This lesson unit is intended to help assess how well students are able to interpret and use scale drawings to plan a garden layout. This involves using proportional reasoning and metric units.
This lesson unit is intended to help you assess how well students are able to use geometric properties to solve problems. In particular, it will support you in identifying and helping students who have the following difficulties: Solving problems relating to using the measures of the interior angles of polygons; and solving problems relating to using the measures of the exterior angles of polygons.
This lesson unit is intended to help you assess how well students are able to: recognize and use common 2D representations of 3D objects and identify and use the appropriate formula for finding the circumference of a circle.
This lesson unit is intended to help you assess how well students are able to: solve simple problems involving ratio and direct proportion; choose an appropriate sampling method; and collect discrete data and record them using a frequency table.
This task was developed by high school and postsecondary mathematics and design/pre-construction educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.
This lesson unit is intended to help you assess how well students are able to: Model a situation; make sensible, realistic assumptions and estimates; and use assumptions and estimates to create a chain of reasoning, in order to solve a practical problem.
This lesson unit is intended to help you assess how well students are able to: Interpret a situation and represent the variables mathematically; select appropriate mathematical methods to use; explore the effects on the area of a rectangle of systematically varying the dimensions whilst keeping the perimeter constant; interpret and evaluate the data generated and identify the optimum case; and communicate their reasoning clearly.
During this problem-based blended learning module students will be designing their dream bedroom as well as creating a scale drawing of the items they chose to be in their bedroom. The launch activity introduces the students to Scale City, which is a video that explores scale models in the real world. Students are then given dimensions for a fictional bedroom to furnish with items of their choosing. Price is not considered in this module, but a budget could be introduced as an extension of the module. Students will then spend time researching items that they would want to place in their bedroom with the area constraints given. Students will have the opportunity to provide each other peer feedback on their bedroom designs. Once students have a rough idea of their bedroom design, they will spend some time creating a scale drawing of their bedroom on graph paper. This will give students the opportunity to use a scale factor to create a scale drawing. Students will again be provided feedback on their designs and be given time to reflect and redesign as needed. If students need extra time to practice using a scale factor and creating scale models, a station rotation lesson has been included as an optional resource.
Students will join the buildings together to form a city with streets and sidewalks running between the buildings. Student groups will make their presentations, provide feedback to other students’ presentations, and get evaluated on their listening skills.Key ConceptsIn this culminating event, students present their project plan and solution to the class. The presentation allows students to explain their problem-solving plan, communicate their reasoning, and construct a viable argument about a mathematical problem.Students also listen to other project presentations and provide feedback to the presenters. Listeners have the opportunity to critique the mathematical reasoning of others.GoalsPresent projects and demonstrate understanding of the unit concepts.Clarify any misconceptions or difficult areas from the Final Assessment.Give feedback on other project presentations.Exhibit good listening skills.Review the concepts from the unit.
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.
Spatial visualization is the study of two- and three-dimensional objects and the practice of mental manipulation of objects. Spatial visualization skills are important in a range of subjects and activities like mathematics, physics, engineering, art and sports! In this lesson, students are introduced to the concept of spatial visualization and measure their spatial visualization skills by taking the provided 12-question quiz. Following the lesson, students complete the four associated spatial visualization activities and then re-take the quiz to see how much their spatial visualization skills have improved.
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 aspects of the task and its potential use.
Accuracy of measurement in navigation depends very much on the situation. If a sailor's target is an island 200 km wide, sailing off center by 10 or 20 km is not a major problem. But, if the island were only 1 km wide, it would be missed if off just the smallest bit. Many of the measurements made while navigating involve angles, and a small error in the angle can translate to a much larger error in position when traveling long distances.
Students will explore scale and use it to find measurements in scale drawings.Key ConceptsScale drawings are drawn proportionally so that there is a ratio between a given length on the drawing and the actual length. This ratio is used to set up a proportion to find other measurements.GoalsUnderstand that scale drawings are proportional.Use scale to find actual measurements.ELL: Define these terms in the context of the discussion:scalescale drawingscaled to fitproportionalAllow ELLs to use the dictionary if they wish.
The evil Scaleo has escaped from prison and is transforming the length, width, and height of objects until they become useless – or dangerous. Who can put things right? Superheroine Scale Ella uses the power of scale factor to foil the villain.
Acting as if they are biomedical engineers, students design and print 3D prototypes of pressure sensors that measure the pressure of the eyes of people diagnosed with glaucoma. After completing the tasks within the associated lesson, students conduct research on pressure gauges, apply their understanding of radio-frequency identification (RFID) technology and its components, iterate their designs to make improvements, and use 3D software to design and print 3D prototypes. After successful 3D printing, teams present their models to their peers. If a 3D printer is not available, use alternate fabrication materials such as modeling clay, or end the activity once the designs are complete.
Students learn how to identify the major features in a topographical map. They learn that maps come in a variety of forms: city maps, road maps, nautical maps, topographical maps, and many others. Map features reflect the intended use. For example, a state map shows cities, major roads, national parks, county lines, etc. A city map shows streets and major landmarks for that city, such as hospitals and parks. Topographical maps help navigate the wilderness by showing the elevation, mountains, peaks, rivers and trails.
Students follow the steps of the engineering design process while learning more about assistive devices and biomedical engineering applied to basic structural engineering concepts. Their engineering challenge is to design, build and test small-scale portable wheelchair ramp prototypes for fictional clients. They identify suitable materials and demonstrate two methods of representing design solutions (scale drawings and simple models or classroom prototypes). Students test the ramp prototypes using a weighted bucket; successful prototypes meet all the student-generated design requirements, including support of a predetermined weight.
The purpose of this task is for students to translate between measurements given in a scale drawing and the corresponding measurements of the object represented by the scale drawing.
Students use bearing measurements to triangulate and determine objects' locations. Working in teams of two or three, they must put on their investigative hats as they take bearing measurements to specified landmarks in their classroom (or other rooms in the school) from a "mystery location." With the extension activity, students are challenged with creating their own maps of the classroom or other school location and comparing them with their classmates' efforts.