NCERT Solutions for Class 5 Mathematics Chapter 7 Shapes And Patterns
NCERT Solutions for Class 5 Mathematics Chapter 7 Shapes And Patterns
NCERT Solutions for Class 5 Mathematics Chapter 7 Shapes And Patterns
This worksheet for Class 5 Mathematics Chapter Shapes And Patterns helps students understand patterns, shapes, and tessellation in a simple and engaging way. This worksheet explains how shapes can be arranged, combined, and repeated to form patterns without gaps or overlaps. It is important because it builds strong foundational skills in geometry, observation, and logical thinking. This worksheet provides complete and accurate NCERT Solutions based strictly on the given content.
Chapter summary: stories, poems & themes
This chapter is activity-based and focuses on hands-on learning through paper weaving, pattern drawing, and shape exploration. Students learn how to create weaving patterns using paper strips and observe repeating designs. The chapter also introduces tessellation, where shapes cover a surface without gaps or overlaps. It includes observation-based questions, grid activities, and shape construction tasks. The main theme is understanding how patterns and shapes work together in mathematics through real-life and visual examples.
What this NCERT chapter covers?
• Understanding weaving patterns using paper strips
• Learning about repeating patterns and sequences
• Exploring tessellation and tiling without gaps or overlaps
• Identifying different shapes and their properties
• Observing angles and sides in triangles and quadrilaterals
• Recognising combinations of shapes in patterns
• Activity-based learning using grids, paper folding, and cutouts
How to use these NCERT solutions?
Students should first try to solve the questions on their own by observing patterns and shapes carefully. After attempting, they can check the answers to understand the correct methods. Parents and teachers can use these solutions to guide students step by step. The solutions follow the exact NCERT order and structure, making them useful for revision and concept clarity. This helps students improve accuracy and confidence.
Student tips & learning tricks
• Carefully observe patterns before answering
• Follow row-wise instructions in weaving patterns
• Check angles to understand tessellation
• Avoid skipping steps in pattern sequences
• Use drawing and colouring to understand designs better
• Pay attention to shape properties like sides and angles
Why NCERT solutions are important?
NCERT Solutions help students understand concepts clearly and correctly. They ensure that answers are aligned with the NCERT curriculum. These solutions strengthen basic concepts in geometry and patterns, which are important for higher classes. They also help students perform better in exams and build confidence in problem-solving.
Complete answer key – NCERT solutions
Weaving mats
1. Let us make paper mats
Fold the paper, cut equal slits, and weave strips by alternating under and over to create a pattern.
2. Can you figure out how to make this mat?
Row 1 – 2 over, 1 under (repeat)
Row 2 – 2 under, 1 over (repeat)
The pattern alternates in each row.
3. Try to weave a pattern
Row 1 – 2 over, 1 under (repeat)
Row 2 – 1 under (start), then 3 over, 3 under (repeat)
Row 3 – 2 under, 1 over (repeat)
Row 4 – 1 over (start), then 3 under, 3 over (repeat)
Follow rows in sequence to continue pattern.
4. Can you work out the steps for these designs?
Observe each design carefully and write the row-wise weaving pattern until it starts repeating.
Let us try
Complete the grid by continuing the same pattern in all directions to maintain symmetry.
Tiling and tessellation
Tessellation means covering a surface using shapes without gaps or overlaps.
No
Explanation:
Each angle of a regular pentagon is 108°.
3 × 108° = 324°, which is less than 360°, so a gap remains.
Adding one more pentagon gives 4 × 108° = 432°, which is more than 360°, so it will overlap.
Hence, one more pentagon cannot fit.
Find out
Can regular triangles fit together at a point? How many of them fit together?
Yes, 6 triangles fit together without gaps.
Explanation:
Each angle is 60°, so 6 × 60° = 360° (no gap or overlap).
Do you see that regular triangles fit around a point?
Yes
Explanation:
They meet perfectly without gaps or overlaps.
Can squares fit together around a point without any gap or overlap? How many squares did you need?
Yes, 4 squares fit together.
Explanation:
Each angle is 90°, so 4 × 90° = 360°.
Can five squares fit together around a point without any gaps or overlaps? Why or why not?
No
Explanation:
5 × 90° = 450°, which is more than 360°, so they overlap.
Can regular hexagons fit together around a point without any gaps or overlaps? How many fit together?
Yes, 3 hexagons fit together.
Explanation:
Each angle is 120°, so 3 × 120° = 360°.
What shapes have been used in this pattern?
Triangles, hexagons
Explanation:
The pattern combines both shapes to fill space without gaps.
Continue the pattern
Extend the design using the same arrangement of triangles and hexagons.
Do regular octagons fit together without any gaps or overlaps?
No, regular octagons do not tessellate.
Explanation:
Their angles do not fit exactly around a point to make 360°.
Look at the pattern
1. What shapes are coming together at the marked points?
Hexagons and small squares
2. Are the same set of shapes coming together at these points?
Yes
Explanation:
The same combination of shapes repeats at every marked point.
Are the triangles equilateral? Why or why not?
No
Explanation:
All sides of the triangles are not equal, so they are not equilateral.
What shapes are coming together at the marked points?
Triangles and squares
Are the same set of shapes coming together at these points?
Yes
What geometrical shapes can you make by fitting 2 of these triangles together?
Triangle, parallelogram, rhombus
1. How many different types of triangles can you make?
3
Explanation:
Isosceles, equilateral, scalene
What do you notice?
Each triangle has 2 equal sides
What do you notice about their angles?
Two angles are equal
2. Is it possible to make a triangle where all three sides are equal?
Yes
3. Is it possible to make a triangle where all three sides are unequal?
Yes
Explanation:
Such triangles are called scalene triangles.
After cutting the equilateral triangle in half, how many sides of each new triangle are equal?
No sides are equal.
The new triangles formed are scalene triangles.
Check in scalene triangles whether any two or more angles are equal?
In a scalene triangle, no two angles are equal—all angles are different.
4. How many different 4-sided shapes (quadrilaterals) can you make?
3
Kite, parallelogram, rectangle
What do you notice about the sides of a kite?
Side 1 = Side 2
Side 3 = Side 4
Adjacent sides are equal.
5. Measure the sides of quadrilaterals A and B. What do you notice?
Opposite sides are equal
Are there any pairs of sides that are equal? Which pairs are equal?
Opposite sides
What types of angles do quadrilaterals A and B have?
Both are parallelograms; B is a rectangle.
7. How many sides do each one of them have?
3-sided, 4-sided, 5-sided shapes
Explanation:
Different arrangements form polygons with different sides.
8. Which of these shapes can be made with all 4 pieces?
Square, rectangle, triangle
Tangram
They are different in shape and size but are made from the same set.
Angles are different
Sides are of different lengths
Which shape am I?
Rectangle
Square
Parallelogram
Kite
What shapes do you see in the kite?
Triangles
Play with circles
What shape is formed?
Rectangle
Explanation:
Joining endpoints of diameters forms a rectangle.
What do you notice about the shape formed?
No matter which diameters are chosen, the shape formed remains a rectangle.
Is it possible to create a 4-sided shape other than a rectangle through this process?
No
Master shapes and patterns with clear NCERT Solutions designed to make learning simple and effective.