2D shapes and tessellation
🎯 In this topic you will
- Investigate how new 2D shapes can be formed by combining two or more shapes.
- Develop an understanding of the key properties of common 2D shapes.
- Explore how 2D shapes tessellate to cover a surface without gaps or overlaps.
🧠 Key Words
- 2D shape
- parallel
- polygon
- regular
- tessellation
Show Definitions
- 2D shape: A flat shape that has only length and width, with no thickness.
- parallel: Lines that are always the same distance apart and never meet, even if extended.
- polygon: A closed 2D shape made from straight line segments joined end to end.
- regular: A description of a shape where all sides are equal in length and all angles are equal.
- tessellation: A repeating pattern of shapes that covers a surface completely with no gaps or overlaps.
🔷 Building New Shapes
U nderstanding how to combine 2D shapes to make new shapes helps you see how shapes can be broken down into smaller parts, making it easier to solve problems.
🧩 Tessellation in Design
T essellation is important in many designs because repeating shapes can cover a surface completely without gaps or overlaps.
❓ EXERCISES
$1$. Copy and complete each sentence to name the small shapes and name the shape that has been made by putting them together.
a. The four ____ make a ____.
b. The two ____ make a ____.
c. The four ____ make ____.
👀 Show answer
a. The four triangles make a square.
b. The two trapeziums make a hexagon.
c. The four triangles make a trapezium.
$2$. Name a $2$D shape that has each of these characteristics.
a. At least one right angle.
b. At least one curved side.
c. At least one pair of parallel sides.
d. At least $7$ vertices.
e. Not a polygon.
👀 Show answer
a. Rectangle
b. Circle
c. Parallelogram
d. Heptagon
e. Circle
❓ EXERCISES
$3$. Can each shape be made by putting this rectangle and these two triangles together? Answer ‘yes’ or ‘no’.
👀 Show answer
a. Yes
b. Yes
c. No
d. No
$4$. Name the shapes in these tessellating tile patterns.
👀 Show answer
a. Hexagons
b. Triangles and hexagons
c. Octagons and squares
d. Octagons, squares, and diamonds
$5$. Make a template by drawing a triangle onto card. You could trace and copy one of these triangles.
Cut out your template and draw around it ten times to make a tessellating pattern.
Try doing the same with a different triangle.
Do all the triangles tessellate?
👀 Show answer
Yes. All triangles tessellate because copies of the same triangle can fit together around a point to make a full turn of $360^\circ$ with no gaps.
🧠 Think like a Mathematician
Statement: Marcus says, “If I cut this rectangle into two pieces with one straight cut, I will always make two rectangles.”
Observation: Marcus is not correct.
Investigation:
- Trace and cut out rectangles like Marcus’s. Explore what other pairs of shapes you can make using one straight cut.
- Choose a different shape. Carefully cut the shape out of a piece of paper.
- Write a question to investigate about your shape. For example: What shapes can I make by cutting my shape into two pieces with one straight cut?
- Investigate your question by trying different straight cuts and recording the shapes you make.
- Write a convincing conclusion by copying and completing this sentence: I found out that …
Show Example Conclusion
I found out that a rectangle does not always make two rectangles when cut with one straight line. Depending on where and how the cut is made, it can create other shapes such as triangles, trapeziums, or irregular polygons.
💡 Quick Math Tip
One straight cut can change the shape: Cutting a rectangle with a single straight line does not always make two rectangles. Depending on where and how you cut, you can create other shapes too, such as triangles or trapeziums.