• A paper-and-pencil formative assessment can be used to guide instruction (M-2-5-1_Shape Sorting Assessment and KEY.doc).
• Use an exit ticket (M-2-5-1_Exit Ticket Lesson 1 and KEY.doc) to assess student understanding. Make a copy of the exit ticket for each student. Hand out the tickets at the end of the lesson and collect them as students leave the classroom.
• Have students sort shapes according to attributes using the Shape Sorting and Patterning Cards (M-2-5-1_ Shape Sorting and Patterning Cards.doc). They should create and label categories on a large piece of paper and glue the cards to the appropriate place.

The focus of this lesson is identifying and describing two-dimensional shapes. Students get an opportunity to review familiar shapes at the beginning of the lesson. Then they find those shapes in the environment using geometry shape finders. After identifying known shapes in a new setting, they create unfamiliar shapes by folding paper. This is intended to help students understand that there are many kinds of shapes, and they can be described according to their attributes. Students then reflect on their understanding of shapes by sorting the shapes and discussing their common attributes.

“Today we are going to continue our work on geometry. We will discuss a few geometry vocabulary words. During our unit we will continue to add to our geometry concepts wall. We will talk about shapes that we find in the classroom. Then we will make new shapes by folding paper, and we will sort them according to their attributes. There are many shapes in the world around us. You have already learned about some shapes. Let’s make a list of shapes on this chart.”

Record student responses on chart paper. Review vocabulary words such as side and vertex as students share and remind them that we describe shapes by their attributes. (You might say, for example, “A square has four sides and four vertices, or corners.”)

Geometry Shape Finder Hunt

“Shapes are everywhere. For the next several minutes you are going to be looking for shapes in our classroom. I’m going to give each of you a geometry shape finder” (M-2-5-1_Geometry Shape Finders.doc). Hold up the shape finders and review the shape on each one. “You are to find only the shapes that match your geometry shape finder and write them down in your math journal. For example, my geometry shape finder has a circle at the top. I will look through it to find something in the room that has the shape of a circle.”

Hold the geometry shape finder up to your eye and look through it—just like a magnifying glass.

“Oh, look! I see a penny. It has the same shape as my geometry shape finder. I will need to record it in my math journal.”

Pass out the geometry shape finders and allow students to look for shapes for about 5–7 minutes. Students should record their results in their math journals. Bring the class back together and discuss the shapes found in your classroom. Encourage students to describe the shapes and their attributes using proper vocabulary. Ask students to trade shape finders and look for a new shape, repeating the activity so that each student has the opportunity to look for several kinds of shapes.

Folding Paper to Make New Shapes

For this activity, you will need two 8-inch square pieces of paper for you, one 8-inch square piece of paper for each student, and one 12-inch by 18-inch piece of drawing paper for each student.

Say, “Let’s take a look at some different shapes. When we look at each shape, let’s find the number of sides and the number of vertices it has. Let’s start with my square.”

Show one of the 8-inch squares to the students. “How many sides does this square have?” (4) “How many vertices, or corners, does this square have?” (4) As students provide the answers, write the information on the board or on chart paper, as shown below.

Shape	Name	Sides	Vertices
	Square	4	4

Have students copy the chart into their math journal, leaving room to add additional rows later. “Now I am going to fold my paper multiple times. Watch carefully how I fold my paper. After I finish, each of you will get a square piece of paper, and I will give you step-by-step instructions on how to fold it. Right now, watch how I fold my square.”

Hold the 8-inch square piece of paper so the entire class can see the folding process.

Follow the steps below to fold the paper. Visual instructions are provided in the Folding Square Example (M-2-5-1_Folding Square Example.doc). As you fold, explain to students what you are doing.

1. Fold the square in half, along the vertical line of symmetry. Be sure to make a good crease.
2. Open the square.
3. Fold the square in half, along the horizontal line of symmetry. Be sure to make a good crease.
4. Open the square.
5. Bring each corner vertex to the intersection of both lines of symmetry. Fold and crease well.
6. Repeat step 5 for each corner vertex.
7. Open up the square so you can see all of the folds.

