From a young age, children are interested in equal or fair sharing to avoid unhappiness. This creates concrete hands-on experiences of sharing cookies or sweets, laying the foundation for fraction knowledge. Fractions can be conceptualized in multiple ways, beyond the common “part–whole” concept. These include fractions as ratios, operators, measures, and quotients, each offering a unique perspective on their meaning and application (Lamon, 2007). Understanding these diverse conceptualizations is crucial for developing a comprehensive understanding of fractions.
In early years teaching, emphasis should be placed on part–whole, division, and measurement interpretations (Van de Walle et al., 2014). Children should be given opportunities to experience different meanings of fractions through practical, play-based, and experiential activities. At this stage, learners typically describe fractions informally using terms such as “piece” or “equal sharing”, rather than formal fraction notation, which is introduced later in primary education.
The part–whole interpretation is the most familiar representation, in which a fraction describes a portion of a whole object, set, or quantity. For example, 1/2 represents one of two equal parts of an orange that has been shared.
The ratio interpretation describes a fraction as a relationship between two quantities expressed as a comparison (e.g., 1 in 4 learners) (Lamon, 2007). The operator interpretation treats a fraction as an operation applied to a quantity; for example, “half of 10” involves dividing 10 into two equal parts, resulting in 5 (Van de Walle et al., 2018). Fractions can also be understood as a quotient, where the numerator is divided by the denominator; for example, 5/2 represents 5 divided by 2, which equals 2.5 (Charles et al., 2012). In the measure interpretation, a fraction represents a position or length on a number line; for example, 3/4 is located between 0 and 1 on a number line (Lamon, 2007).
These conceptualisations are interconnected and mutually reinforcing. For example, understanding fractions as both part–whole and ratios can support learners in solving proportion problems more effectively.
Teaching fraction concepts in early childhood education (ECE) should therefore emphasise hands-on, visual, and experiential learning, focusing on understanding parts of a whole rather than abstract symbols (Clements & Sarama, 2014). The use of real objects, manipulatives, and everyday contexts helps learners develop an intuitive understanding of fractions as equal parts of a whole.
A useful starting point for preschool learners is sharing concrete quantities, such as distributing six beans between two or three dolls. Through such activities, learners observe that increasing the number of recipients reduces the amount each receives. Formal fraction notation is introduced later, once learners have developed sufficient conceptual understanding of numerators and denominators through repeated practical experiences and verbal explanations.
Food items provide meaningful contexts for exploring fractions. Learners can physically divide items into equal parts, with emphasis placed on equal partitioning and fairness (Van de Walle et al., 2018).
Visual representations such as circles, strips, fraction walls, and number lines support conceptual understanding (Charles et al., 2012).
Fractions can be linked to everyday experiences such as sharing food, dividing fruit, or measuring ingredients in recipes (Clements & Sarama, 2014).
Activities involving cutting, folding, and manipulating fraction materials help reinforce understanding. Games and playful activities can further support engagement and conceptual learning (National Council of Teachers of Mathematics [NCTM], 2013).
By combining varied hands-on activities with meaningful real-world examples, teachers can support young learners in developing a strong foundational understanding of fractions before progressing to symbolic representation.
Learning measurement is best supported through concrete experiences and exploration of length, area, mass, and volume/capacity. Early measurement instruction begins with direct comparison of objects, as this helps children understand that different attributes can be measured and ordered according to mathematical properties (Clements & Sarama, 2021).
Instruction should then progress to the use of non-standard units (e.g., body parts, sticks, or informal tools), which help learners understand relationships between attributes such as length and number, mass and number, and volume and number (Sarama & Clements, 2009; Cheeseman et al., 2014). Measurement learning should also include the use of appropriate tools such as balancing scales and containers of different shapes and sizes, which should be made available for play and exploration (Parviainen et al., 2024).
Learners also need to develop awareness of the attribute being measured (i.e., measurement concepts). Concrete exploration of measurable attributes supports conceptual development when teachers intentionally connect measurement language to real-life situations (Cheeseman et al., 2014; Lee et al., 2016). For example, length can be explored through direct comparison (shorter/longer, taller/shorter) and ordering (from shortest to longest) (Clements & Sarama, 2021).
Similar approaches apply to other measurement domains. In area, learners compare objects using terms such as smaller/larger. In mass, comparisons may include lighter/heavier or lightest/heaviest. In volume or capacity, learners use terms such as fuller/emptier, more/less, or fewer/greater. The consistent use of accurate mathematical language by teachers is important in supporting the development of measurement concepts.
Practicing these concepts can take place through both free play and guided play. Below are examples of each:
Provide materials such as cups, bowls, spoons, sand, sticks of equal length, plastic toys of varying heights, boxes, shapes of equal size, balancing scales, and stones of different sizes.
Provide materials and scaffold learning through guided questioning, for example:
As children develop a more sophisticated understanding of time and time-related terminology (Lyytinen, 2014; Mulligan & Mitchelmore, 2013), measurement instruction should also include time concepts. Time can be explored using concrete tools, such as timers and hourglasses, while collecting toys or doing physical exercise. Providing such tools for play further supports understanding of time as a measurable concept (Parviainen et al., 2024).
Time understanding also includes sequencing events. Learners can practise ordering sequences of familiar activities, such as morning routines, puzzle completion, or baking, by arranging pictures from beginning to end. Such activities support the development of temporal reasoning and understanding of chronological order.
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Mulligan, J., & Mitchelmore, M. (2013). Early awareness of mathematical pattern and structure. In L. Y. English & J. T. Mulligan (Eds.), Reconceptualizing early mathematics learning (pp. 29–45). Springer.
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