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Patterns and relationships units of work

Level 1 Patterns and Relationships

Achievement ObjectivesLearning OutcomesUnit title
NA1-5
NA1-1
NA1-2
  • recognise that counting tells how many objects are in the set irrespective of how they are arranged or the order in which they are counted.
  • solve problems involving one more or less to a given set using their knowledge of the forward and backward number sequences
  • skip count in 2s
Counting on counting
NA1-5
NA1-1
  • see what a number pattern is
  • be able to guess and check the next number in a pattern
  • skip count in 2s, 5s, and 10s
Ten in a bed
NA1-5
NA1-1
  • continue a sequential pattern
  • systematically count to establish rules for sequential patterns
  • skip count in 2s, 5s and 3s
The three pigs
NA1-5
NA1-1
  • continue a skip-counting pattern
  • describe skip-counting patterns
  • use graphs to illustrate skip-counting patterns
Beetle wheels
NA1-5
NA1-6
NA2-7
NA2-8
  • investigate and recognise the results of adding and subtracting combinations of odd and even numbers
  • state generalisations about the addition and subtraction of combinations of odd and even numbers
  • apply generalisations about odd and even number patterns to problem solving situations
Early number patterns
NA1-6
  • describe patterns
  • continue a pattern
  • create patterns
Pattern makers
NA1-6
  • record patterns on grid paper
  • make predictions about ‘missing’ sections of a pattern
  • use words to describe linear patterns
Snakes and scarves
NA1-6
  • "read" a repeating pattern and predict what may come next
  • create a repeating pattern with two elements
  • create a repeating pattern with three elements
Mary, Mary quite contrary

Level 2 Patterns and Relationships

Achievement ObjectivesLearning OutcomesUnit title
NA2-7
GM2-2
  • partition numbers less than 10
  • know and use "teen" facts
  • solve addition problems by making a ten, or making a decade
  • solve addition problems involving measurements
Partitions
NA2-7
  • 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
Letter patterns
NA2-7
  • identify patterns in number sequences
  • systematically "count" to establish rules for sequential patterns
  • use rules to make predictions
Supermarket displays
NA2-7
NA2-8
  • create, describe and continue a single-attribute repeating pattern
  • identify the unit of repeat in a repeating pattern, and apply known patterning language
  • identify and describe the composite pattern
  • describe and explain the rule for the pattern in the composite pattern
Dual patterns
NA2-7
NA2-8
  • recognise situations in which there is a relationship between two number sets
  • transfer mapped values onto a graph (an xy coordinate system)
  • explain a simple relationship graph with reference to mapped values
Mapping relationships
NA2-8
  • 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
Letter Patterns
NA2-8
NA2-6
  • continue a sequential pattern
  • develop bar charts to show relationships
Staircases
NA2-8
NA2-6
  • continue a simple pattern
  • generalise the pattern
Pede patterns

Level 3 Patterns and Relationships

Achievement ObjectivesLearning OutcomesUnit title
NA3-7
NA3-6
  • consolidate understanding of simple properties of addition, subtraction, multiplication and division
  • discover and use some more complex properties of addition, subtraction, multiplication and division
Properties of operations
NA3-8
  • predict the next term of a spatial pattern
  • find a rule to give the number of matchsticks (tiles) in a given member of the pattern
  • find the member of the pattern that has a given number of matchsticks (tiles)
Matchstick patterns
NA3-8
  • show number patterns using the hundred’s board and other grid arrangements for whole numbers
  • find the rule for a pattern of numbers shown on a hundred’s board or for input/output pairs from a calculator;
  • relate sequential spatial patterns to how they appear as a number sequence on a hundreds board
Hundreds of patterns
NA3-8
  • continue a patterns
  • find the recurrence rule of a pattern
  • look at relations between two patterns
  • have some idea of what a general rule is
Building patterns incrementally
NA3-8
  • continue a pattern
  • find the recurrence rule of a pattern
  • look at relations between two patterns
  • have some idea of what a general rule is
Building patterns constantly
NA3-8
  • use a "cups and cubes" model to describe relationships
Cups and cubes

