In this lesson, students learn to sort shapes by comparing and contrasting the two-dimensional shapes that make up the fundamental three-dimensional shapes. At the end of this lesson, they are going to:
- sort blocks by attributes.
- draw outlines of three-dimensional objects' faces.
- determine and address figures and shapes that exist in the real world.
- make three-dimensional forms with clay or Play-Doh.
- contrast two- and three-dimensional shapes.

- How are spatial relationships, such as shape and dimension, used to draw, build, model, and represent real-world situations or solve problems?
- How do geometric properties and theorems help to describe, model, and analyze situations?
- What relationships in mathematical contexts can patterns be used to describe?
- How can identifying regularity or repetition help with problem-solving efficiency?
- How can the use of geometric shape attributes aid in mathematical reasoning and problem-solving?

- Cone: A solid figure that has a circular base and one vertex. 
- Cube: A rectangular solid having six congruent square faces. 
- Cylinder: A three-dimensional figure with two circular bases, which are parallel and congruent. 
- Rectangular Prism: A solid figure in which all six faces are rectangles. 
- Sphere: A solid figure that has all points the same distance from the center. 
- Three-Dimensional Shapes: Figures with measurable lengths, heights, and depths.

- a collection of real-world objects such as an oatmeal box, a cereal box, a Kleenex box, a paper towel roll, a tennis ball, a six-sided number cube, etc.
- one cereal box opened flat
- classroom building blocks
- three-dimensional plastic shapes
- Vocabulary Cards (M-K-4-2_Vocabulary Cards)
- modeling clay or Play-Doh, a small ball for each pair of students
- large plastic lid or other flat surface for clay work
- large pieces of white paper (11" x 24")
- crayons (or other drawing tools)
- Tana Hoban.(1996). Shapes, Shapes, Shapes. Greenwillow Books.
- J. Feldman.(1991). Shapes in Nature. Children’s Press.
- Stuart J. Murphy.(1997). Circus Shapes. HarperCollins.
- Assessment (M-K-4-2_Assessment and KEY)

- Assessing student mastery may be made easier by the teacher observing during workstations, one-on-one conferences with students, and class discussions. 
- To determine whether a student has mastered the material or needs more practice, a formative assessment can be utilized with paper and pencil (M-K-4-2_Assessment and KEY). This formative assessment can also be used to guide instruction.

Explicit instruction, modeling, scaffolding, and active engagement 
W: Set out an assortment of varying-sized boxes and containers. Draw comparisons between them as well as with classroom blocks. 
H: Choose a rectangular prism box and ask students to describe it, pointing out all of its features. For cubes, cylinders, cones, pyramids, and spheres, repeat these steps and provide instances of actual objects with similar shapes. 
E: Assign students to work in pairs to create two-dimensional impressions of the block shapes using modeling clay and toy blocks. Determine which shapes result in circles, squares, etc. 
R: Go over what the students learned from the exercise. Assemble workstations for a related exercise where students will trace the edges of different blocks on paper. If a block has different shapes, make sure they are tracing more than one side of the block. 
E: Show a few of the student's tracings and inquire as to the shapes' names and possible building blocks. Talk about arranging the blocks according to the shapes they have traced. 
T: To reinforce vocabulary and characteristics of two- and three-dimensional shapes and objects, a variety of books are available for the class to read aloud. You can apply paint or ink pads to boxes or blocks and then transfer the mixture to paper to see the shapes of the blocks as an additional hands-on exercise that resembles class work. 
O: Using a variety of attributes, students first sort and investigate two- and three-dimensional figures. Students discuss the qualities of three-dimensional objects while learning to use their formal names. Students can connect the nets of three-dimensional figures to the two-dimensional shapes that make them up through practical exercises. Students can learn to quickly identify the two-dimensional shape made up of one face of a three-dimensional figure through repeated exposure. 

Create a collection of items using classroom building blocks, three-dimensional plastic shapes, and actual items from your home or classroom. Every student should receive a tiny ball of modeling clay or Play-Doh.

