The purpose of this task is for students to select 2 numbers from a set of 3 that sum to 9. The task can be completed for sums equaling any number. Teachers may choose to ask students to write the simple equations they select.

In this lesson students will use their knowledge of decimals to solve problems in a real- world setting.

In this activity, learners work in groups to determine the mass and volume of four samples: glass marbles, steel washers or nuts, pieces of pine wood, and pieces of PVC pipe. Learners then plot the data points on a large class graph of mass vs. volume to discover that data points for a particular material form a straight line, the slope of which gives the density of the material.

Popcorn pops due to the moisture in the kernel that explodes when heated.  In this lesson students will compare kernels soaked in water before popping with dry kernels to see whether it makes a difference in the number of unpopped kernels. 

Students learn about population density within environments and ecosystems. They determine the density of a population and think about why population density and distribution information is useful to engineers for city planning and design as well as for resource allocation.

During this activity students will learn how to estimate population size using two techniques, density extrapolation and the mark-recapture method.

Prior to 1990, the performance of a student in precalculus at the University of Washington was not a predictor of success in calculus. For this reason, the mathematics department set out to create a new course with a specific set of goals in mind:

A review of the essential mathematics needed to succeed in calculus.
An emphasis on problem solving, the idea being to gain both experience and confidence in working with a particular set of mathematical tools.
This text was created to achieve these goals and the 2004-05 academic year marks the eleventh year in which it has been used. Several thousand students have successfully passed through the course.

This book is full of worked out examples. We use the the notation “Soluion.” to indicate where the reasoning for a problem begins; the symbol ?? is used to indicate the end of the solution to a problem. There is a Table of Contents that is useful in helping you find a topic treated earlier in the course. It is also a good rough outline when it comes time to study for the final examination. The book also includes an index at the end. Finally, there is an appendix at the end of the text with ”answers” to most of the problems in the text. It should be emphasized these are ”answers” as opposed to ”solutions”. Any homework problems you may be asked to turn in will require you include all your work; in other words, a detailed solution. Simply writing down the answer from the back of the text would never be sufficient; the answers are intended to be a guide to help insure you are on the right track.

In the first half of this module, students identify measurable attributes of objects in terms of length, weight, and capacity.  Students learn words such as small, big, short, tall, empty, full, heavy, and light so that they will have the vocabulary needed to describe objects (PK.MD.1).  The comparison of length, weight, and capacity naturally leads to discussions about quantity and number.  In the second half, measurement is connected to quantity as students reason if there are enough, more than, less than, or the same number of objects in a set using matching and counting strategies (PK.CC.5).  Comparing concrete sets leads to comparing quantities and abstract numbers.  Children will also focus on identifying first and last in quantities up to 5 and 10 in different configurations (PK.CC.6).

Students will begin to think about probability by considering how likely it is that their house will be struck by lightning. They will consider the relative likelihood of familiar events (e.g., outdoor temperature, test scores) on the continuum between impossible and certain. Students will discuss where on the continuum "likely," "unlikely," and "equally likely as unlikely" areGoals and Learning ObjectivesThink about the concept of likelihood.Understand that probability is a measure of likelihood.Informally estimate the likelihood of certain events.Begin to think about why one event is more likely than another.SWD: Students with disabilities may need additional support seeing the relationships among problems and strategies. Throughout this unit, keep anchor charts available and visible to assist them in making connections and working toward mastery. Provide explicit think alouds comparing strategies and making connections. In addition, ask probing questions to get students to articulate how a peer solved the problem or how one strategy or visual representation is connected or related to another.

Learn about the dynamic relationships between a jet engine's heat loss, surface area, and volume in this video adapted from Annenberg Learner's Learning Math: Patterns, Functions, and Algebra.

Students learn about the concept of pushing, as well as the relationship between force and mass. Students practice measurement skills using pan scales and rulers to make predictions about mass and distance. A LEGO MINDSTORMS(TM) NXT robot is used to test their hypotheses. By the end of the activity, students have a better understanding of robotics, mass and friction and the concept of predicting.

This video lesson presents a real world problem that can be solved by using the Pythagorean theorem. The problem faces a juice seller daily. He has equilateral barrels with equal heights and he always tries to empty the juice of two barrels into a third barrel that has a volume equal to the sum of the volumes of the two barrels. This juice seller wants to find a simple way to help him select the right barrel without wasting time, and without any calculations - since he is ignorant of Mathematics. The prerequisite for this lesson includes knowledge of the following: the Pythagorean theorem; calculation of a triangles area knowing the angle between its two sides; cosine rule; calculation of a circle's area; and calculation of the areas and volumes of solids with regular bases.

How is psychology influenced by the digitalization of almost everything? What can frequent digital measurements and novel statistical techniques mean for 21st century psychology?

In this tutorial students conduct both an N=1 time-series case study and experiment, measuring some aspects of their daily life, such as mood, food intake, social activities, exercise, attention, alertness, sleep, or anything else they like. The experiment will result in (1) a linear graph depicting the effect of the chosen intervention through time and (2) a network depicting relationships between the chosen variables through time.

With this personal case study and experiment students get some insights into the new possibilities of frequently repeated measurements for studying (individual) human behavior.

The topic of this video is energy in general, and specifically the ways we can quantify it. In order to make the concepts accessible to a broad audience, this video focuses on everyday things and events. How is it that energy plays a part in a child riding a scooter? How is the energy we consume in playing related to the energy on the food we eat? This video poses these questions to the class and challenges them to put a list of five such items into an ordering from most energy to least.

In this video from Cyberchase, the CyberSquad figures out how fast their broom must go so they can reach Motherboard before Wicked.

An important consideration when sampling from a population is that of random error (also known as sampling error), which results from chance variation in the members of any sample taken from a larger population. Random error may affect the conclusions you draw from a study by affecting the precision of a descriptive study, or the power of an analytic study. However, although the magnitude of random error can be quantified to some degree, its direction cannot be predicted due to its random nature. Random errors can be accounted for to some degree through the application of inferential statistics when presenting and interpreting results.

In this video segment from Cyberchase, the CyberSquad learns how to read a thermometer as they try to keep their chocolate sculpture from melting.

This short video and interactive assessment activity is designed to teach fourth graders about reading the compound units in pounds and ounces.

Students will use their knowledge of operations and estimation to solve real world problems.

Students practice human-centered design by imagining, designing and prototyping a product to improve classroom accessibility for the visually impaired. To begin, they wear low-vision simulation goggles (or blindfolds) and walk with canes to navigate through a classroom in order to experience what it feels like to be visually impaired. Student teams follow the steps of the engineering design process to formulate their ideas, draw them by hand and using free, online Tinkercad software, and then 3D-print (or construct with foam core board and hot glue) a 1:20-scale model of the classroom that includes the product idea and selected furniture items. Teams use a morphological chart and an evaluation matrix to quantitatively compare and evaluate possible design solutions, narrowing their ideas into one final solution to pursue. To conclude, teams make posters that summarize their projects.