Rate

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Solve problems involving all four operations with rational numbers.
Understand quantity as a number used with a unit of measurement.
Solve problems involving quantities such as distances, intervals of time, liquid volumes, masses of objects, and money, and with the units of measurement for these quantities.
Understand that a ratio is a comparison of two quantities.
Write ratios for problem situations.
Make and interpret tables, graphs, and diagrams.
Write and solve equations to represent problem situations.

Lesson Flow

In this unit, students will explore the concept of rate in a variety of contexts: beats per minute, unit prices, fuel efficiency of a car, population density, speed, and conversion factors. Students will write and refine their own definition for rate and then use it to recognize rates in different situations. Students will learn that every rate is paired with an inverse rate that is a measure of the same relationship. Students will figure out the logic of how units are used with rates. Then students will represent quantitative relationships involving rates, using tables, graphs, double number lines, and formulas, and they will see how to create one such representation when given another.

In this lesson, students watch a video of a runner and express his speed as a rate in meters per second. Students then use the rate to determine how long it takes the runner to go any distance.Key ConceptsSpeed is a rate that is expressed as distance traveled per unit of time. Miles per hour, laps per minute, and meters per second are all examples of units for speed. The measures of speed, distance, and time are all related. The relationship can be expressed in three ways: d = rt, r = dt, t = dr.Goals and Learning ObjectivesExplore speed as a rate that measures the relationship between two aspects of a situation: distance and time.In comparing distance, speed, and time, understand how to use any two of these measures to find the third measure.

Students will create go-carts and calculate the speed, then change a variable and record the differences in speed.

Students explore the physics utilized by engineers in designing today's roller coasters, including potential and kinetic energy, friction, and gravity. First, students learn that all true roller coasters are completely driven by the force of gravity and that the conversion between potential and kinetic energy is essential to all roller coasters. Second, they also consider the role of friction in slowing down cars in roller coasters. Finally, they examine the acceleration of roller coaster cars as they travel around the track. During the associated activity, the students design, build, and analyze a roller coaster for marbles out of foam tubing.

In this video from Cyberchase, the CyberSquad figures out how fast their broom must go so they can reach Motherboard before Wicked.

Students conduct an experiment to determine the relationship between the speed of a wooden toy car at the bottom of an incline and the height at which it is released. They observe how the photogate-based speedometer instrument "clocks" the average speed of an object (the train). They gather data and create graphs plotting the measured speed against start height. After the experiment, as an optional extension activity, students design brakes to moderate the speed of the cart at the bottom of the hill to within a specified speed range.

Students use their understanding of projectile physics and fluid dynamics to find the water pressure in water guns. By measuring the range of the water jets, they are able to calculate the theoretical pressure. Students create graphs to analyze how the predicted pressure relates to the number of times they pump the water gun before shooting.

In this activity, students will play a game to review the conversation skills acquired this past semester. This activity will be a review of questions, introductions, and basic information. The goal is for students to be able to sign a response to the questions as fast as they can.

A simple lesson to introduce pupils to speed-time graphs using aspects of SDG9 relating to transport. Suitable for Y7 - Y9.Three levels of differentiation. 

Lesson plan detailing on speed and energy by using toy race cars, with and without weight, to describe speed and electromagnetic energy.  

As if they are engineers, students are tasked to design solar-powered model vehicles that are speedy and compact in order to make recommendations to a local car sales company. Teams familiarize themselves with the materials by building solar-panel model car prototypes, following kit instructions, which they test for speed. After making design improvements, they test again. Then they take measurements and calculate the volume of each team’s vehicle. They rank all teams’ vehicles by speed and by size. After data analyses, reflection and team discussion, students write recommendations to the car company about the vehicle they think is best for consumers. Youngsters experience key portions of the engineering design process and learn the importance of testing and collaborating in order to make better products. Pre/post-quizzes and numerous worksheets and handouts are provided.

Students act as engineers to solve a hypothetical problem that has occurred in the Swiss Alps due to a seismic event. In research groups, students follow the steps of the engineering design process as teams compete to design and create small-size model sleds that can transport materials to people in distress who are living in the affected town. The sleds need to be able to carry various resources that the citizens need for survival as well as meet other design requirements. Students test their designs and make redesigns to improve their prototypes in order to achieve final working designs. Once the designs and final testing are complete, students create final technical reports.

Students see how different levels of surface tension affect water's ability to move. Teams "race" water droplets down tracks made of different materials, making measurements, collecting data, making calculations, graphing results and comparing to their predictions and the properties of each surface, determining which surface exhibits the highest (or lowest) level of surface tension with water. They apply their results to make engineering recommendations for real-world applications.

Students learn about wind as a source of renewable energy and explore the advantages and disadvantages wind turbines and wind farms. They also learn about the effectiveness of wind turbines in varying weather conditions and how engineers work to create wind power that is cheaper, more reliable and safer for wildlife.

Students strengthen their communicate skills about measurements by learning the meaning of base units and derived units, including speed one of the most common derived units (distance/time). Working in groups, students measure the time for LEGO MINDSTORMS(TM) NXT robots to move a certain distance. The robots are started and stopped via touch sensors and programmed to display the distance traveled. Using their collected data, students complete a worksheet to calculate the robots' (mean/average) speeds at given motor powers.

Students are introduced to the concepts of torque, power, friction and gear ratios. Teams modify two robotic LEGO® MINDSTORMS® vehicles by changing their gear ratios, wheel sizes, weight and engine power, while staying within a limit of points to spend on modifications. The robots face each other on a track with a string attaching one to the other. The winning robot, the one with the best adjustments, pulls the other across the line.

Students study the physical properties of different fluids and investigate the relationship between the viscosities of liquid and how fast they flow through a confined area. Student groups conduct a brief experiment in which they quantify the flow rate to understand how it relates to a fluid's viscosity and ultimately chemical composition. They explore these properties in milk and cream, which are common fluids whose properties (and even taste!) differ based on fat content. They examine control samples and unknown samples, which they must identify based on how fast they flow. To identify the unknowns requires an understanding of the concept of viscosity. For example, heavy cream flows at a slower rate than skim milk. Ultimately, students gain an understanding of the concept of viscosity and its effect on flow rate.

Students are introduced to the concepts of force, inertia and Newton's first law of motion: objects at rest stay at rest and objects in motion stay in motion unless acted upon by an unbalanced force. Examples of contact and non-contact types of forces are provided, specifically applied, spring, drag, frictional forces, and magnetic, electric, gravitational forces. Students learn the difference between speed, velocity and acceleration, and come to see that the change in motion (or acceleration) of an object is caused by unbalanced forces. They also learn that engineers consider and take advantage of these forces and laws of motion in their designs. Through a PowerPoint® presentation and some simple teacher demonstrations these fundamental science concepts are explained and illustrated. This lesson is the first in a series of three lessons that are intended to be taught as a unit.

Students learn about friction and drag two different forces that convert energy of motion to heat. Both forces can act on a moving object and decrease its velocity. Students learn examples of friction and drag, and suggest ways to reduce the impact of these forces. The equation that governs common frictional forces is introduced, and during a hands-on activity, students experimentally measure a coefficient of friction.

Expanding on the topic of objects in motion covering Newton's laws of motion, acceleration and velocity, which are taught starting in third grade, students are introduced to new concepts of speed, density, level of service (LOS) (quality of roadways), delay and congestion. Every day we are affected by congestion even if we do not step out of our homes. For example, the price we pay for goods increases due to increases in shipping costs caused by congestion delays. A congestion metric would help us to compare roadways and assess improvement methods. A common metric used to measure congestion is called level of service (LOS).