### Year 5/6 Year Planner

Year Planner              Years 5 & 6                 Terms 1-4

Each term revisits concepts and teaching and learning takes individual students to higher level of understanding.

Individual student growth documented against VELS Progression Points for each topic each term.

 Addition   Strategies include Counting forwards on 100’s Chart, Open Number Lines, Partial Sums addition, Counting on Addition using Place Value  (Jump strategy). Subtraction   Strategies include Counting Backwards on 100’s Chart, Open Number Lines, Counting Up or Counting Back to find difference, Counting Up using Place Value. Multiplication   Strategies    include Making Arrays, Multiplication as Repeated Addition. Partial Products Multiplication and the Area Model for Multiplication (box method). Division   Strategies include division as sharing, what to do with left overs, sharing one place value at a time (left to right). Inverse of multiplication (2x?=6). Fractions   Making explicit links to division and multiplication. (½ of 6 is 3, 6÷2=3, 2x3=6, 3+3=6, 6-3-3=0). Denominator is number of groups shared between. Numerator number of groups selected. (Group is the whole & One is the whole). Shape Location Chance Data Decimals & Percent Identify and sort shapes by properties such as parallel and perpendicular lines (for example, quadrilaterals). They use the ideas of angle, size and scale to describe the features of shapes and solids.  Classify and sort shapes and solids (for example, prisms, pyramids, cylinders and cones) using the properties of lines (orientation and size), angles (less than, equal to, or greater than 90°), and surfaces. Visualise and describe relative location and routes between places shown on a map. They create and interpret simple networks  such as a road network to show connectednessbetween towns. Estimate and describe the chance of random  events using words, percentages and fractions or decimals between 0 and 1. Plan and conduct questionnaires to collect data for a specific purpose. Calculate and interpret measures of centre (mean, median  and mode) and spread (range) for ungrouped data. Explore ideas of ratio (as a comparison) and percentage (comparing to 100). They use materials to explore decimals, ratios and percentages as equivalent forms of fractions (for example, 1/2 = 0.5 = 50% ). Identify symmetry  by reflection or rotation. They create and compare pairs of enlarged shapes using simple scale factors and describe the features that change (for example, side lengths) and features that remain the same (for example, angles). Develop and follow instructions to draw shapes and nets of solids using simple scale. Investigate the sample  space (possible outcomes) for simple chance events and calculate theoretical probability. Recognise different data types such as categorical and numerical,  discrete and  They organise and present grouped and ungrouped data using displays such as simple frequency tables and histograms. Use decimals, ratios and percentages to find equivalent representations of common fractions (for example,  9/12 =3/4 = 0.75 = 75%) 1 : 3 = 4 parts =1/4 and 3/4. Represent solids (for example, prisms,pyramids, cylinders and cones) as two-dimensional drawings and nets. Create two-dimensional representations of three dimensional shapes and objects found in the surrounding environment. Explain how symmetry in chance situations (for example, the roll of a die) creates equally likely outcomes. Students identify relationships between variables and describe them with language and words (for example, how hunger varies with time of the day). Construct and use rules for sequences based on the previous term, recursion (for example, the next term is three times the last term plus two), and by formula (for example, a term is three times its position in the sequence plus two). Develop simple procedures to determine the perimeter and area of simple shapes (for example, counting squares in a grid to determine area). create simulations of chance events to estimate probability (for example, randomly selecting a card from a pack without kings to choose a month). Form and specify sets of numbers, shapes and objects according to given criteria and conditions (for example, 6, 12, 18, 24 are the even numbers less than 30 that are also multiples of three). They use venn diagrams and karnaugh maps to test the validity of statements using the words none, some or all (for example, test the statement ‘all the multiples of 3, less than 30, are even numbers’). ·         Contexts include Whole Number, Length, Time, Mass, Volume, Money. ·         Money used to develop concepts of Decimals within Operations. ·         All strategies emphasise use of Place Value components. ·         Teachers need to make explicit the links between the four operations and Fractions. ·         All activities emphasise the use of Number in student relevant authentic open contexts. ·         Differentiation built into every lesson extending understanding for all students.

Warm Up Activities emphasise the following throughout the year.

Patterns (Counting and Shape), Probability games, Automatic recall of simple number facts (Doubling, adding two one digit numbers, compliments of ten, odd and even, etc), Matching Analogue, Digital and Written time.

Problem Solving activities aligned to topics under investigation presented to students weekly to further develop Proficiency Strands of Australian Curriculum (Understanding, Fluency, Problem Solving & Reasoning). Resources include Exemplars, Pictures/Numbers/Words.com)

Literacy emphasised for each topic. Students to become fluent in vocabulary of each topic.

