Introduction of the concept: Working with proportions
Prior Knowledge: Multiplication, division, knowledge and understanding of ratios
Materials needed:
– 1/28 Scale Radio Control (R/C) Car
– Chalk line cord
– Stopwatch
Explanation: I chose these manipulatives because proportions can be a little intimidating. By using an R/C car, students can connect with this lesson in a different way. Most kids have toys, and many times the toys are used to mimic real life. This is exactly what will be occurring here. A toy is going to be mimicking real life in 1/28th scale.
Standards:
– Numbers and Operations
– Connections
Illinois Standards:
6.B.3a Solve practical computation problems involving whole numbers, integers and rational numbers
6.C.3a Select computational procedures and solve problems with whole numbers, fractions, decimals, percents and proportions
6.C.3b Show evidence that computational results using whole numbers, fractions, decimals, percents and proportions are correct an/or that estimates are reasonable
6.D.3 Apply ratios and proportions to solve practical problems.
Explanation: I chose these objectives and standards for the fact that they parallel nicely the concepts that will be covered in this lesson.
Lesson objectives:
– Students will demonstrate how to solve proportions
– Students will demonstrate an understanding of scale
– Students will demonstrate the ability to solve proportions in real life situations
Class set up: This activity should be done as a whole group lesson, though groups of four students can work as well, provided there are enough materials available
Anticipatory set: Show the students the car and set it up on a scale ¼ mile drag strip. Ask the students how fast they think the car can go. Tell the students: “I bet you that this car can go nearly 900 miles per hour.” Drive the car down the track. When they all notice the car did not in fact appear to travel at the mentioned speed, have someone clock the speed of the car as you run it again. (The car can go about 30 miles per hour). When they show you the speed, tell them: “the gun is right. The car went about 900 miles per hour.” Then mention the car is 1/28th scale.
Procedure:
1) Review ratios with the class
2) Pose the anticipatory set.
3) Have the students attempt to figure out how long the track is without measuring it. Remind them that the car is 1/28th scale and the track is ¼ mile scaled to 1/28th. Eventually they will determine the track is about 47 feet.
4) Run the car the second time. Have students record the time it takes for the car to travel the scale drag strip.
5) Ask the students to try to determine how you made the claim of a speed of 900mph.
6) After listening to explanations, explain to the class that proportions deal with equality of ratios. An R/C car going 30mph is equivalent to a full size car going 900mph. As you increase any one factor, everything goes up proportionally (i.e. equally).
Question: How is it that I came up with the distance of 47 feet for the track?
7) Run the car a few more times at different speeds. Have the students determine the speed of the car in the current size. This is a good exercise in algebraic reasoning as they need to solve for the speed
8) Have the students explain their algorithms for determining the scale speed. Accuracy is not of paramount importance. What you are trying to convey is the idea of how proportions work.
During the procedure: The teacher should constantly be making assessments during the activity. If at any point a student seems lost, a step can be repeated.
Checking for understanding: The teacher can observe the calculations and estimations that are being made when determining the full scale speed of the car. Simply pausing to ask if everyone understands works as well. Repetition of this should not be a big deal as the students will more than likely enjoy repeatedly racing the cars.
Assessment: Students will demonstrate understanding of proportion by calculating the proportions needed to determine scale speed. An accompanying worksheet can be made to augment the lesson.
Conclusion: Proportions deal with equality of ratios and can be found everywhere, even in toys.
Meeting the needs of diverse learners:
Limited English Proficiency: As there is very little, if any reading involved in this lesson, the only difficulty could be in explaining the concept. In this case I can simply give the solutions first and have the students work backwards to the concept. (Ex: If I explain that this toy car going 30mph is the same as this real car going 900mph, the student can see the proportion by seeing the size difference. If you are getting bigger, you’re adding a lot. If you’re adding a lot, you’re multiplying.)
LD in Math: Luckily the strategy for Limited English also works nicely with Math LD. I would use the same strategy here.
Gifted in Math: In this case, I would have the students measure all major parts of the R/C car (body, hood, doors, wheels, axel, drive train) to see if it is properly to scale with a the full size counterpart.
Extensions: The students can take a field trip to the Revell-Monogram model factory. There, the students can see proportions in real life application as they learn about how the factory determines how big to make the parts for their models based on the scale being used as well as the size of the original vehicle.
Analysis: I chose proportions because it is something that is used more often than we realize. Especially as an R/C enthusiast, I didn’t realize how much I used proportions until I sat down to write this. I feel that this lesson is strong in that the use of cool toys is a great way to keep students’ attention. It can also be a weakness too, in that the novelty of the car overshadows what is being taught. I feel that the concept was taught without burying the students in overcomplicated explanations. They can see the scale and make the connections visually as well as in their heads. I feel that proportion is challenging no matter what, so keeping it as simple as possible is key.
Resources:
http://www.revell-monogram.com
VanDeWalle, John. Elementary and Middle School Mathematics: Teaching Developmentally. Pearson Education, Inc. 2004
