This is the second version of a task asking students to find the areas of triangles that have the same base and height. This presentation is more abstract as students are not using physical models.

The purpose of this task is to provide an opportunity for students to reason about equivalence of equations. The instruction to give reasons that do not depend on solving the equation is intended to focus attention on the transformation of equations as a deductive step.

This real world word problem requires students to figure out the scale ratio and unit rate.

Last year the Siuslaw 97J School District changed our food service operation from a national supplier (Chartwell’s) to in-house food service. Our Food Service Manager instituted an organic philosophy and wanted to source local produce. Utilizing our school garden program we now help supply fresh produce for our Siuslaw Elementary School cafeteria. Crop production is stronger in the 4/5 wing because of wind protection from the building. Florence experiences high winds and we are located close to the beach so we have constant sand blowing into our crops. The K-3 garden beds do not have the same protection as the 4/5 beds, and as a result have a lower yield. Our goal is to have students design and engineer wind barriers for these beds and then present the best solutions to our school board so that we can get funding to implement our ideas. This project can be used in any school with a garden by using preexisting barriers on a the school property. The unique environment of the school would dictate the lessons required to be adapted to fit the environmental needs of the community. If the school is lacking a garden, the students can focus on an at home garden project.

The task provides an opportunity for students to engage in Mathematical Practice Standard 4: Model with mathematics.

The purpose of this task is to give students experience in using simulation to determine if observed results are consistent with a given model (in this case, the Ňjust guessingÓ model). Part (i) also addresses the role of random assignment in the design of an experiment and assesses understanding of this concept.

This task involves two aspects of statistical reasoning: providing a probabilistic model for the situation at hand, and defining a way to collect data to determine whether or not the observed data is reasonably likely to occur under the chosen model. When guessing between two choices, there is no reason to suspect that one outcome is more likely than the other. Thus, a model that assumes the two outcomes to be equally likely (such as flipping a coin) is appropriate.

This task is an example of applying geometric methods to solve design problems and satisfy physical constraints. This task models a satellite orbiting the earth in communication with two control stations located miles apart on earthsŐ surface.

The context of this task is a familiar one: a cold beverage warms once it is taken out of the refrigerator. Rather than giving the explicit function governing this warmth, a graph is presented along with the general form of the function. Students must then interpret the graph in order to understand more specific details regarding the function.

In this challenging instructional task students relate addition and subtraction problems to money and to situations and goals related to saving money.

This word problem may be used for instructional or assessment purposes, depending on where students are in their understanding of addition and how the teacher supports them.

In this task students use ratio and rate reasoning to solve the real-world problem of placing a security camara in a shop.

The purpose of this task is to identify the structure in the two algebraic expressions by interpreting them in terms of a geometric context. Students will have likely seen this type of process before, so the principal source of challenge in this task is to encourage a multitude and variety of approaches, both in terms of the geometric argument and in terms of the algebraic manipulation.

The purpose of this task is to help students see that 4_(9+2) is four times as big as (9+2). Though this task may seem very simple, it provides students and teachers with a very useful visual for interpreting an expression without evaluating it.

Our school, Kelly Middle School, is one of the oldest middle school buildings in 4J (primary construction was completed in 1945). Each year we practice earthquake drills. Why? Why should we be concerned about earthquakes? Where might an earthquake occur in the northwest area? Might it be minor or violent? How might this be measured? Is an earthquake a singular event, or a series of events? What increases or decreases an earthquake hazard? Do we have any early-warning systems? Is the school earthquake drill correct? Considering these questions students need to develop an understanding of how to prepare for, and react to an earthquake event. When students are comfortably informed, who should they report to?

There are a couple of ways to solve this real world word problem.

This task is a modeling problem which ties in to financial decisions faced routinely by businesses, namely the balance between maintaining inventory and raising short-term capital for investment or re-investment in developing the busines

Dope the semiconductor to create a diode. Watch the electrons change position and energy.

This modeling task involves several different types of geometric knowledge and problem-solving: finding areas of sectors of circles (G-C.5), using trigonometric ratios to solve right triangles (G-SRT.8), and decomposing a complicated figure involving multiple circular arcs into parts whose areas can be found (MP.7).