Lesson 1.5 · Figures made up of squares — multi-square blocks
Hua's Classroom for Shanghai Maths — One Lesson One Exercise (English edition, pages 10–11).
Lesson Alignment
How this Shanghai Maths lesson connects to learning goals, Common Core, and Eureka Math.
Learning Objectives
Students will be able to:
- 01Name two-, three-, and four-square blocks (polyominoes). (Question 1)
- 02Grow a block by adding one square (2→3, 3→4). (Question 2)
- 03Compose a $4 \times 3$ rectangle and a $4 \times 4$ square from multi-square blocks. (Question 2)
- 04Find combinations of blocks that make a $3 \times 5$ rectangle. (Question 2)
- 05Tile a larger square using given blocks, each used once. (Enhancement)
Common Core Standards
| Code | Standard (focus for this lesson) |
|---|---|
| 3.MD.C.5 / 3.MD.C.6 | Recognize area as attribute; measure area by counting unit squares. (All) |
| 3.MD.C.7 | Relate area to multiplication and addition; compose rectangles. (Question 2) |
| 3.G.A.2 | Partition shapes into parts with equal areas. (Question 2, Enhancement) |
| 1.G.A.2 (revision) | Compose two-dimensional shapes. (Question 1–2) |
Eureka Math Correspondence
| Shanghai Maths 1.5 | Focus | Eureka Math (corresponding) |
|---|---|---|
| Question 1 | Name multi-square blocks | G3 M4 unit squares / area language |
| Question 2 | Add a square; compose rectangles | G3 M4 Topics A–B; tiling & composing |
| Enhancement | Tile a square with given pieces (each once) | G3 M4 / M7 spatial problem solving |
Core Concepts
Multi-square blocks (polyominoes) — naming, growing, and tiling.
Naming Multi-square Blocks
| Name | Made of | Also called | Figure |
|---|---|---|---|
| Two-square block | $2$ unit squares joined edge-to-edge | Domino |
|
| Three-square block | $3$ unit squares | Tromino |
|
| Four-square block | $4$ unit squares | Tetromino |
|
Growing Blocks
- Two-square → three-square: add one square touching a full side.
- Three-square → four-square: add one more square the same way.
Different places to add a square create different shapes (straight, L, T, skew…).
Composing Rectangles & Squares
| Target | Area (unit squares) | Teaching focus |
|---|---|---|
| $4 \times 3$ rectangle | $12$ | Pieces must fill without gaps or overlaps |
| $4 \times 4$ square | $16$ | Total area of pieces $= 16$ |
| $3 \times 5$ rectangle | $15$ | Find which combination of blocks works |
Enhancement Ideas
Use the given multi-square blocks in the upper diagram to build the square underneath. Each block is used only once.
- First check: do the pieces’ areas add up to the target square’s area?
- Then try placements; rotate pieces if the book allows.
Key Terms & Definitions (Reference)
Quick glossary for Lesson 1.5 language.
| Term | Definition |
|---|---|
| Unit square | One square of the grid; the basic area unit. |
| Multi-square block | Several unit squares joined along full sides. |
| Two- / three- / four-square block | Block made of 2 / 3 / 4 unit squares. |
| Area | Number of unit squares that cover a figure. |
| Compose / Tile | Put shapes together to fill a larger shape without gaps or overlaps. |
Key Answers
Quick reference for this lesson’s exercise answers.
1. two-square; three-square; $4$ unit squares.
2. Add one square to grow $2\to3$ and $3\to4$ (any edge-joined placement). Sample tilings: $4\times3$ as three $2\times2$; $4\times4$ as four $2\times2$; $3\times5$ as three $1\times5$ strips or five $3\times1$ strips.
3. Tile the target square using each given block at most once (areas must match: $4\times4=16$, $5\times5=25$). Drawings may vary.