This short video and interactive assessment activity is designed to teach third graders about identifying and naming 3d figures.
This lesson unit is intended to help teachers assess how well students are able to identify and use geometrical knowledge to solve a problem. In particular, this unit aims to identify and help students who have difficulty in: making a mathematical model of a geometrical situation; drawing diagrams to help with solving a problem; identifying similar triangles and using their properties to solve problems; and tracking and reviewing strategic decisions when problem-solving.
This short video and interactive assessment activity is designed to give fifth graders an overview of squares and rectangles.
This unit is a multidisciplinary unit created for a high school math classroom, designed to combine statistics and hydrology. In this unit, students will learn about the water cycle and water budgets within the watershed. The unit starts with learning about basic budgeting in a watershed, comparable to financial budgeting, and expands to creating linear regressions based on the relationship between precipitation, discharge, and evapotranspiration in a watershed system. Students will be able to synthesize the information they learn about the watershed to learn about topics such as graphing points, lines, creating scatterplots, and creating linear regressions for the line of best fit. By teaching statistics through the lens of the watershed, the primary objective is to facilitate active, engaged learners who understand how math can be usefully applied to various contexts in the world around us while gaining a deeper appreciation for the water resources on Earth.
This was designed for a Geometry classroom, but could be modified for Pre-Algebra- Statistics based on student needs and interest level.
This unit consists of five lessons covering architecture and structural engineering. Each lesson includes goals, anticipatory set, learner objectives, guided practice, procedure instructions, closing activities, and extensions. Student handouts and worksheets are also included.
Lesson 1: Animal Structures
Lesson 2: Homes
Lesson 3: Stability
Lesson 4: Local Towers & Bridges
Lesson 5: Schools
NGSS: K-2-ETS1-1, K-2-ETS1-2, K-2-ETS1-3, 3-5-ETS1-1, 3-5-ETS1-2, 3-5-ETS1-3
Materials: blocks or other building toys, ruler, book or ball (for weight), graph paper, pencils, and floor plan of school or hand-drawn approximation featuring highlights.
An interactive applet and associated web page that demonstrate supplementary angles (two angles that add to 180 degrees.) The applet shows two angles which, while not adjacent, are drawn to strongly suggest visually that they add to a straight angle. Any point defining the angle scan be dragged, and as you do so, the other angle changes to remain supplementary to the one you change. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.
Playing the role of engineers in collaborations with the marketing and production teams in a chocolate factory, students design a container for a jumbo chocolate bar. The projects constraints mean the container has to be a regular trapezoidal prism. The design has to optimize the material used to construct the container; that is, students have to find the dimensions of the container with the maximum volume possible. After students come up with their design, teams present a final version of the product that includes creative branding and presentation. The problem-solving portion of this project requires students to find a mathematical process to express the multiple variables in the prism’s volume formula as a single variable cubic polynomial function. Students then use technology to determine the value for which this function has a maximum and, with this value, find the prism’s optimal dimensions.
This task presents a foundational result in geometry, presented with deliberately sparse guidance in order to allow a wide variety of approaches. Teachers should of course feel free to provide additional scaffolding to encourage solutions or thinking in one particular direction. We include three solutions which fall into two general approaches, one based on reference to previously-derived results (e.g., the Pythagorean Theorem), and another conducted in terms of the geometry of rigid transformations.
The construction of the tangent line to a circle from a point outside of the circle requires knowledge of a couple of facts about circles and triangles. First, students must know, for part (a), that a triangle inscribed in a circle with one side a diameter is a right triangle. This material is presented in the tasks ''Right triangles inscribed in circles I.'' For part (b) students must know that the tangent line to a circle at a point is characterized by meeting the radius of the circle at that point in a right angle: more about this can be found in ''Tangent lines and the radius of a circle.''
This short video and interactive assessment activity is designed to give fourth graders an overview of tessellations.
This short video and interactive assessment activity is designed to give fifth graders an overview of tessellations.
This short video and interactive assessment activity is designed to teach third graders an overview of tessellations.
This short video and interactive assessment activity is designed to teach third graders about determining unknown angles in composite figures.
This short video and interactive assessment activity is designed to teach fourth graders about determining unknown angles in composite figures.
ile patterns will be familiar with students both from working with geometry tiles and from the many tiles they encounter in the world. Here one of the most important examples of a tiling, with regular hexagons, is studied in detail. This provides students an opportunity to use what they know about the sum of the angles in a triangle and also the sum of angles which make a line.
This task aims at explaining why four regular octagons can be placed around a central square, applying student knowledge of triangles and sums of angles in both triangles and more general polygons.
This is a solver for problems involving the time value of money (TVM). It emulates the TVM solver on the TI-83+ and TI-84 graphing calculators. Updated 6 November 2011 to work correctly when I% = 0.
The purpose of this task is to engage students in geometric modeling, and in particular to deduce algebraic relationships between variables stemming from geometric constraints. The modelling process is a challenging one, and will likely elicit a variety of attempts from the students.
Students overlay USGS topographic maps into Google Earth’s satellite imagery. By analyzing Denali, a mountain in Alaska, they discover how to use map scales as ratios to navigate maps, and use rates to make sense of contour lines and elevation changes in an integrated GIS software program. Students also problem solve to find potential pathways up a mountain by calculating gradients.
An interactive applet and associated web page showing how to find the area and perimeter of a trapezoid from the coordinates of its vertices. The trapezoid can be either parallel to the axes or rotated. The grid and coordinates can be turned on and off. The area and perimeter calculation can be turned off to permit class exercises and then turned back on the verify the answers. The applet can be printed as it appears on the screen to make handouts. The web page has a full description of the method for determining area and perimeter, a worked example and has links to other pages relating to coordinate geometry. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.