Chapter 6 · Consolidation and enhancement
Lesson 6.6 · Tessellations of figures
Hua's Classroom for Shanghai Maths — One Lesson One Exercise (English edition).
Lesson Alignment
How this Shanghai Maths lesson connects to learning goals, Common Core, and Eureka Math.
Learning Objectives
Students will be able to:
- 01Name common plane figures in a tessellation context.
- 02Divide a square into identical smaller squares; find side and area.
- 03Combine pieces (tangram / two squares → larger square).
Common Core Standards
| Code | Standard (focus for this lesson) |
|---|---|
| 3.G.A.2 | Partition shapes. |
| 4.G.A.3 | *(preview)* Line symmetry. |
| 3.MD.C.5–7 | Area concepts and rectangle area. |
| 3.MD.A.2 | *(related)* Measure/solve with units. |
Eureka Math Correspondence
| Shanghai Maths | Focus | Eureka Math |
|---|---|---|
| Compose shapes | Tessellate / tile | G3 M7 / M4 |
Core Concepts
Tessellations — covering without gaps; dissecting and rejoining squares.
Name Figures
Identify shapes used in tiling patterns.
Tile / Divide Squares
Square side $6\ \text{dm}$ ÷ into $4$ identical squares → side and area of each.
Tangram & Cut-Join
Four-piece tangram boards; cut two $1\ \text{dm}$ squares and join into a larger square — draw the result.
Key Terms & Definitions (Reference)
Quick glossary for this lesson.
| Term | Definition |
|---|---|
| Tessellation | Repeating shapes that cover a plane without gaps or overlaps. |
| Tangram | Puzzle of polygons that form a square. |
Key Answers
Quick reference for this lesson’s exercise answers.
Key answers
- Name figures: circle; rectangle; triangle; rhombus; triangle; square; hexagon; octagon
- Common feature: line symmetry
- Draw: draw all lines of symmetry on the figures
- Tessellation: continue the hexagon tiling
- Fill brackets: (1) length $15$ cm, width $5$ cm, area $75$ cm²;\; (2) $2$ different rectangles
- Square divided: side $3$ dm; area $9$ dm²
- Tangram sailboat: A (can)
- Tiles: $600$ tiles
- Display board: at most $60$ artworks
- Enhancement: (9) rearrange two $1$ dm squares into one larger square;\; (10) divide T-pentomino into $4$ congruent pieces (each area $1\frac14$ small squares)