Water Quality Lessons
68th
2
Classroom
Math
Summary
This is an inquirybased lesson that asks students to play with a table of Celsius and Fahrenheit values and see what conclusions they can draw about the relationship between the two sets of numbers. They also have the opportunity to discuss their ideas of “hot” and “cold” and examine what values correspond to those concepts.
Objectives
 To determine the formula for converting from Celsius to Fahrenheit.
Materials and Resources
Supplies
4 beakers
Thermometers
Graph paper
Rulers
Hint cards
Data table for Celsius and Fahrenheit (010 degrees Celsius)
Hot plate and ice for prep
Before you get started
Tips for Teachers
 Allow students to experiment with the numbers. Do your best to not lead them to the formula and allow them to spend time playing with the numbers and their relationship. It will be tempting to tell them the answer. Don’t do it! They will learn much more from engaging with the math.
Preparation
Fill at least three (and possibly four) large beakers of water at the following approximate temperatures: “hot,” “warm,” “cool,” and “cold.” The warm beaker should be around 70 degrees. Place them in a location in the room where students can touch the beakers in small groups. (Note: it’s important to use large beakers because small samples will quickly change temperature and students will be unable to do the experiment.)
 Create hint cards to distribute if students need help figuring out how to convert Fahrenheit to Celsius. For example: “Try doubling the Celsius!” or “Why is the number 32 important? What operation do you think is used on 32?”
Background
 Too often, unit conversions are rote formulas that students use with little understanding. This lesson allows students to consider how the numbers are changing and experiment on their own with the math of the conversion formula.
Instruction Plan
Engage
Ask students the following questions, putting all temperatures that students mention on the board:
“What’s the hottest thing you’ve ever felt?”
“What’s the coldest thing you’ve ever felt?”
“What’s the hottest you personally have ever been?”
“Can you put a number to any of these experiences?” (Most will probably be in Fahrenheit).
Compare 70 degrees air and water. Discuss that it is about 70 degrees in the room right now. Have students put their finger in a beaker of water that is also 70 degrees. Does it feel the same?
Ask students, “What questions do you have about temperature so far?”
Explore
Students should come to the front of the room in small groups to feel the beakers.
Ask students:
“What is the difference between them?”
“What words would you use to describe these temperatures?”
“Are these words accurate descriptions? Why or why not?”
Explain that there are differents units for temperature. In the US, temperature is usually measured using the Fahrenheit scale (unit = degrees Fahrenheit), whereas scientists use the Celsius scale (unit = degrees Celsius).
Now, ask the following questions about the beakers:
“Which are getting warmer and which are getting colder?”
“Do the beakers heat up or cool down more quickly? Why?”
Take the temperature of the four beakers with a digital thermometer and put them up on the board. They should be something like this:
40 degrees Fahrenheit
60 degrees Fahrenheit
80 degrees Fahrenheit
90 degrees Fahrenheit.
Convert all four temperatures to Celsius and put them on the board in a table.
Make sure that Celsius is the first column of the table and Fahrenheit is the second column.
Have the students copy the table and add the data point 0, 32.
Explain that their goal is to figure out how to move from Celsius to Fahrenheit (or how the two sets of numbers relate to each other).
Now, give a pep talk. Explain to the students that they are looking for patterns in the data. They might or might not actually come up with a formula or a representation for the data. That doesn’t matter! What matters is finding a pattern. Explain that if the students get frustrated or worried, you will provide hint cards but that they can do it! Their goal is to think about the mathematical relationship between Celsius and Fahrenheit and write a sentence describing it. They could also represent it in any other way, as a point on a line, as a mathematical description (double and add 32), or anything else they can think of.
Distribute the following materials, scaffolded appropriately for your class:
Graph paper (possibly with axes labeled)
Calculators
A table of all the conversions from 0 degrees Celsius to 10 degrees Celsius. (For more advanced students, maybe provide a larger set of data).
If students get frustrated during this process, pass out a hint card.
Meanwhile, move around the room and ask the following questions to get them thinking:
“Is the space between a degree Celsius or a degree Fahrenheit bigger?”
“Is 50 degrees Celsius hotter or colder than 50 degrees Fahrenheit?”
“Is a Fahrenheit temperature always hotter than a Celsius temperature? Explain.”
Explain
When students are ready, have them share their results for conversion from Celsius to Fahrenheit.
Once students have all presented, show them the formula.
Ask students to practice five conversions.
Elaborate
Give students the temperature on Mercury (427 degrees Celsius) and on Pluto (229 degrees Celsius).
Ask students:
“What are the extremes on Earth versus these 2 planets?”
“What are the extremes in NYC?”
“What do those numbers mean? How many times bigger are they than the coldest thing you have ever experienced?”
Then, have the students convert them to Fahrenheit. Discuss whether or not the difference is meaningful at the extreme and why or why not?
Standards
CCLS  ELA Science & Technical Subjects

 Integrate quantitative or technical information expressed in words in a text with a version of that information expressed visually (e.g., in a flowchart, diagram, model, graph, or table).
CCLS  Mathematics

 Reporting the number of observations.
NGSS  CrossCutting Concepts

Cause and Effect
 Cause and effect relationships may be used to predict phenomena in natural or designed systems.
NGSS  Disciplinary Core Ideas

PS3.A: Definitions of Energy
 Temperature is a measure of the average kinetic energy of particles of matter. The relationship between the temperature and the total energy of a system depends on the types, states, and amounts of matter present. ETS1.B: Developing Possible Solutions
 The term “heat” as used in everyday language refers both to thermal energy (the motion of atoms or molecules within a substance) and the transfer of that thermal energy from one object to another. In science, heat is used only for this second meaning; it refers to the energy transferred due to the temperature difference between two objects. (secondary)
NGSS  Science and Engineering Practices

Analyzing and Interpreting Data
 Analyze and interpret data to provide evidence for phenomena.

Developing and Using Models
 Develop a model to predict and/or describe phenomena
NYC Science Scope & Sequence  Units

Grade 6, Unit 1
 Energy and Simple Machines

Grade 6, Unit 2
 Weather and Atmosphere

Grade 7, Unit 2
 Energy and Matter
NYS Science Standards  Key Ideas

PS Key Idea 3
 Matter is made up of particles whose properties determine the observable characteristics of matter and its reactivity

PS Key Idea 4
 Energy exists in many forms, and when these forms change energy is conserved.
NYS Science Standards  Major Understandings

 A liquid has definite volume, but takes the shape of a container.
 Heat can be transferred through matter by the collisions of atoms and/or molecules (conduction) or through space (radiation). In a liquid or gas, currents will facilitate the transfer of heat (convection).
NYS Science Standards  MST

 Students will understand the relationships and common themes that connect mathematics, science, and technology and apply the themes to these and other areas of learning.
 Students will apply the knowledge and thinking skills of mathematics, science, and technology to address reallife problems and make informed decisions.