Building Conceptual Understanding through Multiple Representation, Modeling, and Manipulatives

Any student who can perform simple memorization can recall that 4 + 3 = 7. But what does it mean to truly understand the concept of addition? And how can teachers help students achieve this deep understanding? In line with the latest research, we have found that the three pillars upon which conceptual understanding is […]

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Elementary School Sets the Foundation for Future Achievement

Education is like building a skyscraper — the strength of its foundation determines how high and sturdy the building can become. According to “Preschool Education and Its Lasting Effects: Research and Policy Implications”1 written by W. Steven Barnett, “preschool education programs produce long-term improvements in school success, including higher achievement test scores, lower rates of […]

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Grade 5 Overview: Fractions, Rounding and Data Analysis

In Grade 5, students start to combine familiar and new math skills for problem-solving. Happy Numbers includes many exercises with interconnection of different skills so that students learn to fluently operate their knowledge. You’ll also find tasks in which they can choose the next step in problem-solving, which reinforces their independence in math.   The […]

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Properties of Multiplication

One of the most important skills teachers can equip their students with is the ability to apply a general math concept to problem-solving. However, students often learn the properties of arithmetic operations without appreciation of their real importance and application. That’s why Happy Numbers pays a lot of attention to clear, step-by-step guidance for learning […]

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The Relationship between Multiplication and Division

Mathematics is a very logical science, built on rules, principles, and relationships. Mathematical thinking is based on the sequential study of procedures, first with concrete objects, then with visual models, and only then with abstract symbols and concepts. This systematic approach to learning allows students to grasp the meaning of mathematical operations and the connection […]

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Numbers to 1000 Part 1: Two-Digit Numbers

Math mindset or mathematical thinking is a logical process that isn’t necessarily related to numbers, but basic math language is absolutely dependant on them. That’s why Happy Numbers prepared a comprehensive summary on how numbers to 1000 are taught in its curriculum. This overview unifies counting, number sequencing, notation, and place value. For Part 1, […]

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Comparison of Whole Numbers within 1000

In Pre-K and Kindergarten, students learn a lot about numbers: their names, notation, sequencing, and counting. With a foundation of different visual representations, they grasp that each number can answer the question, “How many objects are in a group?” This logically brings students to a new mathematical skill, comparison.   There are two widely-known pedagogical […]

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