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* *Reflection: Diverse Entry Points
Speed Demon Investigation (Part 2/2) - Section 2: Explain/Extend

Using math to teach physics is considered best practice. However, the level of complexity involved with using mathematics can create a significant barrier to student learning of physics concepts. It is tempting to disentangle the math from the physics to promote student learning, however there are several strategies that can help scaffold the mathematics:

1) Provide students with opportunities to use "clean data" or data that is fabricated to be easier to manipulate. For example, when calculating the speed of a car, give students data sets like:

A car travels 55 miles in 1 hour and 110 miles in 2 hours. What is the speed of the car?

This "clean data" allows students to practice calculations using whole numbers and shorter division rather.

2) Start simple and progress to complex. Once students master "clean data", give them structured practice with more complex data sets. Depending on the level of your students, data sets might include decimals, opportunities for long division or order of operations.

3) Allow students to collect data and calculate using their own "dirty data" (decimals, inaccurate measurements, etc.). By using "real" numbers, students can start looking for patterns and errors; practice using calculators; and become more comfortable with decimals, significant figures and rounding of decimals.

4) Create structured graphic organizers with example problems as shown here Speed Demon Investigation Math Notes.

*Diverse Entry Points: Providing Scaffolding for Mathematics in Physics*

# Speed Demon Investigation (Part 2/2)

Lesson 9 of 18

## Objective: SWBAT design an investigation to practice calculating speed/velocity.

*100 minutes*

"Are we there yet?" is a common middle school refrain when on a road trip - especially when the destination is anticipated. The Speed Demon Investigation provides students an opportunity to solve the authentic problem of, "When will we get there?" This series of lessons is designed to allow practice planning and carrying out scientific investigations (**SP3**) while exploring fundamental concepts (calculating speed of objects by collecting data) related to the performance expectation that states, "a change in an object's motion depends on the sum of the forces on the object" (**MS-PS2-2**). While this series of lessons does not directly teach or assess MS-PS2-2, it does provide a sound basis for understanding motion, which students need in order to understand forces.

From beginning to end, students are engaged in investigation to collect, analyze and interpret data (**SP4**); use mathematics and computational thinking (**SP5**); and engage in argument from evidence (**SP7**).

Additional connections to Common Core Mathematical Standards in Measurement and Data occur when students use measurement of time and distance to collect data and then analyze their data. In this lesson, students also access **WHST.6-8.1** Common Core Language Arts Standards, Writing in Science and Technical Subjects when writing arguments from evidence.

While I use this series of lessons as an introduction to calculating speed, the lessons can also be used or re-used to explore many different concepts including: mass, weight, displacement, forces and Newton's Laws of Motion (**PS2.A: Forces and Motion**). Rather than trying to teach all of these concepts at one time, I choose to concentrate on scientific practice learning objectives and tailor the activities, discussions and assessment to match the objectives.

The Speed Demon Investigation series of lessons is a scientific inquiry investigation taught over the span of 1 week. To help manage the magnitude of this activity, you will find the project split into 2 parts.

- Part 1 includes the ENGAGE and EXPLORE components of the lesson; Time: 2-3 50-minute lessons or equivalent block periods.

- Part 2 includes the EXPLAIN/EXTEND and EVALUATE components of the lesson; Time: 2-3 50-minute lessons or equivalent block periods.

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#### Explain/Extend

*50 min*

The EXPLAIN stage provides students with an opportunity to communicate what they have learned so far and figure out what it means. This stage of the lesson presents a great place for a quick formative assessment. The EXTEND stage allows students to apply new knowledge to a novel situation. The novel situation in this case is using the data collected during the investigation to solve the problem of:

**What time Bob will have to leave his house (in room 209/210 at Platt) to arrive at Water World by opening time (at 10:00 am)?**

During this stage of the investigation, students work together to solve the problem by completing Data Table 3: Time of Speed Demon Investigation. During this part of the investigation, students explain to each other the mathematics required to:

1) Calculate the average speed of the tiny car.

2) Convert the distance from Platt to Water World from miles to the units used in your average speed.

3) Calculate the time it will take Bob to get from Platt to Water World.

4) Convert the time into hours and minutes.

An example of student discussion is here:

The calculations required to solve this problem can be way beyond the abilities of many middle school students. From this video, collaboration and "group-think" supports students in tackling this challenging math. Because students share their thinking and work together to problem solve, they are apt to pick up on errors and may be compelled - because of the need to organize thinking in order to speak - to dig more deeply into their own thinking. For additional ideas about how to scaffold the use of mathematics to teach physics can be found here: Providing Scaffolding for Mathematics in Physics.

#### Resources

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#### Evaluate

*50 min*

The EVALUATION stage is for both students and teachers to determine how much learning and understanding has taken place. During this stage of the investigation, students complete Part 3: Communicating Scientifically of the Speed Demon Investigation.

At this point, students have solved the final problem of what time Bob will have to leave. Now, Students will write a one paragraph PACER argument describing the process they used to solve the problem. For additional resources, visit Writing Arguments from Evidence (PACER Arguments).

For examples of final arguments, view: Speed Demon Investigation Final PACER Argument - Proficient Exemplar and Speed Demon Investigation Final PACER Argument - Advanced Exemplar.

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- LESSON 1: Forces and Motion Assessment Review
- LESSON 2: Float-a-Boat: Introduction to Scientific Inquiry and Design (Part 1/2)
- LESSON 3: Float-a-Boat: Introduction to Scientific Inquiry and Design (Part 2/2)
- LESSON 4: Float-a-Boat: Student Rubric Creation and Authentic Data Analysis
- LESSON 5: Float-a-Boat: Student Choice Assessments and Cooperative Grading
- LESSON 6: Motion of the Ocean (Part 1/2)
- LESSON 7: Motion of the Ocean (Part 2/2)
- LESSON 8: Speed Demon Investigation (Part 1/2)
- LESSON 9: Speed Demon Investigation (Part 2/2)
- LESSON 10: Wild Water Slide: Engineering and Experimental Design (Part 1/3)
- LESSON 11: Wild Water Slide: Engineering and Experimental Design (Part 2/3)
- LESSON 12: Wild Water Slide: Engineering and Experimental Design (Part 3/3)
- LESSON 13: Newton's Second and Third Laws of Motion: Bumper Boats Investigation
- LESSON 14: Newton's Laws Graffiti
- LESSON 15: Newton's First Law: Inertia Kills Investigation
- LESSON 16: Newton's Laws of Motion Simulation Investigation
- LESSON 17: Forces and Motion Assessment Choices
- LESSON 18: Force and Motion Essential Questions