Level 4 Patterns and Relationships

Achievement ObjectivesLearning OutcomesUnit title
NA4-8
NA5-2
  • use powers of two in problem situations
  • find number patterns in practical situations
  • experiment to find patterns
Two's company
NA4-9
NA4-7
  • devise a rule for ensuring that sets of numbers can be arranged into 3-by-3 magic squares
  • represent 3-by-3 magic squares algebraically
  • devise rules for determining the Magic Number for magic squares
  • represent magic squares using parametric equations
  • solve equations that have been formed from magic squares
Magic squares
NA4-9
GM4-3
  • explore the relationship between rows and columns in finding the areas of rectangles
  • calculate the area of rectangles, parallelograms and triangles
You can count on squares
NA4-9
  • develop, justify and use rules to solve problems that involve number strips
  • identify and clearly articulate patterns, and make generalisations based on these
Matilda's waltz
NA4-9
  • find a rule to describe any member of a number sequence and express it in words
The truth about triangles and squares
NA4-9
  • find the number of crosses in Tukutuku panels by using areas of squares and rectangles
  • find the number of crosses in repeating Tukutuku panels by using linear formulae
Tukutuku panels
NA4-9
  • solve problems using linear relationships shown on tables and graphs
Drive

Level 5 Patterns and Relationships

Achievement ObjectivesLearning OutcomesUnit title
NA5-9
  • solve linear equations
  • describe a linear relationship between two variables in words and as an equation
  • make a table of one variable against another
  • use a graph to find the value of y, given x, and x, given y
Holistic algebra
NA5-9
  • devise an algebraic rule to identify tilted squares that can fit on geoboards of different sizes
  • devise an algebraic rule to identify the size of the smallest square geoboard on which tilted squares can fit
  • devise and use an algebraic rule for Pythagoras’ theorem
  • devise algebraic rules to find Pythagorean triples
Fences and posts
NA5-9
  • find pairs of whole number co-ordinates and use them to draw graphs in problem contexts
  • link the graphs to formulae of the kind ax±by=c
  • find the nth whole number pairs in a context that solve ax-by=c
Linear graphs and patterns
NA5-7
NA5-9
  • make a table of one variable against another to describe a quadratic relationship
  • describe a quadratic relationship between two variables in words and as an equation
  • show a quadratic relationship as a parabola on the Cartesian Plane
  • recognise the key features of a parabola
  • use the graph of a parabola to find unknowns
  • find unknowns from a simple quadratic equation.
Mary's Garden

Level 6 and 7 Patterns and Relationships

Achievement ObjectivesLearning OutcomesUnit title
NA6-7
GM6-6
  • devise an algebraic rule to identify tilted squares that can fit on geoboards of different sizes
  • devise an algebraic rule to identify the size of the smallest square geoboard on which tilted squares can fit
  • devise and use an algebraic rule for Pythagoras’ theorem
  • devise algebraic rules to find Pythagorean triples
Tilted squares and triangles
M7-3
  • find the recurrence relation for simple sequences
  • construct tables of values for a pattern
  • find the value of the general term of a sequence algebraically
  • find the value of the general term of a sequence geometrically
The why and how of general terms
M7-3
  • find the smaller Fibonacci numbers by using the recurrence relation
  • find the initial members of other sequences that can be found using a recurrence relation like the Fibonacci one
  • find the general term of these recurrence relations using quadratic equations
  • understand the concept of a limit of a sequence
  • find various limits relating to sequences
Fibonacci II
M7-3
  • find patterns in the lengths of the sides of standard paper formats
  • use patterns relating to the lengths of the sides of standard paper formats
  • see that fractions can be ‘continued’ in order to calculate basic surds
All shapes and sizes