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

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Elaboration on this Achievement Objective

This means students will explore sequential patterns, either spatial, for example, spatialsequence. , ... 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, spatial3. in the pattern above, and use this to predict the shape in a given ordinal position, for example, the next shape is spatialsquare. , the eleventh shape will be spatial circle. . 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
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A long dinner

Level Two
Number and Algebra
Rich learning activities
The purpose of this activity is to engage students in identifying a (simple linear) pattern and using this to solve a problem.
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A Spot of Sickness

Level Two
Number and Algebra
Figure It Out activities
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

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Building Graphs

Level Two
Number and Algebra
Figure It Out activities
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

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Cannon balls

Level Two
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • 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 a list).
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Dual patterns

Level Two
Number and Algebra
Units of Work
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 single-attribute and two-attribute repeating patterns with varying numbers of elements.
  • Identify and replace missing elements in a repeating pattern.
  • Identify, describe, and create composite patterns.
  • Identify the unit of repeat in a repeating pattern and apply known300
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Entertaining Patterns

Level Two
Number and Algebra
Figure It Out activities
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

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Fair and Square

Level Two
Number and Algebra
Figure It Out activities
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

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Flipping Fish

Level Two
Number and Algebra
Figure It Out activities
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

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Follow that Arrow

Level Two
Number and Algebra
Figure It Out activities
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

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Food for Thought

Level Two
Number and Algebra
Figure It Out activities
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)

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Jo's table

Level Two
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Continue patterns.
  • Describe number patterns.
  • Devise and use problem solving strategies (guess and check, make a table, look for patterns).
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Letter patterns

Level Two
Number and Algebra
Units of Work
In this unit we look at number patterns from letters and numbers. We use a table of values to help record our thinking. 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.
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Mapping relationships

Level Two
Number and Algebra
Units of Work
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 relationships 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.
  • Transfer mapped values onto a graph (an300
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Odd and even numbers

Level Two
Number and Algebra
Units of Work
The purpose of this unit is to explore a pattern that is central to our number system: odd and even numbers.
  • Identify 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 and300
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Pede patterns

Level Two
Number and Algebra
Units of Work
This unit is about generating number patterns for certain creatures 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.
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Perfect Patterns

Level Two
Number and Algebra
Figure It Out activities
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

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Pick the Pattern

Level Two
Number and Algebra
Figure It Out activities
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

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Punching Numbers

Level Two
Number and Algebra
Figure It Out activities
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

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Puzzling Picnics

Level Two
Number and Algebra
Figure It Out activities
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

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Quacky Questions

Level Two
Integrated
Figure It Out activities
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)

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Scaling Up

Level Two
Number and Algebra
Figure It Out activities
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

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Staircases

Level Two
Number and Algebra
Units of Work
In this unit ākonga look for and describe patterns they see in different types of staircases and other patterns.
  • Continue a sequential pattern.
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Sticky Moments

Level Two
Number and Algebra
Figure It Out activities
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

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Supermarket displays

Level Two
Number and Algebra
Units of Work
In this unit students explore the number patterns created when tins are stacked in different arrangements and keep track of the numbers involved by drawing up a table of values.
  • Identify patterns in number sequences.
  • Systematically “count” to establish rules for sequential patterns.
  • Use rules to make predictions.
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Table Time

Level Two
Number and Algebra
Figure It Out activities
This is a level 2 algebra strand activity from the Figure It Out series.A PDF of the student activity is included.

using tables to show patterns