Set up a 4 corners activity.. Hand out shape pattern cards to all students. For 30 seconds each corner does an exercise corresponding to their first shape, then they will change depending on their second, third, and fourth shape... then they switch through the circuit until they have completed their pattern. They will go through the pattern  2 times. 

In this game activity students practice comparing shapes and naming something that is alike or different about them.

This video is part of the Learn and Grow with WHRO TV series. Watch Carolyn Harris teach about sorting shapes according to one or two attributes.

Create your own shapes using colorful blocks and explore the relationship between perimeter and area. Compare the area and perimeter of two shapes side-by-side. Challenge yourself in the game screen to build shapes or find the area of funky figures. The PDF from VDOE was added to create an activity which reviews area and perimeter of triangles and rectangles on paper prior to delving into the fun, interactive activity.

Students learn about isometric drawings and practice sketching on triangle-dot paper the shapes they make using multiple simple cubes. They also learn how to use coded plans to envision objects and draw them on triangle-dot paper. A PowerPoint® presentation, worksheet and triangle-dot (isometric) paper printout are provided. This activity is part of a multi-activity series towards improving spatial visualization skills.

This challenging problem and brainteaser gives first graders an opportunity to compose and decompose squares.

This hands-on activity shows you how to build basic architectural shapes out of toothpicks and gumdrops. Learners explore how different shapes are more stable than others, and are introduced to ideas about "stretching and squashing"--that is, about tension and compression.

This task presents students with some creative geometric ways to represent the fraction one half. The goal is both to appeal to students' visual intuition while also providing a hands on activity to decide whether or not two areas are equal.

In Unit 5, students explore concepts of perimeter and geometry. Students have gradually built their understanding of geometric concepts since Kindergarten, when students learn to name shapes regardless of size and orientation. They also learn to distinguish between flat and solid shapes. In Grade 1, students’ understanding grows more nuanced, as they learn to distinguish between defining and non-defining attributes, as well as compose and decompose both flat and solid shapes. In Grade 2, students draw and identify shapes with specific attributes. All of this understanding gets them ready for Grade 3, in which students begin their journey of measuring those attributes, including area (addressed in Unit 4), and perimeter (explored here), as well as classification of shapes based on attributes into one or more categories.

Students begin the unit by defining perimeter as the boundary of a two-dimensional shape and measure it by finding its length. For a polygon, the length of the perimeter is the sum of the lengths of the sides. They develop their understanding of perimeter by measuring it with a ruler, finding it when all side lengths are labeled, and then finding it when some information about the length of a shape’s side lengths needs to be deduced, such as when a rectangle only has its length and width labeled. Students then solve real-world and mathematical problems, both given a figure and without one, involving perimeters of polygons (3.MD.8). With this understanding of perimeter, they are able to compare the measurement of area and perimeter of a rectangle, seeing that a rectangle with a certain area can have a variety of perimeters and, conversely, a rectangle with a certain perimeter can have a variety of areas, connecting the additional cluster content of perimeter to the major cluster content of area. Students then solve various problems involving area and perimeter. The last topic of the unit explores geometry. Students build on Grade 2 ideas about polygons and their properties, specifically developing and expanding their knowledge of quadrilaterals. They explore the attributes of quadrilaterals and classify examples into various categories (3.G.1), then explore attributes of polygons and classify examples into various categories, now including quadrilaterals. Students also draw polygons based on their attributes. Students next use tetrominoes and tangrams to compose and decompose shapes.

In this unit, students reason abstractly and quantitatively, translating back and forth between figures and equations in the context of perimeter problems (MP.2). Students will also construct viable arguments and critique the reasoning of others as they develop a nuanced understanding of the difference between area and perimeter, as well as when they classify shapes according to their attributes and justify their rationale (MP.3). Lastly, students will use appropriate tools strategically by using rulers to measure the side lengths of polygons to find their perimeter, as well as use rulers and right angle templates to find attributes of shapes to determine their classification (MP.5).

Unit 4 in Grade 4 introduces students to the more abstract geometric concepts of points, lines, line segments, rays, and angles. Students learn to measure angles and then use this skill to classify shapes based on their angle measure, a geometric property. Students also develop an understanding of reflectional symmetry, identifying line-symmetric shapes and drawing their lines of symmetry.

