Students connect polynomial arithmetic to computations with whole numbers and integers. Students learn that the arithmetic of rational expressions is governed by the same rules as the arithmetic of rational numbers. This unit helps students see connections between solutions to polynomial equations, zeros of polynomials, and graphs of polynomial functions. Polynomial equations are solved over the set of complex numbers, leading to a beginning understanding of the fundamental theorem of algebra. Application and modeling problems connect multiple representations and include both real world and purely mathematical situations.
Students are introduced to statics and dynamics, free-body diagrams, combustion and thermodynamics to gain an understanding of the forces needed to lift rockets off the ground. They learn that thrust force is needed to launch rockets into space and the energy for thrust is stored as chemical energy in the rocket's fuel. Then, using the law of conservation of energy, students learn that the chemical energy of the fuel is converted into work and heat energy during a rocket launch. A short PowerPointÂ® presentation is provided, including two example problems for stoichiometry review. An optional teacher demonstration is described as an extension activity.
In this unit of study students learn that in the horizontal direction a projectile moves at a constant speed with nothing to cause acceleration. In the vertical direction a projectile accelerates due to the earth’s gravitational field. And combining these two type of motions together you can determine the parabolic arch of a projectile. This unit integrates nine STEM attributes and was developed as part of the South Metro-Salem STEM Partnership's Teacher Leadership Team. Any instructional materials are included within this unit of study.
Using paper, paper clips and tape, student teams design flying/falling devices to stay in the air as long as possible and land as close as possible to a given target. Student teams use the steps of the engineering design process to guide them through the initial conception, evaluation, testing and re-design stages. The activity culminates with a classroom competition and scoring to evaluate how each team's design performed.
Students create and analyze composite materials with the intent of using the materials to construct a structure with optimal strength and minimal density. The composite materials are made of puffed rice cereal, marshmallows and chocolate chips. Student teams vary the concentrations of the three components to create their composite materials. They determine the material density and test its compressive strength by placing weights on it and measuring how much the material compresses. Students graph stress vs. strain and determine Young's modulus to analyze the strength of their materials.
In this lesson students are introduced to Architect, Jeremy Peang-Meth. Mr. Peang-Meth was asked to design a local, renewable energy source for building located in the heart of New York City. While the tall buildings surrounding the site caused some obvious problems, there were also some benefits to the site. Students are asked to consider the constraints posed by the location of the building and then, based on their analysis of those constraints, to find a roof location that will provide good energy capture from the wind. After they have made that choice, students are invited to view Mr. Peang-Meth’s solution as he presents it in the provided video.
This interactive activity helps learners visualize the role of electrons in the formation of ionic and covalent chemical bonds. Students explore different types of chemical bonds by first viewing a single hydrogen atom in an electric field model. Next, students use sliders to change the electronegativity between two atoms -- a model to help them understand why some atoms are attracted. Finally, students experiment in making their own models: non-polar covalent, polar covalent, and ionic bonds. This item is part of the Concord Consortium, a nonprofit research and development organization dedicated to transforming education through technology.
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...
Building on an introduction to statics, dynamics free-body diagrams, combustion and thermodynamics provided by the associated lesson, students design, construct and test their own rocket engines using sugar and potassium nitrate an opportunity to apply their knowledge of stoichiometry. This activity helps students understand that the energy required to launch a rocket comes from the chemical energy stored in the rocket fuel. The performance of each engine is tested during a rocket launch, after which students determine the reasons for the success or failure of their rockets.
This lesson unit is intended to help teachers assess how well students are able to: interpret a situation and represent the constraints and variables mathematically; select appropriate mathematical methods to use; make sensible estimates and assumptions; investigate an exponentially increasing sequence; and communicate their reasoning clearly.
In this module, students synthesize and generalize what they have learned about a variety of function families. They extend the domain of exponential functions to the entire real line (N-RN.A.1) and then extend their work with these functions to include solving exponential equations with logarithms (F-LE.A.4). They explore (with appropriate tools) the effects of transformations on graphs of exponential and logarithmic functions. They notice that the transformations on a graph of a logarithmic function relate to the logarithmic properties (F-BF.B.3). Students identify appropriate types of functions to model a situation. They adjust parameters to improve the model, and they compare models by analyzing appropriateness of fit and making judgments about the domain over which a model is a good fit. The description of modeling as, the process of choosing and using mathematics and statistics to analyze empirical situations, to understand them better, and to make decisions, is at the heart of this module. In particular, through repeated opportunities in working through the modeling cycle (see page 61 of the CCLS), students acquire the insight that the same mathematical or statistical structure can sometimes model seemingly different situations.
This task, while involving relatively simple arithmetic, codes to all three standards in this cluster, and also offers students a good opportunity to practice modeling (MP4), since they must attempt to make reasonable assumptions about the average length of vehicles in the traffic jam and the space between vehicles. Teachers can encourage students to compare their solutions with other students.
The principal purpose of the task is to explore a real-world application problem with algebra, working with units and maintaining reasonable levels of accuracy throughout.
Students will investigate renewable and non-renewable energy options as they develop a plan to reduce the energy consumption of their household.
Students learn about the separation techniques of sedimentation and centrifugation and investigate whether blood is a homogeneous or a heterogeneous mixture. Working in groups as if they are biomedical researchers, they employ the scientific method and make observations about the known characteristics of urine, milk and blood. They probe further by analyzing research on the properties and fractionation modes of blood. As students learn about certain strange characteristics with the fractionation behavior of blood, they formulate hypotheses on the unique nature of blood. Using provided materials âolive oil, tomato juice and petroleum jellyâthey design an experiment and construct a blood model. They test their hypotheses by conducting experiments on the blood model, and then propose theories for the nature of blood as a mixtureâarriving at the theory of mixture dualism in bloodâthat blood is a complex mixture system. An activity-guiding handout and PowerPointÂ® presentation are provided for this student-directed, project-based activity.
This is a challenging task, suitable for extended work, and reaching into a deep understanding of units. The task requires students to exhibit MP1, Make sense of problems and persevere in solving them. An algebraic solution is possible but complicated; a numerical solution is both simpler and more sophisticated, requiring skilled use of units and quantitative reasoning. Thus the task aligns with either A-CED.1 or N-Q.1, depending on the approach.
Modeling Our World with Mathematics Unit 2: Environmental Science Topic 2 - Sustainable Forestry
Students will investigate the properties of matter too small to see, as well as how it behaves when present in different quantities. Students will design a procedure to measure the thickness of a thin film of oil on the surface of water.