Say, "We discussed two-dimensional shapes like squares, circles, triangles, and trapezoids in a previous lesson. Recall that shapes in two dimensions are flat. We will be studying three-dimensional shapes today. I've gathered items from both our classroom and my home. We are going to take a close look at them to determine their similarities and differences. Subsequently, we will contrast them with the classroom blocks."

Select an object from the list that resembles a rectangular prism. Make it visible to the class. Distribute it to people for more in-depth analysis. "What information about this figure can you provide?" Allow students to react, restating their findings in appropriate language, such as:

"Yes, a rectangle is depicted on the side of the picture. There are four corners and four sides on the flat side. Are there any additional items in the collection that have rectangular-shaped sides?" Permit students to choose boxes that are similar to each other. "All right, there are a few boxes similar to this one. This shape is known as a rectangular prism. Together, let's call this a "rectangular prism." How does this box's name aid in our memory of its shape?" Allow students to react, then assist them in realizing that the word "rectangle" sounds similar to "rectangle."

Present to the class a flattened-out box with all of its sides' shapes exposed. "Are you able to observe how the rectangle prism is constructed from rectangles? "How many rectangles do you have?" (6) Count them all together, tracing around each rectangular side with your finger or a marker. "Observe the outcome when we combine all of these rectangles." Refold the box into the three-dimensional configuration it was in before.

"Are there any other rectangular, prism-shaped objects in our room?" Permit a few pupils to reply, identifying and/or pointing to various items within the classroom.

Use the cube, cylinder, cone, pyramid, and sphere examples to reenact the previous dialogue. Allow students to identify comparable forms in classroom building blocks, real-world objects, and three-dimensional plastic shapes. Using vocabulary, explain the surfaces as triangles, rectangles, squares, and circles. Ask students to make the shapes out of clay or Play-Doh as you go over each three-dimensional shape.

Give each three-dimensional shape its name on a large word card, then place the cards on the ground so that objects can be arranged in groups around the cards. As you begin with a single shape—the rectangular prism, for instance—give each student a turn locating an object or a block to add to that group. "On this card, I have the word 'rectangular prism' along with an image of what it looks like. Let's search through our collection to locate every item that also has a rectangular prism and group them."

Give students some time to make any necessary revisions after ensuring that everyone is happy with the final groups.

Take out the real-world boxes from each group. "Let's focus just on the classroom blocks. Could someone please locate a cube?" Select a student to find a cube from the collection while you flatten a piece of clay on a flat surface. "If I insert one side of this cube into the clay, what shape will we observe?" Take a few guesses. "Let's find out." To make a square, press the flat side into the clay. "Did we make accurate predictions? How many square sides does this cube have? (6) Let's use clay to discover more about each of these blocks."

Assign students to pairs, and ensure that each pair has a modeling clay ball and a variety of classroom blocks (one for each shape). Let them experiment with creating shapes with the clay by pressing blocks into it and describing them. While they are working, move around and talk about what they are doing using the vocabulary words for the two- and three-dimensional shapes. "Which block has a level side shaped like a circle? That's right, the cone. Cones and cylinders are the two forms that have circles; you're correct. When you use the rectangular prism, what shapes do you get?" Gather the clay and blocks, then quickly go over the discoveries made by the students.

"What observations did you make regarding the cone, cylinder, and sphere?" (They roll because, among other things, only one side forms a shape; the sides are round rather than all flat.)
"What took place when these shapes were pressed into the clay?" (Other shapes were formed by the sides that were compressed in.)
"What is the number of corners in a triangle?" (3)
"What is the number of corners on a pyramid?" (5)

"We have examined a variety of items from both our classroom and mine. You succeeded in organizing the items into similar groupings. Let's go over the names of the shapes we employed." Say the name of each three-dimensional shape while holding up an example of it. "You also examined the sides of the shape blocks closely. Let's recall the shapes these blocks' sides reveal to us." Name the two-dimensional shapes that correspond to each block's sides while holding up an example of each block.

