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Where to Look From - Dot Grid Shapes

Grade 3CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Different Views of Objects: An object can look different depending on where you look at it from. For example, a car from the side shows its wheels and doors, but from the top, it looks like a large rectangle with a roof in the middle.

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Top View: This is the view of an object as seen from directly above. A round table appears as a simple circle from the top, while a staircase might look like a set of parallel rectangular strips from above.

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Front and Side Views: These views are seen from the front or the side of an object. A bus seen from the front looks like a rectangle with two headlights and a windshield, whereas from the side, it appears as a long rectangle with many windows.

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Dot Grid Patterns: A dot grid is a set of dots arranged in rows and columns at equal distances. We can use these dots to draw shapes like squares, rectangles, and triangles by connecting the dots with straight lines. For example, a square is made by connecting the same number of dots horizontally and vertically, like 33 dots by 33 dots.

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Creating Designs (Rangoli): On a dot grid, we can create beautiful patterns called Rangoli. These can be made of straight lines forming geometric shapes or curved lines forming floral patterns by connecting dots in different sequences.

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Mirror Halves and Symmetry: Some shapes can be divided into two identical parts by a line. These are called mirror halves. If you place a mirror on the dividing line, the reflection completes the other half of the shape. For example, the letter 'M' has a vertical line of symmetry down the middle.

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Line of Symmetry: This is an imaginary dotted line that divides a figure into two parts such that one part is the mirror image of the other. Some shapes, like a circle, can have many lines of symmetry, while others, like the letter 'P', have no line of symmetry.

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Incomplete Shapes on Dot Grid: We can complete a symmetrical shape on a dot grid by counting the number of dots from the line of symmetry on one side and mirroring the same count on the other side to ensure both halves are identical.

📐Formulae

Length of a segment=(Number of dots in a row−1) unitsLength\ of\ a\ segment = (Number\ of\ dots\ in\ a\ row - 1)\ units

Total Dots in a Rectangle=(Dots along length)×(Dots along width)Total\ Dots\ in\ a\ Rectangle = (Dots\ along\ length) \times (Dots\ along\ width)

Perimeter of square on grid=4×(Number of gaps between dots on one side)Perimeter\ of\ square\ on\ grid = 4 \times (Number\ of\ gaps\ between\ dots\ on\ one\ side)

Area by counting squares=Number of complete squares enclosed by dotsArea\ by\ counting\ squares = Number\ of\ complete\ squares\ enclosed\ by\ dots

💡Examples

Problem 1:

On a dot grid, draw a rectangle where the length covers 55 dots and the width covers 33 dots. How many total dots are used for the boundary?

Solution:

  1. Place the first dot as a corner.
  2. Move horizontally and count 55 dots to form the length.
  3. From the corners of the length, move vertically down and count 33 dots to form the width.
  4. Connect the remaining dots to close the rectangle.
  5. The boundary dots are the 55 dots on top, 55 dots on the bottom, and the 11 extra dot in the middle of each side (since the corner dots are already counted).
  6. Total dots = 5+5+(3−2)+(3−2)=5+5+1+1=125 + 5 + (3 - 2) + (3 - 2) = 5 + 5 + 1 + 1 = 12 dots.

Explanation:

To find the dots on the boundary, we sum the dots on all four sides while being careful not to double-count the corner dots.

Problem 2:

Identify the line of symmetry for the letter 'H' and explain if it has more than one mirror half.

Solution:

  1. If we draw a horizontal line through the middle of 'H', the top part is the mirror image of the bottom part.
  2. If we draw a vertical line through the center of 'H', the left part is the mirror image of the right part.
  3. Therefore, 'H' has 22 lines of symmetry.

Explanation:

A shape can have multiple mirror halves if it can be folded in more than one way to make the parts match perfectly.