Unit Conversion Algorithms

Time 1 block periods (90 mintues) Level 9 Physics Purpose Students will explore different units made to make measurements in physics and generate a general algorithm to convert between basic SI prefixes (kilo-, centi- and milli-) as well as familiar distance units (inches, miles and feet) in one or two steps Overview Explain in general terms what will happen during this activity (i.e., brief summary of ‘Teaching Notes’) Student Outcomes - Students will be able to explain and apply a set of “rules” for to convert between distance units

- Standards addressed: - CT-STEM Skills - Computational Problem-Solving (Generating/Applying algorithmic solutions, developing modular computational tools, simplifying/reframing/generalizing problems) - Data and information (manipulating data)

-Next Generation Science Standards - Planning Investigations (Evaluate data collection methods) - Constructing Solutions -Illinois State Science Standards - PSAE 13A, IOD

Prerequisites Students will have just completed a measurement lab where they measure the length of the hallway using a variety of different units (strides, m, cm, feet/inches) and explored how different methods result in more/less accurate and precise results. Background Students will need to be able to use a ruler, be comfortable with the algebra concept that when a variable is divide by itself it is equivalent to 1 or “cancels out”. 1 Teaching Notes

During the previous course, students will have completed the investigation from Active Physics Chapter 1, section 2 (LINK). As a result, data will be collected for hallway measurements using strides, meters centimeters and feet/inches. This data will be available for all students via google docs. It may need to be “cleaned up” so students can see the relevant relationships depending on the accuracy/precision

Independent warm-up (5 minutes): 1) Using the data table from last class, how did we describe the different measurements? 2) Describe, in words and using math, how you changed the number of strides into a measurement using meters.

Discussion (10 minutes): After students have had a chance to complete the warm- up, go over the questions with the class. For question 1, some students may push back and say they’re not related because they are different measures. Be sure to remind students that each measurement used a different method but still represented the same distance. Build off student ideas to find a consensus process used to “convert” from strides to meters. Leave this process on the board for the rest of class.

Small group work (15 minutes): Tell the students that they are to use the class data to figure out a process that can change the cm measurement to m. They will need to test this on at least 3 data points and write their process on the white board. After about 10 minutes, students should start to notice a pattern: multiply by 100. It may not be perfect but this is a discussion we can have with groups re: accuracy of the lab results. If the students still struggle seeing the pattern hand them a meter stick. Tell them it is 1 meter long and have them notice that it is also 100 cm long. Select two groups to present their findings and ask questions to the rest of the class to look for agreement in process. Write down the “master process” on the board next to the strides example from the warm-up.

Individual work (5 minutes): Give students two sample problems: 1 converting m -> cm and 1 converting cm -> m. Have students self-assess after 5 minutes. Pause here if the process isn’t clear for students. Have some a sample problem prepared to work through for students as an example if necessary.

Small group work/whole class discussion (20 minutes): Tell students that they are now to make a list on their whiteboard of similarities between the stride length <-> m “conversion” and the cm<-> m “conversion”. Students may notice that multiplication was used, that they can multiply by the same number for to convert all of the time, that the units are just “related,” to go from cm<->m we divided instead of multiply. They will also point out that the numbers to multiply are different. After students share out they are asked to make a second list of other ways they could measure distance. Miles, feet, kilometers may come up as well as other more creative examples using the height or length of people or common objects. This leads to the question, ‘Can we use what the process above to change from any 2 distance unit to any other distance unit?’ Take a silent poll of students. If there are a lot of ‘no’ students ask why they say that and see if ‘yes’ peers can convince them. Students may identify that more information is needed as a big hang-up.

Direct instruction (15 minutes) Introduce students to the unit conversions handout (km, cm, m, inches, feet, and miles). Finally, give this “changing” process a name—Unit Conversion. Introduce students to flow chart through sample problem. Check that students see the connection between their processes earlier and this flow chart with questions while giving the sample.

Individual and small work time (20 minutes) Students work on practice problems using the unit conversion handout and flow chart. Problems focus on SI unit to base unit. Some converting distances between meters and “familiar” distances (e.g. home to school, length of car, and height of person). To scaffold this, early questions could have students finding information off the charts before asking them to convert. Harder questions could ask students convert more steps (e.g. a nanometer is 10^-9 m….. The radius of DNA is 0.5 nm, how many km is this?) or more complex units (e.g. m/s to mph). Have the students work independently for the first 10 minutes, talk with their tables for the last 10 minutes.

Homework: More practice for students and more looking at the algorithm.

3 Pre-class Preparation Check the data from the previous lab—clean it up as you see fit based on student understanding of accuracy and precision of measurements. For a group that has a harder time finding patterns they may need to see perfect data Materials and Tools Technology including software and files Suggested resources or equipment needed Web links and/or video links Supplementary documents or handouts

Assessment How will the teacher evaluate if the objectives have been met? Include homework assignment handouts, in-course discussion questions, and/or exam questions.

Acknowledgements -If this lesson uses any software or curricular materials that you didn’t develop yourself, please attribute the source here.

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