Te Kete Ipurangi
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# 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 sequencesskip count in 2s Counting on counting NA1-5NA1-1 see what a number pattern isbe able to guess and check the next number in a patternskip count in 2s, 5s, and 10s Ten in a bed NA1-5NA1-1 continue a sequential patternsystematically count to establish rules for sequential patternsskip count in 2s, 5s and 3s The three pigs NA1-5NA1-1 continue a skip-counting patterndescribe skip-counting patternsuse graphs to illustrate skip-counting patterns Beetle wheels NA1-5NA1-6NA2-7NA2-8 investigate and recognise the results of adding and subtracting combinations of odd and even numbersstate generalisations about the addition and subtraction of combinations of odd and even numbersapply generalisations about odd and even number patterns to problem solving situations Early number patterns NA1-6 describe patternscontinue a patterncreate patterns Pattern makers NA1-6 record patterns on grid papermake predictions about ‘missing’ sections of a patternuse words to describe linear patterns Snakes and scarves NA1-6 "read" a repeating pattern and predict what may come nextcreate a repeating pattern with two elementscreate 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 10know and use "teen" factssolve addition problems by making a ten, or making a decadesolve addition problems involving measurements Partitions NA2-7 draw the next shape in a pattern sequencesee how the pattern continues from one shape to the nextdraw up a table of values Letter patterns NA2-7 identify patterns in number sequencessystematically "count" to establish rules for sequential patternsuse rules to make predictions Supermarket displays NA2-7NA2-8 create, describe and continue a single-attribute repeating patternidentify the unit of repeat in a repeating pattern, and apply known patterning languageidentify and describe the composite patterndescribe 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 setstransfer 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 sequencesee how the pattern continues from one shape to the nextdraw up a table of values Letter Patterns NA2-8NA2-6 continue a sequential patterndevelop bar charts to show relationships Staircases NA2-8NA2-6 continue a simple patterngeneralise 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 divisiondiscover and use some more complex properties of addition, subtraction, multiplication and division Properties of operations NA3-8 predict the next term of a spatial patternfind a rule to give the number of matchsticks (tiles) in a given member of the patternfind 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 numbersfind 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 patternsfind the recurrence rule of a patternlook at relations between two patternshave some idea of what a general rule is Building patterns incrementally NA3-8 continue a patternfind the recurrence rule of a patternlook at relations between two patternshave 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 Objectives Learning Outcomes Unit title NA4-8NA5-2 use powers of two in problem situationsfind number patterns in practical situationsexperiment to find patterns Two's company NA4-9NA4-7 devise a rule for ensuring that sets of numbers can be arranged into 3-by-3 magic squaresrepresent 3-by-3 magic squares algebraicallydevise rules for determining the Magic Number for magic squaresrepresent magic squares using parametric equationssolve 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 rectanglescalculate 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 stripsidentify 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 rectanglesfind 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 Objectives Learning Outcomes Unit title NA5-9 solve linear equationsdescribe a linear relationship between two variables in words and as an equationmake a table of one variable against anotheruse 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 sizesdevise an algebraic rule to identify the size of the smallest square geoboard on which tilted squares can fitdevise and use an algebraic rule for Pythagoras’ theoremdevise 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 contextslink the graphs to formulae of the kind ax±by=cfind 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 relationshipdescribe a quadratic relationship between two variables in words and as an equationshow a quadratic relationship as a parabola on the Cartesian Planerecognise the key features of a parabolause the graph of a parabola to find unknownsfind 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 sizesdevise an algebraic rule to identify the size of the smallest square geoboard on which tilted squares can fitdevise and use an algebraic rule for Pythagoras’ theoremdevise algebraic rules to find Pythagorean triples Tilted squares and triangles M7-3 find the recurrence relation for simple sequencesconstruct tables of values for a patternfind the value of the general term of a sequence algebraicallyfind 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 relationfind the initial members of other sequences that can be found using a recurrence relation like the Fibonacci onefind the general term of these recurrence relations using quadratic equationsunderstand the concept of a limit of a sequencefind various limits relating to sequences Fibonacci II M7-3 find patterns in the lengths of the sides of standard paper formatsuse patterns relating to the lengths of the sides of standard paper formatssee that fractions can be ‘continued’ in order to calculate basic surds All shapes and sizes