Measuring Up Math Teacher Leader Kick-Off 28-29 August 2006 Henry Kepner Kevin McLeod Connie Laughlin DeAnn Huinker This material is based upon work supported by the National Science Foundation under Grant No. 0314898. 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 (NSF). Session Goals Consider the relationship among measurement, geometry, and other mathematics strands. Examine big ideas of measurement. Generate, use, and refine measurement benchmarks. Developed by the Milwaukee Mathematics Partnership (MMP) with support from the National Science Foundation under Grant No. EHR-0314898. 2006–2007 MMP Content Themes Measurement and Geometry Reflect upon teaching and learning measurement and geometry, identify: Big ideas and concepts Important skills Connections between them Developed by the Milwaukee Mathematics Partnership (MMP) with support from the National Science Foundation under Grant No. EHR-0314898. How long is a meter? Developed by the Milwaukee Mathematics Partnership (MMP) with support from the National Science Foundation under Grant No. EHR-0314898. Big Ideas of Measurement Read “Big Ideas” section on page 315. Consider how these ideas relate to the “How Long is a Meter Activity” Read “The Meaning and Process of Measuring” section on page 317. Developed by the Milwaukee Mathematics Partnership (MMP) with support from the National Science Foundation under Grant No. EHR-0314898. Big Ideas of Measurement 1. Measurement involves a comparison of an attribute of an item or situation with a unit that has the same attribute. ◊ Lengths are compared to units of length, ◊ Areas are compared to units of area, ◊ Time is compared to units of time, etc. 2. Meaningful measurement and estimation of measurements depend on a personal familiarity with the unit of measure being used. 3. Estimation of measures and the development of personal benchmarks for frequently used units of measure help students increase their familiarity with units, prevent errors in measurement, and aid in the meaningful use of measurement. 4. Measurement instruments are devices that replace the need for actual measurement units. It is important t to understand how measurement instruments work so that they can be used correctly and meaningfully. Developed by the Milwaukee Mathematics Partnership (MMP) with support from the National Science Foundation under Grant No. EHR-0314898. A Measurement is . . . . . . a number that indicates a comparison between the attribute of the object (or situation or event) being measured and the same attribute of a given unit of measure. Process of Measurement 1. Decide on attribute to be measured. 2. Select a unit that has that attribute. 3. Fill, cover, or match the unit to the attribute of the object. (Van de Walle, 2004, p. 316) Developed by the Milwaukee Mathematics Partnership (MMP) with support from the National Science Foundation under Grant No. EHR-0314898. Scavenger Hunt Directions: K-2 Weight • Use the balance scale to determine which book is heavier • Use the books, beakers, and videos. Put everything in order from lightest to heaviest. 3-5 Mass • Use the balance scale to determine the weight of several objects at your table in grams. • Order your objects from lightest to heaviest Reflect: In what ways did measurement ideas grow across the grades? Developed by the Milwaukee Mathematics Partnership (MMP) with support from the National Science Foundation under Grant No. EHR-0314898. Personal Benchmarks Why? 1. Increases students’ familiarity with units. 2. Helps prevent error in measurement 3. Aids in the meaningful use of measurement. 4. Help students answer simple measurement questions. What? 1. Personally determine a benchmark for involving seconds(e.g., 3 seconds or 20 seconds). 2. Share these benchmarks with the other teachers at your table. Developed by the Milwaukee Mathematics Partnership (MMP) with support from the National Science Foundation under Grant No. EHR-0314898. A Brief Walk-Through of the Scavenger Hunts PreK – 2 pp. 16-17 and p. 70 Goals • Identify objects that are longer, shorted, heavier, lighter, hold more and hold less • Understand the use of comparative vocabulary • Order objects by a specific attribute Materials • Copy of “Scavenger Hunt List” for each student. • Paper clip and crayon, penny and a wood block, spoon and small cup, rice beans or sand. • Objects of various lengths, weights, and capacities at three stations. Scavenger Hunt Part 1 (Explore) Students work in pairs. They find objects that fit each of the comparisons on the student sheet. Class discussion of objects that they found. Scavenger Hunt Part 2 ( Extend) Create three stations (length, weight, capacity). Determine objects that are longer then, shorter than, and the same length as the given object. Challenge more capable students to order the whole set of objects according to the stated attribute. Developed by the Milwaukee Mathematics Partnership (MMP) with support from the National Science Foundation under Grant No. EHR-0314898. A Brief Walk-Through of the Scavenger Hunts Grades 3-5 pp. 34-38 and pp. 112-117 Goals • Select objects with attributes whose measurements are approximately equal to a given length, weight, of angle, as measured in standard units. • Develop a familiarity with standard units of length, weight, and angle. • Classify measurements as “same as”, “more than’ or “less than” a given length, weight, or angle in standard units. • Understand the use of comparative vocabulary. • Order objects by a specific attribute. Materials Assorted objects depending on items to be measured. Scavenger Hunt Part 1 (Engage and Explore) Students work small groups of 3 to 4 students. They find five objects that are close to their standard unit. Measure to find which object is closest to the unit that the group received. (Ex: 1 cm, 1 inch, 1 foot, 1 yard). Scavenger Hunt Part 2 ( Extend) Change the scavenger hunt to find 5 objects with weight as close to that of a given standard measure. (Ex: 1 gram, 1 pound, 1 ounce, 1 kilogram). Observe how students report the measures and how they measure the attributes of objects. Developed by the Milwaukee Mathematics Partnership (MMP) with support from the National Science Foundation under Grant No. EHR-0314898. My Benchmarks Grades 3-5 pp. 39 – 42, pp. 118 – 121 Goals • Generate ways of using familiar objects as measurement devices, or benchmarks, in daily life. • Use the benchmarks to estimate the measurements of selected attributes of familiar objects. • Develop a familiarity with objects with standard units by measuring particular attributes in familiar objects. Materials Various materials depending on the objects to be measured. Activity • Students work in pairs. They will be finding benchmarks to estimate measurements such as length, area, volume, or weight in standard units. • Perform the tasks on the black-line masters. • Whole group reporting when they are finished. Record the various benchmarks that students used. Developed by the Milwaukee Mathematics Partnership (MMP) with support from the National Science Foundation under Grant No. EHR-0314898. Assignment for September With colleagues and students, fill out a copy of the Personal Measurement Benchmarks chart. Try to find 2-3 benchmarks for each unit. Bring these charts to the September meeting. Developed by the Milwaukee Mathematics Partnership (MMP) with support from the National Science Foundation under Grant No. EHR-0314898.