Measurement
Imminently hands-on yet elusively abstract, measurement skills and concepts can be engaging but challenging to teach. What can be measured? Time, energy, space, and matter. Each of these physical aspects of our world has its measurable aspects, their respective measurement tools, and units of measure (see Figure 1.7). Some textbooks and curriculum frameworks classify money as a measurement topic; however, money is not measured but counted (unless all quantification is considered a form of measurement). Measurement is a critical topic for other mathematics applications and is related to many other topics outside mathematics. Both customary (U.S.) and metric systems are referenced in the standards (the customary system reinforces fraction concepts and metrics reinforce the base-ten place value system and decimal concepts).
Measurement: Subject, Tools, and Units
| Category | Subject | Example Tool | Example Unit | |
| Time | long periods short periods shorter periods tempo | calendar clock stopwatch metronome | months hours seconds beats per bar* | |
| Energy | atmospheric electric temperature earthquake hearing atomic radiation | pressure barometer electric meter thermometer seismograph audiometer Geiger-Müller tube | millibars kilowatts degrees moment magnitude decibels, Hertz* particles per minute | |
| Space | length height of elevation capacity distance angle | meter stick altimeter tape measure odometer protractor | centimeters meters cubic feet miles degrees | |
| Matter | volume (capacity) mass (weight) density (liquid) | flask scale hydrometer | milliliters pounds specific gravity units | |
| When we want to measure something, there may be a standard unit (as above), more than one unit (e.g., meters or yards), or a unit and scale can be created. *The items indicated are actually ratios of measures. Scientists tend to focus on mass, length, and time and ways they combine. For example: speed = distance (length) / time (short periods) density = volume (three-dimensional space) / mass Vectors represent quantities with both magnitude and direction such as force, velocity, and acceleration. | ||||
Try This!
Select a test item from a state or district mathematics test and analyze the content knowledge required. For example, the following item requires facility with number and operation, geometry, and possibly measurement concepts.
Draw a rectangle and a triangle that have the same area. Label the dimensions. Show that the areas are the same.
Young children develop the concept that objects have various attributes, some of which can be measured. They develop the language to express measurement ideas such as longer or more. They begin to associate specific attributes with units and tools of measurement and make simple measurements fairly accurately. Elementary students gain experience with a variety of tools and measurement concepts, in both metric and customary systems. They work with formulas for perimeter, area, and volume of various shapes. By the secondary grades students gain experience with derived attributes (ratios of measurements), conversions, formulas, precision, and error concepts.
Data analysis, statistics, and probability
A group of four- and five-year-olds was recently observed "doing" data analysis using probability and statistics. They were discussing their ice cream choices for the monthly parent's night. On the wall was a chart, a pictograph, with little white, brown, and pink ice cream cones depicting their predictions the previous day of their parents' preferences for vanilla, chocolate, or strawberry ice cream. (Chocolate was by far the winner.) That day the children were sharing results of asking their parents about their favorite flavors. As the new graph evolved, the children exclaimed about the prevalence of vanilla. These young children made predictions, collected data, represented data on a graph, and analyzed those data. They discussed their findings in ways that were mathematically powerful. Like the other content strands, data analysis, statistics, and probability are developed across all grade level spans.
Data are quantifications of aspects of the world. It seems that everything is quantified: sports scores, weather records, income levels, test scores, stock market trends, population patterns, and political views. Data analysis and the application of statistical methods are used across the curriculum. Students are taught how to collect and record data, to represent data in various forms, and to interpret and use data. Students are taught to describe their data collections with frequency charts, measures of central tendency, and various graphs and charts. Higher-level concepts include variability, significance, correlation, sampling, and transformations.
The study of probability assists us in making more accurate estimations with problems involving uncertainty. Probability helps answer the question, "How likely is some event?" Applications range from educational assessment, business, politics, and medicine to scientific phenomena. Students engaged in probability activities will use their knowledge of number and operations, variables and algebraic equations, problem-solving skills, measurement and graphing, and logical reasoning. Ultimately, skill with probability and statistics should enable students to make more informed decisions in all aspects of their lives.
Further enhance your math curriculum with more Professional Development Resources for Teaching Measurement, Grades K-5.
