ePortfolio Maths - Knowledge

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.

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 am able to know the divisibility rules for 2,3,4,5,6,8,9,10 and am able to know what numbers are divisible from a number.

My next step is to be able to know the divisibility rules of by heart for all numbers.