Estimating the Weight of Steel

Lesson Rubric
Lesson Powerpoint
Calculator Spreadsheet
Student Sample One
Student Sample Two
Student Sample Three

Name: John Austin
Grade: WELDING I (High School Juniors)
School: SWT BOCES

1. Title/Context Of Learning Experience
   The lesson was developed to be an aid in determining the weight of a piece of steel. Welders often have weight and size constraints on the projects they weld and this lesson was meant to show them an easy way to determine the weight of a piece of steel or several pieces of steel if their thickness are known.

   Some of the relevant math standards addressed are:
   MST.S3.C8 use addition, multiplication etc. with real numbers and algebraic expressions
   MST.S3.C23 derive and apply formulas to find area etc

   In order to be successful, students need to be able to:

   • use a calculator
   • accurately read a tape measure or ruler marked off in inches
   • convert halves, quarters and eighths to sixteenths of an inch
   • convert fractional measurements to their decimal equivalents
   • realize that a piece of steel has three dimensions and that all three affect the final weight of the piece of steel
   • know how to find the area of a rectangle and know that that area is measured in square units
   • judge what a reasonable estimate for the weight of steel might be
2. Essential Question
   The essential question is “How can we determine the weight of a piece of steel before we cut it?”
3. Assessment Plan
   The students were given the task of calculating the weights of several pre-cut pieces of steel in the welding shop. Arriving at the correct value depended on two processes: first, accurately measuring the 3 dimensions of the piece of steel, and then entering those values (with length and width converted to decimals) into the weight-calculating spreadsheet. The welding teacher and I monitored the students as they measured and used the computers. Some had to be helped to do one process or the other.

   A worksheet was handed out with spaces for the dimensions, as well as the final answer. Students were required to state the area in square inches, and the weight to the nearest hundredth of a pound.

   Students were questioned when their measurements did not seem to be in the same range as what we would consider a “reasonable” estimate. Most of the students compared their initial answers with those of other students, just to make sure they were in the “ballpark”. Some students needed very direct one-on-one guidance, and the welding instructor was very helpful in providing it.

4. Procedure
   First, the teacher establishes the anticipatory set for the lesson by asking questions like “Does anyone know the legal weight limit for a single axle trailer?” and “How thick should the steel bed of a trailer be if it is going to haul firewood” and “Is there ever a time when the tailgate of a trailer might need to be thicker, or longer than the other pieces?”

   Then a quick review of the concept of area: how to measure it and what units do we use. Following that, the teacher introduces the scenario of someone building a steel trailer and talks about why a welder would want to know required thickness and weights of the different pieces that make up the trailer. He mentions the legal weight constrictions, the practical problems of moving large pieces of steel and the fact that a shop owner would not be very happy if a piece of steel were cut the wrong size.

   Then, a powerpoint presentation follows which discusses some of the considerations that have to be made when designing and building a trailer. The powerpoint presentation points out the fact that there are really 5 pieces of steel required for a trailer, and that those pieces share certain dimensions.

   Without mentioning the term “density”, the teacher shows that the weight of a piece of steel can be estimated by multiplying the area by a multiplier related to its thickness.

   At the end of the powerpoint, the teacher displays a spreadsheet, which was designed to calculate the weight of a trailer (or just a single piece of steel) by using the area and thickness (as measured in 16ths of an inch). A few examples are done using the spreadsheet to show how it automatically calculates the weight. This spreadsheet is loaded onto 10 wireless computers.

   After taking any questions, the teacher has the students spread out in the shop and begin to measure 10 pieces of steel labeled A through J. Once measured, they go to a laptop computer and enter the dimensions. The resulting weight calculations (along with the measurements) are recorded on an answer sheet provided. During the exercise, the concept of accuracy and rounding are discussed, as is the process of converting fractions to decimals.

