España 
Italia 
United States 
Brasil 
Chile
Ecuador
Mexico
Colombia
Perú
Traditionally, in mathematics, content strands (number, geometry, statistics, etc.) were compartmentalized as if they were separate worlds. But what if measurement were precisely a bridge that connects numbers with geometry? Measurement allows students to construct meaning from an early age and develop key skills such as estimation, comparison, and making mathematical connections.
In this article, we will explore in depth how the learning of measurement in mathematics is constructed throughout the entire school stage. From early childhood through middle school, we will explore the five key ideas that structure this journey and discover how to turn measurement into a genuine foundation for mathematical thinking.
Explore how these ideas unfold across the school years.
The five big ideas of measurement
Last November, at the 2024 Mathematical Education Conference of the APMCM, we offered a talk about the learning progression of the concept of measurement throughout the entire school stage.
In our talk, we discussed the term “big idea,” which, citing Charles Randall (2005), is defined as the formulation of a central idea in mathematics learning that links multiple mathematical concepts into a coherent whole.
The following five big ideas form the foundation of measurement learning.
Compare and order
Before measuring, one must observe, manipulate, and reason. Which object weighs more? Which occupies more space? These comparisons, whether direct or indirect, lay the foundation for metric thinking and enable the development of logical strategies before introducing formal instruments or units.
Units and equivalences
Using informal units, such as hand spans, bottle caps, or pencils, helps students construct the notion of a unit of measure. From there, the transition to conventional units becomes meaningful, and with it, the need to establish equivalences, such as between centimeters and meters, between grams and kilograms, or between hours and minutes.
Estimation
Estimation involves anticipating, validating, and testing prior assumptions. It forms part of an essential and cross-cutting mathematical practice. It allows us to tell if a result makes sense, if a measurement is coherent with reality, or if there are errors that should be reviewed. That’s why it should be part of regular classroom work.
Measurement with instruments
Selecting appropriate tools, using them correctly, and determining the required precision are essential components of measurement. Here, there is not only technique, but also decision-making and reading context.
Deduction of formulas
A formula is a generalized relationship derived through experience. Observing patterns, experimenting with shapes and measurements, deducing relationships… Only afterward is it formalized. This approach connects directly with algebraic thinking.
Measurement: a trajectory that grows with students
These big ideas are not all worked on at once, nor are they approached linearly. They interweave, evolve, and mutually reinforce each other throughout the entire school stage. In fact, throughout compulsory education, the content of measurement evolves as students’ thinking develops. In this journey, we can identify certain key moments:
Early Childhood Education and early elementary
In the early grades, students engage with measurement through bodily experience and exploration. Comparing directly, ordering by size or weight, using objects from the environment as personal units… Learning is grounded in perception and hands-on manipulation. Simple instruments are introduced (such as strings, containers, and stopwatches), but the focus remains on developing effective strategies.
Middle elementary
In the middle grades, the first conventional units appear, and simple equivalences are also consolidated, always from authentic and meaningful contexts. At this stage, it is also key to continue fostering estimation.
Upper elementary
The work expands to other magnitudes, such as length (cm, mm), mass (kg, g), or volume (L, mL). Here, rational numbers are introduced more explicitly, and understanding of the decimal system is deepened. Operations with decimals are introduced, which allows for addressing situations that lay the foundations for understanding proportionality.
In this sense, measurement ceases to be solely a concrete practice and becomes a tool for analysis and prediction.
Middle school
Finally, in middle school, measurement is connected to geometry, algebra, and statistics. Formulas are deduced, compound units are interpreted (km/h, g/cm³), and work is done with scales and complex conversions.
The focus shifts to applying metric thinking to real contexts and solving more abstract situations. Estimation, comparison, and validation strategies reach their maximum expression here.
