Tools & Mathematics

Nature of Science & Engineering
Interactions Among Science, Technology, Engineering, Mathematics, and Society

Tools and mathematics help scientists and engineers see more, measure more accurately, and do things that they could not otherwise accomplish.

Benchmark: Tools to Improve Observations

Use tools, including rulers, thermometers, magnifiers and simple balances, to improve observations and keep a record of the observations made. 


Standard in Lay Terms 

Tools and mathematics are used by scientists and engineers to ensure accurate observations and record keeping. (J. Panichi)

Big Ideas and Essential Understandings 

Big Idea:

Students will measure length, mass, volume, and temperature, using the appropriate tool  and unit of measurement.

Students will use the metric system as the standard system of measurement.

Students will record their observations.

Students will employ tools to gather, analyze, and interpret data.    

Students will use data to construct reasonable explanations.

Students will use mathematics in scientific inquiry.

Students will understand that scientists use different kinds of investigations and tools to develop explanations using evidence and knowledge.

(adapted from National Science Education Standards)

Benchmark Cluster 

MN Standard Benchmarks   Use tools, including rulers, thermometers, magnifiers, and simple balances, to improve observations and keep a record of the observations made.


Video clip: Cool Conservation Tools

A short clip depicting some of the newest, coolest tools for gathering data for conservation.


NSES Standards

Simple instruments, such as magnifiers, thermometers, and rulers, provide more information than scientists obtain using only their senses.  NSES

Objects have many observable properties, including size, weight, shape, color, temperature, and the ability to react with other substances.  Those properties can be measured using tools, such as rulers, balances, and thermometers.  NSES

AAAS Atlas

NSDL Science Literacy Maps

Describing things as accurately as possible is important in science because it enables people to compare their observations with those of others. 1B/P3 (ID: SMS-BMK-1901)

One reason for following directions carefully and for keeping records of one's work is to provide information on what might have caused differences in investigations. 1B/E2b (ID: SMS-BMK-1710)

Clear communication is an essential part of doing science.  It enables scientists to inform others about their work, expose their ideas to criticism by other scientists, and stay informed about scientific discoveries around the world.  1C/E2 (ID: SMS-BMK-1907)

Keep written or electronic records of information so that the records are understandable weeks or months later.  12C/E3 (ID: SMS-BMK-0813)

Measuring instruments can be used to gather accurate information for making scientific comparisons of objects and events and for designing and constructing things that will work properly.  3A/E3 (ID: SMS-BMK-0080)

Benchmarks for Science Literacy Project 2061

By the end of 2nd grade, students should know that:

  • People can often learn about things around them by just observing those things carefully, but sometimes they can learn more by doing something to the things and noting what happens. 1B/P1
  • Tools such as thermometers, magnifiers, rulers, or balances often give more information about things than can be obtained by just observing things unaided. 1B/P2
  • Describing things as accurately as possible is important in science because it enables people to compare their observations with those of others. 1B/P3

By the end of the 5th grade, students should know that:

  • Scientific investigations may take many different forms, including observing what things are like or what is happening somewhere, collecting specimens for analysis, and doing experiments. 1B/E1*
  • One reason for following directions carefully and for keeping records of one's work is to provide information on what might have caused differences in investigations. 1B/E2b
  • Scientists do not pay much attention to claims about how something they know about works unless the claims are backed up with evidence that can be confirmed, along with a logical argument. 1B/E4

Common Core Standards

Minnesota Grade 3 Math Standards

Strand: Mathematical Reasoning

Standard: Apply skills of mathematical representation, communication and reasoning throughout the remaining four content strands.


  1. Communicate, reason and represent situations mathematically.
  2. Solve problems by distinguishing relevant from irrelevant information, sequencing and prioritizing information and breaking multi-step problems into simpler parts.
  3. Evaluate the reasonableness of the solution by considering appropriate estimates and the context of the original problem.
  4. Know when it is appropriate to estimate and when an exact answer with whole numbers, fractions or decimals is needed.
  5. Express a written problem in suitable mathematical language, solve the problem and interpret the result in the original context.
  6. Support mathematical results using pictures, numbers and words to explain why the steps in a solution are valid and why a particular solution method is appropriate.

