MiddleSchoolPortal/Measurement Sliced and Diced
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Measurement Sliced and Diced - Introduction
Middle school teachers tell us that there are important practical skills and understanding that students need before they engage in the abstractions of algebra. These skills are found in the blurry area where measurement, basic geometry, and the arithmetic of decimals and fractions come together in the real world. To move forward mathematically, middle school students need hands-on experiences with measuring, using scale and proportionality, and estimating with benchmarks.
How can online resources support the need for hands-on experiences with measurement? Read on! Students can use web resources to see the quantifying components in life, to visualize mathematics concepts, and to get instant feedback on calculations. The web is a friendly place to practice computational skills with fractions, decimals, and formulas. But perhaps most importantly, the Internet can expand the realm of possible real-world problem solving. Here we feature activities, lesson plans, and projects to help students understand how measurement and mathematical problem solving are part of life.
A class measurement project can wrap together many important components of mathematics learning into a very memorable experience. Who can forget measuring their school gym to see how many pennies it could hold or finding the volume of the community swimming pool to see how many ping-pong balls it would take to fill it? A class measurement project allows students to first make choices about which tools and units to use, and then to do the measuring, use the data to find an answer, and communicate results. They apply measurement skills and concepts to solve everyday questions that can involve estimation, decimals, fractions, and proportional reasoning. A solid foundation in measurement in the middle school years enables students to think about their world in quantitative, geometric terms and see the usefulness of mathematics.
Background Information for Teachers
You are not alone if the idea of teaching measurement makes you uncomfortable; after all, doesn't everyone know how to measure? We selected these resources to help you refresh your approach to teaching measurement.
Learning math: measurement Feel like you need a little review? This free online course examines critical concepts related to measurement. The 10 sessions feature video lessons, activities, and online demonstrations to review procedures used in conducting measurements, along with other topics such as the use of nonstandard measurement units, precision and accuracy, and the metric system. Circles, angles, volume formulas, and relationships between units of measurement are also explored. The final session presents case studies that help you examine measurement concepts from the perspective of your students.
Measurement fundamentals This module, developed for the Virtual Machine Shop, offers a great deal of practical information about linear and angular measurement and the use of standard and metric units. It introduces the unique math used by engineers and tradespeople and presents a very practical focus to the study of measurement.
How Many? A Dictionary of Units of Measurement This handy reference from the Center for Mathematics and Science Education at the University of North Carolina at Chapel Hill features a clickable list of defined terms related to units of measure. You'll also find FAQs, commentary, and news related to measurement units.
Animations and Interactive Online Activities
With these animations and interactive resources, students can find length, area, and perimeter at their own pace with as many repetitions as needed to create understanding.
Measuring Henry's cabin When students want to know why they need to learn to measure, show them this cabin blueprint and ask them what they think a builder needs to know to start constructing a building. Students examine the cabin blueprint and find the surface area of the walls.
Powers of ten What student isn't interested in very large numbers! Before your very eyes see the perspective expand from a 1-meter view of a rose bush to an expanded vision of 10 to the 26 power and then decrease to 10 to the negative 15. The site, also available in German and Italian, uses the meter as the unit of measurement. This visualization can help students see the results of increasing and decreasing scale. It is an engaging way to demonstrate scale and is a nice illustration of the meaning of exponents.
Jigsaw puzzle size-up This online interactive jigsaw puzzle activity requires students to enlarge or shrink puzzle pieces before placing them in a puzzle. The choices for enlarging are 1.5, 2, and 4 times larger, while the sizes for shrinking are one-quarter, one-third, and one-half.
These next two resources are from the site Figure This! that features 81 activities for middle schoolers. The activities, presented by colorful, animated characters, feature mathematics found in real-life situations. Students work with paper and pencil to answer the multiple questions posed in each activity. From the Figure This! home page you can go to a math index for a correlation of activities to important math topics. Printable versions of the activities are available in English and Spanish.
Access ramp: how steep can a ramp be? The activity opens with an animation of a Figure This! character in a wheelchair using an access ramp over a three-step staircase, with steps 7 inches high and 10 inches wide. Students are challenged to think about dimensions of an access ramp to determine where the ramp should start to go up the three steps at a reasonable slope. Information about handicap accessibility is included.
Windshield wipers: it's raining! Who sees more? The driver of the car or the truck? Here's something that the future drivers in middle school will relate to. Geometric shapes are used to compare the areas cleaned by different styles of windshield wipers.
Open-Ended Questions and Hands-On Activities
Teachers can use the printable open-ended questions and hands-on activities to get students thinking about measurement concepts.
Approximating the Circumference and Area of a Circle If you have students who think they know everything about area, perimeter, circles, and pi, make a copy of this Geometry Problem of the Week and see what they can figure out.
Wacky ruler Here's a good starter activity for students who lack the most fundamental understanding of measurement. They print out a "wacky ruler" and a page that features eight wiggly pink worms. The model ruler is marked with two, four, and seven units. Students can enter their measurements online to check their accuracy.
Measuring (Const) These six worksheets introduce students to fractional units on a standard ruler and millimeters on a metric ruler. There is also a short, colorful PowerPoint slide show that demonstrates the fractional parts of an inch.
