Students will use a stopwatch to time themselves performing in various events, record data, and then compare and order decimals to determine bronze, silver and gold medal winners.
Simple machines are devices with few or no moving parts that make work easier, and which people have used to provide mechanical advantage for thousands of years. Students learn about the wedge, wheel and axle, lever, inclined plane, screw and pulley in the context of the construction of a pyramid, gaining insights into tools that have been used since ancient times and are still important today. Through numerous hands-on activities, students imagine themselves as ancient engineers building a pyramid. Student teams evaluate and select a construction site, design a pyramid, perform materials calculations, test a variety of cutting wedges on different materials, design a small-scale cart/lever transport system to convey building materials, experiment with the angle of inclination and pull force on an inclined plane, see how a pulley can change the direction of force, and learn the differences between fixed, movable and combined pulleys. While learning the steps of the engineering design process, students practice teamwork, creativity and problem solving.
The purpose of this task is for students to show they understand the connection between fraction and decimal notation by writing the same numbers both ways.
The purpose of this task is to provide students with an opportunity to explain fraction equivalence through visual models in a particular example.
Students conduct an experiment to study the acceleration of a mobile Android device. During the experiment, they run an application created with MIT's App Inventor that monitors linear acceleration in one-dimension. Students use an acceleration vs. time equation to construct an approximate velocity vs. time graph. Students will understand the relationship between the object's mass and acceleration and how that relates to the force applied to the object, which is Newton's second law of motion.
Students observe multiple examples of capillary action. First they observe the shape of a glass-water meniscus and explain its shape in terms of the adhesive attraction of the water to the glass. Then they study capillary tubes and observe water climbing due to capillary action in the glass tubes. Finally, students experience a real-world application of capillary action by designing and using "capillary siphons" to filter water.
Students are introduced to the concept of energy conversion, and how energy transfers from one form, place or object to another. They learn that energy transfers can take the form of force, electricity, light, heat and sound and are never without some energy "loss" during the process. Two real-world examples of engineered systems light bulbs and cars are examined in light of the law of conservation of energy to gain an understanding of their energy conversions and inefficiencies/losses. Students' eyes are opened to the examples of energy transfer going on around them every day. Includes two simple teacher demos using a tennis ball and ball bearings. A PowerPoint(TM) presentation and quizzes are provided.
Students learn about kinetic and potential energy, including various types of potential energy: chemical, gravitational, elastic and thermal energy. They identify everyday examples of these energy types, as well as the mechanism of corresponding energy transfers. They learn that energy can be neither created nor destroyed and that relationships exist between a moving object's mass and velocity. Further, the concept that energy can be neither created nor destroyed is reinforced, as students see the pervasiveness of energy transfer among its many different forms. A PowerPoint(TM) presentation and post-quiz are provided.
Students will explore the concepts of place value using their bodies as tools. They will time themselves performing various kinesthetic tasks like jumping jacks and sit ups and use the numbers that they record from these activities in their exploration. Working in groups, they will practice adding and subtracting and comparing numbers. They will also come up with creative ways to represent numbers using the properties of operation and the rules of place value.
Students will explore the concepts of place value using their bodies as tools. They will time themselves performing various kinesthetic tasks like jumping jacks and sit ups and use the numbers that they record from these activities in their exploration. Working in groups, they will practice adding and subtracting and comparing numbers. They will also come up with creative ways to represent numbers using the properties of operation and the rules of place value.
Context based exponential growth and decay questions.
(This is used as a test of OER)
In this task students prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
This problem illustrates how an exponentially increasing quantity eventually surpasses a linearly increasing quantity.
In this task students observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
This problem shows that an exponential function takes larger values than a cubic polynomial function provided the input is sufficiently large.
The purpose of this task is twofold: first using technology to study the behavior of some exponential and logarithmic graphs and secondly to manipulate some explicit logarithmic and exponential expressions. Although not asked in the task body, the teacher may wish to prompt students to explain why the two graphs behave as they do as the base b varies: that is, a larger value of b between 1 and 2 makes the exponential graph grow faster and the logarithmic graph grow more slowly as x increases.
The task provides a reasonably straight-forward introduction to interpreting the parameters of an exponential function in terms of a modeling context. In general, an exponential function f(t)=ab^t has two parameters. The parameter a is interpreted as the starting value (when t represents time), and b represents the growth rate -- the amount the quantity is multiplied by each time the value of t is incremented by 1.
The purpose of this task is to help students see the "why" behind properties of logs that are familiar but often just memorized (and quickly forgotten or misremembered). The task focuses on the verbal definition of the log, helping students to concentrate on understanding that a logarithm is an exponent, as opposed to completing a more computational approach.
This task and its companion, F-BF Exponentials and Logarithms I, is designed to help students gain facility with properties of exponential and logarithm functions resulting from the fact that they are inverses.
According to the GED testing service, test takers struggle with “applying rules of exponents in numerical expressions with rational exponents to write equivalent expressions with rational exponents.” (https://www.gedtestingservice.com/uploads/files/09738c12fe4e4accd9a16bab7cb99a3c.pdf )
Students do “fairly well” with simple squares and square roots, but there is a “sharp drop-off” when things get more complicated.
These are questions included in the “no calculator” portion of the test.
These skills are Mathematics Standards Level D in the College and Career Readiness Standards for Adult Education (https://www.educateiowa.gov/sites/files/ed/documents/CCRStandardsAdultEd.pdf ) under “Expressions and Equations.”
This curriculum guide will offer opportunities to build the deeper understanding necessary to understand the rules of exponents such as (xm)n = xmn .
Write and evaluate numerical expressions involving whole-number exponents. (6.EE.1)
Know and apply the properties of integer exponents to generate equivalent numerical expressions. (8.EE.1)