C. Measurement

Standard: Measure and calculate length, time, weight, temperature and money using appropriate tools and units to solve real-world and mathematical problems.

The student will:

  1. Select an appropriate tool and identify the appropriate unit to measure time, length, weight and temperature.
  2. Find the perimeter of a polygon with whole number sides.
  3. Know relationships between units of length in a system of measurement, such as 12 inches equals one foot or 100 centimeters equals one meter.
  4. Tell time to the minute using digital and analog time.
  5. Determine elapsed time to the minute.
  6. Make change using as few coins as possible up to a dollar.


Student Misconceptions 

Students may mix-up the meaning of observation in science.  The word observation generally means something that we've seen with our own eyes.  In science, the term is used more broadly.  Scientific observations can be made directly with our own senses or may be made indirectly through the use of tools like thermometers, pH test kits, Geiger counters, etc.  We can't actually see beta particles, but we can observe them using a Geiger counter.  To learn more about the role of observation in science, visit Observation beyond our eyes. From Understanding Science: How Science Really Works


It is an exciting day in Ms. A.'s 3rd grade classroom: their monarch eggs have begun to hatch and the students can begin collecting data on the small caterpillar larva.  The students have been paired up and given a caterpillar to observe and collect data throughout its short life before it turns into a butterfly.  The students are excitedly getting their caterpillar cups and hand lenses to make their observations and measurements.  Ms. A. leads a discussion with the class about the appropriate way to measure their small organisms.  Would a bathroom scale be appropriate?  A meter stick?  She has students do a think-pair-share to discuss the best way to measure, and then records their answers on the SMART board.  They decide that grams would be the best unit of measure for the larva's mass and millimeters would be the best unit of measure for length.   Ms. A. uses the document camera to demonstrate how to carefully pick up the caterpillar with a paintbrush.  She models how to use a gram scale and weigh the larva.  Next Ms. A. models how to measure their caterpillars using the millimeters on the ruler.  She has a few students come up to the document camera to try it and reminds her students that they have learned about measurement in math.  Finally, Ms. A. and the students set up data tables in their science notebooks to record their daily observations of date, length and mass of their caterpillar, and any other observations they make.  She turns the students loose in the science lab and they can't wait to explore their caterpillars! (G. Keenan, 2011; pictures used with permission from Alicia Schumacher)


Instructional Notes 

Instructional suggestions:

Children should be taught to make careful measurements, but they also need to learn that some errors in measurement are unavoidable.  Sometimes errors arise through carelessness, misuse of measurement instruments, or recording mistakes.  These human errors can be minimized by instruction and practice in measuring carefully and properly and by double (or triple) checking of measurements.  Even then, errors may be introduced because of limitations in the precision of the instruments used to make the measurements.  Students should be taught how to make the most precise measurements possible with the tools available.  They should also repeat their measurements several times.  Sometimes they will obtain results that are different each time.  If those differences are significant, students should examine their measurement methods to see whether an obvious error occurred.  Science Framework for California Public Schools, 2004

FOSS Correlations:

Matter and Energy

  • Investigation 3, Parts 2-3, pp. 139-160
  • Investigation 4, Part 1, pp. 174- 180

Magnetism and Electricity

  • Investigation 1, Part 3, pp. 23- 34


  • Investigation 4, Part 1, pp. 8-13

Structures of Life

  • Investigation 1, Part 3, pp. 28- 33


  • Investigation 1, Parts 2-3, pp. 16-24
  • Investigation 2, Parts 2-3, pp. 14-24
  • Investigation 3, Parts 2-3, pp. 14-21
  • Investigation 4, Parts 1-3, pp. 8- 21

Selected activities

Float My Boat  An activity on FETCH! by PBS.

Students are challenged to build tinfoil boats and test different designs to see how          many pennies their boats can hold without sinking.

The Science of Puddles  Debra Hornfeldt, Como Park Elementary, St Paul MN

Based on original activities from The Wonders of Wetlands (pp. 152-156) and Aquatic Project Wild (pp.ages 21-26).  Summary: Children will look at their schoolyard and determine where a puddle will form after a heavy rain.  They will map the school yard and draw chalk lines to demonstrate their predictions.  After a rain, children will check their predictions and begin to investigate a puddle over a period of time.  Children will graph water temperature, diameter, and depth data and be able to explain the changes in data over time as measured by teacher observation.

