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 operation signs appear (plus and minus). Students will reinforce and expand their knowledge of basic geometry. They’ll learn principles of sorting objects and comparing them, which will be 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 up to 10 and begin to learn numbers up 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 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 HappyNumbers.com to explore our full curriculum and sign up for a free trial.

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

To see the full exercise, follow this link.

To see the full exercise, follow this link.

    In addition, students review counting in various exercises, including those with manipulatives. A tangible experience helps them understand the meaning of the process before they move to more abstract math operations.

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     In Module 1, students work with numbers from 0 to 10. Tasks are simple, and the curriculum includes many repetitions of similar scenarios with different numbers. Practice makes perfect, doesn’t it? Using repetition, Happy Numbers leads students to master the concept.

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     Happy Numbers varies the notation to make the task just a little harder. Look at those octopuses! Is it possible not to fall in love with math in such a scenario?

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

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    Students have already reviewed material about objects that are the same or different. They also begin learning to count unlike and unaligned objects, a skill that is now merged with number matching. 

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     Module 1 of the Kindergarten curriculum ends with addition and subtraction of 1 with abstract visual models and numerical notation. Students use familiar representations (cubes, base-10 blocks, a number path, and real-world objects) to explore the concept of one more…

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…and one less to solve +/- 1 equations.

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     The next Module is dedicated to “Two-Dimensional and Three-Dimensional Shapes.” Students review shapes and their names learned in Pre-K…

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 …as well as become familiar with polygons and hexagons and their properties.

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      They choose specific shapes to complete and decorate the picture. This helps them memorize shape names and learn to identify them quickly.

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     Then Happy Numbers increases the complexity of the task by asking students to color figures with different colors depending on their shape.

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    In topic B, students explore spatial orientation. They learn such terms as above/below and also up/down, in front of/behind, between/beside, and near:

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    In topic C, students apply their previous understanding of flat and solid shapes to distinguish between the two.

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    Kindergarteners are not yet ready to learn comparison properly, but they can notice differences such as longer, taller, and shorter. Several tasks with visually highlighted attributes of objects will prepare them for formal comparison in Grade 1.

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In topic B, students work with familiar linking cubes to count cubes to determine the length of sticks. They compare lengths using longer, shorter, and the same.

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    At this stage, they also learn to identify heavier and lighter objects.

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    In topic D, students learn the word capacity and use it to measure the amount of liquid a container can hold.

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    Then, to prepare for comparing numbers, students work with real-world objects to determine if there are "enough" to make pairs.

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

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    Happy Numbers includes manipulatives to push students toward grasping the pattern. They now 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.

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    First, students learn to count totals using concrete and familiar objects, like cars. They work with real-world objects in two colors to learn how to differentiate addends. 

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    Then, for the first time, Happy Numbers introduces “+” and “-” signs and teaches how to use them. 

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    Then students  build models using real-world objects and math cubes

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    In Topic D, students progress into subtraction.

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    They also model subtraction with cubes...

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    Students compose number bonds, addition statements, and equations.

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

To see the full exercise, follow this link.

To see the full exercise, follow this link.

    At the end of the Kindergarten curriculum, Happy Numbers presents students with 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 the numbers 10 to 20.

    We start by introducing ten-frames first.

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    Students learn new numbers with a model of a ten frame. 

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    Students also use Base-10 Blocks to practice numbers. If students make a mistake, Happy Numbers will remind them of the pattern of tens and ones they mastered previously. 

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    Place value oriented exercises help students to practice two digit numbers: here, for example, they need to put a certain number of cubes in the box.

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    Students decompose numbers 11-20 using models involving 10-frames.

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    Then, students explore how multiples of 10 are represented by 10-frames or number names. Students begin to order multiples of 10 on a number path to practice skip-counting by 10s. 

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    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 with 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, which are so important for a teacher. Happy Numbers will be glad to become a part of your Kindergarten curriculum and do our best for your students!

    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:

    If you have any additional questions, our support team is always here to assist you. Click the blue messenger icon in the bottom right corner of this page to start a conversation with them.