This problem is the fifth in a series of seven about ratios. In the first problem students define the simple ratios that exist among the three candidates. It opens an opportunity to introduce unit rates. The subsequent problems are more complex. In the second problem, students apply their understanding of ratios to combine two pools of voters to determine a new ratio. In the third problem, students apply a known ratio to a new, larger pool of voters to determine the number of votes that would be garnered.

This is the sixth problem in a series of seven that use the context of a classroom election. While it still deals with simple ratios and easily managed numbers, the mathematics surrounding the ratios are increasingly complex.

This is the last problem of seven in a series about ratios set in the context of a classroom election. Since the number of voters is not known, the problem is quite abstract and requires a deep understanding of ratios and their relationship to fractions.

This is the first and most basic problem in a series of seven problems, all set in the context of a classroom election. Every problem requires students to understand what ratios are and apply them in a context. The problems build in complexity and can be used to highlight the multiple ways that one can reason about a context involving ratios.

This is the second in a series of tasks that are set in the context of a classroom election. It requires students to understand what ratios are and apply them in a context. The simple version of this question just asked how many votes each gets. This has the extra step of asking for the difference between the votes.

This problem, the third in a series of tasks set in the context of a class election, is more than just a problem of computing the number of votes each person receives. In fact, that isnŐt enough information to solve the problem. One must know how many votes it takes to make one half of the total number of votes. Although the numbers are easy to work with, there are enough steps and enough things to keep track of to lift the problem above routine.

This is the fourth in a series of tasks about ratios set in the context of a classroom election. What makes this problem interesting is that the number of voters is not given. This information isnŐt necessary, but at first glance some students may believe it is.

As the standards in statistics and probability unfold, students will not yet know the rules of probability for compound events. Thus, simulation is used to find an approximate answer to these questions. In fact, part b would be a challenge to students who do know the rules of probability, further illustrating the power of simulation to provide relatively easy approximate answers to wide-ranging problems.

This task is meant to be a straight-forward assessment task of graph reading and interpreting skills. This task helps reinforce the idea that when a variable represents time, t=0 is chosen as an arbitrary point in time and positive times are interpreted as times that happen after that.

This problem asks the student to evaluate six numerical expressions that contain the same integers and operations yet have differing results due to placement of parentheses. It helps students see the purpose of using parentheses.

This problem asks the student to evaluate three numerical expressions that contain the same integers yet have differing results due to placement of parentheses.

Make waves with a dripping faucet, audio speaker, or laser! Add a second source or a pair of slits to create an interference pattern.

Watch a string vibrate in slow motion. Wiggle the end of the string and make waves, or adjust the frequency and amplitude of an oscillator. Adjust the damping and tension. The end can be fixed, loose, or open.

Learning Goals/Outcomes/Objectives:
Observable features of the student performance by the end of the grade: 1). Obtaining information: Students use books and other reliable media to gather information about: i. Climates in different regions of the world (e.g., equatorial, polar, coastal, mid-continental). ii. Variations in climates within different regions of the world (e.g., variations could include an area’s average temperatures and precipitation during various months over several years or an area’s average rainfall and temperatures during the rainy season over several years). 2 Evaluating information a Student's combine obtained information to provide evidence about the climate pattern in a region that can be used to make predictions about typical weather conditions in that region. 3 Communicating information a Students use the information they obtained and combined to describe*: i. Climates in different regions of the world. ii. Examples of how patterns in climate could be used to predict typical weather conditions. iii. That climate can vary over years in different regions of the world.

The principal purpose of the task is to explore a real-world application problem with algebra, working with units and maintaining reasonable levels of accuracy throughout.

These problems give students the opportunity to construct and compare linear, quadratic, and exponential models.

In this lesson, students will first participate in a chalk talk to elicit initial ideas about climate and Antarctica and the types of data scientists collect. Next, they will explore images of Antarctica and make initial noticings and wonderings about what they’re seeing. Students will be introduced to important vocabulary through matching terms to components or features of a satellite image. Finally, students will synthesize their initial ideas about how satellite imagery can help us understand climate change in Antarctica. This is the first lesson of a five-part curriculum about Antarctic physical environments and ecosystems.

When a division problem involving whole numbers does not result in a whole number quotient, it is important for students to be able to decide whether the context requires the result to be reported as a whole number with remainder or a mixed number.

The words compose and decompose are used to describe actions that young students learn as they acquire knowledge of small numbers by putting them together and taking them apart. This understanding is a bridge between counting and knowing number combinations. It is how instant recognition of small numbers develops and leads naturally to later understanding of fact families. This task helps them develop an understanding of number combinations.