Written Share/Reflections of developed understandings are standard practice and completed at the end of every lesson.

All lessons to explicitly identify to students the Learning Intentions for each lesson.

## Mathematics - Level 4

### Learning focus

As students work towards the achievement of Level 4 standards in Mathematics, they describe their investigations with correct mathematical terms, symbols and notations. They use mathematical procedures to construct and systematically investigateconjecture or hypotheses.

In Number, students extend their understanding of whole numbers, fractions and decimals. They use patterns and arrays to develop understanding of multiples (including lowest common multiple), factors (including highest common factor), prime andcomposite numbers. They recognise and use simple powers (for example, 23 = 8).

Students investigate and use equivalent forms of common fractions. They order fractions and decimals and locate them on a number line. They investigate temperature and other contexts to develop the concept of negative numbers. They explore ideas ofratio (as a comparison) and percentage (comparing to 100). They use materials to explore decimals, ratios and percentages as equivalent forms of fractions (for example, 1/2 = 0.5 = 50% = 1 : 2).

Students devise and use mental and written methods (algorithms) to add, subtract, multiply and divide whole numbers. For divisionthey recognise remainders as common fractions or decimals. They devise and use mental and written methods to add and subtract decimals. They use materials and number lines to develop understanding of multiplication and division of decimals (to two decimal places) and simple common fractions. They routinely make estimations and approximations in calculations and make judgments about their accuracy.

In Space, students identify and sort shapes by properties such as parallel and perpendicular lines (for example, quadrilaterals). They use the ideas of angle, size and scale to describe the features of shapes and solids. They identify symmetry by reflection orrotation. They create and compare pairs of enlarged shapes using simple scale factors. They describe the features that change (for example, side lengths) and features that remain the same (for example, angles). They represent solids (for example, prisms,pyramids, cylinders and cones) as two-dimensional drawings and nets. They visualise and describe relative location and routes between places shown on a map. They create and interpret simple networks such as a road network to show connectednessbetween towns.

In Measurement, chance and data, students estimate and measure lengths (including perimeter), area (including surface area), volumes, capacity, time (including duration), and temperature in metric units using appropriate instruments and scales. They determine and use the level of accuracy required for the purpose of the measurement. They develop simple procedures to determine the perimeter and area of simple shapes (for example, counting squares in a grid to determine area).

Students estimate and describe the chance of random events using words, percentages and fractions or decimals between 0 and 1. They investigate the sample space (possible outcomes) for simple chance events and calculate theoretical probability. They explain how symmetry in chance situations (for example, the roll of a die) creates equally likely outcomes. They create simulationsof chance events to estimate probability (for example, randomly selecting a card from a pack without kings to choose a month).

Students plan and conduct questionnaires to collect data for a specific purpose. They recognise different data types such as categorical and numerical, discrete and continuous. They organise and present grouped and ungrouped data using displays such as simple frequency tables and histograms. They calculate and interpret measures of centre (mean, median and mode) andspread (range) for ungrouped data.

In Structure, students use venn diagrams and tables (karnaugh maps) to test the validity of statements involving the quantifiersnone, some and all. They develop algorithms involving words, diagrams and mathematical symbols (for example, for testing the divisibility of a number).

Students create number sequences by computing the next term from the previous term or terms (recursion). They develop function rules for the terms in sequences based on their position in the sequence.

Students recognise that the ‘identity’ for each operation has no effect: the number 0 for addition and subtraction, and 1 for multiplication and division. They form and solve equations using words and symbols.

When Working mathematically, students make and test conjectures and generalisations about numbers, shapes and mathematical structure using concrete materials and diagrams. For example:

• in Number, the factors of primes and composites
• in Space, the properties of shapes
• in Measurement, chance and data, the probability of outcomes in games of chance
• in Structure, the patterns of remainders formed by division.

Students identify and investigate real life, practical and historical applications of mathematics. They pose and solve mathematical problems using a range of strategies (for example, make a list, find a pattern, work backwards). They solve new problems based on familiar problem structures.

Students develop and use estimation procedures to check the results of computations made using technology. They use technology for complex and extended computations. They use appropriate technology to explore puzzles involving numbers (for example, solve a magic square using a spreadsheet) and to generate drawings of shapes, solids, nets and geometric designs.

### National Statements of Learning

This learning focus statement incorporates the Year 5 National Statement of Learning for Mathematics.

