In this lesson, students will experiment with combining several of the same shapes to create larger, similar shapes. At the end of this lesson, they are going to:
- Investigate how smaller shapes can be combined to form larger shapes.
- Compare and contrast different combinations and designs of shapes.
- Classify drawings according to shape characteristics.

- How can the study of mathematics aid in clear communication? 
- In mathematical contexts, how can relationships be described using patterns? 
- How do we represent, compare, quantify, and model numbers using mathematics? 
- What does it mean to evaluate or estimate a numerical quantity? 
- 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?

- Hexagon: A shape with six sides. 
- Pentagon: A shape with five sides. 
- Quadrilateral: A shape with four sides. 
- Rhombus: A parallelogram with four equal sides. 
- Trapezoid: A quadrilateral with exactly one pair of parallel sides. 
- Triangle: A shape with three sides. 
- Vertex: The corner of a shape.

- pattern blocks 
- large paper models of pattern blocks, at least four of each shape (You will need to prepare these before the lesson.) 
- three or four sheets of drawing paper for each pair of students 
- colored pencils 
- pattern block stickers (optional) 
- pattern block designs (M-K-4-3_Duck, Turtle, and Fish Patterns)

- Teacher observation in classroom discussions, workstations, and one-on-one conferences with students will help assess student mastery. 
- One-on-one conferences could make use of student drawings. Call attention to the places where smaller shapes resulted in larger shapes and ask the student to explain his or her design.

Explicit instruction, modeling, scaffolding, and active engagement 
W: Explain to the class that they will be seeing how different shapes can be combined to create new ones. 
H: Instruct students to sketch a square that symbolizes a cake. Then, draw a straight line through the square to form two new shapes. Draw attention to any forms that the students might be familiar with. 
E: Show a collection of pattern block shapes and go over each one's characteristics and names. Students should locate two shapes that can be used to form a rhombus by focusing on it and coming to the conclusion that two triangles will cover it without overlapping or hanging over the edge. 
R: Let students play with the triangles and rhombuses using smaller pattern blocks. Give students additional examples to practice, demonstrating how some shapes may need to be flipped or turned to fit correctly. Ask students to draw fresh patterns and new shapes on paper, then trace them. 
E: Show the group the pattern drawings and talk about the parallels and discrepancies. 
T: Give students a piece of chart paper, an easel, or a whiteboard to draw something on. Then, see if any other students can draw the same design. You can find tangram puzzles online by clicking the provided link. 
O: In order to create new shapes from smaller or different shapes, students will apply their visual discrimination skills to take what they have learned about shapes and attributes to a higher level. When students start learning about area and perimeter in the future, the capacity to discern particular shapes within other shapes will become increasingly significant.

Say, "We've been working with shapes a lot. You have seen how shapes are used to create real-world objects, and you have created animal pictures using shapes. We will examine how to combine shapes to create new shapes today."

Give the class the following problem to read: "Mario baked a cake in a rectangular pan with his mother. Mario separates the pan into two large pieces by making a straight cut through it. If Mario cut a straight line through the cake, what shapes could he create?"

Assign each student a piece of paper, pencil, and marker set, or a whiteboard and markers, and instruct them to draw a line that represents chopping the cake. Ask students to illustrate how Mario might cut the cake by drawing a straight line across the paper. Ask a student to demonstrate how they drew a large rectangle for the class on a whiteboard or chart paper. Make sure to draw attention to any discernible shapes, such as triangles or rectangles. "Observe how your line splits the rectangle in half." Repeat with two or three more students.

Form a big circle with the students on the ground, and place the large paper pattern block shapes in the middle. Present every shape to the class one at a time, asking them to identify it, count its corners and sides, and provide any additional comments.

Create a rhombus on the floor in the center of the shapes after moving them all to one side. "What shapes would the pieces take if I cut this rhombus into two pieces like I would a cake? Is there anybody among us who can identify two shapes that, when combined, would form a rhombus? Let's see if these work with our rhombus cake." As students select shapes, have them fit onto the rhombus to check if there are any gaps or overlaps. Try out the shapes that students suggest until the right ones (two green triangles) are selected. After placing the triangles on the rhombus, discuss how they cover it without overlapping or protruding past the edge.

