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.
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.
Written
All lessons
to explicitly identify to students the
## Mathematics - Level 4## Learning focusAs 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 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 In 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 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 - 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 LearningThis learning focus statement incorporates the Year 5 National Statement of Learning for Mathematics. ## Standards## NumberAt 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, 2 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. ## SpaceAt 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 dataAt 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). ## StructureAt 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 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 mathematicallyAt 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. |