This problem requires a comparison of rates where one is given in terms of unit rates, and the other is not.

For this interactive, students determine if the values in the table are proportional. Students enter an answer and can click the Check Answer button to see if their answer is correct.

Sample Learning Goals
Use a ratio as a descriptive characteristic
Compare the meaning of a ratio in different contexts
Use scaling to build proportions or find a missing value in a proportion
Simplify ratios to build proportions or find a missing value in a proportion
Use multiplicative reasoning to solve problems

Students are creating a proportional and non proportional real world context and representing each example through multiple representations.

Students are creating a proportional and non proportional real world context and representing each example through multiple representations.

This lesson unit is intended to help teachers assess whether students are able to: identify when two quantities vary in direct proportion to each other; distinguish between direct proportion and other functional relationships; and solve proportionality problems using efficient methods.

Sample Learning Goals
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two hand heights.
Understand the concept of a unit rate a/b associated with a ratio a:b, and use rate language in the context of a ratio relationship.
Recognize and represent proportional relationships between hand heights.

This course was created by the Rethink Education Content Development Team in partnership with the North Carolina Virtual Public Schools. This course is aligned to the NC Standards for 7th Grade Math. 

This course was created by the Rethink Education Content Development Team in partnership with the North Carolina Virtual Public Schools. This course is aligned to the NC Standards for 7th Grade Math. 

This course was created by the Rethink Education Content Development Team in partnership with the North Carolina Virtual Public Schools. This course is aligned to the NC Standards for 7th Grade Math.

Within the physical science strand of 7th grade science, students focus on forms of energy, energy transfer, and transformation and conservation in mechanical systems—in other words, potential and kinetic energy, work, and mechanical advantage and efficiency in simple machines. In this task, students working in groups design a simple machine or simple machine system that would be able to lift and relocate a 13 kg cinder block after reading an excerpt from Mrs. Frisby and the Rats of NIMH by Robert O'Brien, a novel about genetically engineered rats who assist a mouse by moving her home out of danger in a farmer’s field. The interdisciplinary and inquiry based nature of this activity allows students to build meaningful connections while promoting creativity and 21st Century Skills. This lesson was developed by NCDPI as part of the Academically and/or Intellectually Gifted Instructional Resources Project. This lesson plan has been vetted at the state level for standards alignment, AIG focus, and content accuracy.

There is a non-mathematical fact that students must know about mixtures in order to answer this question. When salt is dissolved in water, the salt disperses evenly through the mixture, so any sample from the mixture that has the same volume will have the same amount of salt.

Engineers design and implement many creative techniques for managing stormwater at its sources in order to improve and restore the hydrology and water quality of developed sites to pre-development conditions. Through the two lessons in this unit, students are introduced to green infrastructure (GI) and low-impact development (LID) technologies, including green roofs and vegetative walls, bioretention or rain gardens, bioswales, planter boxes, permeable pavement, urban tree canopies, rainwater harvesting, downspout disconnection, green streets and alleys, and green parking. Student teams take on the role of stormwater engineers through five associated activities. They first model the water cycle, and then measure transpiration rates and compare native plant species. They investigate the differences in infiltration rates and storage capacities between several types of planting media before designing their own media mixes to meet design criteria. Then they design and test their own pervious pavement mix combinations. In the culminating activity, teams bring together all the concepts as well as many of the materials from the previous activities in order to create and install personal rain gardens. The unit prepares the students and teachers to take on the design and installation of bigger rain garden projects to manage stormwater at their school campuses, homes and communities.

Students reinforce an antenna tower made from foam insulation so that it can withstand a 480 N-cm bending moment (torque) and a 280 N-cm twisting moment (torque) with minimal deflection. During one class period, students discuss the problem, run the initial bending and torsion tests and graph the results. During the following class periods, students design, construct and test sturdier towers, and graph the results.