This tasks is an example of a mathematical modeling problem (SMP 4) and it also illustrates SMP 1 (Making sense of a problem). Students are only told that there are two ingredients in the pasta and they have a picture of the box. It might even be better to just show the picture of the box, or to bring in the box and ask the students to pose the question themselves.

This activity can be played by pairs of students to support writing numbers.

Working individually or in pairs, students compete to design, create, test and redesign free-standing, weight-bearing towers using Kapla(TM) wooden blocks. The challenge is to build the tallest tower while meeting the design criteria and minimizing the amount of material used all within a time limit. Students experiment with different geometric shapes used in structural designs and determine how design choices affect the height and strength of structures, becoming comfortable with the concepts of structural members and modeling.

How does energy flow in and out of our atmosphere? Explore how solar and infrared radiation enters and exits the atmosphere with an interactive model. Control the amounts of carbon dioxide and clouds present in the model and learn how these factors can influence global temperature. Record results using snapshots of the model in the virtual lab notebook where you can annotate your observations.

The purpose of the task is to show students a situation where squaring both sides of an equation can result in an equation with more solutions than the original one. The reason for this is that it is possible to have two unequal numbers whose squares are equal.

Spreadsheets Across the Curriculum module. Students build spreadsheets to forward model an example of exponential decay and interpret the meaning of the decay constant.

This activity is a guided inquiry investigation where students gather data on rate of water falling on erosion. Student will interpret their data, and develop a conclusion from the data. The data will lead to further questions, which can be developed by the students.

This task uses the same situation to explore different concepts of probability theory.

In this inquiry lab activity, the students will attempt to layer 6 different kinds of soda pops in a large test tube. The students will have to use prior knowledge of the physical properties of liquids, in particular density, to accomplish this task.

In this number tracing activity students create a rainbow number line. This can be a colorful tool with a personal connection to the student that may be used as a reference. It can serve as a visual and motor reminder when reading and writing numbers because the student went through the tracing motion.

In this task students are asked to analyze a function and its inverse when the function is given as a table of values. In addition to finding values of the inverse function from the table, they also have to explain why the given function is invertible.

In this hands-on activity rolling a ball down an incline and having it collide into a cup the concepts of mechanical energy, work and power, momentum, and friction are all demonstrated. During the activity, students take measurements and use equations that describe these energy of motion concepts to calculate unknown variables, and review the relationships between these concepts.

In this hands-on activity rolling a ball down an incline and having it collide into a cup the concepts of mechanical energy, work and power, momentum, and friction are all demonstrated. During the activity, students take measurements and use equations that describe these energy of motion concepts to calculate unknown variables and review the relationships between these concepts.

This task requires interpreting a function in a non-standard context. While the domain and range of this function are both numbers, the way in which the function is determined is not via a formula but by a (pre-determined) sequence of coin flips. In addition, the task provides an opportunity to compute some probabilities in a discrete situation.

The task is better suited for instruction than for assessment as it provides students with a non standard setting in which to interpret the meaning of functions. Students should carry out the process of flipping a coin and modeling this Random Walk in order to develop a sense of the process before analyzing it mathematically.

This task provides a context to calculate discrete probabilities and represent them on a bar graph. It could also be used to create a class activity where students gather, represent, and analyze data, running simulations of the random walk and recording and then displaying their results.

This task completes the line of reasoning of Random Walk III in a situation where the numbers become too large to calculate and so abstract reasoning is required in order to compare the different probabilities. It is intended for instructional purposes only with a goal of understanding how to calculate and compare the combinatorial symbols.

The nature and scientific measurement of geological and cosmological time are among the most misunderstood and difficult to teach concepts in all of K-12 science education. To address this issue, a multi-disciplinary team of geologists, astronomers and education professionals at Western Kentucky University developed a series of professional development workshops for pre- and in-service middle grades teachers. The goals of those workshops were to 1) to develop teacher's content understanding of rates of change and the ages of the earth and universe; and 2) to provide teachers with materials, activities and teaching strategies to help them more effectively educate students about rates of change and the concepts of deep time. Two four-day workshops were held, with each workshop divided into two two-day sessions. Each workshop day consisted of a blend of in-depth content discussions, hands-on activities, and classroom implementation forums. The teachers were provided with all the materials necessary to implement the lessons learned during the workshops as well as publications pertaining to deep time and evolution. Teachers were assessed prior to and immediately after each workshop day and were required to submit a classroom implementation plan as part of their involvement in the workshops.

We have been successful in meeting our workshop goals. The participants clearly advanced their content understanding of geological and cosmological time and the implementation plans received clearly show a desire to apply many of the activities learned in the workshop. Ironically, and despite state science standards mandating coverage of concepts of rates of change and deep time, teachers find that they do not have the time to fully educate their students about geological and cosmological time. We are currently assessment results and are working to disseminate the workshop materials (http://astro.wku.edu/universe).

(Note: this resource was added to OER Commons as part of a batch upload of over 2,200 records. If you notice an issue with the quality of the metadata, please let us know by using the 'report' button and we will flag it for consideration.)

This task makes for a good follow-up task on rational irrational numbers after that the students have been acquainted with some of the more basic properties. In addition to eliciting several different types of reasoning, the task requires students to rewrite radical expressions in which the radicand is divisible by a perfect square (N-RN.2).

In some textbooks, a distinction is made between a ratio, which is assumed to have a common unit for both quantities, and a rate, which is defined to be a quotient of two quantities with different units (e.g. a ratio of the number of miles to the number of hours). No such distinction is made in the common core and hence, the two quantities in a ratio may or may not have a common unit. However, when there is a common unit, as in this problem, it is possible to add the two quantities and then find the ratio of each quantity with respect to the whole (often described as a part-whole relationship).