Student teams locate a contaminant spill in a hypothetical site by measuring the pH of soil samples. Then they predict the direction of groundwater flow using mathematical modeling. They also use the engineering design process to come up with alternative treatments for the contaminated water.

Throughout this problem-based learning module students will address real world skills. Students will be asked to brainstorm ideas and think innovatively both independently and collaboratively in addressing a real-world problem that is relevant to their daily lives and surroundings.  Students/teams will be encouraged to use the internet for research purposes in their design phase. What components should be included for a modern, updated classroom? Students will utilize various online platforms to design an ideal, modern, 21st century “dream classroom”.  Students will incorporate components that would meet the needs of all learners and a classroom that would be able to integrate technology. These classrooms can be shared with relevant individuals in the community and others in the school building.

Students capture and examine air particles to gain an appreciation of how much dust, pollen and other particulate matter is present in the air around them. Students place "pollution detectors" at various locations to determine which places have a lot of particles in the air and which places do not have as many. Quantifying and describing these particles is a first step towards engineering methods of removing contaminants from the air.

Students use scaling from real-world data to obtain an idea of the immense size of Mars in relation to the Earth and the Moon, as well as the distances between them. Students calculate dimensions of the scaled versions of the planets, and then use balloons to represent their relative sizes and locations.

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.

This lesson is an introduction to scale copies for Math 7 students. This is a Desmos lesson. Some images and content were obtained from Open Up Resources: Download for free at openupresources.org. 

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.

Students learn about one-axis rotations, and specifically how to rotate objects both physically and mentally to understand the concept. They practice drawing one-axis rotations through a group exercise using cube blocks to create shapes and then drawing those shapes from various x-, y- and z-axis rotation perspectives on triangle-dot paper (isometric paper). They learn the right-hand rule to explore rotations of objects. A worksheet is provided. This activity is part of a multi-activity series towards improving spatial visualization skills.

In this activity, students design an innovative human shelter that is inspired and informed by an animal structure. Each group is assigned an animal class, and they gather information about shelters used by the animals in that class. After researching the topic and brainstorming ideas, students build small prototypes (models) of the structures. Finally, they present their products, explaining what attribute of the animal structure influenced their design.

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.

In this problem-based learning module, students will work collaboratively to improve the accessibility or safety of their school or community. For example, students could identify that accessibility ramps need to be added to the school property or additional sidewalks need to be created/repaired to increase the safety of students as they walk to school. Students would work together to create models of these improvements and create a communications plan that informs the stakeholders of the materials needed to create these improvements (i.e. using volume to determine the amount of concrete, using angles to determine measurements for ramps, etc..).

Four full-year digital course, built from the ground up and fully-aligned to the Common Core State Standards, for 7th grade Mathematics. Created using research-based approaches to teaching and learning, the Open Access Common Core Course for Mathematics is designed with student-centered learning in mind, including activities for students to develop valuable 21st century skills and academic mindset.

Zooming In On Figures

Unit Overview

Type of Unit: Concept; Project

Length of Unit: 18 days and 5 days for project

Prior Knowledge

Students should be able to:

Find the area of triangles and special quadrilaterals.
Use nets composed of triangles and rectangles in order to find the surface area of solids.
Find the volume of right rectangular prisms.
Solve proportions.

Lesson Flow

After an initial exploratory lesson that gets students thinking in general about geometry and its application in real-world contexts, the unit is divided into two concept development sections: the first focuses on two-dimensional (2-D) figures and measures, and the second looks at three-dimensional (3-D) figures and measures.
The first set of conceptual lessons looks at 2-D figures and area and length calculations. Students explore finding the area of polygons by deconstructing them into known figures. This exploration will lead to looking at regular polygons and deriving a general formula. The general formula for polygons leads to the formula for the area of a circle. Students will also investigate the ratio of circumference to diameter ( pi ). All of this will be applied toward looking at scale and the way that length and area are affected. All the lessons noted above will feature examples of real-world contexts.
The second set of conceptual development lessons focuses on 3-D figures and surface area and volume calculations. Students will revisit nets to arrive at a general formula for finding the surface area of any right prism. Students will extend their knowledge of area of polygons to surface area calculations as well as a general formula for the volume of any right prism. Students will explore the 3-D surface that results from a plane slicing through a rectangular prism or pyramid. Students will also explore 3-D figures composed of cubes, finding the surface area and volume by looking at 3-D views.
The unit ends with a unit examination and project presentations.

