The Ministry is migrating nzmaths content to Tāhurangi.
Relevant and up-to-date teaching resources are being moved to Tāhūrangi (tahurangi.education.govt.nz).
When all identified resources have been successfully moved, this website will close. We expect this to be in June 2024.
e-ako maths, e-ako Pāngarau, and e-ako PLD 360 will continue to be available.
For more information visit https://tahurangi.education.govt.nz/updates-to-nzmaths
This means students will recognise the features of tabular, graph and equation representations of linear and quadratic relationships. This includes connecting constant first or second order difference in tables with linear and quadratic relations respectively, with the graph (linear and parabolic) and standard equation forms (y = mx + c and y = a x 2 + bx + c) for such relations. For example, given the spatial pattern below students can use a table, graph or equation to represent the relation and solve problems.
This means students will understand that to generalise means to establish properties that hold for all occurrences. This involves the ability to examine a number of cases, define the variables involved, use appropriate mathematical terminology and symbols, and ultimately reason with the properties themselves. Fractional numbers, for the purpose of this objective, are defined as rational numbers in the form a/b, where a and b are whole numbers and b ≠ 0.
This means students will describe the function rule for a linear relationship as well as recognise recursive relationships where more complex relationships are involved. For example, given the pattern of fish made with matchsticks and counters below, students should be able to represent the relationships in a table and graph and use these representations to predict the terms in the sequence:
This means students will generalise, which means to establish properties that hold for all occurrences. This involves the ability to look at several examples, notice what changes (variables) and what does not, use appropriate mathematical terminology and symbols to describe the pattern, and apply the generalisation to other examples. At Level Four students should be able to describe and apply the properties of multiplication and division as these operations apply to whole numbers. These properties include commutativity, distributivity, associativity, inverse and identity.
This means students will recognise that a sequential pattern can be either spatial, for example .gif){kind=small}
.., or numeric, for example 1, 3, 5, 7... A pattern has consistency so further terms of it can be anticipated from those already known. The focus in this thread is that students become increasingly sophisticated at describing the relationships between variables found in sequential patterns.
This means students will generalise, which means to establish properties that hold for all instances. Generalisation begins with noticing patterns and relationships in a few specific instances, defining the variables involved, noticing the relationships between the variables, then using appropriate mathematical terminology and symbols to describe the relationships. At Level Three students develop many generalisations that allow them to perform mental strategies effectively.
This means students will explore sequential patterns, either spatial, for example, .gif){kind=small}
, ... or numeric, for example, 1, 3, 5, 7 ... A pattern has consistency so further terms of it can be anticipated from those already known. In spatial patterns students should be able to identify the repeating element, for example,