"I'll demonstrate another method for creating an image of the shapes found on each block's sides. We can draw a picture with paper and crayons instead of clay." Display a sheet of paper for everyone to see. Select a form and place a flat side against the paper. "Observe how I can draw around this block's flat side." Place the block down after tracing it. "What shape did I draw?"

"There is an option for you at the workstations. At workstations, you can use clay, blocks, and boxes to draw shapes. Make sure you examine every side of every block or box, and if at all possible, draw or stamp multiples of each. Take a look at this pyramid. With this block, how many shapes could you draw or stamp? Yes, a square and a triangle are two distinct shapes. Fill one sheet of paper at a time at each station with shapes that you trace with the objects or stamp into clay, just like we did in class earlier."

Each student should have an identical-shaped object at their workstation (all cubes, all rectangular prisms, etc.). At each station, add three-dimensional plastic shapes, blocks, and actual objects. Every station needs to have supplies of white paper, clay, and crayons.

Place students at workstations. Before moving on to the next station, give students time to trace or stamp each item. Make your way around the room, reviewing vocabulary related to the two- and three-dimensional shapes they are studying.

Organize a class discussion of everyone's work at the stations. Show the students a page of work and ask them to identify the two-dimensional shapes by pointing at them. To find out what kind of object created these shapes, ask, "What is the name of this three-dimensional shape?" Continue with several more student papers.

Start a conversation with the class about how they could use the pictures they have traced to sort the blocks in the classroom. For instance, cutout shapes could be used as labels on the shelves to indicate the proper stacking order for each kind of block.

There are numerous ways to achieve this.

Whole group: students could be given a mixed set of blocks to sort and label before bringing them to the shelves.
Small groups: each group could be in charge of finding every block and stacking it on the shelf, or they could be in charge of just one shape.
Workstation: As each group goes around the station, they could sort one bag containing sets of mixed blocks that have been placed inside grocery bags.

Extension:

Routine: Reading aloud would be a good way to continue practicing the names and identification of two- and three-dimensional shapes. Consider the following books:

- Tana Hoban. (1996). Shapes, Shapes, Shapes. Greenwillow Books.
- J. Feldman. (1991). Shapes in Nature. Children’s Press.
- Stuart J. Murphy. (1997). Circus Shapes. HarperCollins.
- Susan Mascall and Bob Mascall. (1999). Big Shapes for Little Kids. Fundangles.
- Marilyn Burns. (1995). The Greedy Triangle. Scholastic.

I Spy: Look for a two- or three-dimensional shape in the classroom and provide hints to the students about what it is. It is up to the students to guess what shape you are considering. As students gain more experience with this game, ask them to provide hints.

Expansion: Provide big sheets of paper, paint, and boxes or blocks. Students should paint one side of a box or block and then transfer the design onto paper. If there were smaller, three-dimensional shapes available, ink pads would also function. Ask students to identify the shape they are printing and to indicate how many sides and corners it has while they are working. Find out if any other surfaces in the box have this shape.

Utilizing both two- and three-dimensional shapes, play Shape Bingo.

Give each student a copy of a Venn diagram on an 11 x 17 (or bigger) piece of paper in pairs. Give the students two three-dimensional shapes to choose from. Give the students instructions to contrast and compare the two shapes orally. "How are the shapes the same?" ask them. "What makes them distinct from one another?" Put the ideas of the students on a Venn diagram.

Small Group: Shape Detectives: Give a variety of shaped cards to small groups. Encourage them to search the room for objects that match the shapes on the cards to become "Shape Detectives." Encourage groups to yell "Shape Detective, (name of shape)!" as they locate each shape. The class as a whole must stop when a group yells and waits for you to verify that they are correct.

Students can use the vocabulary cards (M-K-4-2_Vocabulary Cards) as practice if they need more learning opportunities.