Cluster 1: Draw, construct, and describe geometrical figures and describe the relationships between them. (Additional Cluster)Archived

Students are asked to determine if given lengths will determine a triangle.

Type: Formative Assessment

Students are asked to draw a triangle with given side lengths, and explain if these conditions determine a unique triangle.

Type: Formative Assessment

Students are asked to draw a triangle given the lengths of two of its sides and the measure of a nonincluded angle and to decide if these conditions determine a unique triangle.

Type: Formative Assessment

Students are asked to draw a triangle given the measures of two sides and their included angle and to explain if these conditions determine a unique triangle.

Type: Formative Assessment

Students are asked to draw a triangle given the measures of two angles and their included side and to explain if these conditions determine a unique triangle.

Type: Formative Assessment

Students are asked to draw a triangle given the measures of two angles and a non-included side and to explain if these conditions determine a unique triangle.

Type: Formative Assessment

Students are asked to draw a triangle with given angle measures, and explain if these conditions determine a unique triangle.

Type: Formative Assessment

Students are asked to find the ratio of the area of an object in a scale drawing to its actual area and then relate this ratio to the scale factor in the drawing.

Type: Formative Assessment

Students are asked to find the length and area of an object when given a scale drawing of the object.

Type: Formative Assessment

Students are asked to sketch and describe the two-dimensional figures that result from slicing a square pyramid.

Type: Formative Assessment

Students are asked to sketch and describe two-dimensional figures that result from slicing a rectangular prism.

Type: Formative Assessment

Students are asked to reproduce a scale drawing using a different scale.

Type: Formative Assessment

Students are asked to sketch and describe the two-dimensional figures that result from slicing a cylinder.

Type: Formative Assessment

Students are asked to sketch and describe the two-dimensional figures that result from slicing a cone.

Type: Formative Assessment

In this lesson, you will find clip art and various illustrations of polygons, circles, ellipses, star polygons, and inscribed shapes.

Type: Image/Photograph

Students will create a proportional self portrait from a photo using a gridded drawing method and learn how a grid system can help accurately enlarge an image in a work of art. Students will use the mathematical concepts of scale, proportion and ratio, to complete their artwork.

Type: Lesson Plan

This set of geometry challenges focuses on creating a variety of polygons as students problem solve and think as they learn to code using block coding software.  Student will need to use their knowledge of the attributes of polygons and mathematical principals of geometry to accomplish the given challenges. The challenges start out fairly simple and move to more complex situations in which students can explore at their own pace or work as a team. Computer Science standards are seamlessly intertwined with the math standards while providing “Step it up!” and “Jump it up!” opportunities to increase rigor.

Type: Lesson Plan

This set of geometry challenges focuses on using area/perimeter as students problem solve and think as they learn to code using block coding software.  Student will need to use their knowledge of the attributes of polygons and mathematical principals of geometry to accomplish the given challenges. The challenges start out fairly simple and move to more complex situations in which students can explore at their own pace or work as a team. Computer Science standards are seamlessly intertwined with the math standards while providing “Step it up!” and “Jump it up!” opportunities to increase rigor.

Type: Lesson Plan

This set of geometry challenges focuses on scaled drawings and area as students problem solve and think as they learn to code using block coding software.  Student will need to use their knowledge of the attributes of polygons and mathematical principals of geometry to accomplish the given challenges. The challenges start out fairly simple and move to more complex situations in which students can explore at their own pace or work as a team. Computer Science standards are seamlessly intertwined with the math standards while providing “Step it up!” and “Jump it up!” opportunities to increase rigor.

Type: Lesson Plan

This set of geometry challenges focuses on creating a variety of polygons using the coordinate plane as students problem solve and think as they learn to code using block coding software.  Student will need to use their knowledge of the attributes of polygons and mathematical principals of geometry to accomplish the given challenges. The challenges start out fairly simple and move to more complex situations in which students can explore at their own pace or work as a team. Computer Science standards are seamlessly intertwined with the math standards while providing “Step it up!” and “Jump it up!” opportunities to increase rigor.

Type: Lesson Plan

In this lesson, students create a fish tank for a fish supply company for a future sales campaign. They will use scale drawings and proportions to design the perfect fish tank.

• First, students have to complete a ranking activity of items that will be included in their scale drawing along with three types of fish.
• Next, students will conduct a pH lab activity to gain knowledge about how pH levels will affect population and the ecosystem within the tank.
• Finally, students will adjust their item selection and re-engineer their tank drawing to support their findings and additional information provided by the client. Students must determine what objects would be beneficial to the living things that the students chose in relation to available space and pH balance.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

In this STEM design project, students will design and build a 3D model of an ecofriendly community in an existing ecosystem, taking into account the organisms that live there and applying their knowledge of the ecosystem and the needs of the organisms living in it to preserve the biodiversity there. Students will build a 3D model using their understanding of scale and size, create an electronic presentation, and write a summary of their findings.

Type: Lesson Plan

Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Students will use modeling clay to explore the cross sections that result from slicing a 3-dimensional figure.

Type: Lesson Plan

Objective: Students will create a detailed scale drawing. Context: Students have used tools to measure length, solve proportions, and interpret scale drawings. They will continue to use ratio and proportion in the study of similar figures, percent, and probability.

Type: Lesson Plan

This lesson provides students the opportunity of creating the floor plan of a stage for a future school play. The students will use scale ratio and proportions to find the size of scaled geometric shapes. Then, students will create a scale drawing of the objects required on the stage. Finally, students will reason and compute the size of the actual stage.

