Introduction to Geometry

2-Dimensional and 3-Dimensional Shapes

(cube, sphere, rectangular prism, pyramid)


Rose Cavaliere: Internship I – Observed Lesson 2



·       whiteboard and markers

·       class list w/ assessment objectives to record results

·       pop up cube (starts flat, then pops open)

·       Brown paper shopping bag w/ groceries in that are 3-D shapes

·       Poster Board labeled “Shapes Museum” with one side labled 2D and one 3D; have pics from magazines as examples to glue on

·       Models of items to illustrate 3-D and sides, lines segments, vertices that unfold flat to show sides (plastic 3D shapes are in classroom)

·       Toothpicks and marshmallows

·       Cards to hand to pairs assigned them 3-D shapes to build with the marshmallows and toothpicks

·       Worksheet to cut-out and tape together 3-D shapes, scissors, tape

·       Magazines, scissors, glue

·       Tessalation coloring sheet

·       Worksheet to assess w/ 3-D shapes and 2-D shapes


Timing Outline

10:30-11:20: 50 minutes

10:30-10:45: hook & discussion                    15

10:45-10:50: Shapes Museum                                     5

10:50-11:10: Marshmallow Activity             20

11:10-11:20: assessment worksheet              10

                                                                        50 minutes



This lesson will introduce children to the concept of 3-D shapes through the analysis of physical items as well as opportunities to build and create these shapes themselves.  2-D items were discussed in a math lesson earlier this week and this lesson is intended to build upon that to add to their schema about geometric shapes and jargon.






Reason with shapes and their attributes.

Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.

Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) 



Analysis of Prior Knowledge

This is the second of three lessons on basic geometry principles (Lesson 1 was geometric shapes (2-D);  Lesson 3 will be about symmetry). I spoke with Mrs. Cortez who informed me that she has introduced them to the shapes (2-D and 3-D) in a previous lesson but it has not been extended since then.  During Lesson 1 almost all of these students knew the names of the basic 2-D shapes (triangle, circle, square, diamond, rectangle, oval).  We discussed attributes of shapes (size, sides, angles) but did not go into comparing and contrasting 2-D and 3-D.  We discussed what dimension means and I could tell it was the first time they were looking at shapes this analytically.





have students understand difference between 2-D and 3-D shapes

oral responses explaining 2-D and 3-D;

pointing out objects that are 2-D and 3-D when presented with 2 choices

have students match correct name to correct shape (sphere, rectangular prism, cube, pyramid)

have students complete sheet where they color in the object I name; 

have students count sides and corners of 3-D objects

have students count sides of 3-D objects (two opportunities will exist for this: during marshmallow activity or closing activity)

have students explore 3-D shapes in the real world

oral discussion and items brought in for Shapes Museum




Remind them that we discussed shapes and their names on Monday and Tuesday. Be quick and brief—no discussion.  Then I will bring in a pop up cube that will start out flat, then open to illustrate 2-D and 3-D. While it is flat we will count sides and corners.  While cube is open we will count sides and corners.





·       Bring out a brown paper bag w/ groceries/household items packed in it.  Grocery items represent 3-D shapes. Shapes discussed today will be: sphere, rectangular prism, cube, cone, pyramid.

·       Establish “Shapes Museum” w/ these items. Invite them to bring in items from home (or draw items or cut pictures out of newspapers or magazines) to add to the museum.

·       Show them and pass around 3-D shapes; count the sides, discuss lines, corners, intersection of lines (vertices).

·       Unfold one of the above shapes (one of the boxes of cereal for example) and count the sides and lines again.

·       Marshmallow shapes (2-D and 3-D): give the children baggies with toothpicks and marshmallows.  Send them off in pairs w/ assigned shapes to make (see pairings below)—they need to make the 2-D and 3-D version.  Set timer for 10 minutes.  At end of 10 minutes as them to show the 2-D and 3-D version of shape (for ex. make a square—make another square—turn this into a cube)

·       Early Finishers: Challenge activity cut-out 3-D shape and tape together OR look for 2-D and 3-D items in magazine, OR tessalation coloring sheet. 



Have children return to their desks to complete an assessment worksheet that requires them to label shapes as either 2-D or 3-D.



·       Early Finisher activities have two levels of complexity, one much more challenging, one more basic.  Challenging activity: cut out, fold and tape together 3-D shapes.  Basic Activity 1:  look through magazines for 3-D shapes to glue into Shapes Museum. Basic Activity 2: tessalation coloring sheet .  Students like Meisner, Yosvany, Jocelyn may quickly get the marshmallow activity and need something more challenging to engage them while the rest of the class explores 3-D shapes.  Yosvany, while bright, can become disruptive when he finishes well in advance of the class.  Students like Jonathan D., Harlan, Nancy, Cathleen may need something they can more readily succeed at.

·       For the whole class assessment I will use a worksheet.  When I name a shape they mark whether it is 2D or 3D; then we have them match the 2D shapes to the 3D shapes.

·       The marshmallow activity allows students who still need reinforcement of basic 2-D shapes to continue exploring at that level.  Students this may be necessary for are Nancy, Omar, Harlan, Stephanie.  This should be permitted and the concept of 3-D can be continually reinforced with them in future lessons (if I had future lessons).

·       By pairing students, they can assist each other.  Stronger students are paired with students who may need more support.  3-D shapes assigned during marshmallow activity will be by design based on students in pairs.  For example, Yosvany, Pedro, Meisner, Jocelyn could probably handle a pyramid.  Some will get rectangular prisms, others cubes.  Instructions will include allowing some to make the 2-D shape that starts the 3-D shape, then they help each other finish the 3-D shape.

·       In general, I have tried to make this lesson as hands on and as visual as possible, with a little seatwork and whiteboard discussion included as well.  For students like Yosvany and Hector the 3D marshmallow shapes will come easily and will the cube cut-out.  For students like Kathleen, Omar, Jonathan A. and Harlan, working with strategies besides a worksheet will help them acquire this information. The most basic activity, the coloring sheet, will allow students such as Kathleen to participate and still work within the topic.

·       Very strategic pairing needs to occur with Hector (who is a behavior problem) and the following students who, for every activity consistently exhibit delays:  Jonathan A., Nancy, Kathleen, Harlan, Vincent, Stephanie, Omar, Jonathan A.

·       All pairs were selected w/ a stronger/needs support combination in mind (mixed ability).  During Marshmallow activity one person makes the 3D and one person makes the 2D;  2D and 3D shapes are also assigned strategically.

·       Also, by making three groups with mixed ability pairs, groups are heterogenous.  Then, by making the lesson about 2D and 3D shapes I can assign the students who need more support the task of making the 2D shapes.



Groups are designed to pair a stronger performing student w/ ne who needs more support either academically or behaviorally.  Student name on top is stronger student.









Jonathan A.

Eric Chaj






Jonathan D.






Eric Cuzco