-Kindergarten Module 3 — Topic A: exercise b)


(see Pre-Kindergarten Module 3 — Topic A: exercise e)

Along with the exercise with strawberries, this one with pencils boosts students forward to addition. They count a sum of objects by dragging them into an answer box. On the second level of the task, Happy Numbers asks them to do the inverse operation, that is, break the total number of pencils into two groups according to conditions given.

Happy Numbers introduces zero through animation, which builds an associative line between the number and real objects.

By the end of Module 3, students become familiar with all numbers from 0 to 10. They repeat counting by distributing 10 identical objects aligned in two rows.


(see Pre-Kindergarten Module 3 — Topic H: exercise d)

Some New Object Properties

Students continue to expand their knowledge of real object properties by studying terms such as length, weight, and capacity. Happy Numbers explains how to make comparisons.


(see Pre-Kindergarten Module 4 — Topic A: exercise b)

Since students are familiar with such characteristics as the same and different, Happy Numbers asks them to build a visual model using manipulatives, which will match conditions given. That helps to develop conceptual understanding of new terms.

They progress to abstract modeling with cubes, which will soon become a frequently used instrument called Base-10 Blocks.

Such properties as lighter or heavier Happy Numbers explains using a scenario with a seesaw, which is familiar and pleasant for young students. It looks like a game, but it perfectly explains the concept with a lifestyle example.

Building Math Scenarios

The last step before learning addition is presented in this exercise. Students count like objects separately, making numbers which will soon become addends, and then count a sum.


(see Pre-Kindergarten Module 5 — Topic B: exercise b)

They prepare for subtraction by moving through an inverse scenario, where part of a group of the same objects disappears.

In Topic D, students learn to match real objects with cubes and then count them. This is how Happy Numbers transitions them to more abstract visual modeling and, accordingly, to a higher math level.

The Pre-Kindergarten curriculum ends with exercises fully describing the development of an abstract scenario. Students mentally translate conditions given in numerical and word notation into an abstract visual model and build it with manipulatives. Here is what it looks like for an addition equation:


(see Pre-Kindergarten Module 5 — Topic D: exercise f)

… and for a subtraction task:


(see Pre-Kindergarten Module 5 — Topic E: exercise a)

Such exercises, which require using models of different levels of abstraction, help to develop mathematical thinking, which also contributes to the growth of creativity.

Build up a Solid Foundation

Pre-Kindergarten is a starting level, which lays the basis for subsequent development of the student in the field of mathematics. According to recent research, children who have low math marks at the beginning of math education continue to lag behind their better-prepared peers. By 8th grade, they may perform at a level their peers had surpassed by grade 5. That is why laying a mathematical foundation at the Pre-K level should be given the greatest attention. It’s important to not only teach math procedures but to also develop a math dialogue, which will allow students to form a conceptual understanding and initiate a flexible mathematical mindset. For that reason, Happy Numbers developed the Pre-K curriculum taking into account the interests of students as well as teachers’ priorities. Based on actual scientific developments and widely available technical capabilities, Happy Numbers offer exercises with a variety of engaging scenarios, memorable examples, and what is not less important – great pedagogy that will help students feel the strong connection between the familiar world around them and mathematics. 

How can you enhance your instruction with Happy Numbers?

It’s incredibly easy to bring Happy Numbers to your class, and you can do so at any point in the school year. Sign up now or watch a 1-minute video that will guide you through the setup:

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