In this real world problem students solve questions based on the relationship between production costs and price.
Students use their senses to describe what the weather is doing and predict what it might do next. After gaining a basic understanding of weather patterns, students act as state park engineers and design/build "backyard weather stations" to gather data to make actual weather forecasts.
This task provides a real world context for interpreting and solving exponential equations. There are two solutions provided for part (a). The first solution demonstrates how to deduce the conclusion by thinking in terms of the functions and their rates of change. The second approach illustrates a rigorous algebraic demonstration that the two populations can never be equal.
This series of word problems requires students to apply the concepts of factors and common factors in a context.
This word problem requires students to use fractions to solve it.
The purpose of this activity is to bring together the students' knowledge of engineering and airplanes and the creation of a glider model to determine how each modification affects the flight. The students will use a design procedure whereby one variable is changed and all the others are kept constant.
The purpose of this task is to provide students with a multi-step problem involving volume and to give them a chance to discuss the difference between exact calculations and their meaning in a context.
The purpose of this task is to provide students with a concrete situation they can model by dividing a whole number by a unit fraction.
This real world task requires students to answer questions about equations for calculating compound interest.
This task asks students to use similarity to solve a problem in a context that will be familiar to many, though most students are accustomed to using intuition rather than geometric reasoning to set up the shot.
The purpose of this task is to help students understand what is meant by a base and its corresponding height in a triangle and to be able to correctly identify all three base-height pairs.
This task could be put to good use in an instructional sequence designed to develop knowledge related to students' understanding of linear functions in contexts. Though students could work independently on the task, collaboration with peers is more likely to result in the exploration of a range of interpretations.
This task involves a fairly straightforward decaying exponential. Filling out the table and developing the general formula is complicated only by the need to work with a fraction that requires decisions about rounding and precision.
This task describes two linear functions using two different representations. To draw conclusions about the quantities, students have to find a common way of describing them. We have presented three solutions (1) Finding equations for both functions. (2) Using tables of values. (3) Using graphs.
Using gumdrops and toothpicks, students conduct a large-group, interactive ozone depletion model. Students explore the dynamic and competing upper atmospheric roles of the protective ozone layer, the sun's UV radiation and harmful human-made CFCs (chlorofluorocarbons).
In this activity, students learn about their heart rate and different ways it can be measured. Students construct a simple measurement device using clay and a toothpick, and then use this device to measure their heart rate under different circumstances (i.e., sitting, standing and jumping). Students make predictions and record data on a worksheet.
Students learn about material properties, and that engineers must consider many different materials properties when designing. This activity focuses on strength-to-weight ratios and how sometimes the strongest material is not always the best material.
Climate change is an urgent problem. Because it is causing new weather extremes and fatal catastrophes, climate change is better termed climate disruption. Bending the curve to flatten the upward trajectory of pollution emissions responsible for climate disruption is essential in order to protect billions of people from this global threat. Education is a key part of the solution.
Students toss coins to determine what traits a set of mouse parents possess, such as fur color, body size, heat tolerance, and running speed. Then they use coin tossing to determine the traits a mouse pup born to these parents possesses. Then they compare these physical features to features that would be most adaptive in several different environmental conditions. Finally, students consider what would happen to the mouse offspring if those environmental conditions were to change: which mice would be most likely to survive and produce the next generation?
This task presents a simple but mathematically interesting game whose solution is a challenging exercise in creating and reasoning with algebraic inequalities. The core of the task involves converting a verbal statement into a mathematical inequality in a context in which the inequality is not obviously presented, and then repeatedly using the inequality to deduce information about the structure of the game.