Kindergarten Overview: Objects, Positions, and Quantity

Kindergarten students make a very important step in their mathematical education — in this grade, they transition to abstract thinking. Whereas in Pre-Kindergarten they lightly touched upon cubes as abstract objects, in Kindergarten they will become familiar with the Number Line and Base-10 Blocks. Here, the first math signs appear (plus and minus). Students will reinforce and expand their knowledge of basic geometry and learn principles of sorting objects and comparing them, which will be very necessary for Grade 1, where students begin to compare numbers. In the second half of the Kindergarten curriculum, work with simple equations based on various visual models begins. Students strengthen their knowledge of numbers to 10 and begin to learn numbers to 20, which prepares them for Grade 1.

Emerging readers can easily work with Happy Numbers on their own, as our app features text read aloud in English and Spanish as many times as your students need.

Happy Numbers provides Kindergarten teachers with robust and comprehensive software, which can be used for whole-group instruction, independent centers, and at-home practice. It also helps to collect personalized data about the learning path of each student. Learn more about the Happy Numbers curriculum for Kindergarten in this overview!

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

Review Pre-K

First of all, students will briefly repeat Pre-K materials. Happy Numbers reminds them of basic logical terms, such as same and different, and also principles of sorting.


(see Kindergarten Module 1 — Topic A: exercise b)


(see Kindergarten Module 1 — Topic B: exercise c)

Then they move on to a review of numbers up to 5. Here appears the Number Line, a new visual model, which is more abstract than others students saw before. In this task, students match numbers written differently:


(see Kindergarten Module 1 — Topic C: exercise d)

They review counting in an exercise with a visual model of real objects, such as oranges. They are presented as manipulatives, which students need to drag into a box.

Along with the repetition of material covered, students also become familiar with new tasks. Happy Numbers introduces “sharing candies,” a great exercise for building fluency with basic addition! As students have not yet learned equation notation, they write an answer without the equal sign. Watch the video below to get a full understanding of how it works:


Students work with numbers to 5. At this stage, the task is very simple, as students need to understand and grasp the principle of solving it first.

There are so many ways to apply the Number Line! Previously, students used it for matching. Here, they review number sequencing on the Number Line with the help of a friendly grasshopper.

Now that students are sufficiently prepared, Happy Numbers introduces the first equations! They are absolutely the same as in the “sharing candies” exercise, but now the equations are written out completely, including all signs, and an abstract model with cubes is used as visual support.


(see Kindergarten Module 1 — Topic D: exercise i)

Then, students proceed to review numbers up to 10. Happy Numbers varies the notation to make the task just a little harder. Look at those octopuses! How is it possible not to fall in love with math with such a scenario?


(see Kindergarten Module 1 — Topic E: exercise d)

It’s really important for Kindergarten students to have a strong mental grasp on numbers to 10. That is why in the next exercise Happy Numbers asks them to count the birds while they are flying away.

Students have already reviewed material about same and different objects. They are learning to count unlike and unaligned objects, a skill which is now merged with number matching. What a pleasure to count cute kittens!


(see Kindergarten Module 1 — Topic F: exercise f)

Module 1 of the Kindergarten curriculum ends with addition and subtraction of 1 with abstract visual models and with numerical notation. Students try it on a Number Line:


(see Kindergarten Module 1 — Topic G: exercise f)

…  with a model of Base-10 Blocks:

… and using equations with just numerals:


(see Kindergarten Module 1 — Topic G: exercise h)

Extension of Basic Geometry Knowledge

The sneak peek into geometry starts with reviewing shapes and their names:


(see Kindergarten Module 2 — Topic A: exercise b)

In this grade, students also learn a new shape called hexagon. Ravenous elephants are ready to help!


(see Kindergarten Module 2 — Topic A: exercise k)

There are several engaging tasks with a game-like framework. For example, students fill figures with different colors depending on their shape. In doing so, they build fluency with geometric figures and their names.

Then Happy Numbers transitions students to spatial orientation. In exercises with friendly animals, they learn such terms as above/below:

… and between/beside:


There are also tasks on positions in front/behind and up/down.

