NA2-8: Find rules for the next member in a sequential pattern.
Elaboration on this Achievement Objective
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, 
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?
Teaching resources for this Achievement Objective
The purpose of this activity is to engage students in identifying a (simple linear) pattern and using this to solve a problem.
Rich learning activities
Number and Algebra
Level Two
This is a level 2 algebra strand activity from the Figure It Out series. A PDF of the student activity is included.
continue a sequential pattern show a pattern on a graph
Figure It Out activities
Number and Algebra
Level Two
This is a level 2 algebra strand activity from the Figure It Out series. A PDF of the student activity is included.
continue a sequential pattern continue a spatial pattern show a pattern on a graph
Figure It Out activities
Number and Algebra
Level Two
Identify a pattern and describe this using their own words Use equipment appropriately when exploring mathematical ideas; devise and use problem solving strategies to explore situations mathematically (guess and check, make an list).
Problem solving activities
Number and Algebra
Level Two
This unit develops pattern-based thinking through the exploration of a pattern that has more than one attribute and more than one unit of repeat.
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 the composite...
Units of Work
Number and Algebra
Level Two
The purpose of this unit of is to develop pattern-based thinking through the exploration of a pattern that is central to our number system: odd and even numbers.
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 adding and...
Units of Work
Number and Algebra
Level One
This is a level 2 number and algebra activity from the Figure It Out theme series. A PDF of the student activity is included.
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
Figure It Out activities
Number and Algebra
Level Two
This is a level 2 algebra strand activity from the Figure It Out series. A PDF of the student activity is included.
find the rule to continue a pattern
Figure It Out activities
Number and Algebra
Level Two
This is a level 2 algebra activity from the Figure It Out theme series. A PDF of the student activity is included.
continue a spatial pattern and describe the rule continue a sequential pattern and describe the rule
Figure It Out activities
Number and Algebra
Level Two
This is a level 2 algebra strand activity from the Figure It Out series. A PDF of the student activity is included.
find the rule connecting members in a pattern
Figure It Out activities
Number and Algebra
Level Two
These are level 2 number and algebra problems from the Figure It Out series. A PDF of the student activity is included.
use additive strategies to solve problems (Problems 1,2 and 4) predict next member in a sequence (Problem 3)
Figure It Out activities
Number and Algebra
Level Two
Continue patterns Describe number patterns Devise and use problem solving strategies (guess and check, make a table, look for patterns)
Problem solving activities
Number and Algebra
Level Two
In this unit we look at the number patterns we get from letters and numbers. We keep track of the numbers involved by drawing up a table of values. It’s important here to look for the pattern and see how the number of tiles changes from letter to letter.
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.
Units of Work
Number and Algebra
Level Two
The purpose of this unit of two lessons is to develop relational thinking through the exploration and expression of the relationship between two related number patterns.
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 sets....
Units of Work
Number and Algebra
Level Two
This unit provides you with a range of opportunities to assess the entry level of achievement of your students.
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....
Units of Work
Number and Algebra
Level Two
This unit is about generating number patterns for certain ‘insects’ from the mythical planet of Elsinore. Each ‘Pede’ is made up of square parts and has a number of feet. The patterns range from counting by 2s and 3s to being the number of feet plus three.
Continue a simple pattern. Generalise the pattern.
Units of Work
Number and Algebra
Level Two
This is a level 2 algebra strand activity from the Figure It Out series. A PDF of the student activity is included.
continue a sequence of basic facts equations
Figure It Out activities
Number and Algebra
Level Two
This is a level 2 algebra strand activity from the Figure It Out series. A PDF of the student activity is included.
continue a spatial pattern continue a sequential pattern
Figure It Out activities
Number and Algebra
Level Two
This is a level 2 algebra strand activity from the Figure It Out series. A PDF of the student activity is included.
create a number pattern
Figure It Out activities
Number and Algebra
Level Two
This is a level 2 algebra strand activity from the Figure It Out series. A PDF of the student activity is included.
continue a pattern and find a rule
Figure It Out activities
Number and Algebra
Level Two
These are level 2 number, algebra, and geometry problems from the Figure It Out series. A PDF of the student activity is included.
find rectangles within a shape (Problem 1) solve problems using additive strategies (Problem 2) continue a spatial pattern (Problem 3)
Figure It Out activities
Geometry and Measurement
Level Two
This is a level 2 algebra activity from the Figure It Out theme series. A PDF of the student activity is included.
continue a sequential pattern
Figure It Out activities
Number and Algebra
Level Two
In this unit students look for and describe the patterns they see in different types of staircases.
Continue a sequential pattern. Develop bar charts to show relationships.
Units of Work
Number and Algebra
Level Two
This is a level 2 algebra strand activity from the Figure It Out series. A PDF of the student activity is included.
find rules for sequential patterns
Figure It Out activities
Number and Algebra
Level Two
In this unit the students look at the number patterns created when tins are stacked in different arrangements. The aim of the unit is for students to keep track of the numbers involved by drawing up a table of values. They are then encouraged to look for patterns in the numbers.
Identify patterns in number sequences. Systematically “count” to establish rules for sequential patterns. Use rules to make predictions.
Units of Work
Number and Algebra
Level Two