This is a task from the Illustrative Mathematics website that is one …
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Below is a picture of the (elliptical) orbit of a planet around the sun: The sun is at point $A$, point $P$ is where the planet is closest to the sun d...
Natural Resources Biometrics begins with a review of descriptive statistics, estimation, and …
Natural Resources Biometrics begins with a review of descriptive statistics, estimation, and hypothesis testing. The following chapters cover one- and two-way analysis of variance (ANOVA), including multiple comparison methods and interaction assessment, with a strong emphasis on application and interpretation. Simple and multiple linear regressions in a natural resource setting are covered in the next chapters, focusing on correlation, model fitting, residual analysis, and confidence and prediction intervals. The final chapters cover growth and yield models, volume and biomass equations, site index curves, competition indices, importance values, and measures of species diversity, association, and community similarity.
Students work in teams to design a tabletop supply organizer inspired by …
Students work in teams to design a tabletop supply organizer inspired by the natural home of an insect species. Their prototype stores the group’s classroom supplies (scissors, crayon boxes, pencils, and glue sticks). In addition to following measurement constraints that apply to their prototype, students must design their supply organizer with the idea that supplies must be easily retrievable and the organizer must be sturdy enough to withstand everyday classroom wear and tear. Students test their prototype in the classroom for a period of 5 days and evaluate its effectiveness.
In this lesson, students will learn that math is important in navigation …
In this lesson, students will learn that math is important in navigation and engineering. Ancient land and sea navigators started with the most basic of navigation equations (Speed x Time = Distance). Today, navigational satellites use equations that take into account the relative effects of space and time. However, even these high-tech wonders cannot be built without pure and simple math concepts basic geometry and trigonometry that have been used for thousands of years. In this lesson, these basic concepts are discussed and illustrated in the associated activities.
This task applies geometric concepts, namely properties of tangents to circles and …
This task applies geometric concepts, namely properties of tangents to circles and of right triangles, in a modeling situation. The key geometric point in this task is to recognize that the line of sight from the mountain top towards the horizon is tangent to the earth. We can then use a right triangle where one leg is tangent to a circle and the other leg is the radius of the circle to investigate this situation.
Students find the volume and surface area of a rectangular box (e.g., …
Students find the volume and surface area of a rectangular box (e.g., a cereal box), and then figure out how to convert that box into a new, cubical box having the same volume as the original. As they construct the new, cube-shaped box from the original box material, students discover that the cubical box has less surface area than the original, and thus, a cube is a more efficient way to package things.
Students learn about two-axis rotations, and specifically how to rotate objects both …
Students learn about two-axis rotations, and specifically how to rotate objects both physically and mentally about two axes. A two-axis rotation is a rotation of an object about a combination of x, y or z-axes, as opposed to a single-axis rotation, which is about a single x, y or z-axis. Students practice drawing two-axis rotations through an exercise using simple cube blocks to create shapes, and then drawing on triangle-dot paper the shapes from various x-, y- and z-axis rotation perspectives. They use the right-hand rule to explore the rotations of objects. A worksheet is provided. This activity is part of a multi-activity series towards improving spatial visualization skills. At activity end, students re-take the 12-question quiz they took in the associated lesson (before conducting four associated activities) to measure how their spatial visualizations skills improved.
The coffee cooling experiment is a popular example of an exponential model …
The coffee cooling experiment is a popular example of an exponential model with immediate appeal. The model is realistic and provides a good context for students to practice work with exponential equations.
This number after bingo activity increases student flexibility with the number sequence …
This number after bingo activity increases student flexibility with the number sequence and their ability to start counting sequences at various points.
This lesson discusses how to identify sets of numbers as natural numbers, …
This lesson discusses how to identify sets of numbers as natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers.
This site teaches Quantities to High Schoolers through a series of 116 …
This site teaches Quantities to High Schoolers through a series of 116 questions and interactive activities aligned to 4 Common Core mathematics skills.
This site teaches The Complex Number System to High Schoolers through a …
This site teaches The Complex Number System to High Schoolers through a series of 2195 questions and interactive activities aligned to 16 Common Core mathematics skills.
This site teaches The Real Number System to High Schoolers through a …
This site teaches The Real Number System to High Schoolers through a series of 1090 questions and interactive activities aligned to 8 Common Core mathematics skills.
This site teaches Vector and Matrix Quantities to High Schoolers through a …
This site teaches Vector and Matrix Quantities to High Schoolers through a series of 2195 questions and interactive activities aligned to 16 Common Core mathematics skills.
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