AC9M7N01

See also: Learning Areas / Mathematics / Mathematics / Number / Year 7

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

Elaborations

• AC9M7N01_E1 - investigating squares of natural numbers from one to \(20\), and connecting them to visual representations such as dots arranged in a square pattern
• AC9M7N01_E2 - using the square and square root notation, and the distributive property and area diagrams to calculate the squares of two-digit numbers; for example, \(43^2=(40+3)^2=40^2+2\times40\times3+3^2=1600+240+9=1849\)
• AC9M7N01_E3 - 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 \(7\)
• AC9M7N01_E4 - 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
• AC9M7N01_E5 - 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

Achievement Standard Components

• ASMAT702 - They solve problems involving squares of numbers and square roots of perfect square numbers.