5. Resources
   Some of the resources used to create this lesson included:
   • the expertise of professors at Clarkson University who helped design the powerpoint and spreadsheet
   • a mobile computer and a powerpoint projector
   • mobile, wireless computers on which the spreadsheet was loaded
   • class sets of tape measures and scientific calculators
   • 10 rectangular pieces of steel of varying thickness
   • a laminated chart showing conversions of fractional measures into their decimal equivalents
6. Instructional/Environmental Modifications
   This was one of the weaknesses of the lesson that will have to be addressed before the lesson is taught again. Individual help and slight modifications to the length of the assignment were done to help slower students finish on time. As in many classes, there was quite a range of abilities, with a large component of students who struggled with the measuring and converting data.

   There is no question that more effort will have to be made to determine the math and reading abilities of the students well in advance of the lesson. Also, there should be some sort of pre-test to help determine the skill level regarding reading a ruler, equivalent fractions and converting fractions to decimals.

7. Time Required
   Once the powerpoint lesson and spreadsheet were loaded onto a mobile computer cart and projector, the amount of planning time was not much more than for a typical lesson. The Welding instructor had to cut (or find) 10 fairly rectangular pieces of steel, measure them, label them and spread them around the shop. The only extra materials required besides a handout were enough measuring tapes to go around for 17 students.

   The class period is approximately 2 hours 15 minutes, but few lessons can hold any student’s attention more than an hour, so the entire lesson (including the measuring and calculations) was designed to take 60 minutes or so.

   The wrap-up was a very short comparison of answers and discussion of why there were a few variations in weight estimates.

   The assessment was really just the completed handout listing the dimensions and final weight estimates for each piece of steel. A few students were not able to complete all 10 pieces, but their assessment was done by judging the ones they had accomplished.

8. Reflection
   This lesson was developed as an attempt to use some technology to help welding students get answers to real questions without using a lot of classroom instructional time. A spreadsheet was developed to speed up the process of estimating how much a piece of steel might weigh, so that the actual design process could proceed. There is a fine line between forcing students to manually do repetitious calculations and providing a “thought-proof” calculator, which could accomplish a task “magically”.

   There were several aspects of this lesson, which were not well thought out and should be addressed before the lesson is used again. Most of the problems with the lesson do not involve the powerpoint or spreadsheet themselves (although they could always use a little bit of “tweaking” to improve their effectiveness). Instead, the biggest problems with the lesson were basics, which needed to be addressed far in advance of the lesson.

   First, the students needed to be assessed on their ability to read and record a measuring tape. This included not only the basics of how to read a tape, but also the idea of 16ths, 8ths 4ths and halves all being recorded on the same scale.

   Next, the students should have been tested and primed on the process of converting common measuring tape dimensions into 16ths of an inch, since the spreadsheet calculator required all thickness data to be expressed in that measure.

   Also, the students should have reviewed the process of changing a fraction into a decimal so that a measurement like “3/16” could be entered decimally into the spreadsheet. A chart was found which listed many fraction-to-decimal conversions; so many students used it to make the conversions. This sped up the lesson and reduced the number of errors caused by simple arithmetic mistakes.

   Next, there should have been much more effort spent on adapting the lesson to those students who have learning disabilities and/or I.E.P.’s. There were no classroom aides available during the lesson, so the CTE instructor and the math consultant had to try to provide guidance to all 17 students, including some with very low math skills, while keeping the lesson moving along.

   The lesson was enjoyable from my perspective because it seemed to interest the students and provide them a tool that they may be able to use in the future. They seemed to enjoy doing the lesson and some were a little surprised at their own weaknesses in being able to use a measuring tape. Because most had not seen a spreadsheet before, they were quite impressed with the automatic calculations. Some other changes in the lesson may be called for. For example, the concept of density was not addressed, even though that was the underlying concept for the entire exercise. The reason for that omission is that that particular concept is often misunderstood and I thought that a detailed discussion of what it meant might be more of a distraction than an aid to understanding. However, different groups may find that sort of background material to be quite useful.