Students will resume their project and decide on dimensions for their buildings. They will use scale to calculate the dimensions and areas of their model buildings when full size. Students will also complete a Self Check in preparation for the Putting It Together lesson.Key ConceptsThe first part of the project is essentially a review of the unit so far. Students will find the area of a composite figure—either a polygon that can be broken down into known areas, or a regular polygon. Students will also draw the figure using scale and find actual lengths and areas.GoalsRedraw a scale drawing at a different scale.Find measurements using a scale drawing.Find the area of a composite figure.SWD: Consider what supplementary materials may benefit and support students with disabilities as they work on this project:Vocabulary resource(s) that students can reference as they work:List of formulas, with visual supports if appropriateClass summaries or lesson artifacts that help students to recall and apply newly introduced skillsChecklists of expectations and steps required to promote self-monitoring and engagementModels and examplesStudents with disabilities may take longer to develop a solid understanding of newly introduced skills and concepts. They may continue to require direct instruction and guided practice with the skills and concepts relating to finding area and creating and interpreting scale drawings. Check in with students to assess their understanding of newly introduced concepts and plan review and reinforcement of skills as needed.ELL: As academic vocabulary is reviewed, be sure to repeat it and allow students to repeat after you as needed. Consider writing the words as they are being reviewed. Allow enough time for ELLs to check their dictionaries if they wish.

Students further explore scale, taking a scale drawing floor plan and redrawing it at a different scale.Key ConceptsStudents explore change from one scale to another, focusing on the ratios. Students will draw a scale model of a house.GoalsRedraw a scale drawing at a different scale.Find measurements using a scale drawing.

Students are introduced to real-world applications of geometry and measurement by looking at architectural plans. Students also begin to get familiar with reading architectural plans and thinking about scale.Key ConceptsSince this lesson is exploratory, all of the mathematics discussed will be informal. However, most of the mathematics that students will see in the unit is introduced in this lesson. Students look at length, area, surface area, and volume and examine how these measurements pertain to architectural plans and determining building costs. Students will also consider scale and how scale is used in architectural plans and math drawings.GoalsThink about what measurements are needed to build a building.Think about what measurements determine the cost of a building.Think about how scale is used in math drawings.SWD: Check in to ensure that students understand the meaning of domain-specific vocabulary terms such as dimensions, scale, and area. You may also need to clarify the meaning of the word contract for some students.ELL: Consider having students compile a list or resource with key vocabulary terms for this unit.

Lesson OverviewStudent groups make their presentations, provide feedback on 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 project to the class.Give feedback on other project presentations.Exhibit good listening skills.Reflect on the problem-solving process.

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.

Students critique their work from the Self Check and redo the task after receiving feedback. Students then take a quiz to review the goals of the unit.Key ConceptsStudents understand how to find the area of figures such as rectangles and triangles. They have applied that knowledge to finding the area of composite figures and regular polygons. The area of regular polygons was extended to understand the area of a circle. Students also applied ratio and proportion to interpret scale drawings and redraw them at a different scale.GoalsCritique and revise student work.Apply skills learned in the unit.Understand two-dimensional measurements:Area of composite figures, including regular polygons.Area and circumference of circles.Interpret scale drawings and redraw them at a different scale.SWD: Make sure all students have the prerequisite skills for the activities in this lesson.Students should understand these domain-specific terms:composite figuresregular polygonsareacircumferencescale drawingstwo dimensionalIt may be helpful to preteach these terms to students with disabilities.ELL: As academic vocabulary is reviewed, be sure to repeat it and allow students to repeat after you as needed. Consider writing the words as they are being reviewed. Allow enough time for ELLs to check their dictionaries if they wish.

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.