Measure a picture, number 1: inch, half, quarter of an inch This student worksheet is the first in a series of five worksheets offering practical experience reading units on a ruler.
Visualizing the Metric System How can you make the metric system more understandable for your students? Tell them to think of a gram as the mass of a jelly bean and a liter as one quart. This list can help students retain a visual picture to approximate various metric units.
National Institute of Standards and Technology metric pyramid Take the mystery out of the metric system by having students create their own reference tool. They can use this paper cutout to make a 3-D pyramid printed with metric conversion information for length, mass, area, energy, volume, and temperature.
Projects
The next four resources can be used to support a student project that explores big trees and the mathematics related to circumference and pi. A student exploration question can be "How big is the biggest tree in our neighborhood?"
Big tree: have you ever seen a tree big enough to drive a car through? Even if your students have never seen a tree large enough to drive a car through, they can practice using fractions and decimals and the formula for the circumference of a circle. This activity lists the girth and height of 10 National Champion giant trees and asks students to determine which of the trees is large enough for a car to drive through.
NPR: Bushwhacking with a Big-Tree Hunter Some people hunt animals and others hunt for trees. In this National Public Radio story, one in a special series called Big Trees and the Lives They've Changed, visit the Olympic Peninsula and learn about the life of a big tree hunter and the death of a giant Douglas fir.
Project Shadow
Here is a project idea that can be huge and interdisciplinary with the science or social studies department or that can be a one-day event where students can experience practical measurement. You may want to register as part of an online worldwide one-day event to calculate the circumference of the Earth (see first resource) or simply use all the resources to put together a class activity for replicating Eratosthenes' experiment. However you choose to approach it, you can tie measurement to real life by highlighting the historical connections and relating the activity to the modern technology of global positioning systems.
The noon day project This Internet site presents the necessary mathematics and science information teachers need to re-create the measurement of the circumference of the Earth as done by the Greek librarian Eratosthenes more than 2000 years ago. Shadow measurements taken at high noon local time on a designated day in March are posted online and used to calculate the circumference of the Earth. Teachers can sign up and have their students participate in this annual spring event.
Measuring the Circumference of the Earth This web page illustrates how data and mathematics were used in Eratosthenes' famous experiment.
Money: Large Amounts Project
Finally, how about using pennies as a unit of measure and asking big questions such as "What would the national debt look like if it were a pile of pennies—would it reach farther than the moon?" Once you start thinking in terms of using pennies, or any other size coins, to represent quantities, you may decide to start with a smaller quantity than the national debt. In any event, these web sites are a great place to begin.
The megapenny project Visit this site to begin to appreciate the magnitude of large numbers. It shows and describes arrangements of large quantities of U.S. pennies. You'll see that a stack of 16 pennies measures one inch and a row of 16 pennies is one foot long. The site builds excitement for learning the size of the mass found in one quintillion (written as a one followed by eighteen zeroes) pennies. All pages have tables at the bottom, listing things such as the value of the pennies on the page, size of the pile, weight, and area (if laid flat). All weights and measurements are U.S. standards, not metric.
The silver mile Here is a Math Forum middle school Problem of the Week that challenges students to think about the coins involved in creating a mile-long trail of silver coins. The authors include a few rules that require students to use fractions as they construct their mile using nickels, dimes, quarters, half-dollars, or silver dollars in specific proportions. MSP full record
SMARTR: Virtual Learning Experiences for Students
Visit our student site SMARTR to find related virtual learning experiences for your students! The SMARTR learning experiences were designed both for and by middle school aged students. Students from around the country participated in every stage of SMARTR’s development and each of the learning experiences includes multimedia content including videos, simulations, games and virtual activities. Visit the virtual learning experience on Measurement.
Careers
The FunWorks Visit the FunWorks STEM career website to learn more about a variety of math-related careers (click on the Math link at the bottom of the home page).
NCTM Measurement Standard
In the discussion of the measurement standard, the National Council of Teachers of Mathematics states that "In the middle grades, students should build on their formal and informal experiences with measurable attributes like length, area, and volume; with units of measurement; and with systems of measurement." (Principles and Standards for School Mathematics, NCTM, 2000, p. 241)
At its simplest, measurement in grades 6-8 begins with what appears to be a basic need for the student to know how to use a ruler to measure length. The reality is that even this apparently simple measurement task requires the use of multistep mathematics thinking. Many students lack the computational skills and conceptual understanding necessary to take on the more sophisticated tasks of finding surface area and volume and using units and converting units in metric and customary systems. The suggested online resources may help your students develop a conceptual understanding of area, perimeter, and volume and learn to use formulas and measurement units. The resources can also help you plan a really worthwhile class project. Check out the nine specific expectations that NCTM describes for middle school students related to the measurement standard.
Author and Copyright
Judy Spicer is the mathematics education resource specialist for digital library projects at Ohio State University. She has taught mathematics in grades 9-14.
Please email any comments to msp@msteacher.org.
Connect with colleagues at our social network for middle school math and science teachers at http://msteacher2.org.
Copyright November 2004 - The Ohio State University. This material is based upon work supported by the National Science Foundation under Grant No. 0424671 and since September 1, 2009 Grant No. 0840824. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
