While students need to be able to write sentences describing ratio relationships, they also need to see and use the appropriate symbolic notation for ratios. If this is used as a teaching problem, the teacher could ask for the sentences as shown, and then segue into teaching the notation. It is a good idea to ask students to write it both ways (as shown in the solution) at some point as well.

A gear is a simple machine that is very useful to increase the speed or torque of a wheel. In this activity, students learn about the trade-off between speed and torque when designing gear ratios. The activity setup includes a LEGO(TM) MINDSTORMS(TM) NXT pulley system with two independent gear sets and motors that spin two pulleys. Each pulley has weights attached by string. In a teacher demonstration, the effect of adding increasing amounts of weight to the pulley systems with different gear ratios is observed as the system's ability to lift the weights is tested. Then student teams are challenged to design a gear set that will lift a given load as quickly as possible. They test and refine their designs to find the ideal gear ratio, one that provides enough torque to lift the weight while still achieving the fastest speed possible.

Students will investigate the concepts of ratio and rate. They use multiple forms of ratio language and ratio notation, and formalize understanding of equivalent ratios.

Students begin their sixth grade year investigating the concepts of ratio and rate. They use multiple forms of ratio language and ratio notation, and formalize understanding of equivalent ratios.

In this lesson, students will understand that a ratio is an ordered pair of non-negative numbers, which are not both zero. Students will understand that a ratio is often used instead of describing the first number as a multiple of the second. Students will use the precise language and notation of ratios (e.g., 3:2, 3 to 2). Students will understand that the order of the pair of numbers in a ratio matters and that the description of the ratio relationship determines the correct order of the numbers. Students conceive of real-world contextual situations to match a given ratio.

In this lesson, students will reinforce their understanding that a ratio is an ordered pair of non-negative numbers, which are not both zero. Students continue to learn and use the precise language and notation of ratios (e.g., 3:2, 3 to 2). Students demonstrate their understanding that the order of the pair of numbers in a ratio matters. Students create multiple ratios from a context in which more than two quantities are given. Students conceive of real-world contextual situations to match a given ratio.

Students are presented with a guide to rain garden construction in an activity that culminates the unit and pulls together what they have learned and prepared in materials during the three previous associated activities. They learn about the four vertical zones that make up a typical rain garden with the purpose to cultivate natural infiltration of stormwater. Student groups create personal rain gardens planted with native species that can be installed on the school campus, within the surrounding community, or at students' homes to provide a green infrastructure and low-impact development technology solution for areas with poor drainage that often flood during storm events.

This lesson will allow students to become familiar with the concept of equivalent ratios and similar objects. Through an open investigation students will develop methods to find equivalent ratios. This is a lesson to be used as part of a unit with Painter Problems and How Far Can You Leap found in ALEX.

This lesson will allow students to become familiar with the concept of unit rate. Through an open investigation students will develop methods to find unit rate with a table, equivalent ratios, or an equation. This is a lesson to be used as part of a unit with "Painter Problems" and "How Big Should It Be?"

In this lesson, students view a picture or video of the Statue of Liberty and are asked how long the arm would be if the nose measures 4 feet 6 inches. They measure the length of their own nose and the length of their arm and form a ratio. Using proportions, students compute the length of the statue's arm. In addition to the lesson plan, the site includes ideas for teacher discussion, extensions of the lesson, and additional resources.

Through multi-trial experiments, students are able to see and measure something that is otherwise invisible to them seeing plants breathe. Student groups are given two small plants of native species and materials to enclose them after watering with colored water. After being enclosed for 5, 10 and 15 minutes, teams collect and measure the condensed water from the plants' "breathing," and then calculate the rates at which the plants breathe. A plant's breath is known as transpiration, which is the flow of water from the ground where it is taken up by roots (plant uptake) and then lost through the leaves. Students plot volume/time data for three different native plant species, determine and compare their transpiration rates to see which had the highest reaction rate and consider how a plant's unique characteristics (leaf surface area, transpiration rate) might figure into engineers' designs for neighborhood stormwater management plans.

In this ratios and proportions video lesson, students will practice reading and understanding the language of word problems; they will use specific words as clues to the mathematical operations embedded in the proportions and ratios problems and use them in context. This resource supports English language development for English language learners.

In this math video lesson, students will analyze and write data for "beans counting" rate of three classmates, then, they will formalize ways to represent rates and develop arguments for comparing and making more elaborated conclusions about them.This resource supports English language development for English language learners.

In this Math video lesson on rates, students will explore ways of writing rates, then, they will develop arguments for comparing and making conclusions about them; finally, they formalize their ideas by making justifications recording the data in complete sentences. This resource supports English language development for English language learners.

Students use everyday building materials sand, pea gravel, cement and water to create and test pervious pavement. They learn what materials make up a traditional, impervious concrete mix and how pervious pavement mixes differ. Groups are challenged to create their own pervious pavement mixes, experimenting with material ratios to evaluate how infiltration rates change with different mix combinations.

As a weighted plastic egg is dropped into a tub of flour, students see the effect that different heights and masses of the same object have on the overall energy of that object while observing a classic example of potential (stored) energy transferred to kinetic energy (motion). The plastic egg's mass is altered by adding pennies inside it. Because the egg's shape remains constant, and only the mass and height are varied, students can directly visualize how these factors influence the amounts of energy that the eggs carry for each experiment, verified by measurement of the resulting impact craters. Students learn the equations for kinetic and potential energy and then make predictions about the depths of the resulting craters for drops of different masses and heights. They collect and graph their data, comparing it to their predictions, and verifying the relationships described by the equations. This classroom demonstration is also suitable as a small group activity.

This lesson assess how well students are able to solve real-life mathematical problems. Students use proportional relationships to solve multistep ratio and percent problems, draw inferences about a population from random sample of data, and make and state assumptions based on real-life situations.

Students will be introduced to the concept of Ratio using an activity with newspapers. They will also reinforce their understanding of fractions as well as fraction to decimal conversions.

Normally we find things using landmark navigation. When you move to a new place, it may take you awhile to explore the new streets and buildings, but eventually you recognize enough landmarks and remember where they are in relation to each other. However, another accurate method for locating places and things is using grids and coordinates. In this activity, students will come up with their own system of a grid and coordinates for their classroom and understand why it is important to have one common method of map-making.