Measuring Cloud Coverage from Science Netlinks

Purpose: To review what clouds are and then use fractions to describe cloud coverage.

Measuring and Comparing Matter (A MnSTEP Activity)

Summary: In this physical science lab activity, students will measure a variety of different materials from the classroom to determine how much matter is found in these materials. Using the same volume for each type of material they investigate, students will determine the mass of these materials by using an elementary balance.  The data (the masses of the different materials) will be compiled in graph form and analyzed to determine which materials contain more matter.  The investigative results will be shared with other classmates using a gallery approach as students walk around the room looking at other students' graphs and charts.  Students will then draw conclusions from the data about mass, volume, and density during a class discussion and write about their findings in a science journal.

Instructional Resources 

Additional Resources

Video Clips from NeoK12:

Metric and Standard Measurement Systems

Shows how nonstandard units of measurement systems evolved to standard systems in order to create accuracy in science investigations.

How Telescopes WorkWays to Gather Light

Simple clip that shows how telescopes gather more light so that human eyes can see distant objects.

New Vocabulary 


Balance: a tool for weighing objects.

Celsius (°C): the temperature scale used in the metric system. Water freezes at 0°C and boils at 100°C.

Centimeter (cm): one one-hundredth of a meter.

Distance: how far it is between two points.

Estimate: an approximate value for a measurement.

Graduated cylinder: a transparent cylinder marked with evenly spaced lines for determining the volumes of liquids.

Gram (g): the basic unit of mass in the metric system.

Height: the distance on a person from the top of the head to the bottom of the feet.

Kilogram (kg): one thousand grams, or the mass of 1 liter of water.

Kilometer (km): one thousand meters.

Length: the distance of something from end to end, usually the longest dimension.

Liter (l): the basic unit of fluid volume in the metric system.

Mass: a quantity of matter.

Measurement standard: a unit agreed upon and used by a large number of people.

Meter (m): the basic unit of distance or length in the metric system.

Metric system: a system of weights and measures based on multiples of ten.

Milliliter (ml): one one-thousandth of a liter; 1000 milliliters equal 1 liter.

Millimeter (mm): one one-thousandth of a meter.

Scale: something divided into regular spaces as a tool for measuring. (SS)

Standard measurements: units agreed upon and used by a large number of people.

Temperature: a measure of how hot or cold something is. (TG, SS)

Thermometer: a tool used to measure temperature. (TG, SS)

Volume: three-dimensional space. (TG, SS)

Weigh: to find the mass of.  You weigh an object to find its mass. (SS)

Width: the distance from side to side, a dimension shorter than the length. (TG)

Vocabulary from FOSS Measurement Module Glossary 2005 Edition

Technology Connections 

PBS Fetch! Episode 12: That Doesn't Float My Boat  

Trying to relieve a bad case of "Game Show Host Block," Ruff has fallen asleep and left the water in the bathtub running!  The flooded doghouse is filled with floating junk, giving him the perfect idea for today's challenge: Khalil, Anna, and Julia must design a boat out of materials they find at the dump.  Their boat has to float; it has to be stable and steer-able; and it has to be propelled by something other than oars.  Find Program TV schedule at: PBS Fetch! Episode 12: That Doesn't Float My Boat

The Science Spot

PowerPoint lessons for teachers to use to teach about measurement.

Johnnie's Math Page

This site has interactive tools and activities to introduce length, mass, and volume.  Great visuals to teach about rulers, standard vs. non-standard measurements, balances, thermometers, and much more can be found on this site.