Type: Lesson Plan

This is the third lesson of the Unit, "Makeover, Home Edition."This lesson is designed to teach students how to put ideas into reality by creating and using scale drawings in the real world. In Part I (#48705) students determine backyard dimensions for fence installation. Part II (#48967) concentrates on inserting a pool and patio into this backyard. In Part III (#49025) students create a scale drawing of this backyard. Part IV (#49090) focuses on inserting a window and painting walls inside the house.

Type: Lesson Plan

Students use hands-on materials to understand that only certain combinations of lengths will create closed triangles.

Type: Lesson Plan

In this lesson, students will sketch, model, and describe cross-sections formed by a plane passing through a three-dimensional figures. Students will create a cube, right rectangular prism, and right rectangular pyramid using modeling clay or Play-doh, slice the model using parallel, perpendicular, and intersecting lines and describe the two-dimensional figure resulting from slicing the three-dimensional models.

Type: Lesson Plan

In this lesson, students will design two outdoor gardens, 1) a raised garden bed and 2) a ground level garden (traditional). Students will, with help of the teacher, till the ground with removal of ground cover, build border for garden, add soil, attach poles with string to create a life size graph all so they can grow tomatoes and plot the data easily in their survival journals.This is Part 2 of a 4-Part Project on Survival.

Type: Lesson Plan

In this lesson, students will investigate a contextual problem in which they will need to construct a 2-dimensional polygon, compute actual lengths and areas and then reproduce a scale drawing of the figure at a different scale. Students will also use the free application, GeoGebra (see download link under Suggested Technology) to help them design their parks.

Type: Lesson Plan

This MEA requires students to formulate a comparison-based solution to a problem involving finding the fastest driving routes from home to work considering different aspects. Students are provided the context of the problem, a request letter from a client asking them to provide a recommendation, and data relevant to the situation. Students utilize the data to create a defensible model solution to present to the client.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

In this lesson plan, students will observe and record the linear dimensions of similar figures, and then discover how the values of area and perimeter are related to the ratio of the linear dimensions of the figures.

Type: Lesson Plan

In this 2 part lesson, students will learn about scale drawings/models, scales, and scale factors culminating in an activity where they will produce an enlargement of an image they choose.

Type: Lesson Plan

Learn to use architectural scale drawings to build a new horse arena and solve problems involving scale drawings in this interactive tutorial. By the end, you should be able to calculate actual lengths using a scale and proportions.

Type: Original Student Tutorial

Did you know that altering computer code can increase 3D printing efficiency? Check it out!

Type: Perspectives Video: Professional/Enthusiast

Set sail with this math teacher as he explains how kites were used for lessons in the classroom.

Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set [.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth [.KML]

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Teaching Idea

Before the lesson, students attempt the Gold Rush task individually. You then look at their responses and formulate questions for students to think about as they review their work. At the start of the lesson, students reflect on their individual responses and use the questions posed to think of ways to improve their work. Next, students work collaboratively in small groups to produce, in the form of a poster, a better solution to the Gold Rush task than they did individually. In a whole-class discussion students compare and evaluate the different methods they used. Working in small groups, students analyze sample responses to the Gold Rush task, then, in a whole-class discussion, review the methods they have seen. Finally, students reflect on their work.

Type: Problem-Solving Task

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. If used in an instructional setting, it would be good for students to have an opportunity to see other solution methods, perhaps by having students with different approaches explain their strategies to the class. Students who can only solve this by first converting the linear measurements will have a hard time solving problems where only area measures are given.

Type: Problem-Solving Task

Students explore the formation of craters on the lunar surface using real world imaging data and mathematical reasoning. Students make observations and inferences about the time that impact craters were formed using probability and percentages.

Type: Problem-Solving Task

This web page features activities that compare the Great Pyramid to such modern structures as the Statue of Liberty and the Eiffel Tower. In the first activity, students use a template to construct a scale model of the Great Pyramid. They must find the scale heights for the tallest building in their neighborhood or for their height. In the remaining activity, students are given the dimensions for two other pyramids and challenged to create models.

Type: Teaching Idea

In this engineering task, students will apply concepts of volume to decide what they will need to take on a 2-1/2 year journey to Mars. Then plan how to fit everything into a 1-cubic-meter box, using only a measuring tape, pencil and paper, and math.

Type: Teaching Idea

This video discusses constructing a right isosceles triangle with given constraints and deciding if the triangle is unique.

Type: Tutorial

This video demonstrates drawing a triangle when the side lengths are given.

Type: Tutorial

In this lesson, students will be viewing a Khan Academy video that will show how to convert ratios using speed units.

Type: Tutorial

In this lesson (or series of lessons), students interpret and use scale drawings to plan a garden layout. Students start by producing their own layout and then work together to refine their garden design. The activity requires that students use short rules (rulers), meter rules (meter sticks), string, protractors, scissors, glue, card, plain paper, graph paper, and colored pencils. Students work individually for 20 minutes, engage in a 100-minute lesson (or two 50-minute lessons), and complete a 10-minute follow up lesson or homework.

Type: Unit/Lesson Sequence

This manipulative allows you to create shapes using colorful blocks to explore the relationship between perimeter and area. The game screen challenges you to build shapes or find the area of figures.

Type: Virtual Manipulative

With this online Java applet, students use slider bars to move a cross section of a cone, cylinder, prism, or pyramid. This activity allows students to explore conic sections and the 3-dimensional shapes from which they are derived. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Virtual Manipulative

Explore the effect on perimeter and area of two rectangular shapes as the scale factor changes.

Type: Virtual Manipulative