This unit builds on lots of work in prior grades with shape recognition and categorization (1.G.1, 2.G.1, 3.G.1). In order to differentiate a square from a rhombus, students must attend to the angle measure of the corners, or vertices. Thus, this unit introduces students to the vocabulary that will allow them to talk about angle measure as an attribute of plane figures (both polygons and more abstract figures, such as sets of intersecting lines), as well as the measurement system used to quantify angle measure precisely.

The unit begins with students drawing points, lines, line segments, rays, and angles, and continues to general classifications based on angles, including distinguishing between right, obtuse, acute, and straight angles as well as parallel, perpendicular, and intersecting lines. Then, students develop a more precise idea of angles as geometric figures that can be measured, and learn to do so. Students also learn to think of angles not just as objects but as actions—they can indicate a turn or change in direction. Students also see that angles are additive, just like other geometric measures they’ve explored in prior grades, such as length in Grade 2 (2.MD.1—6) and area in Grade 3 (3.MD.5—7). Next, students use their deepened understanding of angles to classify and draw triangles according to their angle measure (right, obtuse, and acute) as well as side length (equilateral, isosceles, and scalene) and quadrilaterals according to the parallel and/or perpendicular nature of their sides. Lastly, students explore lines of symmetry, finding and drawing them in figures.

This unit allows for particular focus on MP.2, MP.5 and MP.6. For example, when students are “shown two sets of shapes and asked where a new shape belongs,” they are reasoning abstractly and quantitatively (MP.2) (G Progression, p. 16). Students also learn to use a new tool, the protractor, precisely, ensuring they line up the vertex and base correctly and read the angle measure carefully (MP.5, MP.6).

This work continues to formalize much of the work students have already done in understanding geometric figures, which will continue to formalize in coming years. This unit prepares students to hierarchically classify two-dimensional figures in Grade 5 (5.G.3, 5.G.4). It also introduces students to drawing geometric figures, which they will see again in Grade 7 (7.G.1—3) and even high school Geometry and the trigonometric aspects of Algebra II. Thus, while all of the standards addressed in the unit are additional cluster standards, they lay an important foundation for geometric work in years to come.

Note: This lesson was designed for students with autism. The students will review a few elements of art, specifically colors, shapes, and different types of lines. They will identify these elements in Vincent van Gogh's painting Irises. The students will then practice drawing different types of lines and shapes in different colors, and will use these elements of art to produce an original crayon-resist piece inspired by Irises.

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.

This instructional task gives students a hands-on experience with composing and decomposing geometric figures.

Video Description:  Discover how NASA's Earth-observing satellites gather data to monitor food growth. Dr. Inbal Becker-Reshef describes how mathematics is used to interpret satellite data and describe vegetation and crop yield. Dr. Hannah Kerner shares how algorithms and models use NASA data to describe and predict food supply and food shortages. This work through NASA Harvest provides tools for farmers and governments to describe and predict food security worldwide. Video Length:  2:09.NASA eClipsTM is a suite of online student-centered, standards-based resources that support instruction by increasing STEM literacy in formal and nonformal settings.  These free digital and downloadable resources inform and engage students through NASA-inspired, real-world connections.NASA eClips Real World segments (grades 6-8) connect classroom mathematics to 21st Century careers and innovations.  They are designed for students to develop an appreciation for mathematics through real-world problem solving.

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 lesson begins by introducing Olympics as the unit theme. The purpose of this lesson is to introduce students to the techniques of engineering problem solving. Specific techniques covered in the lesson include brainstorming and the engineering design process. The importance of thinking out of the box is also stressed to show that while some tasks seem impossible, they can be done. This introduction includes a discussion of the engineering required to build grand, often complex, Olympic event centers.

This challenging problem and brainteaser gives students an opportunity to compose and decompose polygons to make rectangles.

Using shapes to make animals, students will graph the colors used in their animals to practice collecting data and analyzing graphs. 

Students apply several methods developed to identify and interpret patterns to the identification of fingerprints. They look at their classmates' fingerprints, snowflakes, and "spectral fingerprints" of elements. They learn to identify each image as unique, yet part of a group containing recognizable similarities.