DIssection of composite figures

Prior knowledge and understanding

Students are assumed to be able to:

• recall and identify various triangles and special quadrilaterals (including rectangles and squares, parallelograms, rhombuses, trapeziums and kites)

10:00 Introduction

(10 mins, LIT): Review of how to dissect simple composite figures into plane shapes and definitions

• Composite figure: any figure or shape that may be divided into at least two basic figures.
• Dissect: to methodically separate or 'cut up'

Have students group their dissections on the board (using Blu-Tack or otherwise) based on the combination of the two shapes they dissected the hexagon into. As a class discussion, ask:

• How many main ways were there to dissect the hexagon into two shapes?
• Which shapes did we cut them into?
• What do we call a shape that is made up of smaller, basic shapes? (Composite figure/shape)

Students collect their dissections from the board and paste them into their workbooks.

Segue into a discussion about dissecting it into three or more triangles and special quadrilaterals. Ask:

• Could we cut these shapes up further?
• What other shapes could we cut it into?
  • Triangles
  • Quadrilaterals: Squares, rectangles, parallelograms, rhombuses, kites, trapeziums

10:10 Body activity 1

(20 mins): Dissection of composite figures into at least three basic shapes

(15 mins) Provide students with the same composite figure from the introduction. In pairs, students work together to separate it into three or more basic shapes and must come up with at least three different variations of dissections. They then identify and label each basic shape and paste/draw these dissections into their workbooks.

As students work, go around the class and ask students (AFL)

• How many smaller shapes have you cut the hexagon into?
• Which shapes have you cut them into?/What type of shape?
• What are the features of this shape?
• Could you cut this shape further into smaller basic shapes?

Sample dissections by students may include:

(5 mins) Come back together for class discussion. Ask:

• What kind of new ways of cutting the hexagon did you come up with? (Have students show the class their dissections. Try to highlight examples that use a variety of triangles and quadrilaterals) Ask for examples using:
  • 3 shapes
  • 4 shapes
  • 5 shapes
• What shapes did you use?
• Are any of the shapes identical to each other?
• Are there more or less ways to dissect the hexagon than before?

Discuss how since this shape was able to be cut into basic shapes, it is a composite shape. The more shapes you cut the figure into, the more dissection possibilities there are.

10:30 Body activity 2

They copy by hand/take a photo of their dissection. On a blank piece of grid paper, they trace the outline of their composite figure.

(10 mins) Students swap their outline with a partner and using the tangram pieces, they reconstruct their partner's composite figures. Once they have succeeded, they compare their reconstructions to their partner's original dissection. As students are working, ask (AFL):

• How many shapes do you think your partner used?
• Which shapes are you using?
• Are there any clues in your partner's composite figure that might indicate that the used certain shapes? (e.g. corners, length of sides, etc.)
• How are your dissections different?
• Did you use the same number of shapes?

(2 mins) Students copy their composite figure and dissections as well as their partner's dissection into their workbook and label each shape. They repeat this for their partner's composite figure.

(5 mins) Come back together for class discussion. Ask:

• Did everyone end up with the same dissection as their partner?
• What does this tell us about the number of possible dissection for a given composite shape?

Discuss how there are multiple ways for a composite figure to be dissected.

10:50 - Conclusion

(5 mins) Exit card

Provide students with the following exit card. Collect cards before the end of class and look over to gauge students' understanding of the dissection of composite figures. (AFL)

(5 mins) Homework and pack up

Students select three or four different pieces from the tangram kit. Using these basic shapes, they create at least three composite shapes. They draw the composite figures and the dissections into their workbook.