Students often refer to Class 5 Maths Notes and Chapter 7 Shapes and Patterns Class 5 Notes during last-minute revisions.
Class 5 Maths Chapter 7 Notes Shapes and Patterns
Class 5 Maths Notes Chapter 7 – Class 5 Shapes and Patterns Notes
We see different shapes and patterns everywhere in the nature around us! They can be seen everywhere, from growing plants to the petals of flowers, stripes of zebra, the way birds fly and in arrangement of leaf in trees, these are nature made patterns. We can also see different man-made pattern around us, like: different floor pattern, weaving mat patterns, doormats, baskets, floor mats, hand fans etc. Weaving techniques and patterns are often passed down through generations, preserving cultural heritage and craftsmanship.
→ Weaving is the process of interlacing two sets of threads or strips to make fabric, mats, or baskets. It is a repeated pattern of over and under movements.
→ Weaving patterns are often repeating and symmetrical, and follow certain mathematical rules, like: over, under, over, under….Advanced patterns may include triangles, diamonds, hexagons, etc.
→ Closed figures made up of straight line segments are called polygons.
→ In regular polygons all sides are equal in length, and all angles are equal in measure, (e.g., equilateral triangle, square, regular pentagon).
→ In irregular polygons, sides and/or angles are not all equal.
→ Naming of polygons (number of its sides or vertices) like: Triangle (3), Quadrilateral (4), Pentagon (5), Hexagon (6), Heptagon (7), Octagon (8), Nonagon (9), Decagon (10), etc.
- Square: 4 equal sides, 4 right angles.
- Rectangle: 4 right angles, opposite sides equal.
- Parallelogram: Opposite sides parallel and equal. (It includes squares, rectangles, and rhombus)
- Rhombus: 4 equal sides, opposite angles equal. (A special type of parallelogram)
- Kite: It is a quadrilateral whose four sides can be grouped into two pairs of adjacent equal-length sides.
→ Triangles: Polygon of three sides:
→ Classification of triangles by Sides:
- Equilateral: 3 equal sides, 3 equal angles (60 degrees each).
- Isosceles: 2 equal sides, 2 equal base angles.
- Scalene: No equal sides, no equal angles.
→ A circle is a fundamental two-dimensional geometric shape consisting of all points in a plane that are at a fixed distance from a central point. This fixed distance is called the radius, and the distance across the circle, passing through the center, is the diameter.
→ A repeating pattern of shapes that fit together without any gaps or overlaps are called tessellations. Shapes that tessellate are: Squares, Equilateral Triangles, and Regular Hexagons.
→ A net is a 2D pattern that can be folded to make a 3D solid.
→ The icosahedron and dodecahedron are two of the five platonic solids, meaning they are convex polyhedral with identical faces that are all regular polygons. The icosahedron has 20 faces, all equilateral triangles, and 12 vertices. The dodecahedron has 12 faces, all regular pentagons, and 20 vertices.
Weaving Patterns
→ Weaving involves creating mats or designs by interlacing strips of paper or other materials in a repeating way.
Triangles
→ There are three types of triangle on the basis of sides.
- Equilateral triangle All 3 sides and angles are equal.
- Isosceles triangle Isosceles triangle has 2 equal sides and 2 equal angles.
- Scalene triangle All sides and angles are unequal.
Quadrilaterals
- Parallelogram Opposite sides and opposite angles are equal.
- Rectangle A type of parallelogram with opposite sides equal and all right angles.
- Square All sides are equal and all angles are right angles (a special case of rectangle and rhombus).
- Rhombus All sides and opposite angles are equal.
- Kite Two pairs of adjacent sides are equal.
Tiling or Tessellation
→ Tiling refers to covering a surface with shapes without gaps or overlaps.
→ Regular shapes and Irregular shapes
→ A regular polygon has all sides equal and all interior angles equal while an irregular polygon does not have all sides and angles equal.
→ Regular shapes in Tessellation
- Equilateral Triangles Fit perfectly around a point i.e. 6 triangles meet at a vertex.
- Square Fit without gaps i.e. 4 squares meet at a vertex.
- Regular Hexagons Fit perfectly i.e. 3 hexagons meet at a vertex.
- Regular pentagons and octagons Do not tessellate as they leave gaps.
→ Irregular Tessellations
Combinations of different shapes e.g. squares and triangles can tessellate if arranged properly.
3-D Shapes
→ Cube A cube is a regular hexahedron, it has six square faces. All its faces are identical and all its angles are right.
It has 6 faces, 12 edges and 8 vertices.
Note A large cube with $n$ small cubes along each edge contains $n^3$ small cubes.
→ Icosahedron An icosahedron is a polyhedron with twenty faces.
It has 20 equilateral triangular faces, 30 edges and 12 vertices.
→ Dodecahedron A dodecahedron is a polyhedron with 12 faces.
It has 12 regular pentagonal faces, 30 edges and 20 vertices.
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