# Patterns and relationships units of work

### Level 1 Patterns and Relationships

 Achievement Objectives Learning Outcomes Unit title NA1-5NA1-1NA1-2 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 NA1-5NA1-1 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 the bed - patterns NA1-6NA1-1 continue a sequential pattern systematically count to establish rules for sequential patterns skip count in 2s, 5s and 3s The three pigs NA1-6NA1-1 continue a skip-counting pattern describe skip-counting patterns use graphs to illustrate skip-counting patterns Gecko feet 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 Objectives Learning Outcomes Unit title NA2-7GM2-2 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 NA2-7NA2-8 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 Odd and even numbers NA2-7NA2-8 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 NA2-7NA2-8 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 NA2-8NA2-6 continue a sequential pattern Staircases NA2-8NA2-6 continue a simple pattern generalise the pattern Pede patterns

### Level 3 Patterns and Relationships

 Achievement Objectives Learning Outcomes Unit title NA3-7NA3-6 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 Continue a linear growth pattern from a few examples. Find the recursive rule of a linear growth pattern from table of values. Explain why the graph of relationships in the pattern is linear. Use the table and recursive rule, and/or the graph to make predictions about other terms of the pattern. Attempt to create a general rule that connects term number and number of tiles for any term of the pattern. Building patterns NA3-8 use a "cups and cubes" model to describe relationships Cups and cubes

### Level 4 Patterns and Relationships

 Achievement Objectives Learning Outcomes Unit title NA4-8 describe and represent the commutative property and distributive properties of multiplication . recognise that multiplication and division are inverse operations, and interpret division as either equal sharing or measuring. find relationships in the difference of perfect squares, e.g. 7 x 7 = 49 so 8 x 6 = 48. What's going on? Properties of multiplication and division NA4-8NA4-1GM4-3 use a recursive rule to generate the sequence of Fibonacci numbers create a Fibonacci spiral using squares with Fibonacci side lengths find a pattern of odd and even numbers in the sequence identify and represent patterns we find for consecutive numbers in the sequence Fascinated by Fibonacci NA4-9NA4-7 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 NA4-9GM4-3 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 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

### Level 5 Patterns and Relationships

 Achievement Objectives Learning Outcomes Unit title NA5-2 use powers of two in problem situations find number patterns in practical situations experiment to find patterns Two's company 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 find areas of shapes find simple two-variable linear patterns relating to areas 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 NA5-7NA5-9 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 Objectives Learning Outcomes Unit title NA6-7GM6-6 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 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