Group 8 Knowledge Sample Term 2
Achievement objectives:
NA4-1: Use a range of multiplicative strategies when operating on whole numbers.
Elaboration on this Achievement Objective:
This means students will apply the properties of multiplication and division (commutative, distributive,
associative and inverse) to number problems, particularly those requiring multiplication and division.
Students should exercise critical choice in their method of calculation - mental, machine or paper - and
recognise situations in which estimation should be used, including the checking of calculated answers.
Strategies expected at Level Four include: using common factors and multiples, for
example 37 + 41 + 40 + 38 = as 4 x 40 – 4, using the distributive property, for example
24 x 36 = 20 x 36 + 4 x 36, 9 x 78 = 9 x 80 – 9 x 2, or 276 ÷ 12 = 240 ÷ 12 + 36 ÷ 12, using the associative
property, for example 12 x 33 = 4 x 99, or 216 ÷ 12 = 216 ÷ 2 ÷ 2 ÷ 3, and inverse operations (reversing), for example
354 ÷ 6 = as 6 x = 354. This objective also involves calculating powers, for example
43 = 4 x 4 x 4 = 64, and factorials, for example 4! = 1 x 2 x 3 x 4 = 24. Students should have strong
mental strategies for operations on whole numbers but also accurately carry out standard written algorithms,
particularly for multi-digit multiplication and division. Level Four corresponds to the
Advanced Multiplicative stage of the number framework.
associative and inverse) to number problems, particularly those requiring multiplication and division.
Students should exercise critical choice in their method of calculation - mental, machine or paper - and
recognise situations in which estimation should be used, including the checking of calculated answers.
Strategies expected at Level Four include: using common factors and multiples, for
example 37 + 41 + 40 + 38 = as 4 x 40 – 4, using the distributive property, for example
24 x 36 = 20 x 36 + 4 x 36, 9 x 78 = 9 x 80 – 9 x 2, or 276 ÷ 12 = 240 ÷ 12 + 36 ÷ 12, using the associative
property, for example 12 x 33 = 4 x 99, or 216 ÷ 12 = 216 ÷ 2 ÷ 2 ÷ 3, and inverse operations (reversing), for example
354 ÷ 6 = as 6 x = 354. This objective also involves calculating powers, for example
43 = 4 x 4 x 4 = 64, and factorials, for example 4! = 1 x 2 x 3 x 4 = 24. Students should have strong
mental strategies for operations on whole numbers but also accurately carry out standard written algorithms,
particularly for multi-digit multiplication and division. Level Four corresponds to the
Advanced Multiplicative stage of the number framework.
We have specifically been learning the divisibility rules for 2, 3, 4, 5, 6, 8, 9, 10, e.g. 276 is divisible by 3
because 2 + 7 + 6 = 15. By knowing these rules, we can use our knowledge to solve problems. Below
are examples of work showing how this skill has been mastered.
Self Reflection:
In this sample of learning I have shown that I have a capability to learn divisibility rules including: 2,3,4,5,6,8,9,10.
My next step is to be capable of knowing some rules of by heart or at least without difficulty or reference.
Always good to have future goals. Well done for your achievements to date :)
ReplyDeleteAyla, you have understood divisibility rules to 10. You know some off by heart but your next step is to continue to learn and memorise them so that you can solve problems quickly.
ReplyDelete