NCERT Class 5 Mathematics Maths Mela Chapter 07 Shapes and Patterns PDF Download

Chapter 7: Shapes and Patterns

Weaving Mats

You may have seen woven baskets of different kinds. If you look closely, you will notice different weaving patterns on each basket.

We will try weaving some mats with paper strips.

1. Let us make paper mats.

You will need - A coloured paper (30 cm long and 20 cm wide) and eight paper strips of two different colours (3 cm wide and longer than 20 cm).

1. Take a coloured paper 30 cm long and 20 cm wide.
2. Fold the coloured paper in half along the longer side.
3. Draw vertical lines at equal distances from the closed end and cut slits leaving a gap of 3 cm at the top.
4. Carefully unfold the paper. There will be no cuts in the paper at the top and the bottom.
5. Now cut 8 paper strips of 3 cm width in 2 colours and of length slightly longer than 20 cm.
6. Take one colour strip and weave it across the slits going 1 under and 1 over, and again 1 under and 1 over. Repeat it for the first row.
7. Take one more strip of another colour and weave it across the slits going 1 over and 1 under, and again 1 over and 1 under. Repeat it for the second row.
8. Weave all the strips in the same alternating pattern. Neatly fold any extra strip ends behind the mat. Your mat is ready!

We can describe the pattern of the above weave as follows.
Row 1-1 under, 1 over, 1 under, 1 over, ... (repeat)
Row 2 - 1 over, 1 under, 1 over, 1 under, ... (repeat)

2. Can you figure out how to make this mat?

Let us try to understand how this mat is woven by looking at the pattern in the first two rows.
Row 1 - 2 over, 1 under, 2 over, 1 under, ...
Row 2-2 under, 1 over, 2 under, 1 over, ...
You can use strips of the same colour or 2 different colours, one for each row.

3. Try to weave a pattern, using the rules given below.

Row 1 - 2 over, 1 under, 2 over, 1 under, ... (repeat).
Row 2 - 1 under (do not repeat), 3 over, 3 under, 3 over, 3 under, ... (repeat).
Row 3 - 2 under, 1 over, 2 under, ... (repeat).
Row 4 - 1 over (do not repeat), 3 under, 3 over ... (repeat). Continue weaving in this order.

4. Can you work out the steps for any of these designs and weave the pattern?

Write the steps of the pattern in your notebook for each row until it starts repeating.

Let Us Try

Draw the following pattern on a grid paper. Part of it is done for you. Now, complete the rest of the grid to get the full design.

[Figure: Grid pattern with partial design completed, See in your textbook]

Teacher's Note

When you write down the weaving pattern for a row, look carefully at whether each strip goes over or under as you move across. Start from one end and count in order: if the first movement is "over", the second will be "under" in a basic pattern. Write down the repeating part only, not the whole row - that saves time and helps you see the pattern's structure.

Tiling and Tessellation

We often use tiles of the same shape or a combination of shapes to cover a region.

You can see pentagons (5-sided figures) in this figure. As all its sides are equal it is a regular pentagon.

Shapes that have equal sides are called regular shapes.

We have placed 3 pentagons around a point. Can we fit one more into the empty space?

Pentagons cannot fill a region without leaving gaps. So, we say that regular pentagons do not tessellate.

Find Out

Can regular triangles fit together at a point without any gap? How many of them fit together? (A sample triangle is given at the end of the book).

Do you see that regular triangles fit around a point as shown here?

Regular triangles when fitted around a point leave no gaps and there is no overlap.

Triangles with all equal sides are also called equilateral triangles.

Therefore, equilateral triangles tessellate. Can squares (a regular 4-sided shape) fit together around a point without any gap or overlap? Try it out using cutouts of squares (a sample square is given at the end of the book). How many squares did you need?

Can five squares fit together around a point without any gaps or overlaps? Why or why not?

Can regular hexagons (6-sided shapes with equal sides) fit together around a point without any gaps or overlaps? Try and see (a sample hexagon is given at the end of the book). How many fit together at a point?

Here is a tessellating pattern with more than one shape.

What shapes have been used in this pattern? _____________, _____________.

Continue the pattern given below and colour it appropriately.

[Figure: Tessellating pattern with hexagons and triangles in yellow and blue, See in your textbook]

A regular octagon means a shape with eight equal sides.

Do regular octagons fit together without any gaps or overlaps? Try drawing the same and check.

Regular octagons do not tessellate.

Look at the pattern given below. What shapes are coming together at the marked points? Are the same set of shapes coming together at these points? Continue the pattern and colour it appropriately.

[Figure: Hexagonal and diamond pattern with marked points, See in your textbook]

What shapes are coming together at the marked points?

Are the same set of shapes coming together at these points?

Continue the pattern and colour it appropriately.

Create similar patterns using other cutouts of shapes.

A rhombus is a shape with all equal sides. It has been divided into four triangles.

[Figure: Rhombus divided into four triangles, See in your textbook]

Here is a tiling pattern made using two different shapes - squares and triangles. Are the triangles equilateral? Why or why not?

[Figure: Tiling pattern with squares and triangles, See in your textbook]

Teacher's Note

A tessellating pattern works when shapes fit together with no gaps or overlaps around each point. Test whether a shape tessellates by checking a single point first: if the angles meeting at that point add up to exactly 360 degrees, the shape can tessellate. For example, six equilateral triangles (each 60 degrees) meet at a point: 6 × 60 = 360 degrees, so triangles tessellate.

Key Points

• A weaving pattern repeats in each row, following a rule of alternating "over" and "under" or other combinations. Write down just the repeating part to describe the pattern clearly.
• A regular shape has all sides equal. Tessellate means shapes fit together with no gaps or overlaps.
• Equilateral triangles, squares, and regular hexagons tessellate on their own, but regular pentagons and regular octagons do not. Different shapes can tessellate together if their angles at a meeting point add up to 360 degrees.

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