Samacheer Kalvi Class 5 Maths Solutions Term 1 Chapter 3 Patterns InText Questions

Activity (Text Book Page No. 53)

Question 1. Continue the colours pattern as shown.
Answer: The patterns follow a clear sequence of shapes and colors.
1. The first pattern is a repeating sequence of triangles: upright, inverted, right-pointing, left-pointing. The colors also repeat in sequence: orange, blue, green, yellow. To continue, you would repeat this set of four triangles and colors.
2. The second pattern uses three shapes: a horizontal rectangle, a vertical rectangle, and a diamond. The colors are pink, light blue, and dark blue, repeating with these shapes. To continue, you would repeat this set of three shapes and colors.
3. The third pattern is a series of circles. The colors repeat as blue, pink, orange. To continue, you would repeat these three colors for the circles.
Observing and understanding the repeating unit is key to extending any pattern correctly.
In simple words: Look at the shapes and colors that come one after another. Find the part that repeats. Then, just keep drawing that same repeating part to continue the pattern.

🎯 Exam Tip: Always identify the basic repeating unit (the 'core' of the pattern) for both shape and color before attempting to extend it.

Do Yourself (Text Book Page No. 56)

Question 1. Count and write the tiles for each figure.
Answer: The table below shows the count of tiles for each figure. Each figure represents a square number, which is a number multiplied by itself.

🎯 Exam Tip: Recognize that these tile counts are square numbers (\(1^2=1, 2^2=4, 3^2=9\), etc.), which is a common pattern in such visual problems.

Question 2. Circle the square numbers.
Answer: Square numbers are the result of multiplying a whole number by itself (e.g., \(1 \times 1 = 1\), \(2 \times 2 = 4\)). In a multiplication table, square numbers appear along the diagonal where the row number is the same as the column number. These numbers are highlighted below.

🎯 Exam Tip: Remember that square numbers are always found on the main diagonal of a multiplication table, from top-left to bottom-right.

Try These (Text Book Page No. 60)

Question a. Find the sum: \( 1 + 3 + 5 + 7 + 9 + 11 \)
Answer: The sum of the first \( n \) odd numbers is \( n^2 \). Here, we are adding the first 6 odd numbers.
\( 1 + 3 + 5 + 7 + 9 + 11 = 36 \)
This can also be written as \( 6 \times 6 = 6^2 \).
In simple words: When you add a string of odd numbers starting from 1, the total is always a square number. Count how many odd numbers you added, and then multiply that count by itself. Here, there are 6 odd numbers, so the sum is \( 6 \times 6 = 36 \).

🎯 Exam Tip: The sum of the first 'n' odd numbers is always equal to 'n' squared (\(n^2\)), which is a useful shortcut for such problems.

Question b. Find the sum: \( 1 + 3 + 5 + 7 + 9 + 11 + 13 \)
Answer: This is the sum of the first 7 odd numbers.
\( 1 + 3 + 5 + 7 + 9 + 11 + 13 = 49 \)
This is equal to \( 7 \times 7 = 7^2 \). This pattern simplifies calculations greatly.
In simple words: Add up all the odd numbers given. There are 7 odd numbers, so the answer is \( 7 \times 7 = 49 \).

🎯 Exam Tip: Recognize the pattern: the sum of the first 'n' odd numbers is \(n^2\). For 7 odd numbers, the sum is \(7^2=49\).

Question c. Find the sum: \( 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 \)
Answer: This is the sum of the first 8 odd numbers.
\( 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64 \)
This result is \( 8 \times 8 = 8^2 \).
In simple words: Count how many odd numbers are being added. Here there are 8, so the total sum is \( 8 \times 8 = 64 \).

🎯 Exam Tip: Applying the rule \( \text{sum} = n^2 \) helps quickly solve sums of consecutive odd numbers without lengthy addition.