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Middle School    |    Formative Assessment Probe

Mixing Water

By Page Keeley

Assessment Physical Science Middle School

Sensemaking Checklist

This is the new updated edition of the first book in the bestselling Uncovering Student Ideas in Science series. Like the first edition of volume 1, this book helps pinpoint what your students know (or think they know) so you can monitor their learning and adjust your teaching accordingly. Loaded with classroom-friendly features you can use immediately, the book includes 25 “probes”—brief, easily administered formative assessments designed to understand your students’ thinking about 60 core science concepts.

Mixing Water

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The purpose of this assessment probe is to elicit students’ ideas about temperature change in a system. The probe is designed to find out whether students recognize that heat moves from the warm water to the cool water until they both reach the same temperature. Additionally, students’ explanations reveal whether they use an addition, subtraction, or averaging strategy to determine the resulting temperature.

Type of Probe


Related Concepts

Heat, transfer of energy, temperature, thermal equilibrium


The best response is B: 30 degrees Celsius. (In actuality, it would be slightly less, because a small amount of energy is transferred from the water to the glass and the surrounding environment in the process.) Temperature is a measure of the average motion of the particles that make up the water. The two separate samples of water are at different temperatures, meaning the average energy of the particles is less in the cooler (10°C) sample. When the cooler water and the warmer water are mixed together, a transfer of energy occurs between particles when they come in contact with each other. The flow of thermal energy via heat moves from the molecules in the warmer water to the molecules in the cooler water until they have the same average energy (temperature). Because the two samples of water are identical in volume, the thermal equilibrium that is reached is an average of the two temperatures.

Curricular and Instructional Considerations

Elementary Students

In the elementary grades, students use the terms heat, warm, hot, cool, and cold to describe phenomena and interactions with objects and their surroundings. They have experiences mixing same and different amounts of hot and cold water together or putting ice in warm water and finding the resulting temperature. Their experiences with materials and temperature are primarily observational. They learn how to measure temperature with a thermometer. Mixing hot and cold water and predicting and observing the resulting temperature is observational and should initially be approached qualitatively using words like warmer, cooler, hotter, or colder. The emphasis should be on exploring how heat spreads from warmer objects or materials to cooler and how objects or materials of different temperatures can eventually come to the same temperature. Although students at this grade level are not expected to know the difference between heat and temperature, it is helpful to refer to energy transfers in terms of gaining or losing energy in order to help students overcome their intuitive notion that cold is a substance that spreads like heat. The emphasis should be on tracking where the energy manifested as heat goes.

Middle School Students

In middle school, students shift their focus from observing what happens when warm and cold water are mixed together to explaining what happens in terms of thermal energy moving from warmer objects or materials to cooler objects or materials via heat. This is also a time when the term thermal energy is introduced. Students begin to connect the idea of heat with a movement of thermal energy. As middle school students develop a model of particle energy transfer, they can begin to connect the movement of warmer matter to cooler matter to the concept of conduction and convections as mechanisms for the transfer of thermal energy between atoms or molecules. Energy transfer now shifts to quantitative measurements as students see that an energy loss in one material is a gain in energy for the other and that the resulting temperature can be predicted and measured. This probe targets the grade-level expectation of understanding that energy is transferred from warmer regions or objects to cooler ones and that once energy is no longer transferred between objects or materials, they reach thermal equilibrium.

High School Students

Students at this grade level build on their experiences with energy transfer in middle school to investigate a variety of energy transfers more systematically and quantitatively, collecting evidence that confirms that energy is conserved during energy transfers and recognizing the loss of some energy through dissipation. They should be able to predict and quantitatively model how energy moves within a system and toward a more stable state.

Administering the Probe

This probe is best used with grades 5–12 and can be modified for lower elementary grades by changing the answer choices to qualitative descriptors such as (A) A warmer temperature than both cups, (B) A cooler temperature than both cups, and (C) A temperature somewhere between the two cups, followed by asking students to predict the final temperature in their explanation. You may wish to use visual props for this probe to demonstrate the two equal volumes, the pouring of one cup into another, and mixing the combination of the two samples.

Related Disciplinary Core Ideas (NRC 2012; NGSS Lead States 2013)


PS3.B: Conservation of Energy and Energy Transfer

The amount of energy transfer needed to change the temperature of a matter sample by a given amount depends on the nature of the matter, the size of the sample, and the environment.

Energy is spontaneously transferred out of hotter regions or objects and into colder ones.

