Problem: Pose this question: “How would you measure a puddle?” Discuss all the kinds of measurements they might be able to use, then brainstorm some ideas about how to measure. Ask students to make estimates for each kind of measure they have suggested. (How deep? How cold? What is the area? How long to run around it? How long would it be if it were a creek instead? )
Math Topic/Concept: measurement (length, weight, volume, time, temperature, etc. according to the generated suggestions)
Materials: have available a great variety of tools for measuring, such as: yarn, meter and yard sticks, rulers, scales, cups, clock with second hand or stopwatch, paperclips, thermometers, etc. Also provide pencil and paper, and A PUDDLE! (Optional: create a classroom puddle by pouring water onto black plastic that is molded into a box of sand.)
Classroom Use: (Developmental)
Classroom use comments*: Review customary and metric units prior to this activity or during the introductory discussion.
Grade: 4
Grade Cluster: (LateElem)
Illinois Goal: 7
Standard: 7.A.2a, 7.B.2a, 7.B.2b
Applied? (1-4): 3
Source: Creative Publications, “Puddle Questions” Investigation 1 (1994)
Answer: various, according to choices made. Check students’ work for accuracy.
Strategies Listed: logical and critical thinking, estimation, computation, measurement, conversion (within and/or between metric and customary)
Solution: Students consider different ways to measure and select appropriate tools. They work with partners to manipulate the measuring tools and to double check readings for accuracy. They record estimates and actual measurements, label units appropriately, and convert within and/or between customary and metric units. You may want students to measure in both systems to begin developing a sense of reasonableness in comparison.
Extensions or related problems*: Apply to measuring liquid in a wading pool, a bath tub, a swimming pool, and other containers. Apply strategies to estimating and measuring even larger bodies of liquid. What about the water tower? What about grain in the silo?
Intended rubric or assessment method: Analytical Scoring Scale (Jim Olsen, WIU)
Write-up submitted by: Rebecca Cummins (Westmer CUSD 203)
Problem: Pose these questions: What is the biggest angle you can create by spreading your fingers apart? Are there any obtuse angles? Any acute? Any right? How many of each kind of angle? Are your angles different sizes than those of your classmates? What is the measure of the biggest angle you can make? What is the measure of the biggest angle someone in this class might be able to make? (Direct students to make and record estimates of answers for each of the posed questions, and for any other questions generated during this introductory discussion.)
Math Topic/Concept: estimation and measurement of angles
Materials: white paper, pencil, rules, and protractors (optional: math journals)
Classroom Use: (Developmental/Evaluation)
Classroom use comments*: Discuss with students the variance of angles they can create with their spread fingers. Also point out the angles which could be created if one or more of their fingers were folded out of view.
Grade: 4 (developmental) 5 (evaluation)
Grade Cluster: (LateElem)
Illinois Goal: 7
Standard: 7.B.2a and 7.B.1b
Applied? (1-4): 2
Source: www.isbe.state.il.us/ils/benchmarking/mathactivities.htm#LE
Answer: various, according to students’ physical meausre and their chosen “spreads”
Strategies Listed: estimation, measurement, computation, illustration
Solution: Students stretch fingers to examine possible angles, estimate and record responses to the questions posed in introductory discussion, place hand on white paper and trace, use ruler to extend lines to form vertices, measure angles with protractor, and record results next to estimates. Compare results with estimates and then compare final measures with other students’ results. Students then write responses to describe how they estimated angles and how they determined accuracy in measurement.
Other solution methods (if any)*: Students could lay “angle sketchers” over the drawing of their hands. (Angle sketchers can be made by attaching two straight 6” strips of paper together with a brad.)
Extensions or related problems*: Students can examine the angles which the hands of a clock make. Possible inquiries include the following: how many times will a 90 degree angle be formed, at what times will acute angles be formed, at what times will obtuse angles be formed, what times will represent 180 degree angles, what will be the exact measure of 10:22, and others. Let students generate 5 of their own questions and provide a circle chart on which they can create a clock with accurate increments.
Intended rubric or assessment method: Analytic Scoring Scale (Jim Olsen, WIU)
Write-up submitted by: Rebecca Cummins (Westmer CUSD 203)
James R. Olsen, Western Illinois University
E-mail: jr-olsen@wiu.edu
updated Aug. 20, 2001