### Standards

#### Number

At Level 4, students comprehend the size and order of small numbers (to thousandths) and large numbers (to millions). They model integers (positive and negative whole numbers and zero), common fractions and decimals. They place integers, decimals and common fractions on a number line. They create sets of number multiples to find the lowest common multiple of the numbers. They interpret numbers and their factors in terms of the area and dimensions of rectangular arrays (for example, the factors of 12 can be found by making rectangles of dimensions 1 × 12, 2 × 6, and 3 × 4).

Students identify square, prime and composite numbers. They create factor sets (for example, using factor trees) and identify the highest common factor of two or more numbers. They recognise and calculate simple powers of whole numbers (for example, 24 = 16).

Students use decimals, ratios and percentages to find equivalent representations of common fractions (for example, 3/4 = 9/12 = 0.75 = 75% = 3 : 4 = 6 : 8). They explain and use mental and written algorithms for the addition, subtraction, multiplication and division of natural numbers (positive whole numbers). They add, subtract, and multiply fractions and decimals (to two decimal places) and apply these operations in practical contexts, including the use of money. They use estimates for computations and apply criteria to determine if estimates are reasonable or not.

#### Space

At Level 4, students classify and sort shapes and solids (for example, prisms, pyramids, cylinders and cones) using the properties of lines (orientation and size), angles (less than, equal to, or greater than 90°), and surfaces. They create two-dimensional representations of three dimensional shapes and objects found in the surrounding environment. They develop and follow instructions to draw shapes and nets of solids using simple scale. They describe the features of shapes and solids that remain the same (for example, angles) or change (for example, surface area) when a shape is enlarged or reduced. They apply a range of transformations to shapes and create tessellations using tools (for example, computer software).

Students use the ideas of size, scale, and direction to describe relative location and objects in maps. They use compass directions, coordinates, scale and distance, and conventional symbols to describe routes between places shown on maps. Students use network diagrams to show relationships and connectedness such as a family tree and the shortest path between towns on a map.

#### Measurement, chance and data

At Level 4, students use metric units to estimate and measure length, perimeter, area, surface area, mass, volume, capacity time and temperature. They measure angles in degrees. They measure as accurately as needed for the purpose of the activity. They convert between metric units of length, capacity and time (for example, L–mL, sec–min).

Students describe and calculate probabilities using words, and fractions and decimals between 0 and 1. They calculate probabilities for chance outcomes (for example, using spinners) and use the symmetry properties of equally likely outcomes. They simulate chance events (for example, the chance that a family has three girls in a row) and understand that experimental estimates of probabilities converge to the theoretical probability in the long run.

Students recognise and give consideration to different data types in forming questionnaires and sampling. They distinguish between categorical and numerical data and classify numerical data as discrete (from counting) or continuous (from measurement). They present data in appropriate displays (for example, a pie chart for eye colour data and a histogram for grouped data of student heights). They calculate and interpret measures of centrality (mean, median, and mode) and data spread (range).

#### Structure

At Level 4 students form and specify sets of numbers, shapes and objects according to given criteria and conditions (for example, 6, 12, 18, 24 are the even numbers less than 30 that are also multiples of three). They use venn diagrams and karnaugh maps to test the validity of statements using the words none, some or all (for example, test the statement ‘all the multiples of 3, less than 30, are even numbers’).

Students construct and use rules for sequences based on the previous term, recursion (for example, the next term is three times the last term plus two), and by formula (for example, a term is three times its position in the sequence plus two).

Students establish equivalence relationships between mathematical expressions using properties such as the distributive property for multiplication over addition (for example, 3 × 26 = 3 × (20 + 6)).

Students identify relationships between variables and describe them with language and words (for example, how hunger varies with time of the day).

Students recognise that addition and subtraction, and multiplication and division are inverse operations. They use words and symbols to form simple equations. They solve equations by trial and error.

#### Working mathematically

At Level 4, use students recognise and investigate the use of mathematics in real (for example, determination of test results as a percentage) and historical situations (for example, the emergence of negative numbers).

Students develop and test conjectures. They understand that a few successful examples are not sufficient proof and recognise that a single counter-example is sufficient to invalidate a conjecture. For example, in:

• number (all numbers can be shown as a rectangular array)
• computations (multiplication leads to a larger number)
• number patterns ( the next number in the sequence 2, 4, 6 … must be 8)
• shape properties (all parallelograms are rectangles)
• chance (a six is harder to roll on die than a one).

Students use the mathematical structure of problems to choose strategies for solutions. They explain their reasoning and procedures and interpret solutions. They create new problems based on familiar problem structures.

Students engage in investigations involving mathematical modelling. They use calculators and computers to investigate and implement algorithms (for example, for finding the lowest common multiple of two numbers), explore number facts and puzzles, generate simulations (for example, the gender of children in a family of four children), and transform shapes and solids.