Number 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) 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× 40 ×3+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 √43 is between √36 and √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 Represent natural numbers as products of powers of prime numbers using exponent notation (AC9M7N02) developing familiarity with the sequence 1, 2, 4, 8, 16, 32, 64, 128, 256, 512 and powers of 2; the sequence 1, 3, 9, 27, 81, 243, 729 and powers of 3; and the sequence 1, 5, 25, 125, 625 and powers of 5 Represent natural numbers in expanded notation using place value and powers of 10 (AC9M7N03) investigating exponent notation for powers of 10 such as ‘one hundred thousand’ is 100 000=10 × 10× 10× 10 ×10=105 relating the sequences 10, 100, 1000, 100 000 … and 101, 102, 103, 104 ... Use the 4 operations with positive rational numbers including fractions, decimals and percentages to solve problems using efficient calculation strategies (AC9M7N06) developing efficient strategies with appropriate use of the commutative and associative properties, place value, patterning, and multiplication facts to solve multiplication and division problems involving fractions and decimals, for example, using the commutative property to 2 1 1 2 1 calculate of giving of = 3 2 2 3 3 Compare, order and solve problems involving addition and subtraction of integers (AC9M7N07) using less-than and greater-than notation in expressions when comparing and ordering integers; for example, negative 5 is less than positive 2 and can be represented as (−5) < (+2); (−3) > (−6) discussing language such as “addition”, “subtraction”, “magnitude”, “difference”, “sign” and synonyms of these terms © Oxford University Press 2023 Oxford Maths 7 Australian Curriculum Teacher obook pro ISBN 9780190332815 Permission has been granted for this page to be photocopied within the purchasing institution only.
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