Assessment of Students

©Phillip Martin

1.  Sally's third grade class has a pet iguana.  She wants to find out how long his tail is. What unit of measurement would be the best for Sally to use?

a. Millimeters (mm)

b. Meters (m)

c. Centimeters (cm)

d. Kilometers (k)

Answer: c, Level 2: Application

2.  Juan's class is investigating organisms in the pond near the school.  He needs to measure 50 milliliters (ml) of pond water.  What tool should he use?

a. Scale

b. Graduated cylinder

c.  Ruler

d. Hand lens

Answer: b, Level 1: Knowledge

3. The third grade class raised Monarch caterpillars.  Several of the eggs hatched at the end of the first day.  Every day, the class fed each caterpillar three leaves from the milkweed plant.  The class decided that they would monitor the growth rate of the caterpillars.  The students measured the caterpillars at 1:30 p.m. every day for five days.  

a. Measure each Monarch caterpillar.                    


b. Write each measurement in the data table below:

Average Growth

Day 1

Day 2

Day 3

Day 4

Day 5

In (cm)







c. From Day 1 to Day 5 the caterpillar grew ________________________ cm.

d. On Day 4 the caterpillar was ___________________________ cm.

e. If the caterpillar continues to grow at the current rate, how long will the caterpillar be on Day 6?

Level 4: Analysis/Question modified from the following assessment.

Assessment Probe:

Keeley, P. & Tugel, J. (2010). Standing on One Foot. Uncovering Student Ideas in Science Vol 4 (pp. 61-65). NSTA Press.

Essential Questions:

Why are standard units important?

What tools do we use when measuring?

How do we measure, volume, mass, and temperature in the metric system?

Assessment of Teachers

How can I best tap into the various learning modalities (audio, visual, tactile, kinesthetic, etc.) to meet the learning style preferences of as many students as possible?

What materials (books, videos, pneumonic devices, visual aids, props, etc.) are available to me for this lesson?

What relevant vocabulary do I need to present to my students during the lesson?

What will my students need to learn in order to complete the lesson plan's objectives and independent practice activities?

How can I engage my students in the lesson and encourage discussion and participation?


Struggling Learners 

Struggling and At-Risk:

Johnnie's Math Page

This site has interactive tools and activities to introduce length, mass, and volume.  Great visuals to teach about rulers, standard vs. non-standard measurements, balances, thermometers, and much more can be found on this site.

Develop learning stations.  Create areas in the classroom for independent or small-group investigation of tools (rulers, thermometers, magnifiers, and simple balances). Provide necessary materials and resources at each location.  Tasks should emphasize thinking skills and should force students to actively solve problems.  Move among students as they work, asking questions and cementing understanding.  Ref: Teaching Today: How-To Articles

English Language Learners 

Match pictures of tools used for different types of measurement.  For example, pictures of thermometers indicating various temperatures could be matched to various seasonal pictures.

Review the vocabulary of measurement and have students make flashcards for common terms like centimeter, millimeter, meter, and kilometer.

Extending the Learning 

Have students work in cooperative groups of 2-4 to brainstorm and tests ways to measure a tall tree (without climbing the tree).  Have them share their designs and ideas with the class.  Next, share different methods shown on Wikihow to measure a tall tree and have each group try a different method.  Have them record their data and observations in their science notebooks.


Read aloud Twelve Snails to One Lizard: A Tale of Mischief and Measurement by Susan Hightower and Matt Novak to the class and discuss the different units of non-standard measurement that the animals used in the book.

Special Education 

Match pictures of tools used for different types of measurement.  For example, pictures of thermometers indicating various temperatures could be matched to various seasonal pictures.


Classroom Observation 


Administrators can expect to see students engaged in hands-on learning while utilizing tools such as microscopes, magnifying glasses, telescopes, simple balances, rulers, and thermometers.  They can expect to hear students discussing the importance of accurate observations and record keeping of the observations made.  Recording information can take on a variety of forms including charts, tables, and drawings.  A strong connection to math measurement activities should be observed, as well as written stories as to why scientists and engineers rely on tools and mathematics.


Kid Measure

For iPhone, iPod Touch and iPad: Parents measure their kids every week or month and show them how much they have grown.  With this app, the iPhone takes the place of the traditional mark on the wall to see how tall your kids are growing.

Johnnie's Math Page 

This site has interactive tools and activities to introduce measurement concepts using rulers, standard vs. non-standard measurements, balances, thermometers, and much more.


Observation and inference

Benchmark has students distinguish "between actual observations and ideas about what they observed."

biology/elementary science

in grade three is it the intent to differentiate between observation and inference?