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.

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.

Students develop an understanding of the concepts of "push" and "pull" as they "save" stuffed animals from danger using LEGO MINDSTORMS(TM) NXT robots. After learning more about the concepts through a robot demonstration, students explore the concepts themselves in the context of saving stuffed animala from the table edges. They choose to either push or pull the animal to safety, depending on the orientation of the robot and toy. They see the consequences of their choices, learning the importance of understanding these force concepts and the differences between them.

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

Students gain an understanding of the layers of the Earth by designing and building clay models.

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.

Students who are defiant or non-compliant can be among the most challenging to teach. They can frequently interrupt instruction, often do poorly academically, and may show little motivation to learn. There are no magic strategies for managing the behaviors of defiant students. However, research shows that certain techniques tend to work best with these children and youth: (1) Give the student positive teacher recognition. Even actions as simple as greeting the student daily at the classroom door or stopping by the student’s desk to ask ‘How are you doing?’ can over time turn strained relationships into positive ones. (2) Monitor the classroom frequently and intervene proactively to redirect off-task students before their mild misbehaviors escalate into more serious problems. (3) Avoid saying or doing things that are likely to anger or set off a student. Speak calmly and respectfully, for example, rather than raising your voice or using sarcasm. (4) When you must intervene with a misbehaving student, convey the message to the student that you will not tolerate the problem behavior—but that you continue to value and accept the student. (5) Remember that the ultimate goal of any disciplinary measure is to teach the student more positive ways of behaving. Punishment generally does not improve student behaviors over the long term and can have significant and lasting negative effects on school performance and motivation. (6) Develop a classroom ‘crisis response plan’ to be implemented in the event that one or more students display aggressive behaviors that threaten their own safety or the safety of others. Be sure that your administrator approves this classroom crisis plan and that everyone who has a part in the plan knows his or her role. One final thought: While you can never predict what behaviors your students might bring into your classroom, you will usually achieve the best outcomes by remaining calm, following pre-planned intervention strategies for misbehavior, and acting with consistency and fairness when intervening with or disciplining students.

Hyperactive students tend to have a very high energy level, act impulsively and can be behaviorally distracting. They may fidget, play with objects, tap pencils so loudly against their desk that kids from across the room look over at them, or blurt out answers to teacher questions before the instructor is even finished asking them. When working with students who are hyperactive or impulsive, teachers should keep in mind that these students are very often completely unaware that others view their behavior as distracting or annoying. Teachers working with such children can greatly increase their own effectiveness by clearly communicating behavioral expectations to students, by encouraging and rewarding students who behave appropriately, and by being consistent and fair when responding to problem student behaviors. Here are teacher ideas for managing impulsive or hyperactive students who display problem motor or verbal behaviors:

tudents who have chronic difficulties paying attention in class face the risk of poor grades and even school failure. Inattention may be a symptom of an underlying condition such as Attention Deficit Hyperactivity Disorder. However, teachers should not overlook other possible explanations for student off-task behavior. It may be, for example, that a student who does not seem to be paying attention is actually mismatched to instruction (the work is too hard or too easy) or preoccupied by anxious thoughts. Or the student may be off-task because the teacher's lesson was poorly planned or presented in a disorganized manner. It is also important to remember that even children with ADHD are influenced by factors in their classroom setting and that these students' level of attention is at least partly determined by the learning environment. Teachers who focus on making their instruction orderly, predictable, and highly motivating find that they can generally hold the attention of most of their students most of the time.

Students embark on a scavenger hunt around the school looking for indoor air pollution and mapping source locations.

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.

Students will be instructed to make an observation of a flower (tulip) given the one stipulation that they will only be allowed to detect the parts of the plant that are green. Through observation and discussion, students will be led to understand that only seeing parts of the flower leads to an incomplete and even inaccurate understanding of its structure.

Students will construct their own knowledge of the Sun emitting light above and below the visible spectrum by using UV beads to detect ultraviolet radiation coming from the Sun, and, in a second experiment, will record the temperature readings of thermometers placed in the visible and infrared region of a spectrum produced using a prism. An optional M&M Filter Activity is included in the lesson to demonstrate how filter work.