The purpose of this task is to engage students in an open-ended modeling task that uses similarity of right triangles, and also requires the use of technology.
This problem uses the same numbers and asks similar mathematical questions as "6.NS The Florist Shop," but that task requires students to apply the concepts of multiples and common multiples in a context.
This activity helps students learn about the three different types of muscles and how outer space affects astronauts' muscles. They will discover how important it is for astronauts to get adequate exercise both on Earth and in outer space. Also, through the design of their own microgravity exercise machine, students learn about the exercise machines that engineers design specifically for astronaut use.
This problem requires a comparison of rates where one is given in terms of unit rates, and the other is not.
This real world word problem requires multiple steps.
Students are introduced to the concept of the image of music. After listening to a song, they draw images of it by deciding where different musical instruments were placed during recording. They further investigate audio engineering by modeling the position of microphones over a drum set to create a desired musical image.
In this group task students collect data and analyze from the class to answer the question "is there an association between whether a student plays a sport and whether he or she plays a musical instrument? "
Students are introduced to the futuristic concept of the moon as a place people can inhabit. They brainstorm what people would need to live on the moon and then design a fantastic Moon colony and decide how to power it. Students use the engineering design process, which includes researching various types of energy sources and evaluating which would be best for their moon colonies.
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Renee reasons as follows to solve the equation $x^2 + x + 1 = 0$. First I will rewrite this as a square plus some number. x^2 + x + 1 = \left(x+\frac{1...
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: For this task, the letter $i$ denotes the imaginary unit, that is, $i=\sqrt{-1}$. For each integer $k$ from 0 to 8, write $i^k$ in the form $a+bi$. Des...
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Let $z = 1 + i$ where $i^2 = -1$. Calculate $z^2, z^3,$ and $z^4$. Graph $z, z^2, z^3,$ and $z^4$ in the complex plane. What do you notice about the po...
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: A small company wants to give raises to their 5 employees. They have $10,000 available to distribute. Imagine you are in charge of deciding how the rai...
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Three students disagree about what value to assign to the expression $0^0$. In each case, critically analyze the student's argument. Juan suggests that...
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Below is a picture of the (elliptical) orbit of a planet around the sun: The sun is at point $A$, point $P$ is where the planet is closest to the sun d...
Student pairs experience the iterative engineering design process as they design, build, test and improve catching devices to prevent a "naked" egg from breaking when dropped from increasing heights. To support their design work, they learn about materials properties, energy types and conservation of energy. Acting as engineering teams, during the activity and competition they are responsible for design and construction planning within project constraints, including making engineering modifications for improvement. They carefully consider material choices to balance potentially competing requirements (such as impact-absorbing and low-cost) in the design of their prototypes. They also experience a real-world transfer of energy as the elevated egg's gravitational potential energy turns into kinetic energy as it falls and further dissipates into other forms upon impact. Pre- and post-activity assessments and a scoring rubric are provided. The activity scales up to district or regional egg drop competition scale. As an alternative to a ladder, detailed instructions are provided for creating a 10-foot-tall egg dropper rig.
Given an assortment of unknown metals to identify, student pairs consider what unique intrinsic (aka intensive) metal properties (such as density, viscosity, boiling or melting point) could be tested. For the provided activity materials (copper, aluminum, zinc, iron or brass), density is the only property that can be measured so groups experimentally determine the density of the "mystery" metal objects. They devise an experimental procedure to measure mass and volume in order to calculate density. They calculate average density of all the pieces (also via the graphing method if computer tools area available). Then students analyze their own data compared to class data and perform error analysis. Through this inquiry-based activity, students design their own experiments, thus experiencing scientific investigation and experimentation first hand. A provided PowerPoint(TM) file and information sheet helps to introduce the five metals, including information on their history, properties and uses.
The goal of this task is to show that when the whole is not specified, which fraction is being represented is left ambiguous.
Students apply the knowledge gained from the previous lessons and activities in this unit to write draft grant proposals to the U.S. National Institutes of Health outlining their ideas for proposed research using nanoparticles to protect against, detect or treat skin cancer. Through this exercise, students demonstrate their understanding of the environmental factors that contribute to skin cancer, the science and mathematics of UV radiation, the anatomy of human skin, current medical technology applications of nanotechnology and the societal importance of funding research in this area, as well as their communication skills in presenting plans for specific nanoscale research they would conduct using nanoparticles.
Students learn about the biomedical use of nanoparticles in the detection and treatment of cancer, including the use of quantum dots and lasers that heat-activate nanoparticles. They also learn about electrophoresis a laboratory procedure that uses an electric field to move tiny particles through a channel in order to separate them by size. They complete an online virtual mini-lab, with accompanying worksheet, to better understand gel electrophoresis. This prepares them for the associated activity to write draft research proposals to use nanoparticles to protect against, detect or treat skin cancer.
Students learn about frequency and period, particularly natural frequency using springs. They learn that the natural frequency of a system depends on two things: the stiffness and mass of the system. Students see how the natural frequency of a structure plays a big role in the building surviving an earthquake or high winds.