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Related topic
Mathematics / Year 7 / Number
Curriculum content descriptions
describe the relationship between perfect square numbers and square roots, and use squares of numbers and square roots of perfect square numbers to solve problems (AC9M7N01)
Elaborations
- investigating squares of natural numbers from one to \(20\), and connecting them to visual representations such as dots arranged in a square pattern
- using the square and square root notation, and the distributive property and area diagrams to calculate the squares of two-digit numbers; for example, \(43^2=(40+3)^2=40^2+2\times40\times3+3^2=1600+240+9=1849\)
- determining between which \(2\) consecutive natural numbers the square root of a given number lies; for example, \(43\) is between the square numbers \(36\) and \(49\) so \(\sqrt{43}\) is between \(\sqrt{36}\) and \(\sqrt{49}\) and therefore between \(6\) and \(7\)
- generating a list of perfect square numbers and describing any emerging patterns; for example, the last digit of perfect square numbers, or the difference between consecutive square numbers, and recognising the constant second difference
- using the relationship between perfect square numbers and their square roots to determine the perimeter of a square tiled floor using square tiles; for example, an area of floor with \(144\) square tiles has a perimeter of \(48\) tile lengths
General capabilities
ScOT terms
Perfect squares, Square roots