“After you fold your paper to make the creases, you will need to fold the square on the creases you created to make new shapes. For example, if I take my square and fold it in half, I form a shape. What is my shape?” (rectangle) “Yes, I formed a rectangle. Remember a square is a rectangle, also. Now I will record this shape in our chart.” Trace the rectangle onto the chart. Write “Rectangle” in the second column. “Let’s add the number of sides and the number of vertices to our chart. How many sides does a rectangle have?” (4) “How many vertices does it have?” (4) Add this information to the chart. As you record the information on the board, students will fill in their own charts in their math journals.

Shape	Name	Sides	Vertices
	Square	4	4
	Rectangle	4	4

Students should notice that both the square and the rectangle have 4 sides, 4 vertices, and 4 right angles. Say, “Both the square and rectangle are part of a larger group of polygons called quadrilaterals. All quadrilaterals have 4 sides, 4 vertices, and 4 angles.”

Give each student an 8-inch square and a 12-inch by 18-inch piece of drawing paper. “Now it is time for you to do some folding. Let’s start by folding and making creases. Here are the steps.”

Guide students through the folding process. Use the second piece of 8-inch square paper to model each step. This may take a few minutes. When students unfold their square it will have the following creases.

After everyone has folded the square, allow students time to explore the different shapes they can make by folding the square one or more times. Remind students to use only the folds they have already made to create shapes; they should not make any new creases. Have students trace the new shapes they make onto their drawing paper. They should name each shape and list the number of sides and vertices it has. Here are the different shapes they can make:

Shape Categories

As students are creating shapes and tracing them on paper, put several pieces of chart paper up around the room. Label the chart paper with certain attributes, or categories, such as “Shapes with four sides” or “Shapes with more than four vertices.” While reviewing student work, choose several students to trace their shapes on the classroom chart paper in the correct category.

As a class, discuss the shapes in each category. This is a good opportunity to introduce new vocabulary to students, such as quadrilateral, pentagon, and attribute.

As students trace their shapes, discuss which shapes are the “same” and what that means. Introduce the term “congruent,” meaning that one shape will match the other shape when placed on top of it. There will be several opportunities to show (or have students show you) shapes that are congruent:

This discussion will also bring in some of the informal vocabulary of transformations. You might need to explain, “This is the same as that, except it has been turned and flipped over.”

You will have opportunities to assess students through discussions and questions while students are exploring new shapes in the folding activity. You may want to divide students into small groups to further clarify their understanding or assess their learning.

Sample questions include:

• “What shape did you make by folding your square one time? Two times?”
• “Did you make any congruent shapes? How do you know?”
• “I see you have shapes that are similar. Can you tell me why these two shapes are similar?”
• “What do you find challenging about this problem?”
• “I wonder if we can make a shape that has fewer than four sides.”
• “I wonder what shape will have the most vertices.”

Make sure students are recording information about the shapes on their paper. When students share answers, some may say they have a new shape when it is actually a rotation or flip of a shape already mentioned. Make sure to point this out to students by laying shapes on top of each other.

Extension:

Use the activities and strategies listed below to meet the needs of your students during the year.

• Routine: Use the entrance ticket (M-2-5-1_Entrance Ticket Lesson 1 and KEY.doc) to assess students on their knowledge of shapes. An entrance ticket can be used to reinforce skills from a previous lesson, and it can be a helpful preassessment tool.
• Expansion: Students who are ready can use the Shape Sorting and Patterning Cards (M-2-5-1_ Shape Sorting and Patterning Cards.doc) to practice sorting shapes according to their attributes. Students should create categories and then sort cards into the appropriate categories.
• Small Groups: Some students may have a difficult time with the paper-folding activity. If need be, prepare some folded 8-inch squares in advance. Guide students who need more practice through a series of folds in a small group. Reduce the number of folds required. Then help them write down the number of sides and vertices for each shape.
• What’s My Rule?: As a quick transition or warm-up activity, students can play What’s My Rule?. Invite one student to sort a group of shapes into two or more groups. The class will look at the groups and guess what attribute the student used to sort.