The three tasks (including part 1 and part 3) in this set are not examples of tasks asking students to compute using the standard algorithms for multiplication and division because most people know what those kinds of problems look like. Instead, these tasks show what kinds of reasoning and estimation strategies students need to develop in order to support their algorithmic computations.

Students learn about soil properties and the effect biochar—charcoal used as a soil amendment—has on three soil types, sand, loam and clay. They test the soils’ water retention capability before and after the addition of biochar. During the activity, student teams prepare soil mixtures, make observations (including microscopic examinations), compare soil properties, conduct water retention tests, take and record measurements, and analyze their observations and data. They see how the physical properties of soils—color, texture, and particle size—can be indicators of nutrient content and water retention capabilities to support plant growth. From their findings, they consider biochar’s potential benefits for environmental and agricultural applications, especially in conditions of drought and depleted soils. An activity lab sheet is provided to guide experimental data collection and analysis.

Why do we care about air? Breathe in, breathe out, breathe in... most, if not all, humans do this automatically. Do we really know what is in the air we breathe? In this activity, students use M&M(TM) candies to create pie graphs that show their understanding of the composition of air. They discuss why knowing this information is important to engineers and how engineers use this information to improve technology to better care for our planet.

Students create and decode DNA for man’s best friend to observe how variations in DNA lead to the inheritance of different traits. Strips of paper that represent DNA are randomly selected and used to assemble the dog's DNA. Students read the DNA and create a drawing of their pet, and compare it with others in the class to check for similarities and differences.

COERLL has partnered with Rose Potter and Betsy Arnold to publish Recorridos-Don Quijote, a pair of openly-licensed books for the study of Cervantes’ Don Quijote in upper level Spanish courses, including AP. The student workbook, accessible online for free, deepens students’ understanding of the text through reading, pre-reading, and post-reading activities and glosses. The companion teacher support facilitates the teaching of Don Quijote through student-centered strategies and activities, historical and cultural information, quizzes, exams and more.

This tasks gives a verbal description for computing the perimeter of a rectangle and asks the students to find an expression for this perimeter. Students then have to use the expression to evaluate the perimeter for specific values of the two variables.

This task is a natural follow up for task Rectangle Perimeter 1. After thinking about and using one specific expression for the perimeter of a rectangle, students now extend their thinking to equivalent expressions for the same quantity.

The purpose of this task is to ask students to write expressions and to consider what it means for two expressions to be equivalent.

Students learn about material reuse by designing and building the strongest and tallest towers they can, using only recycled materials. They follow design constraints and build their towers to withstand earthquake and high wind simulations.

Students take advantage of the natural ability of red cabbage juice to perform as a pH indicator to test the pH of seven common household liquids. Then they evaluate the accuracy of the red cabbage indicator, by testing the pH of the liquids using an engineer-designed tool, pH indicator strips. Like environmental engineers working on water remediation or water treatment projects, understanding the chemical properties (including pH) of contaminants is important for safeguarding the health of environmental water sources and systems.

Building upon their understanding of forces and Newton's laws of motion, students learn about the force of friction, specifically with respect to cars. They explore the friction between tires and the road to learn how it affects the movement of cars while driving. In an associated literacy activity, students explore the theme of conflict in literature, and the difference between internal and external conflict, and various types of conflicts. Stories are used to discuss methods of managing and resolving conflict and interpersonal friction.

This lesson will start with a brief history of robotics and explain how robots are beneficial to science and society. The lesson then will explore how robots have been used in recent space exploration efforts. The engineering design of the two Mars rovers, Spirit and Opportunity, will be used as prime examples. Finally, the maneuverability of their robotic arms and the functionality of their tools will be discussed.

This task is written so that students have opportunities to use different strategies to determine whether a set has an even or odd number of objects.

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.

Through this lab, students are introduced to energy sciences as they explore redox reactions and how hydrogen fuel cells turn the energy released when hydrogen and oxygen are combined into electrical energy that can be read on a standard multimeter. They learn about the energy stored in bonds and how, by controlling the reaction, this energy can be turned into more or less useful forms.

This task is a reasonably straight-forward application of rigid motion geometry, with emphasis on ruler and straightedge constructions, and would be suitable for assessment purposes.

The goal of this task is to give students an opportunity to experiment with reflections of triangles on a coordinate grid. Students are not prompted in the question to list the coordinates of the different triangle vertices but this is a natural extension of the task.

The goal of this task is to give students experience applying and reasoning about reflections of geometric figures using their growing understanding of the properties of rigid motions. In the case of reflecting a rectangle over a diagonal, the reflected image is still a rectangle and it shares two vertices with the original rectangle.

This activity is one in a series of tasks using rigid transformations of the plane to explore symmetries of classes of triangles, with this task in particular focusing on the class of equilaterial triangles. In particular, the task has students link their intuitive notions of symmetries of a triangle with statements proving that the said triangle is unmoved by applying certain rigid transformations.

This task examines some of the properties of reflections of the plane which preserve an equilateral triangle: these were introduced in ''Reflections and Isosceles Triangles'' and ''Reflection and Equilateral Triangles I''. The task gives students a chance to see the impact of these reflections on an explicit object and to see that the reflections do not always commute.