Question 17 of 19beginner💡 UnderstandShort Answer3 marks

How many little squares are there in each shape of the sequence of Stacked Squares? Which number sequence does this give? Can you explain why?

Correct Answer

Counting little squares in Stacked Squares: First shape: 1 square (1×11 \times 1) Second shape: 4 squares (2×22 \times 2) Third shape: 9 squares (3×33 \times 3) Fourth shape: 16 squares (4×44 \times 4) Fifth shape: 25 squares (5×55 \times 5)

Sequence formed: 1, 4, 9, 16, 25, ... This is the Square numbers sequence.

Explanation: Each shape in the sequence is a square grid. First shape: 1×11 \times 1 grid with 1 square Second shape: 2×22 \times 2 grid with 4 squares Third shape: 3×33 \times 3 grid with 9 squares In general, the nth shape is an n×n grid containing n² small squares ∴ This is exactly the nth square number.

Exercise: Figure it Out (Section 6) | Q: 3 | (Page Page 12)
For More Understanding

Explanation

The Stacked Squares sequence shows progressively larger square grids. Each shape is built by adding another layer of squares around the previous shape. The number of small squares in each shape follows the pattern 1, 4, 9, 16, 25, ... which are perfect squares. This is because each shape is an n×n grid containing n² unit squares.

Solution Steps

  1. Count the little squares in each shape of the Stacked Squares sequence.

  2. Identify the pattern: 1, 4, 9, 16, 25, ...

  3. Recognize this as the Square numbers sequence.

  4. Explain: each shape is an n×n grid containing n² small squares, which is the nth square number.

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