# NA2-8: Find rules for the next member in a sequential pattern.

This means students will explore sequential patterns, either spatial, for example, , ... 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, in the pattern above, and use this to predict the shape in a given ordinal position, for example, the next shape is , the eleventh shape will be . For simple number patterns students should identify the consistent “gap” between the terms (for example, 1, 3, 5, 7... two is added each time), and use this additive difference to find further terms. Students should also develop their concept of relations between variables using spatial patterns that can be represented using numeric tables of values, for example, for this pattern, how many squares make 7 crosses?

continue a sequential pattern

show a pattern on a graph

continue a sequential pattern

continue a spatial pattern

show a pattern on a graph

- Create, describe and continue a single-attribute repeating pattern.
- Identify and describe the composite pattern.
- Create an original composite pattern with a unit of repeat of more than 6 elements (3 and 2) but no more than 12 (3 and 4).
- Describe and explain the rule for the pattern in the300

- Recognise even and odd numbers.
- Independently investigate, recognise and report on the patterns and characteristics of even numbers and of odd numbers.
- State generalisations about the addition and subtraction of even numbers and of odd numbers.
- Investigate and recognise the results of adding300

use repeated addition or skip counting to solve problems

use addition facts to solve problems

describe a rule

use a rule to make a predicition

find the rule to continue a pattern

continue a spatial pattern and describe the rule

continue a sequential pattern and describe the rule

find the rule connecting members in a pattern

use additive strategies to solve problems (Problems 1,2 and 4)

predict next member in a sequence (Problem 3)

- Draw the next shape in a pattern sequence.
- See how the pattern continues from one shape to the next.
- Draw up a table of values.

- Recognise situations in which there is a relationship between two number sets.
- Use a ‘mapping diagram’ to show a number relationship.
- Understand the connection between the coordinate systems of maps and graphs.
- Identify a situation in which there is a unique relationship between two data sets300

- Classify whole numbers as even or odd and generalise the nature of sums when even and odd numbers are added.
- Recognise that sums remain the same if the same amount is added and subtracted to the two addends, e.g. 17 + 19 = 27 + 9.
- Create and follow instructions to make a model made with shapes. 300

- Continue a simple pattern.
- Generalise the pattern.

continue a sequence of basic facts equations

continue a spatial pattern

continue a sequential pattern

create a number pattern

continue a pattern and find a rule

find rectangles within a shape (Problem 1)

solve problems using additive strategies (Problem 2)

continue a spatial pattern (Problem 3)

continue a sequential pattern

- Continue a sequential pattern.

find rules for sequential patterns

- Identify patterns in number sequences.
- Systematically “count” to establish rules for sequential patterns.
- Use rules to make predictions.