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Progressions1st2nd3rd4th5th6th7th8th9th
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Additive thinkingStudents partially recognise number names /sequences. They compare quantities and may subitise. (Stage 0 - Emergent)Students 1-1 match and understand the number of objects in a set. (Stage 1 - 1:1 Counting)Students combine or seperate sets by counting all using materials or imaging. (Stages 2-3 Counting All) Students combine or seperate sets by counting on or back from the largest number. (Stage 4 - Advanced Counting) Students solve problems by partitioning and recombining single digit numbers to form 'tidy numbers'. (Stage 5 - Early Additive)Students solve problems involving two or three digit numbers using place value, partitioning, or compensation strategies. (Stage 6 - Advanced Additive) Students seek the most efficient method to solve problems involving whole numbers and decimals using a range of strategies (including inverse operations). (Stage 7 - Advanced Multiplicative)Students use flexible strategies to solve multi step complex problems involving whole numbers, decimals, fractions, and integers. (Stage 7)
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Multiplicative thinkingStudents say the group of materials is "same" and/or equal. Students do not count objects. Student count all materials or equally share materials into groups of the same size.Students use skip counting and simple addion or subtraction to count a set of objects less than 10. The students solve simple division problems by using known multiplication facts or by trial and error with different-sized groupsStudents instantly recall multiplication and basic facts knowledge and use to solve single-diigit problemsStudents solve word problems with multiplacation/division knowledge. Students begin to use more than one strategy to solve problems.Students use the best strategy to solve multiplication and division problems using whole numbers, common fractions, decimals and percentages.Students are able to decide on the best strategy to solve problems, often using more than one strategy to solve complex problems involving whole numbers, decimals, fractions and integers.Students compare two things using multiplicatve thinking to problem solve involving percentages, rates and rations. Students can use a one and two step algebraic equation to find an unknown.
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Curriculum Level 3
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Patterns and relationshipsThe students repeat a pattern containting 2 units. They may not be able to explain their thinking.Repeating patterns. Creating patterns. Could be a repetition of three or more objects, pictures or numbers. They may be able to explain their thinking.Repeating patterns. Creating patterns. Could be a repetition of three or more objects, pictures or numbers. They may be able to explain their thinking. Students can see the pattern e.g. yellow in first place, blue in second, red in third, pink in fourth.Creating a rule based on identifying a number pattern and the position of the number in sequence and how it fits into the patternStudents use graphs and tables to find rules for the next pattern in the sequential relationship.Students use equations and rules to solve problems. Students graph and understand linear relationships and parabolas, form equations and apply them to solve problems.
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Using symbols and expressions to think mathematicallyThe students recognise some numeral and operation symbols and know what these stand for.Students read and record equations for simple additive and subtraction problems.Students read and record equality (=) and simple inequality (<>) statements for additive and multiplicative problems.Students read and record additive and multiplicative equality and inequality equations for problems involving unknowns, including using inverse operations.Students use algebra (letter symbols) to solve simple proportional problems.Students write equality statements involving terms or factors, including an unknown. They solve equations by operating equally on both sides.Student uses a systematic approach and algebra, including quadratic equations, to model and solve problems.
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Curriculum Level 4
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Geometric thinkingStudents navigate and follow verbal instruction around the classroom. Students identify and interact with a range of shapes.

Students identify different shapes and describe shapes. Students can turn, flip, slide and describe shapes location in relation to other things in their local environment.

Students identify and describe features of shapes and transformations. They solve single-step problems. They are learning to use geometric terms.
Students use the featues of shape and transformations to solve multi-step problems, draw shapes from multiple perspectives, and use the language of geometry accurately.Students use and generalise the properties of shapes and transformations. They reason and justify their solutions using geometric language. Students use scale factors and the relationship of length and angles within shapes (trigonomic approaches) to solve real-world problems. They describe a set of points (locus) mathematically and explain their reasoning.
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Measurement senseStudents hold up two objects and compare their length, temperature, weight, area and volume by physically manipulating the objects.(Beginning Level 1)Students compare the length, temperature, weight etc directly and begin to understand that things can be measured. (Early Level 1)Students compare several objects using self-chosen units of measurement and understand each unit of measurement must be the same. (At Level 1/Early 2)Students are beginning to directly compare objects using standard units of measurements, and apply basic addition facts to standard units.. (Level 2)Students measure time and the attributes of objects choosing appropriate stansard units and working with them to the nearest tenth.Students use an array structure to work out the area of a rectangle. They understand that the number of rows in one column of the rectangle determines the number of rows in the whole rectangle, and use multiplication to calculate the rectangle’s area.(Level 3)Students measure time and the attributes of objects, using metric and other standard measures; make simple conversions between units using whole numbers; use side or edge lengths to find the perimeters and areas of rectangles snd parallelograms and the volumes of cuboids given whole-number dimensions.(Early Level 4)Students use metric and other standard measures; make simple conversions between units, using decimals; use side or edge lengths to find the perimeters and areas of rectangles, parallelograms and triangles and the columes of cuboids. (At Level 4/Early 5)Students split complex shapes into separate parts in order to calculate their length, area, or volume. For example, the surface area of a cylinder can be calculated as sum of the area of two circles and a rectangle. Students develop the ability to compose and decompose shapes in order to find the lengths, areas and volumes of various complex objects.
(Level 5)
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Statistical investigationsStudents undergo a teacher-led investigation collecting, ordering and presenting their data.Students undergo a teacher-led investigation collecting, ordering and presenting their data. They can make summary statements about their findings.Students conduct a collect, organise and display data to ask a given question. They communicate their findings and draw a conclusion. Students pose simple questions to investigate, display whole-number data in different ways and communicate their findings.Student pose comparative questions, and investigate relationships. They collect data on more than one simultaneous variable (multivariate), and display, analyse and communicate their findings.Students pose investigative questions about a wider population, collect samples of (multivariate) data, and analyse thier displays to notice unusual values. They recognise if data needs to be cleaned and discuss the reasons for data variations.
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Interpreting statistical and chance situationsStudents participate in a class investigation, recognise certainty, uncertainty and an incorrect statement.Studetns explain if statements about data displays are correct with reference to the data. They identify and explain different outcomes in simple changce situations. Students identify and explain errors in data displays. They record the results of chance experiments and say which outcomes then seem more likely. Students examine and evaluate the process, results and conclusions of other peoples statistical investigations. They investigate chance situations using experiments and simple models. Students examine the if the process, results and claims of others' statistical investigations are reasonable. They explain why results might be presented in particular ways. They can investigate chance situations by making connections between experimental results and theory.
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