Give each pair of students a few pattern blocks. If pattern blocks are not available, utilize the M-K-4-1_Pattern Block Shape Cards pattern-block-shape cards. Ask them to locate the blue rhombus and use the two shapes that completely enclose it to cover it. Verify that everyone has used two green triangles to indicate understanding.

"Seek out the red trapezoid." Present a paper prototype. "To cover the entire shape, use some of your pattern blocks. To get some of your blocks to fit, you might need to flip or turn them." Turn or flip a paper model to show them how this might appear. Ask partners to come up with another way to cover the trapezoid with different shapes after they have come up with one.

"Now locate the yellow hexagon and identify covering shapes for it." Walk around and watch the pairs at work. To find out which students can name the shapes they are using and whether they understand the main ideas of the activity, pose questions.

"You have been creating larger shapes, like trapezoids, by utilizing shapes like triangles. The pattern block shapes will now be used to create even larger shapes or images. Try to join four squares so that the smaller ones are in contact with one another to create a larger square." Verify if each pair is successful.

"Now, create a larger triangle by using four triangles." Give time for every pair of students to construct the same large triangle after selecting two to use as models for the proper solution using the large paper models. "Now, create a new shape or image design using four triangles. Ensure that every triangle touches at least one other triangle." In groups of two or three, students will present their finished shapes.

Ask students to review their designs and determine which areas, if any, could be covered with additional pattern blocks without affecting the overall design. Make suggestions as needed and stroll around to make sure everyone is understanding.

Select a pair and use the large paper shapes to demonstrate an effective attempt. Talk about how shapes could have been rotated or flipped to obscure the pattern without obscuring or altering it.

Give students some time to experiment with a set of six pattern blocks (there should be at least one triangle) to make new images or patterns. Students need to be reminded that every shape needs to touch another shape. Assign two drawing sheets to each pair of students, and instruct them to use colored pencils to sketch two of their designs. You could suggest that they take a block-by-block route. (Alternatively, pattern block stickers or stencils could be utilized.) Ask them to select one drawing apiece and name it.

Discuss the group's drawings and points of similarity and difference. Have students arrange the drawings in a group based on one of their suggested similarities.

Extension:

Routine: Give one student the task of drawing a picture on an overhead projector using six to ten pattern blocks. Encourage the student to avoid leaving gaps where the edges meet. Switch on the projector. Ask a few students to identify the shapes they used to create the design. Assign a student to duplicate the design on the overhead as well, utilizing some of the same shapes but attempting to construct the same shapes with fresh blocks.

Make sure to fill baggies with various shapes. As a fast-transition activity, distribute baggies to students throughout the year and let them try their hand at creating various shapes.

Small Group: Use a set of four to six pattern blocks to help students construct their pictures. Encourage them to use bigger blocks to cover their designs, or go one step further and use the larger block to replace the smaller shapes, noting that the overall design remains the same. Help them learn how to flip and rotate shapes so that they fit perfectly without overlapping or protruding. Students could use white paper to cover up their designs and then rub their designs with crayons. (The student will use one hand to hold the paper in place while the other is used to rub a crayon across the paper over the shapes until all of the shapes are visible.)

Workstation: Locate published images or supply a set of pattern blocks and blackline masters (M-K-4-3_Duck, Turtle, and Fish Patterns). To cover the larger picture, students will arrange the blocks in various ways. Students can use pattern block stickers to display their work, trace the shapes they used to cover the picture on the blackline master, or cover their design with white paper and rub it with a crayon to present a sample of their work.

Expansion: Students can visit websites to learn more about pattern block manipulation (see Related Resources). Give each student a set of blocks and ask them to try making the same shapes on paper that they are creating online. They are free to trace the designs and shapes they make. Challenge students to show the image using different shapes by having them share their drawings with others.