Teaser of Comparing

Kindergarteners are not yet ready to learn comparison as it is, but they can already notice such differences as more, fewer, and the same. Several tasks with a visually highlighted quantity of objects will prepare them for real comparing in Grade 1.

For example, in this exercise students arrange objects and compare them visually, without counting. There are exercises with similar and dissimilar objects and some with objects that aren’t aligned. These exercises provide training for numerical comparison.

In the next exercise, Happy Numbers labels the picture with the quantity to smoothly transition students from concrete objects to numeric notation.


(see Kindergarten Module 3 — Topic G: exercise f)

Introducing Simple Equations

The second half of the Kindergarten curriculum is mostly devoted to the construction and solution of simple equations. Happy Numbers leads students to translate a visual model with real objects to one with cubes to build the connection between concrete and abstract. They also become familiar with Happy Numbers color-coding, which represents addition and subtraction:

Familiarity with abstract cube models and color-coding helps students solve problems once real objects are removed.


(see Kindergarten Module 4 — Topic A: exercise i)

Students learn to model the task visually by themselves. Here they use the Number Line to build an equation, which will be recorded as an equation by the software.


(see Kindergarten Module 4 — Topic A: exercise l)

As necessary with any learning, the difficulty level and independence increase. Students start to record addition scenarios based on a visual model.


(see Kindergarten Module 4 — Topic C: exercise d)

Happy Numbers combines knowledge of several types of notation and different levels of abstraction in another exercise. It provides an equation scenario represented by real objects, which students need to model with Base-10 Blocks and record as an equation.

In Topic D, students start to progress into subtraction.

Zero is also an important hero in math, so there are special exercises incorporating it. Getting zero as an answer to an equation is clearly shown on a Number Line.

For fluency within addition and subtraction patterns, Happy Numbers offers quite an interesting matching task presented as a test. Students choose an abstract model that correlates to the given model of real objects.

With the expectation that students have learned the skills for solving simple equations, Happy Numbers increases the numbers. Now they are solving equations with numbers up to 10.


(see Kindergarten Module 4 — Topic E: exercise a)


(see Kindergarten Module 4 — Topic G: exercise a)

Numbers up to 20

At the end of the Kindergarten curriculum, Happy Numbers sets up a block of exercises about numbers up to 20. For Kindergarteners, it’s not really necessary to count beyond 10, but in preparation for Grade 1, it will be very helpful. Module 5 is devoted to numbers from 10 to 20. It starts with the formation of a two-digit number on a visual model with real objects shown without mathematical signs.

Students learn new numbers and their sequence on a vertical Number Line.


(see Kindergarten Module 5 — Topic A: exercise d)

Then they move on to a more abstract model of Base-10 Blocks. If there is a mistake, Happy Numbers will remind them of the pattern of tens and ones they mastered previously.


(see Kindergarten Module 5 — Topic C: exercise a)

Happy Numbers also provides high-leveled students with the option to solve equations with numbers up to 20. All of them are connected with ten, which draws the student’s attention to this number. In the next grade, they will work a lot with the strategy of making ten first. Here, they might add 10, subtract 10, or get 10 as an answer.


(see Kindergarten Module 5 — Topic E: exercise c)


(see Kindergarten Module 5 — Topic E: exercise e)
The main aim of the Kindergarten curriculum is to build fluency with whole numbers up to 10 and lay the foundation for further study of numbers beyond 10. Students should master the standard and word forms and easily quantify them by a visual model. That’s why Happy Numbers pays so much attention to the visual representation of numbers and aligns exercises in such a way that students will get a comprehensive understanding of basic numbers and their formation, moving from work with concrete objects to abstract models. Another important goal of this grade is the description of shapes and space. New terms such as above/below, up/down, in front/behind and between/beside allow students to take a fresh look at the world around them, to better navigate in space, and to prepare for more complex tasks in geometry. Mathematics is not just the science of numbers – it allows students to broaden their horizons, strengthen logical thinking, and develop a growth mindset. That is why it’s truly important to provide them with the best educational software which will both help them expand their knowledge and will collect data about their achievements, strengths, and weaknesses, important for a teacher. Happy Numbers will be glad to become a part of your Kindergarten curriculum and do our best for your students!

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