Related Research

  • Middle school students often do not explain the process of heating and cooling in terms of heat energy being transferred. When transfer ideas are involved, some students think cold is being transferred from a colder to warmer object. Other students think both heat and cold are transferred at the same time. Students do not always explain heat-exchange phenomena as interactions. For example, students may say that objects tend to cool down or release heat spontaneously without acknowledging that the object has come in contact with a cooler object or area (AAAS 2009).
  • When considering the final temperature of two beakers of cold water at the same temperature mixed together, children ages 4–6 often judge the temperature to be the same. However, children ages 5–8 often say that the water will be twice as cold because there is twice as much water. At age 12, students describe the water as being the same temperature when mixed together, much like the very young children. One possible explanation for this progression is that young children do not consider amount and judge temperature as if it were an extensive physical quantity. Older children are better able to differentiate between intensive and extensive quantities, understanding that temperature remains unchanged despite the amount of water. It was also found that children tended to make more correct predictions of temperature when equal amounts of hot and cold water were mixed than when two equal amounts of cold water were mixed (Driver et al. 1994).
  • Researchers have found that difficulties experienced by students in response to questions that ask them to predict the final temperature of a mixture of two quantities of water, given the initial temperature of the components, depend on the form in which the temperature problems are presented. Qualitative tasks in which the water is described as warm, cool, hot, or cold are easier than quantitative ones in which specific temperatures are given. Erickson and Tiberghien (1985) found that younger students (ages 8–9) prefer an addition strategy, whereas older students are more apt to use a subtraction strategy, which at least acknowledges that the final temperature lies somewhere in between. However, students ages 12–16 were as likely to use an addition or subtraction strategy as they were to use an averaging strategy.

Related NSTA Resources

Brown, P. 2011. Teaching about heat and temperature using an investigative demonstration. Science Scope 35 (4): 31–35.

German, S. 2016. Predicting, explaining, and observing thermal energy transfer. Science Scope 40 (4): 68–70.

Konicek-Moran, R. 2013. How cold is cold? In Everyday physical science mysteries: Stories for inquiry-based science teaching, R. Konicek- Moran, 113–122. Arlington, VA: NSTA Press

NGSS Archived Webinar: Core Ideas—Energy, www. 8 & l i s t = P L 2 p H c _ B E F W 2 J j W Yu a 2 _ z3ccHEd6x5jIBK. Nordine, J. 2016. Teaching energy across the sciences K–12. Arlington, VA: NSTA Press.

Nordine, J., and D. Fortus. 2017. Core idea PS3: Energy. In Disciplinary core ideas: Reshaping teaching and learning, ed. R. G. Duncan, J. Krajcik, and A. E. Rivet. Arlington, VA: NSTA Press.

NSTA Science Object, Energy: Thermal energy, heat, and temperature. resource/?id=10.2505/7/SCB-EN.3.1.

Suggestions for Instruction and Assessment

  • This probe can be followed up with the science practice of planning and carrying out an investigation. Ask the question, encourage students to commit to a prediction, and then test it with the temperatures stated in the probe (use caution when students are handling hot liquids). The dissonance involved in discovering that their predictions and results may differ can lead to testing other combinations of temperatures, including mixing water at the same temperature, to resolve the dissonance and seek an explanation.
  • Depending on the age of the students, vary their experiences to include mixing same temperatures; mixing samples at two different cold, hot, warm, or cool temperatures; mixing two different temperatures that vary by less than 10 degrees or by more than 50 degrees; mixing unequal volumes at same temperatures and unequal volumes at different temperatures; mixing three of four different samples at same and different volumes; and so on. Ideally, have students come up with the various configurations to test. Have students discover the pattern that results from a variety of mixings, and allow them to use their discovery to develop an explanation.
  • Try juxtaposing two different representational systems. Give one probe in which the prediction is stated as mixing equal amounts of cold and hot water, and give the other stated in quantitative terms as in this probe. Use this conflict-inducing strategy to engage students in argumentation between students whose qualitative prediction differs from their quantitative one and students who predicted the same outcome for both probes.
  • Develop the concept of conduction by providing students with multiple opportunities to mix hot and cold objects and materials, not only liquids. For example, place a hot solid object in contact with a cold solid object. Have students discuss their findings and develop a particle model to support their explanation.
  • For older students, challenge them to predict and explain the outcome of mixing different volumes of water that are also at different temperatures and develop a mathematical model to predict the resulting temperature.

American Association for the Advancement of Science (AAAS). 2009. Benchmarks for science literacy. New York: Oxford University Press. index.php.

Driver, R., A. Squires, P. Rushworth, and V. Wood- Robinson. 1994. Making sense of secondary science: Research into children’s ideas. London: RoutledgeFalmer.

Erickson, G., and A. Tiberghien. 1985. Heat and temperature. In Children’s ideas in science, ed. R. Driver, E. Guesne, and A. Tiberghien, 52–84. Milton Keynes, England: Open University Press.

National Research Council (NRC). 2012. A framework for K–12 science education: Practices, crosscutting concepts, and core ideas. Washington, DC: National Academies Press.

NGSS Lead States. 2013. Next Generation Science Standards: For states by states. Washington, DC: National Academies Press.

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